Joint modelling of repeated measurement and time-to-event data: an introductory tutorial

Associations between modifiable risk factors and cognitive function in middle-aged and older Chinese adults: joint modelling of longitudinal and survival data

Background

Stronger associations between modifiable risk factors and cognitive function have been found in younger than older adults. This age pattern may be subject to mortality selection and non-ignorable missingness caused by dropouts due to death, but this remains unclear.

Methods

Longitudinal data from 9,562 adults aged 50 and older from Waves 1-4 (2011-2018) of the China Health and Retirement Longitudinal Study were used. Cognitive function was assessed repeatedly using a battery of cognitive tests. Joint models of longitudinal and survival data were applied to examine the associations of modifiable risk factors with cognitive function and mortality.

Results

Worse cognitive function score was associated with being female (coefficient[β] = -1.669, 95% confidence interval [CI]: -1.830, -1.511, p < 0.001), low education (β = -2.672, 95%CI: -2.813, -2.530, p < 0.001), rural residence (β = -1.204, 95%CI: -1.329, -1.074, p < 0.001), stroke (β = -0.451, 95%CI: -0.857, -0.051, p = 0.030), probable depression (β = -1.084, 95%CI: -1.226, -0.941, p < 0.001), and current smoking (β = -0.284, 95%CI: -0.437, -0.133, p < 0.001); whereas dyslipidaemia (β = 0.415, 95% CI: 0.207, 0.626, p < 0.001), heart disease (β = 0.513, 95% CI: 0.328, 0.698, p < 0.001), overweight (β = 0.365, 95% CI: 0.224, 0.506, p < 0.001) and obesity (β = 0.264, 95% CI: 0.048, 0.473, p = 0.014) were associated with better cognitive function. These associations changed less than 5% when the longitudinal and survival data were modelled separately. An increase in cognitive function over age was associated with reduced mortality risk (hazard ratio: 0.418, 95%CI: 0.333, 0.537, p < 0.001). The association between socioeconomic disadvantage and cognitive function was more evident in women than in men, while the associations of socioeconomic disadvantage and lifestyle with cognitive function increased with age.

Conclusion

Mortality selection and non-ignorable missingness caused by dropouts due to death played a minor role in the associations between modifiable risk factors and cognitive function in middle-aged and older Chinese adults.

Joint modeling of longitudinal health-related quality of life during concurrent chemoradiotherapy period and long-term survival among patients with advanced nasopharyngeal carcinoma

BACKGROUND

To investigate the prognosis of longitudinal health-related quality of life (HRQOL) during concurrent chemoradiotherapy (CCRT) on survival outcomes in patients with advanced nasopharyngeal carcinoma (NPC).

METHODS

During 2012-2014, 145 adult NPC patients with stage II-IVb NPC were investigated weekly using the European Organization for Research and Treatment of Cancer Quality of Life Questionnaire core 30 (EORCT QLQ-C30) during their CCRT period. The effects of longitudinal trends of HRQOL on survival outcomes were estimated using joint modeling, and hazard ratios (HRs) with 95% confidence intervals (95% CIs) were reported as a 10-point increase in HRQOL scores.

RESULTS

After a median follow-up of 83.4 months, the multivariable models showed significant associations of longitudinal increasing scores in fatigue and appetite loss during the CCRT period with distant metastasis-free survival: 10-point increases in scores of fatigue and appetite loss domains during CCRT period were significantly associated with 75% (HR: 1.75, 95% CI: 1.01, 3.02; p = 0.047) and 59% (HR: 1.59, 95% CI: 1.09, 2.59; p = 0.018) increase in the risk of distant metastasis, respectively. The prognostic effects of the longitudinal HRQOL trend on overall survival and progress-free survival were statistically non-significant.

CONCLUSION

Increases in fatigue and appetite loss of HRQOL during the CCRT period are significantly associated with high risks of distant metastasis in advanced NPC patients. Nutritional support and psychological intervention are warranted for NPC patients during the treatment period.

Associations of CD4 Cell Count Measures With Infection-Related and Infection-Unrelated Cancer Risk Among People With HIV

BACKGROUND

People with HIV are at higher risk of infection-related cancers than the general population, which could be due, in part, to immune dysfunction. Our objective was to examine associations between 4 CD4 count measures as indicators of immune function and infection-related and infection-unrelated cancer risk.

SETTING

We conducted a cohort study of adults with HIV who were diagnosed with cancer in Ontario, Canada. Incident cancers were identified from January 1, 1997 to December 31, 2020.

METHODS

We estimated adjusted hazard ratios (aHR) for the associations between CD4 measures (baseline CD4, nadir CD4, time-updated CD4, time-updated CD4:CD8) and cancer incidence rates using competing risk analyses, adjusted for socio-demographic factors, history of hepatitis B or C infection, baseline viral load, smoking, and alcohol use.

RESULTS

Among 4771 people with HIV, contributing 59,111 person-years of observation, a total of 549 cancers were observed. Low baseline CD4 (<200 cells/µL) (aHR 2.08 [95% CI: 1.38 to 3.13], nadir (<200 cells/µL) (aHR 2.01 [95% CI: 1.49 to 2.71]), low time-updated CD4 (aHR 3.52 [95% CI: 2.36 to 5.24]) and time-updated CD4:CD8 ratio (<0.4) (aHR 2.02 [95% CI: 1.08 to 3.79]) were associated with an increased rate of infection-related cancer. No associations were observed for infection-unrelated cancers.

CONCLUSIONS

Low CD4 counts and indices were associated with increased rates of infection-related cancers among people with HIV, irrespective of the CD4 measure used. Early diagnosis and linkage to care and high antiretroviral therapy uptake may lead to improved immune function and could add to cancer prevention strategies such as screening and vaccine uptake.

A Joint Model Based on Post-Treatment Longitudinal Prognostic Nutritional Index to Predict Survival in Nasopharyngeal Carcinoma

BACKGROUND

a low PNI in patients with NPC is linked to poor survival, but prior studies have focused on single-timepoint measurements. Our study aims to employ joint modeling to analyze longitudinal PNI data from each routine visit, exploring its relationship with overall survival.

METHODS

In this retrospective study using data from the Chang Gung Research Database (2007-2019), we enrolled patients with NPC undergoing curative treatment. We analyzed the correlation between patient characteristics, including the PNI, and overall survival. A joint model combining a longitudinal sub-model with a time-to-event sub-model was used to further evaluate the prognostic value of longitudinal PNI.

RESULTS

A total of 2332 patient were enrolled for the analysis. Separate survival analyses showed that longitudinal PNI was an independent indicator of a reduced mortality risk (adjusted HR 0.813; 95% CI, 0.805 to 0.821). Joint modeling confirmed longitudinal PNI as a consistent predictor of survival (HR 0.864; 95% CI, 0.850 to 0.879). An ROC analysis revealed that a PNI below 38.1 significantly increased the risk of 90-day mortality, with 90.0% sensitivity and 89.6% specificity.

CONCLUSIONS

Longitudinal PNI data independently predicted the overall survival in patients with NPC, significantly forecasting 90-day survival outcomes. We recommend routine PNI assessments during each clinic visit for these patients.

Investigating the Association Between Dynamic Driving Pressure and Mortality in COVID-19-Related Acute Respiratory Distress Syndrome: A Joint Modeling Approach Using Real-Time Continuously-Monitored Ventilation Data

IMPORTANCE AND OBJECTIVES

COVID-19-related acute respiratory distress syndrome (ARDS) is associated with high mortality and often necessitates invasive mechanical ventilation (IMV). Previous studies on non-COVID-19 ARDS have shown driving pressure to be robustly associated with ICU mortality; however, those studies relied on "static" driving pressure measured periodically and manually. As "continuous" automatically monitored driving pressure is becoming increasingly available and reliable with more advanced mechanical ventilators, we aimed to examine the effect of this "dynamic" driving pressure in COVID-19 ARDS throughout the entire ventilation period.

DESIGN SETTING AND PARTICIPANTS

This retrospective, observational study cohort study evaluates the association between driving pressure and ICU mortality in patients with concurrent COVID-19 and ARDS using multivariate joint modeling. The study cohort (n = 544) included all adult patients (≥ 18 yr) with COVID-19 ARDS between March 1, 2020, and April 30, 2021, on volume-control mode IMV for 12 hours or more in a Mass General Brigham, Boston, MA ICU.

MEASUREMENTS AND MAIN RESULTS

Of 544 included patients, 171 (31.4%) died in the ICU. Increased dynamic ΔP was associated with increased risk in the hazard of ICU mortality (hazard ratio [HR] 1.035; 95% credible interval, 1.004-1.069) after adjusting for other relevant dynamic respiratory biomarkers. A significant increase in risk in the hazard of death was found for every hour of exposure to high intensities of driving pressure (≥ 15 cm H2O) (HR 1.002; 95% credible interval 1.001-1.003).

CONCLUSIONS

Limiting patients' exposure to high intensities of driving pressure even while under lung-protective ventilation may represent a critical step in improving ICU survival in patients with COVID-19 ARDS. Time-series IMV data could be leveraged to enhance real-time monitoring and decision support to optimize ventilation strategies at the bedside.

Developing a PRogram to Educate and Sensitize Caregivers to Reduce the Inappropriate Prescription Burden in the Elderly with Alzheimer's Disease (D-PRESCRIBE-AD): Trial protocol and rationale of an open-label pragmatic, prospective randomized controlled trial

CONTEXT

Potentially inappropriate prescribing of medications in older adults, particular those with dementia, can lead to adverse drug events including falls and fractures, worsening cognitive impairment, emergency department visits, and hospitalizations. Educational mailings from health plans to patients and their providers to encourage deprescribing conversations may represent an effective, low-cost, "light touch", approach to reducing the burden of potentially inappropriate prescription use in older adults with dementia.

OBJECTIVES

The objective of the Developing a PRogram to Educate and Sensitize Caregivers to Reduce the Inappropriate Prescription Burden in Elderly with Alzheimer's Disease (D-PRESCRIBE-AD) trial is to evaluate the effect of a health plan based multi-faceted educational outreach intervention to community dwelling patients with dementia who are currently prescribed sedative/hypnotics, antipsychotics, or strong anticholinergics.

METHODS

The D-PRESCRIBE-AD is an open-label pragmatic, prospective randomized controlled trial (RCT) comparing three arms: 1) educational mailing to both the health plan patient and their prescribing physician (patient plus physician arm, n = 4814); 2) educational mailing to prescribing physician only (physician only arm, n = 4814); and 3) usual care (n = 4814) among patients with dementia enrolled in two large United States based health plans. The primary outcome is the absence of any dispensing of the targeted potentially inappropriate prescription during the 6-month study observation period after a 3-month black out period following the mailing. Secondary outcomes include dose-reduction, polypharmacy, healthcare utilization, mortality and therapeutic switching within targeted drug classes.

CONCLUSION

This large pragmatic RCT will contribute to the evidence base on promoting deprescribing of potentially inappropriate medications among older adults with dementia. If successful, such light touch, inexpensive and highly scalable interventions have the potential to reduce the burden of potentially inappropriate prescribing for patients with dementia. ClinicalTrials.gov Identifier: NCT05147428.

Impacts of body weight change on treatment outcomes in patients with multidrug-resistant tuberculosis in Northwest Ethiopia

Measuring body weight during therapy has received insufficient attention in poor resource settings like Ethiopia. We aimed to investigate the association between weight change during therapy and treatment outcomes among patients with multidrug-resistant tuberculosis (MDR-TB) in northwest Ethiopia. This retrospective cohort study analysed data from patients with MDR-TB admitted between May 2015 to February 2022 at four treatment facilities in Northwest Ethiopia. We used the joint model (JM) to determine the association between weight change during therapy and treatment outcomes for patients with MDR-TB. A total of 419 patients with MDR-TB were included in the analysis. Of these, 265 (63.3%) were male, and 255 (60.9%) were undernourished. Weight increase over time was associated with a decrease in unsuccessful treatment outcomes (adjusted hazard ratio (AHR): 0.96, 95% CI: 0.94 to 0.98). In addition, patients with undernutrition (AHR: 1.72, 95% CI: 1.10 to 2.97), HIV (AHR:1.79, 95% CI: 1.04 to 3.06), and clinical complications such as pneumothorax (AHR: 1.66, 95% CI: 1.03 to 2.67) were associated with unsuccessful treatment outcomes. The JM showed a significant inverse association between weight gain and unsuccessful MDR-TB treatment outcomes. Therefore, weight gain may be used as a surrogate marker for good TB treatment response in Ethiopia.

Number of medically prescribed pharmaceutical agents as predictor of mortality risk: a longitudinal, time-variable analysis in the EPIC-Heidelberg cohort

The number of prescribed medications might be used as proxy indicator for general health status, in models to predict mortality risk. To estimate the time-varying association between active pharmaceutical ingredient (API) count and all-cause mortality, we analyzed data from a population cohort in Heidelberg (Germany), including 25,546 participants with information on medication use collected at 3-yearly intervals from baseline recruitment (1994-1998) until end of 2014. A total of 4548 deaths were recorded until May 2019. Time-dependent modeling was used to estimate hazard ratios (HR) and their 95% confidence intervals (CI) for all-cause mortality in relation to number of APIs used, within three strata of age (≤ 60, > 60 to  ≤ 70 and > 70 years) and adjusting for lifestyle-related risk factors. For participants reporting commonly used APIs only (i.e., API types accounting for up to 80% of medication time in the population) total API counts showed no association with mortality risk within any age stratum. However, when at least one of the APIs was less common, the total API count showed a strong relationship with all-cause mortality especially up to age ≤ 60, with HR up to 3.70 (95% CI 2.30-5.94) with 5 or 6 medications and 8.19 (5.61-11.97) for 7 or more APIs (versus none). Between > 60 and 70 years of age this risk association was weaker, with HR up to 3.96 (3.14-4.98) for 7 or more APIs, and above 70 years it was weakened further (HR up to 1.54 (1.34-1.79)). Multiple API-use may predict mortality risk in middle-aged and women and men ≤ 70 years, but only if it includes at least one less frequently used API type. With advancing age, and multiple medication becomes increasingly prevalent, the association of API count with risk of death progressively attenuates, suggesting an increasing complexity with age of underlying mortality determinants.

Software Application Profile: dynamicLM-a tool for performing dynamic risk prediction using a landmark supermodel for survival data under competing risks

MOTIVATION

Providing a dynamic assessment of prognosis is essential for improved personalized medicine. The landmark model for survival data provides a potentially powerful solution to the dynamic prediction of disease progression. However, a general framework and a flexible implementation of the model that incorporates various outcomes, such as competing events, have been lacking. We present an R package, dynamicLM, a user-friendly tool for the landmark model for the dynamic prediction of survival data under competing risks, which includes various functions for data preparation, model development, prediction and evaluation of predictive performance.

IMPLEMENTATION

dynamicLM as an R package.

GENERAL FEATURES

The package includes options for incorporating time-varying covariates, capturing time-dependent effects of predictors and fitting a cause-specific landmark model for time-to-event data with or without competing risks. Tools for evaluating the prediction performance include time-dependent area under the ROC curve, Brier Score and calibration.

AVAILABILITY

Available on GitHub [https://github.com/thehanlab/dynamicLM].

Illustration of association between change in prostate-specific antigen (PSA) values and time to tumor status after treatment for prostate cancer patients: a joint modelling approach

BACKGROUND

Prostate cancer (PCa) is the most prevalent tumor in men, and Prostate-Specific Antigen (PSA) serves as the primary marker for diagnosis, recurrence, and disease-free status. PSA levels post-treatment guide physicians in gauging disease progression and tumor status (low or high). Clinical follow-up relies on monitoring PSA over time, forming the basis for dynamic prediction. Our study proposes a joint model of longitudinal PSA and time to tumor shrinkage, incorporating baseline variables. The research aims to assess tumor status post-treatment for dynamic prediction, utilizing joint assessment of PSA measurements and time to tumor status.

METHODS

We propose a joint model for longitudinal PSA and time to tumor shrinkage, taking into account baseline BMI and post-treatment factors, including external beam radiation therapy (EBRT), androgen deprivation therapy (ADT), prostatectomy, and various combinations of these interventions. The model employs a mixed-effect sub-model for longitudinal PSA and an event time sub-model for tumor shrinkage.

RESULTS

Results emphasize the significance of baseline factors in understanding the relationship between PSA trajectories and tumor status. Patients with low tumor status consistently exhibit low PSA values, decreasing exponentially within one month post-treatment. The correlation between PSA levels and tumor shrinkage is evident, with the considered factors proving to be significant in both sub-models.

CONCLUSIONS

Compared to other treatment options, ADT is the most effective in achieving a low tumor status, as evidenced by a decrease in PSA levels after months of treatment. Patients with an increased BMI were more likely to attain a low tumor status. The research enhances dynamic prediction for PCa patients, utilizing joint analysis of PSA and time to tumor shrinkage post-treatment. The developed model facilitates more effective and personalized decision-making in PCa care.

Association of Lung Function With Cognitive Decline and Incident Dementia in the Atherosclerosis Risk in Communities Study

We examined the associations between lung function and incident dementia and cognitive decline in 12,688 participants in the ARIC Study who provided lung function measurements in 1990-1992. Cognitive tests were administered up to 7 times, and dementia was ascertained through 2019. We used shared parameter models to jointly fit proportional hazard models and linear mixed-effect models to estimate lung-function-associated dementia rate and cognitive change, respectively. Higher forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) were associated with reduced dementia (n = 2,452 persons developed dementia); hazard ratios per 1-L increase in FEV1 and FVC were 0.79 (95% confidence interval (CI): 0.71, 0.89) and 0.81 (95% CI: 0.74, 0.89), respectively. Each 1-L increase in FEV1 and FVC was associated with a 0.08-standard deviation (SD) (95% CI: 0.05, 0.12) and a 0.05-SD (95% CI: 0.02, 0.07) attenuation of 30-year cognitive decline, respectively. A 1% increase in FEV1/FVC ratio was associated with 0.008-SD (95% CI: 0.004, 0.012) less cognitive decline. We observed statistical interaction between FEV1 and FVC, suggesting that cognitive declines depended on values of specific FEV1 and FVC (as compared with FEV1, FVC, or FEV1/FVC ratio models that suggested linear incremental associations). Our findings may have important implications for reducing the burden of cognitive decline that is attributable to environmental exposures and associated lung function impairment.

Association of eGFR and mortality with use of a joint model: results of a nationwide study in Iceland

OBJECTIVES

Prior studies on the association of estimated glomerular filtration rate (eGFR) and mortality have failed to include methods to account for repeated eGFR determinations. The aim of this study was to estimate the association between eGFR and mortality in the general population in Iceland employing a joint model.

METHODS

We obtained all serum creatinine and urine protein measurements from all clinical laboratories in Iceland in the years 2008-16. Clinical data were obtained from nationwide electronic medical records. eGFR was calculated using the Chronic Kidney Disease Epidemiology Collaboration equation and categorized as follows: 0-29, 30-44, 45-59, 60-74, 75-89, 90-104 and >104 mL/min/1.73 m2. A multiple imputation method was used to account for missing urine protein data. A joint model was used to assess risk of all-cause mortality.

RESULTS

We obtained 2 120 147 creatinine values for 218 437 individuals, of whom 84 364 (39%) had proteinuria measurements available. Median age was 46 (range 18-106) years and 47% were men. Proteinuria associated with increased risk of death for all eGFR categories in persons of all ages. In persons ≤65 years, the lowest risk was observed for eGFR of 75-89 mL/min/1.73 m2 without proteinuria. For persons aged >65 years, the lowest risk was observed for eGFR of 60-74 mL/min/1.73 m2 without proteinuria. eGFR of 45-59 mL/min/1.73 m2 without proteinuria did not associate with increased mortality risk in this age group. eGFR >104 mL/min/1.73 m2 associated with increased mortality.

CONCLUSIONS

These results lend further support to the use of age-adapted eGFR thresholds for defining chronic kidney disease. Very high eGFR needs to be studied in more detail with regard to mortality.

Characterization of direct and/or indirect genetic associations for multiple traits in longitudinal studies of disease progression

When quantitative longitudinal traits are risk factors for disease progression and subject to random biological variation, joint model analysis of time-to-event and longitudinal traits can effectively identify direct and/or indirect genetic association of single nucleotide polymorphisms (SNPs) with time-to-event. We present a joint model that integrates: (1) a multivariate linear mixed model describing trajectories of multiple longitudinal traits as a function of time, SNP effects, and subject-specific random effects and (2) a frailty Cox survival model that depends on SNPs, longitudinal trajectory effects, and subject-specific frailty accounting for dependence among multiple time-to-event traits. Motivated by complex genetic architecture of type 1 diabetes complications (T1DC) observed in the Diabetes Control and Complications Trial (DCCT), we implement a 2-stage approach to inference with bootstrap joint covariance estimation and develop a hypothesis testing procedure to classify direct and/or indirect SNP association with each time-to-event trait. By realistic simulation study, we show that joint modeling of 2 time-to-T1DC (retinopathy and nephropathy) and 2 longitudinal risk factors (HbA1c and systolic blood pressure) reduces estimation bias in genetic effects and improves classification accuracy of direct and/or indirect SNP associations, compared to methods that ignore within-subject risk factor variability and dependence among longitudinal and time-to-event traits. Through DCCT data analysis, we demonstrate feasibility for candidate SNP modeling and quantify effects of sample size and Winner's curse bias on classification for 2 SNPs identified as having indirect associations with time-to-T1DC traits. Joint analysis of multiple longitudinal and multiple time-to-event traits provides insight into complex traits architecture.

Predicting Individualized Lung Disease Progression in Treatment-Naive Patients With Lymphangioleiomyomatosis

BACKGROUND

Lung function decline varies significantly in patients with lymphangioleiomyomatosis (LAM), impeding individualized clinical decision-making.

RESEARCH QUESTION

Can we aid individualized decision-making in LAM by developing a dynamic prediction model that can estimate the probability of clinically relevant FEV1 decline in patients with LAM before treatment initiation?

STUDY DESIGN AND METHODS

Patients observed in the US National Heart, Lung, and Blood Institute (NHLBI) Lymphangioleiomyomatosis Registry were included. Using routinely available variables such as age at diagnosis, menopausal status, and baseline lung function (FEV1 and diffusing capacity of the lungs for carbon monoxide [Dlco]), we used novel stochastic modeling and evaluated predictive probabilities for clinically relevant drops in FEV1. We formed predictive probabilities of transplant-free survival by jointly modeling longitudinal FEV1 and lung transplantation or death events. External validation used the UK Lymphangioleiomyomatosis Natural History cohort.

RESULTS

Analysis of the NHLBI Lymphangioleiomyomatosis Registry and UK Lymphangioleiomyomatosis Natural History cohorts consisted of 216 and 185 individuals, respectively. We derived a joint model that accurately estimated the risk of future lung function decline and 5-year probabilities of transplant-free survival in patients with LAM not taking sirolimus (area under the receiver operating characteristic curve [AUC], approximately 0.80). The prediction model provided estimates of forecasted FEV1, rate of FEV1 decline, and probabilities for risk of prolonged drops in FEV1 for untreated patients with LAM with a high degree of accuracy (AUC > 0.80) for the derivation cohort as well as the validation cohort. Our tool is freely accessible at: https://anushkapalipana.shinyapps.io/testapp_v2/.

INTERPRETATION

Longitudinal modeling of routine clinical data can allow individualized LAM prognostication and assist in decision-making regarding the timing of treatment initiation.

DNA methylation markers for kidney function and progression of diabetic kidney disease

Epigenetic markers are potential biomarkers for diabetes and related complications. Using a prospective cohort from the Hong Kong Diabetes Register, we perform two independent epigenome-wide association studies to identify methylation markers associated with baseline estimated glomerular filtration rate (eGFR) and subsequent decline in kidney function (eGFR slope), respectively, in 1,271 type 2 diabetes subjects. Here we show 40 (30 previously unidentified) and eight (all previously unidentified) CpG sites individually reach epigenome-wide significance for baseline eGFR and eGFR slope, respectively. We also develop a multisite analysis method, which selects 64 and 37 CpG sites for baseline eGFR and eGFR slope, respectively. These models are validated in an independent cohort of Native Americans with type 2 diabetes. Our identified CpG sites are near genes enriched for functional roles in kidney diseases, and some show association with renal damage. This study highlights the potential of methylation markers in risk stratification of kidney disease among type 2 diabetes individuals.

Exploring flexible polynomial regression as a method to align routine clinical outcomes with daily data capture through remote technologies

BACKGROUND

Clinical outcomes are normally captured less frequently than data from remote technologies, leaving a disparity in volumes of data from these different sources. To align these data, flexible polynomial regression was investigated to estimate personalised trends for a continuous outcome over time.

METHODS

Using electronic health records, flexible polynomial regression models inclusive of a 1st up to a 4th order were calculated to predict forced expiratory volume in 1 s (FEV₁) over time in children with cystic fibrosis. The model with the lowest AIC for each individual was selected as the best fit. The optimal parameters for using flexible polynomials were investigated by comparing the measured FEV₁ values to the values given by the individualised polynomial.

RESULTS

There were 8,549 FEV₁ measurements from 267 individuals. For individuals with > 15 measurements (n = 178), the polynomial predictions worked well; however, with < 15 measurements (n = 89), the polynomial models were conditional on the number of measurements and time between measurements. The method was validated using BMI in the same population of children.

CONCLUSION

Flexible polynomials can be used to extrapolate clinical outcome measures at frequent time intervals to align with daily data captured through remote technologies.

A two‐level copula joint model for joint analysis of longitudinal and competing risks data

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

Dynamic predictions from longitudinal CD4 count measures and time to death of HIV/AIDS patients using a Bayesian joint model

A Bayesian joint modeling approach to dynamic prediction of HIV progression and mortality allows individualized predictions to be made for HIV patients, based on monitoring of their CD4 counts. This study aims to provide predictions of patient-specific trajectories of HIV disease progression and survival. Longitudinal data on 254 HIV/AIDS patients who received ART between 2009 and 2014, and who had at least one CD4 count observed, were employed in a Bayesian joint model of disease progression. Different forms of association structure that relate the longitudinal CD4 biomarker and time to death were assessed; and predictions were averaged over the different models using Bayesian model averaging. The individual follow-up times ranged from 1 to 120 months, with a median of 22 months and IQR 7-39 months. The estimates of the association structure parameters from two of the three models considered indicated that the HIV mortality hazard at any time point is associated with the rate of change in the underlying value of the CD4 count. Model averaging the dynamic predictions resulted in only one of the hypothesized association structures having non-zero weight in almost all time points for each individual, with the exception of twelve patients, for whom other association structures were preferred at a few time points. The predictions were found to be different when we averaged them over models than when we derived them from the highest posterior weight model alone. The model with highest posterior weight for almost all time points for each individual gave an estimate of the association parameter of -0.02 implying that for a unit increase in the CD4 count, the hazard of HIV mortality decreases by a factor (hazard ratio) of 0.98. Functional status and alcohol intake are important contributing factors that affect the mean square root of CD4 measurements.

Association of leukocyte mitochondrial DNA copy number with longitudinal C-reactive protein levels and survival in older adults: a cohort study

BACKGROUND

Systemic chronic inflammation occurs with age. The association of the leukocyte mitochondrial DNA copy number, a measure of mitochondrial function in aging, with the temporal profile of serum high-sensitivity C-reactive protein and mortality risk remains uncertain. The objectives of this study were to examine the association of the leukocyte mitochondrial DNA copy number with longitudinal high-sensitivity C-reactive protein levels and the association of the longitudinal high-sensitivity C-reactive protein levels with mortality risk.

METHODS

This prospective cohort study included 3928 adults aged ≥ 55 years without systemic inflammation in the baseline examination of the Healthy Aging Longitudinal Study in Taiwan, which started in 2009. Each participant received leukocyte mitochondrial DNA copy number measurement using a fluorescence-based quantitative polymerase chain reaction at baseline, serum high-sensitivity C-reactive protein measurements at baseline and the follow-up examination five years later, and the ascertainment of all-cause death (until November 30, 2021). The relationships among the leukocyte mitochondrial DNA copy number, longitudinal serum high-sensitivity C-reactive protein levels, and time to all-cause mortality were examined using the joint longitudinal and survival modeling analysis.

RESULTS

Of the 3928 participants (mean age: 69 years; 2060 [52%] were women), 837 (21%) died during follow-up. In the adjusted analysis, one standard deviation lower natural log-transformed baseline leukocyte mitochondrial DNA copy number was associated with an increase of 0.05 (95% confidence interval [CI], 0.02 to 0.08) standard deviation in serum high-sensitivity C-reactive protein in subsequent years. An increase of 1 standard deviation in instantaneous high-sensitivity C-reactive protein levels was associated with a hazard ratio (HR) for all-cause mortality of 1.22 (95% CI, 1.14 to 1.30). Similar results were obtained after further adjusting for baseline high-sensitivity C-reactive protein levels (HR [95% CI], 1.27 [1.16 to 1.38]) and after excluding those with serum high-sensitivity C-reactive protein above 10 mg/L (HR [95% CI], 1.21[1.11 to 1.31]) or 3 mg/L (HR [95% CI], 1.19 [1.06 to 1.31]) during follow-up.

CONCLUSIONS

A lower leukocyte mitochondrial DNA copy number was associated with persistently higher high-sensitivity C-reactive protein levels. Moreover, these higher time-varying high-sensitivity C-reactive protein levels were instantaneously associated with a higher risk of death.

The change in Geriatric Nutritional Risk Index is associated with mortality in patients who start hemodialysis: Korean Renal Data Registry, 2016-2018

Malnutrition is common in patients undergoing hemodialysis (HD) and is associated with mortality. This study aimed to investigate the association between changes in nutrition status measured by the Geriatric Nutritional Risk Index (GNRI) and all-cause mortality in patients who started HD. A nationwide retrospective cohort study was conducted based on the Korean Renal Data System database. Patients who started HD from January 2016 to December 2018, and were eligible for GNRI and GNRI trend were included. GNRI trend was a longitudinal change of GNRI, assessed by random slope in a mixed-effect model. Positive and negative random slopes in each patient were assigned to positive and negative GNRI trends. A total of 2313 patients were included and median follow-up period was 3.1 (2.6-3.7) years. GNRI values decreased over time (estimate - 1.212, 95% confidence interval (CI) - 1.116-0.692) and positive GNRI trend was associated with survival benefit (hazard ratio 0.55, 95% CI 0.36-0.84) after multivariate adjustment. These findings show that serial GNRI assessment, besides GNRI, is a useful prognostic factor for mortality in patients who start HD.

Using joint models to study the association between CD4 count and the risk of death in TB/HIV data

Background

The association structure linking the longitudinal and survival sub-models is of fundamental importance in the joint modeling framework and the choice of this structure should be made based on the clinical background of the study. However, this information may not always be accessible and rationale for selecting this association structure has received relatively little attention in the literature. To this end, we aim to explore four alternative functional forms of the association structure between the CD4 count and the risk of death and provide rationale for selecting the optimal association structure for our data. We also aim to compare the results obtained from the joint model to those obtained from the time-varying Cox model.

Methods

We used data from the Centre for the AIDS Programme of Research in South Africa (CAPRISA) AIDS Treatment programme, the Starting Antiretroviral Therapy at Three Points in Tuberculosis (SAPiT) study, an open-label, three armed randomised, controlled trial between June 2005 and July 2010 (N=642). In our analysis, we combined the early and late integrated arms and compared results to the sequential arm. We utilized the Deviance Information Criterion (DIC) to select the final model with the best structure, with smaller values indicating better model adjustments to the data.

Results

Patient characteristics were similar across the study arms. Combined integrated therapy arms had a reduction of 55% in mortality (HR:0.45, 95% CI:0.28-0.72) compared to the sequential therapy arm. The joint model with a cumulative effects functional form was chosen as the best association structure. In particular, our joint model found that the area under the longitudinal profile of CD4 count was strongly associated with a 21% reduction in mortality (HR:0.79, 95% CI:0.72-0.86). Where as results from the time-varying Cox model showed a 19% reduction in mortality (HR:0.81, 95% CI:0.77-0.84).

Conclusions

In this paper we have shown that the “current value” association structure is not always the best structure that expresses the correct relationship between the outcomes in all settings, which is why it is crucial to explore alternative clinically meaningful association structures that links the longitudinal and survival processes.

Data-Driven Chronic Allograft Phenotypes: A Novel and Validated Complement for Histologic Assessment of Kidney Transplant Biopsies

BACKGROUND

No validated system currently exists to realistically characterize the chronic pathology of kidney transplants that represents the dynamic disease process and spectrum of disease severity. We sought to develop and validate a tool to describe chronicity and severity of renal allograft disease and integrate it with the evaluation of disease activity.

METHODS

The training cohort included 3549 kidney transplant biopsies from an observational cohort of 937 recipients. We reweighted the chronic histologic lesions according to their time-dependent association with graft failure, and performed consensus k-means clustering analysis. Total chronicity was calculated as the sum of the weighted chronic lesion scores, scaled to the unit interval.

RESULTS

We identified four chronic clusters associated with graft outcome, based on the proportion of ambiguous clustering. The two clusters with the worst survival outcome were determined by interstitial fibrosis and tubular atrophy (IFTA) and by transplant glomerulopathy. The chronic clusters partially overlapped with the existing Banff IFTA classification (adjusted Rand index, 0.35) and were distributed independently of the acute lesions. Total chronicity strongly associated with graft failure (hazard ratio [HR], 8.33; 95% confidence interval [CI], 5.94 to 10.88; P<0.001), independent of the total activity scores (HR, 5.01; 95% CI, 2.83 to 7.00; P<0.001). These results were validated on an external cohort of 4031 biopsies from 2054 kidney transplant recipients.

CONCLUSIONS

The evaluation of total chronicity provides information on kidney transplant pathology that complements the estimation of disease activity from acute lesion scores. Use of the data-driven algorithm used in this study, called RejectClass, may provide a holistic and quantitative assessment of kidney transplant injury phenotypes and severity.

Full Blood Count Trends for Colorectal Cancer Detection in Primary Care: Development and Validation of a Dynamic Prediction Model

Colorectal cancer has low survival rates when late-stage, so earlier detection is important. The full blood count (FBC) is a common blood test performed in primary care. Relevant trends in repeated FBCs are related to colorectal cancer presence. We developed and internally validated dynamic prediction models utilising trends for early detection. We performed a cohort study. Sex-stratified multivariate joint models included age at baseline (most recent FBC) and simultaneous trends over historical haemoglobin, mean corpuscular volume (MCV), and platelet measurements up to baseline FBC for two-year risk of diagnosis. Performance measures included the c-statistic and calibration slope. We analysed 250,716 males and 246,695 females in the development cohort and 312,444 males and 462,900 females in the validation cohort, with 0.4% of males and 0.3% of females diagnosed two years after baseline FBC. Compared to average population trends, patient-level declines in haemoglobin and MCV and rise in platelets up to baseline FBC increased risk of diagnosis in two years. C-statistic: 0.751 (males) and 0.763 (females). Calibration slope: 1.06 (males) and 1.05 (females). Our models perform well, with low miscalibration. Utilising trends could bring forward diagnoses to earlier stages and improve survival rates. External validation is now required.

TMBcat: A multi-endpoint p-value criterion on different discrepancy metrics for superiorly inferring tumor mutation burden thresholds

Tumor mutation burden (TMB) is a widely recognized stratification biomarker for predicting the efficacy of immunotherapy; however, the number and universal definition of the categorizing thresholds remain debatable due to the multifaceted nature of efficacy and the imprecision of TMB measurements. We proposed a minimal joint p-value criterion from the perspective of differentiating the comprehensive therapeutic advantages, termed TMBcat, optimized TMB categorization across distinct cancer cohorts and surpassed known benchmarks. The statistical framework applies to multidimensional endpoints and is fault-tolerant to TMB measurement errors. To explore the association between TMB and various immunotherapy outcomes, we performed a retrospective analysis on 78 patients with non-small cell lung cancer and 64 patients with nasopharyngeal carcinomas who underwent anti-PD-(L)1 therapy. The stratification results of TMBcat confirmed that the relationship between TMB and immunotherapy is non-linear, i.e., treatment gains do not inherently increase with higher TMB, and the pattern varies across carcinomas. Thus, multiple TMB classification thresholds could distinguish patient prognosis flexibly. These findings were further validated in an assembled cohort of 943 patients obtained from 11 published studies. In conclusion, our work presents a general criterion and an accessible software package; together, they enable optimal TMB subgrouping. Our study has the potential to yield innovative insights into therapeutic selection and treatment strategies for patients.

A Joint Model Considering Measurement Errors for Optimally Identifying Tumor Mutation Burden Threshold

Tumor mutation burden (TMB) is a recognized stratification biomarker for immunotherapy. Nevertheless, the general TMB-high threshold is unstandardized due to severe clinical controversies, with the underlying cause being inconsistency between multiple assessment criteria and imprecision of the TMB value. The existing methods for determining TMB thresholds all consider only a single dimension of clinical benefit and ignore the interference of the TMB error. Our research aims to determine the TMB threshold optimally based on multifaceted clinical efficacies accounting for measurement errors. We report a multi-endpoint joint model as a generalized method for inferring the TMB thresholds, facilitating consistent statistical inference using an iterative numerical estimation procedure considering mis-specified covariates. The model optimizes the division by combining objective response rate and time-to-event outcomes, which may be interrelated due to some shared traits. We augment previous works by enabling subject-specific random effects to govern the communication among distinct endpoints. Our simulations show that the proposed model has advantages over the standard model in terms of precision and stability in parameter estimation and threshold determination. To validate the feasibility of the proposed thresholds, we pool a cohort of 73 patients with non-small-cell lung cancer and 64 patients with nasopharyngeal carcinoma who underwent anti-PD-(L)1 treatment, as well as validation cohorts of 943 patients. Analyses revealed that our approach could grant clinicians a holistic efficacy assessment, culminating in a robust determination of the TMB screening threshold for superior patients. Our methodology has the potential to yield innovative insights into therapeutic selection and support precision immuno-oncology.

Longitudinal Anthropometric Measures and Risk of New-Onset Atrial Fibrillation Among Community-Dwelling Men and Women

OBJECTIVE

To assess the sex-specific evolution of various anthropometric measures and the association of their longitudinal trajectories with new-onset atrial fibrillation (AF).

METHODS

Among 5266 men and 7218 women free of AF at baseline from the prospective population-based Rotterdam Study, each anthropometric measure was measured 1 to 5 times from 1989 to 2014. Anthropometric measures were standardized to obtain hazard ratios per 1 SD increase to enable comparison. Joint models were used to assess the longitudinal association between anthropometric measures and incident AF. Use of the joint models is a preferred method for simultaneous analyses of repeated measurements and survival data for conferring less biased estimates.

RESULTS

Mean (SD) age was 63.9 (8.9) years for men and 64.9 (9.8) years for women. Median follow-up time was 10.5 years. Longitudinal evolution of weight, height, waist circumference, hip circumference, and body mass index was associated with an increased risk of new-onset AF in both men and women. In joint models, larger height in men (hazard ratio [95% credible interval] per 1 SD, 1.27 [1.17 to 1.38]) and weight in women (1.24 [1.16 to 1.34]) showed the largest associations with AF. In joint models, waist to hip ratio was significantly associated with incident AF only in women (1.10 [1.03 to 1.18]).

CONCLUSION

Considering the entire longitudinal trajectories in joint models, anthropometric measures were positively associated with an increased risk for new-onset AF among men and women in the general population. Increase in measure of central obesity showed a stronger association with increased risk of AF onset among women compared with men.

Individually experienced heat index in a coastal Southeastern US city among an occupationally exposed population

Recent studies have characterized individually experienced temperatures or individually experienced heat indices, including new exposure metrics that capture dimensions of exposure intensity, frequency, and duration. Yet, few studies have examined the personal thermal exposure in underrepresented groups, like outdoor workers, and even fewer have assessed corresponding changes in physiologic heat strain. The objective of this paper is to examine a cohort of occupationally exposed grounds and public safety workers (n = 25) to characterize their heat exposure and resulting heat strain. In addition, a secondary aim of this work is to compare individually heat index exposure (IHIE) across exposure metrics, fixed-site in situ weather stations, and raster-derived urban heat island (UHI) measurements in Charleston, SC, a humid coastal climate in the Southeastern USA. A Bland-Altman (BA) analysis was used to assess the level of agreement between the personal IHIE measurements and weather-station heat index (HI) and Urban Heat Island (UHI) measurements. Linear mixed-effect models were used to determine the association between individual risk factors and in situ weather station measurements significantly associated with IHIE measurements. Multivariable stepwise Cox proportional hazard modeling was used to identify the individual and workplace factors associated with time to heat strain in workers. We also examined the non-linear association between heat strain and exposure metrics using generalized additive models. We found significant heterogeneity in IHIE measurements across participants. We observed that time to heat strain was positively associated with a higher IHIE, older age, being male, and among Caucasian workers. Important nonlinear associations between heat strain occurrence and the intensity, frequency, and duration of personal heat metrics were observed. Lastly, our analysis found that IHIE measures were significantly similar for weather station HI, although differences were more pronounced for temperature and relative humidity measurements. Conversely, our IHIE findings were much lower than raster-derived UHI measurements. Real-time monitoring can offer important insights about unfolding temperature-health trends and emerging behaviors during thermal extreme events, which have significant potential to provide situational awareness.

An efficient estimation approach to joint modeling of longitudinal and survival data

The joint models for longitudinal and survival data have recently received significant attention in medical and epidemiological studies. Joint models typically combine linear mixed effects models for repeated measurement data and Cox models for survival time. When we are jointly modeling the longitudinal and survival data, variable selection and efficient estimation of parameters are especially important for performing reliable statistical analyzes, both of which are currently lacking in the literature. In this paper we discuss the pretest and shrinkage estimation methods for jointly modeling longitudinal data and survival time data when some of the covariates in both longitudinal and survival components may not be relevant for predicting survival times. In this situation, we fit two models: the full model that contains all the covariates and the subset model that contains a reduced number of covariates. We combine the full model estimators and the estimators that are restricted by a linear hypothesis to define pretest and shrinkage estimators. We provide their numerical mean squared errors (MSE) and relative MSE. We show that if the shrinkage dimension exceeds two, the risk of the shrinkage estimators is strictly less than that of the full model estimators. Our proposed methods are illustrated by extensive simulation studies and a real-data example.

CKD-MBD Biomarkers and CKD Progression: an Analysis by the Joint Model

BACKGROUND

Biomarkers of the CKD- Bone Mineral Disorder (CKD-BMD have been implicated in CKD progression in follow up studies focusing on single measurements of individual biomarkers made at baseline only. The simultaneous relationship between the time trend of these biomarkers over the course of CKD and renal outcomes has never been tested.

METHODS

We applied the Joint Model (JM) to investigate the longitudinal relationship between repeated measurements of CKD-MBD biomarkers and a combined renal endpoint (eGFR reduction >30%, dialysis or transplantation) in 729 stage 2-5 CKD patients over a 36 months follow up.

RESULTS

In the survival sub-model of the JM the longitudinal series of PTH values was directly and independently related to the risk of renal events [HR (1ln PTH) = 2.0 (from 1.5 to 2.8), p<0.001)] and this was also true for repeated measurements of serum phosphate [HR(1mg/dl) = 1.3924 (from 1.1459 to 1.6918), p = 0.001], serum calcium [HR(1mg/dl) = 0.7487 (from 0.5843 to 0.9593), p = 0.022], baseline FGF23 [HR(1pg/ml) = 1.001 (from 1.00 to 1.002), p = 0.045] and 1,25 dihydroxy Vitamin D [HR (1pg/ml) = 0.9796 (from 0.9652 to 0.9942), p = 0.006].

CONCLUSION

Repeated measurements of serum PTH, calcium and phosphate as well as baseline FGF23 and 1,25 dihydroxy vitamin D are independently related with the progression to kidney failure in a cohort of stage 2-5 CKD patients. This longitudinal study generates the hypothesis that interventions at multiple levels on BMD biomarkers can mitigate renal function loss in this population.

Factors associated to the duration of COVID-19 lockdowns in Chile

During the first year of the COVID-19 pandemic, several countries have implemented non-pharmacologic measures, mainly lockdowns and social distancing, to reduce the spread of the SARS-CoV-2 virus. These strategies varied widely across nations, and their efficacy is currently being studied. This study explores demographic, socioeconomic, and epidemiological factors associated with the duration of lockdowns applied in Chile between March 25th and December 25th, 2020. Joint models for longitudinal and time-to-event data were used. In this case, the number of days under lockdown for each Chilean commune and longitudinal information were modeled jointly. Our results indicate that overcrowding, number of active cases, and positivity index are significantly associated with the duration of lockdowns, being identified as risk factors for longer lockdown duration. In short, joint models for longitudinal and time-to-event data permit the identification of factors associated with the duration of lockdowns in Chile. Indeed, our findings suggest that demographic, socioeconomic, and epidemiological factors should be used to define both entering and exiting lockdown.

Fitting joint models of longitudinal observations and time to event by sequential Bayesian updating

Joint modelling of longitudinal measurements and time to event, with longitudinal and event submodels coupled by latent state variables, has wide application in biostatistics. Standard methods for fitting these models require numerical integration to marginalize over the trajectories of the latent states, which is computationally prohibitive for high-dimensional data and for the large data sets that are generated from electronic health records. This paper describes an alternative model-fitting approach based on sequential Bayesian updating, which allows the likelihood to be factorized as the product of the likelihoods of a state-space model and a Poisson regression model. Updates for linear Gaussian state-space models can be efficiently generated with a Kalman filter and the approach can be implemented with existing software. An application to a publicly available data set is demonstrated.

Kimesurface Representation and Tensor Linear Modeling of Longitudinal Data

Many modern techniques for analyzing time-varying longitudinal data rely on parametric models to interrogate the time-courses of univariate or multivariate processes. Typical analytic objectives include utilizing retrospective observations to model current trends, predict prospective trajectories, derive categorical traits, or characterize various relations. Among the many mathematical, statistical, and computational strategies for analyzing longitudinal data, tensor-based linear modeling offers a unique algebraic approach that encodes different characterizations of the observed measurements in terms of state indices. This paper introduces a new method of representing, modeling, and analyzing repeated-measurement longitudinal data using a generalization of event order from the positive reals to the complex plane. Using complex time (kime), we transform classical time-varying signals as 2D manifolds called kimesurfaces. This kime characterization extends the classical protocols for analyzing time-series data and offers unique opportunities to design novel inference, prediction, classification, and regression techniques based on the corresponding kimesurface manifolds. We define complex time and illustrate alternative time-series to kimesurface transformations. Using the Laplace transform and its inverse, we demonstrate the bijective mapping between time-series and kimesurfaces. A proposed general tensor regression based linear model is validated using functional Magnetic Resonance Imaging (fMRI) data. This kimesurface representation method can be used with a wide range of machine learning algorithms, artificial intelligence tools, analytical approaches, and inferential techniques to interrogate multivariate, complex-domain, and complex-range longitudinal processes.

Early Variation of Respiratory Indexes to Predict Death or ICU Admission in Severe Acute Respiratory Syndrome Coronavirus-2-Related Respiratory Failure

Background

In severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2)-related respiratory failure, the prognostic value of clinically based or blood-gas-based respiratory indexes is unclear.

Objectives

We aimed to assess the prognostic value of Respiratory Index (RI, oxygen saturation [SpO2]/respiratory rate [RR]), RR-oxygenation index (ROX, SpO2/fraction of inspired oxygen [FiO2]/RR), partial pressure of oxygen (PaO2)/FiO2 ratio (P/F), or standard PaO2/FiO2 ratio (_STP/F) at admission and of their variation during hospitalization in SARS-CoV-2-related respiratory failure.

Methods

In 100 consecutive patients hospitalized due to SARS-CoV-2-related respiratory failure, we assessed the association of RI, ROX, P/F and _STP/F, and death; secondary outcome was the composite of 7-day death or intensive care unit (ICU) admission.

Results

ROX <3.85 at admission (hazard ratio [HR] 2.95, 95% confidence interval [CI] 1.29–6.77) and decreasing RI or P/F during hospitalization (RI: HR 1.05, 95% CI: 1.00–1.09; P/F: HR 1.01, 95% CI: 1.00–1.02) were predictors of in-hospital death. RI ≤3.8, ROX <3.85, and P/F <100 at admission were predictors for death or ICU admission (RI: HR 3.77, 95% CI: 1.30–10.98; ROX: HR 4.56, 95% CI: 1.90–10.96; P/F: HR 7.37, 95% CI: 1.59–34.2). The decrease of RI (HR 1.14, 95% CI: 1.03–1.25), ROX (HR 1.45, 95% CI: 1.11–1.88), P/F (HR 1.08, 95% CI: 1.01–1.15), or _STP/F (HR 1.05, 95% CI: 1.01–1.08) during hospitalization was associated with 7-day death or ICU admission.

Conclusions

In patients with SARS-CoV-2-related respiratory failure, easy-to-calculate clinically based respiratory indexes at admission and their variation during hospital stay can be used to assess and monitor the risk for death or ICU admission.

A Joint Model for Unbalanced Nested Repeated Measures with Informative Drop-Out Applied to Ambulatory Blood Pressure Monitoring Data

This study proposes a Bayesian joint model with extended random effects structure that incorporates nested repeated measures and provides simultaneous inference on treatment effects over time and drop-out patterns. The proposed model includes flexible splines to characterize the circadian variation inherent in blood pressure sequences, and we assess the effectiveness of an intervention to resolve pediatric obstructive sleep apnea. We demonstrate that the proposed model and its conventional two-stage counterpart provide similar estimates of nighttime blood pressure but estimates on the mean evolution of daytime blood pressure are discrepant. Our simulation studies tailored to the motivating data suggest reasonable estimation and coverage probabilities for both fixed and random effects. Computational challenges of model implementation are discussed.

Landmarking 2.0: Bridging the gap between joint models and landmarking

The problem of dynamic prediction with time‐dependent covariates, given by biomarkers, repeatedly measured over time, has received much attention over the last decades. Two contrasting approaches have become in widespread use. The first is joint modeling, which attempts to jointly model the longitudinal markers and the event time. The second is landmarking, a more pragmatic approach that avoids modeling the marker process. Landmarking has been shown to be less efficient than correctly specified joint models in simulation studies, when data are generated from the joint model. When the mean model is misspecified, however, simulation has shown that joint models may be inferior to landmarking. The objective of this article is to develop methods that improve the predictive accuracy of landmarking, while retaining its relative simplicity and robustness. We start by fitting a working longitudinal model for the biomarker, including a temporal correlation structure. Based on that model, we derive a predictable time‐dependent process representing the expected value of the biomarker after the landmark time, and we fit a time‐dependent Cox model based on the predictable time‐dependent covariate. Dynamic predictions based on this approach for new patients can be obtained by first deriving the expected values of the biomarker, given the measured values before the landmark time point, and then calculating the predicted probabilities based on the time‐dependent Cox model. We illustrate the approach in predicting overall survival in liver cirrhosis patients based on prothrombin index.

Examining the factors contributing to the association between non-albuminuric CKD and a low rate of kidney function decline in diabetes

BACKGROUND

Studies have shown that among people with diabetes, those with non-albuminuric chronic kidney disease (CKD) have a slower rate of reduction in renal function than do those with normal renal function. This suggests the presence of protective factors, the identification of which may open up targets for intervention. The aim of this study was to identify protective clinical factors and nonclinical biomarkers that contribute to the association between non-albuminuric CKD and the low rate of progression of CKD.

METHODS

We tested for significant associations of several clinical factors and 33 nonclinical biomarkers with (1) normoalbuminuria and (2) a low rate of CKD progression among participants with diabetes and CKD enrolled in the Chronic Renal Insufficiency Cohort (CRIC) Study in the United States. Factors significantly associated with both normoalbuminuria and a low rate of CKD progression were assessed in linear regression to estimate their potential contributions to the association between non-albuminuric CKD and rate of CKD progression.

RESULTS

Systolic blood pressure (SBP), glycated A1c (HbA1c), estimated glomerular filtration rate (eGFR) and six biomarkers [β-trace protein (BTP), kidney injury molecule (KIM-1), fibrinogen, fractalkine, brain natriuretic peptide (BNP) and high-sensitivity troponin-T (hsTnT)] were associated with both normoalbuminuria and a low rate of eGFR decline. The univariate β-coefficient for normoalbuminuria was 0.93 [95% confidence interval (CI): 0.82, 1.05]. When all associated factors and biomarkers were included, the regression coefficient decreased to 0.54 (95% CI: 0.40, 0.67). The factors that contributed to the association between non-albuminuric CKD and low rate of eGFR were lower levels of SBP, HbA1c, BTP, KIM-1, hsTnT, BNP, fibrinogen and fractalkine.

CONCLUSION

Lower levels of SBP and biomarkers that have pro-inflammatory and vascular modulating features may explain up to 40% of the association between non-albuminuric CKD and low rate of CKD progression. Further investigation of these biomarkers may lead to therapeutic interventions.

Associations between depressive symptoms and disease progression in older patients with chronic kidney disease: results of the EQUAL study

Background

Depressive symptoms are associated with adverse clinical outcomes in patients with end-stage kidney disease; however, few small studies have examined this association in patients with earlier phases of chronic kidney disease (CKD). We studied associations between baseline depressive symptoms and clinical outcomes in older patients with advanced CKD and examined whether these associations differed depending on sex.

Methods

CKD patients (≥65 years; estimated glomerular filtration rate ≤20 mL/min/1.73 m²) were included from a European multicentre prospective cohort between 2012 and 2019. Depressive symptoms were measured by the five-item Mental Health Inventory (cut-off ≤70; 0–100 scale). Cox proportional hazard analysis was used to study associations between depressive symptoms and time to dialysis initiation, all-cause mortality and these outcomes combined. A joint model was used to study the association between depressive symptoms and kidney function over time. Analyses were adjusted for potential baseline confounders.

Results

Overall kidney function decline in 1326 patients was –0.12 mL/min/1.73 m²/month. A total of 515 patients showed depressive symptoms. No significant association was found between depressive symptoms and kidney function over time (P = 0.08). Unlike women, men with depressive symptoms had an increased mortality rate compared with those without symptoms [adjusted hazard ratio 1.41 (95% confidence interval 1.03–1.93)]. Depressive symptoms were not significantly associated with a higher hazard of dialysis initiation, or with the combined outcome (i.e. dialysis initiation and all-cause mortality).

Conclusions

There was no significant association between depressive symptoms at baseline and decline in kidney function over time in older patients with advanced CKD. Depressive symptoms at baseline were associated with a higher mortality rate in men.

Individualized prediction for the occurrence of acute kidney injury during the first postoperative week following cardiac surgery

STUDY OBJECTIVE

To develop individualized dynamic predictions for the occurrence of acute kidney injury (AKI) during the first postoperative week after cardiac surgery.

DESIGN

Observational retrospective cohort study.

SETTING

Single university teaching hospital in Madrid, Spain.

PATIENTS

3960 cases of major cardiac surgery performed from January 2002 to December 2013.

MEASUREMENTS

Baseline demographic and clinical characteristics, intraoperative risk factors, and repeated postoperative estimated glomerular filtration rates (eGFR). The primary outcome was AKI during the first postoperative week (stage 1 or higher of the Acute Kidney Injury Network). The dataset was split in two random samples (exploratory and validation). By combining time-to-event outcomes (AKI), and longitudinal data (repeated postoperative eGFR), we developed two different joint models for patients with normal and high baseline levels of serum creatinine (sCr).

MAIN RESULTS

AKI occurred in 1105 patients (31%, 95% confidence interval [CI] 29.5-32.5) in the exploratory sample and 128 (32.2%, 95% CI 27.6-36.8) in the validation sample. For high baseline sCr patients, the risk of an AKI event was associated with the eGFR trajectory (hazard ratio [HR] 0.91, 95% CI 0.90-0.92), as well as with age, and cardiopulmonary bypass time. The normal baseline sCr model incorporated the same covariates and intraoperative transfusion. In this second model, the risk of an AKI event was associated with both the eGFR trajectory (HR 0.91, 95% CI 0.91-0.92, for the current value of eGFR), and with its slope at that point (HR 0.96, 95% CI 0.94-0.99). So AKI risk decreased when the eGFR values increased, in accordance with the speed of this rise. Internal validation showed good discrimination and calibration of both joint models. The AUCs were always higher than 0.7.

CONCLUSIONS

The joint models obtained combining both patient risk factors and postoperative eGFR values, are useful to predict individualized risk of cardiac surgery-associated AKI. Predictions can be updated as new information is gathered.

Dynamic recurrence risk and adjuvant chemotherapy benefit prediction by ctDNA in resected NSCLC

Accurately evaluating minimal residual disease (MRD) could facilitate early intervention and personalized adjuvant therapies. Here, using ultradeep targeted next-generation sequencing (NGS), we evaluate the clinical utility of circulating tumor DNA (ctDNA) for dynamic recurrence risk and adjuvant chemotherapy (ACT) benefit prediction in resected non-small cell lung cancer (NSCLC). Both postsurgical and post-ACT ctDNA positivity are significantly associated with worse recurrence-free survival. In stage II-III patients, the postsurgical ctDNA positive group benefit from ACT, while ctDNA negative patients have a low risk of relapse regardless of whether or not ACT is administered. During disease surveillance, ctDNA positivity precedes radiological recurrence by a median of 88 days. Using joint modeling of longitudinal ctDNA analysis and time-to-recurrence, we accurately predict patients’ postsurgical 12-month and 15-month recurrence status. Our findings reveal longitudinal ctDNA analysis as a promising tool to detect MRD in NSCLC, and we show pioneering work of using postsurgical ctDNA status to guide ACT and applying joint modeling to dynamically predict recurrence risk, although the results need to be further confirmed in future studies.

ctDNA has been shown to identify minimal residual disease (MRD) and is thus dynamically monitored in different types of tumours. Here, the authors show that serial longitudinal ctDNA analysis can be used as a tool to detect MRD, inform the use of adjuvant therapy, and predict recurrence risk in lung cancer.

Improving the investigative approach to polycythaemia vera: a critical assessment of current evidence and vision for the future

Polycythaemia vera is a challenging disease to study given its low prevalence and prolonged time-to-event for important clinical endpoints such as thrombosis, progression, and mortality. Although researchers in this space often rise to meet these challenges, there is considerable room for improvement in the analysis of retrospective data, the development of risk-stratification tools, and the design of randomised controlled trials. In this Viewpoint, we review the evidence behind the contemporary approach to risk stratification and treatment of polycythaemia vera. Frameworks for using data more efficiently, constructing more nuanced prognostic models, and overcoming challenges in clinical trial design are discussed.

Robust joint modelling of longitudinal and survival data: Incorporating a time-varying degrees-of-freedom parameter

Monitoring of individual biomarkers has the potential of explaining the hazard of survival outcomes. In practice, these measurements are intermittently observed and are known to be subject to substantial measurement error. Joint modelling of longitudinal and survival data enables us to associate intermittently measured error-prone biomarkers with risks of survival outcomes and thus plays an important role in the analysis of medical data. Most of the joint models available in the literature have been built on the Gaussian assumption. This makes them sensitive to outliers. In this work, we study a range of robust models to address this issue. Of particular interest is the common occurrence in medical data that outliers can occur with different frequencies over time, for example, in the period when patients adjust to treatment changes. Motivated by the analysis of data gathered from patients with primary biliary cirrhosis, a new model with a time-varying robustness is introduced. Through both the motivating example and a simulation study, this research not only stresses the need to account for longitudinal outliers in the analysis of medical data and in joint modelling research but also highlights the bias and inefficiency from not properly estimating the degrees-of-freedom parameter. This work presents a number of methods in addition to the time-varying robustness, and each method can be fitted using the R package robjm.

Rate of decline in kidney function and known age-of-onset or duration of type 2 diabetes

The association between rate of kidney function decline and age-of-onset or duration of diabetes has not been well investigated. We aimed to examine whether rates of estimated glomerular filtration rate (eGFR) decline differ by age-of-onset or duration in people with type 2 diabetes. Using the Action to Control Cardiovascular Risk in Diabetes study which included those with HbA1c ≥ 7.5% and who were at high risk of cardiovascular events,, rates of eGFR decline were calculated and were compared among groups defined by the known age-of-onset (0–39, 40–49, 50–59, 60–69 and > 70 years) and 5-year diabetes duration intervals. Changes in renal function were evaluated using median of 6 (interquartile range 3–10) eGFR measurements per person. eGFR decline was the slowest in those with known age-at-diagnosis of 50–59 years or those with duration of diabetes < 5 years. The rates of eGFR decline were significantly greater in those with known age-of-onset < 40 years or those with duration of diabetes > 20 years compared to those diagnosed at 50–59 or those with duration of diabetes < 5 years (− 1.98 vs − 1.61 mL/min/year; − 1.82 vs − 1.52 mL/min/year; respectively (p < 0.001). Those with youngest age-of-onset or longer duration of diabetes had more rapid declines in eGFR compared to those diagnosed at middle age or those with shorter duration of diabetes.

Monitoring of plasma concentrations of dabrafenib and trametinib in advanced BRAFV600mut melanoma patients

BACKGROUND

Dabrafenib (D) and trametinib (T) improved survival in patients with BRAFV600^mut melanoma. High plasma concentration of D (PCD) is weakly associated with adverse events (AE). We investigated the relationship between PCD/T and tumour control or AE.

METHODS

We analysed PCD/T in patients treated with D+T for metastatic melanoma. We collected data of tumour response (RECIST 1.1) and AE (CTCAE 4.0) blinded to PCD/T results.

RESULTS

We analysed 71 D and 58T assays from 34 patients. High inter-individual variability of PCD (median: 65.0ng/mL; interquartile range (IQR) [4-945]) and of PCT (median: 8.6ng/mL; IQR [5-39]) was observed. We found a weak relationship between PCD and progression-free survival, taking follow-up time into account (hazard ratio 0.991; 95%CI, 0.981 to 1.000; P=0.06). However, no difference was observed between mean PCD/T of progressing patients (n=21; 125±183ng/mL and 9.3±3.6ng/mL, respectively) and responders (complete, partial or stable response) (n=13; 159±225ng/mL, P=0.58 and 10.6±24.4ng/mL, P=0.29, respectively). No significant relationship was found between PCD/T and most common AEs (fever, lymphopenia, CPK increase, and hepatic cytolysis), body mass index, or age. Mean CPT (n=16) was significantly higher for female subjects (n=18; 11.5±4.8ng/mL) than for male subjects (8.8ng/mL±2.9, P=0.01), but no difference was observed between sex and CPD (P=0.32).

CONCLUSION

Our study showed a weak relationship between PCD and progression-free survival, but no relationship between PCD/T and AE was found. Monitoring PCD and PCT alone is unlikely to be useful in assessing response to treatment.

Long-term kidney function of patients discharged from hospital after an intensive care admission: observational cohort study

The long-term trajectory of kidney function recovery or decline for survivors of critical illness is incompletely understood. Characterising changes in kidney function after critical illness and associated episodes of acute kidney injury (AKI), could inform strategies to monitor and treat new or progressive chronic kidney disease. We assessed changes in estimated glomerular filtration rate (eGFR) and impact of AKI for 1301 critical care survivors with 5291 eGFR measurements (median 3 [IQR 2, 5] per patient) between hospital discharge (2004-2008) and end of 7 years of follow-up. Linear mixed effects models showed initial decline in eGFR over the first 6 months was greatest in patients without AKI (- 9.5%, 95% CI - 11.5% to - 7.4%) and with mild AKI (- 12.3%, CI - 15.1% to - 9.4%) and least in patients with moderate-severe AKI (- 4.3%, CI - 7.0% to - 1.4%). However, compared to patients without AKI, hospital discharge eGFR was lowest for the moderate-severe AKI group (median 61 [37, 96] vs 101 [78, 120] ml/min/1.73m2) and two thirds (66.5%, CI 59.8-72.6% vs 9.2%, CI 6.8-12.4%) had an eGFR of < 60 ml/min/1.73m2 through to 7 years after discharge. Kidney function trajectory after critical care discharge follows a distinctive pattern of initial drop then sustained decline. Regardless of AKI severity, this evidence suggests follow-up should incorporate monitoring of eGFR in the early months after hospital discharge.

Longitudinal-Survival Models for Case-Based Tuberculosis Progression

Introduction: Tuberculosis (TB) disease continues to be responsible for a high global burden with an estimated 10 million people falling ill each year and an estimated 1.45 million deaths. Widely carried out analyses to utilize routine data coming from this disease, and well-established in literature, have paid attention to time-to-event with sputum smear results being considered only at baseline or even ignored. Also, logistic regression models have been used to demonstrate importance of sputum smear results in patient outcomes. A feature presented by this disease, however, is that each individual patient is usually followed over a period of time with sputum smear results being documented at different points of the treatment curve. This provides both repeated measures and survival times, which may require a joint modeling approach. This study aimed to investigate the association between sputum smear results and the risk of experiencing unfavorable outcome among TB patients and dynamically predict survival probabilities.

Method: A joint model for longitudinal and time-to-event data was used to analyze longitudinally measured smear test results with time to experiencing unfavorable outcome for TB patients. A generalized linear mixed-effects model was specified for the longitudinal submodel and cox proportional hazards model for the time-to-event submodel with baseline hazard approximated using penalized B-splines. The two submodels were then assumed to be related via the current value association structure. Bayesian approach was used to approximate parameter estimates using Markov Chain Monte Carlo (MCMC) algorithm. The obtained joint model was used to predict the subject's future risk of survival based on sputum smear results trajectories. Data were sourced from routinely collected TB data stored at National TB Program database.

Results: The average baseline age was 35 (SD: 15). Female TB patients constituted 36.42%. Patients with previous history of TB treatment constituted 6.38% (event: 15.25%; no event: 5.29%). TB/HIV co-infection was at 31.23% (event: 47.87%; no event: 29.20%). The association parameter 1.03 (CI[1.03,1.04]) was found to be positive and significantly different from zero, interpreted as follows: The estimate of the association parameter α = 1.033 denoted the log hazard ratio for a unit increase in the log odds of having smear positive results. HIV status (negative) 0.47 (CI [0.46,49]) and history of TB treatment (previously treated) (2.52 CI [2.41,2.63]), sex (female) (0.82 CI [0.78,0.84]), and body mass index (BMI) categories (severe malnutrition being reference) were shown to be statistically significant.

Conclusion: Sputum smear result is important in estimating the risk to unfavorable outcome among TB patients. Men, previously treated, TB/HIV co-infected and severely malnourished TB patients are at higher risk of unfavorable outcomes.

More than one way: exploring the capabilities of different estimation approaches to joint models for longitudinal and time-to-event outcomes

The development of physical functioning after a caesura in an aged population is still widely unexplored. Analysis of this topic would need to model the longitudinal trajectories of physical functioning and simultaneously take terminal events (deaths) into account. Separate analysis of both results in biased estimates, since it neglects the inherent connection between the two outcomes. Thus, this type of data generating process is best modelled jointly. To facilitate this several software applications were made available. They differ in model formulation, estimation technique (likelihood-based, Bayesian inference, statistical boosting) and a comparison of the different approaches is necessary to identify their capabilities and limitations. Therefore, we compared the performance of the packages JM, joineRML, JMbayes and JMboost of the R software environment with respect to estimation accuracy, variable selection properties and prediction precision. With these findings we then illustrate the topic of physical functioning after a caesura with data from the German ageing survey (DEAS). The results suggest that in smaller data sets and theory driven modelling likelihood-based methods (expectation maximation, JM, joineRML) or Bayesian inference (JMbayes) are preferable, whereas statistical boosting (JMboost) is a better choice with high-dimensional data and data exploration settings.

Reflections on modern methods: Dynamic prediction using joint models of longitudinal and time-to-event data

Individualized prediction is a hallmark of clinical medicine and decision making. However, most existing prediction models rely on biomarkers and clinical outcomes available at a single time. This is in contrast to how health states progress and how physicians deliver care, which relies on progressively updating a prognosis based on available information. With the use of joint models of longitudinal and survival data, it is possible to dynamically adjust individual predictions regarding patient prognosis. This article aims to introduce the reader to the development of dynamic risk predictions and to provide the necessary resources to support their implementation and assessment, such as adaptable R code, and the theory behind the methodology. Furthermore, measures to assess the predictive performance of the derived predictions and extensions that could improve the predictions are presented. We illustrate personalized predictions using an online dataset consisting of patients with chronic liver disease (primary biliary cirrhosis).

Explaining the Sex Effect on Survival in Cystic Fibrosis: a Joint Modeling Study of UK Registry Data

BACKGROUND

Male sex is associated with better lung function and survival in people with cystic fibrosis but it is unclear whether the survival benefit is solely due to the sex-effect on lung function.

METHODS

This study analyzes data between 1996 and 2015 from the longitudinal registry study of the UK Cystic Fibrosis Registry. We jointly analyze repeated measurements and time-to-event outcomes to assess how much of the sex effect on lung function also explains survival. These novel methods allow examination of association between percent of forced expiratory volume in 1 second (%FEV1) and covariates such as sex and genotype, and survival, in the same modeling framework. We estimate the probability of surviving one more year with a probit model.

RESULTS

The dataset includes 81,129 lung function measurements of %FEV1 on 9,741 patients seen between 1996 and 2015 and captures 1,543 deaths. Males compared with females experienced a more gradual decline in %FEV1 (difference 0.11 per year 95% confidence interval [CI] = 0.08, 0.14). After adjusting for confounders, both overall level of %FEV1 and %FEV1 rate of change are associated with the concurrent hazard for death. There was evidence of a male survival advantage (probit coefficient 0.15; 95% CI = 0.10, 0.19) which changed little after adjustment for %FEV1 using conventional approaches but was attenuated by 37% on adjustment for %FEV1 level and slope in the joint model (0.09; 95% CI = 0.06, 0.12).

CONCLUSIONS

We estimate that about 37% of the association of sex on survival in cystic fibrosis is mediated through lung function.

Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation

In this paper, we propose a joint modeling approach to analyze dependency in parallel response data. We define two types of dependency: higher-level dependency and within-item conditional dependency. While higher-level dependency can be estimated with common latent variable modeling approaches, within-item conditional dependency is a unique kind of information that is often not captured with extant methods, despite its potential to shed new insights into the relationship between the two types of response data. We differentiate three ways of modeling within-item conditional dependency by conditioning on raw values, expected values, or residual values of the response data, which have different implications in terms of response processes. The proposed approach is illustrated with the example of analyzing parallel data on response accuracy and brain activations from a Theory of Mind assessment. The consequence of ignoring within-item conditional dependency is investigated with empirical and simulation studies in comparison to conventional dependency analysis that focuses exclusively on relationships between latent variables.

Statistical Joint Modeling for Predicting the Association of CD4 Measurement and Time to Death of People Living with HIV Who Enrolled in ART, Southwest Ethiopia

Background

In much epidemiological HIV research, patients are often followed over a period of time to predict their survival on the basis of repeatedly measured CD4 status. To predict survival, statistical models of the association between mortality and longitudinal CD4 measurement have been conducted widely using time-varying Cox models. However, in the presence of repeated measure, this approach leads to biased estimates. In view of the limitation of time-varying Cox models, in the present study, we considered joint modeling to predict the association of longitudinal CD4 measurement and time to death among patients initiated on ART.

Methods

A retrospective cohort study was employed for five years from 2009 to 2014 on a randomly selected 358 samples. Data were collected from patients’ ART and pre-ART follow-up registration book, database and other clinical records. Data were analyzed using joint latent class modeling of repeated CD4 measurement and time-to-event (HIV death).

Results

We have studied a total of 358 HIV-positive patients. The median and interquartile ranges of the age of patients were 30.31 years and 13.82, respectively. Males constitute the larger proportion, 51.68%. The square root of CD4 count has declined on average over time. This has been indicated with the negative sign of the coefficient for the time effect. The deterioration of health of individuals is severe in class 1, it has been observed with a worse decline in CD4 cell counts over time in this class than other classes (β= −0.488). Women had a larger risk rate than men (β=−2.475, p-value=0.013). Besides, the CD4 counts measurement of patients has been revealed to decrease as age increases (β= −0.016, p=0.008).

Conclusion

The finding indicated that the square root CD4 cell measurement dropped over time in the three classes. This clearly suggested deterioration in the health of individuals. Women were found to have a higher hazard rate than men.