Regression analysis of restricted mean survival time based on pseudo-observations

Dynamic risk prediction of survival in liver cirrhosis: A comparison of landmarking approaches

Electronic health records (EHR) data provides the researcher and physician with the opportunity to improve risk prediction by employing newer, more sophisticated modeling techniques. Rather than treating the impact of predictor variables on health trajectories as static, we explore the use of time-dependent variables in dynamically modeling time-to-event data through the use of landmarking (LM) data sets. We compare several different dynamic models presented in the literature that utilize LM data sets as the basis of their approach. These techniques include using pseudo-means, pseudo-survival probabilities, and the traditional Cox model. The models are primarily compared with their static counterparts using appropriate measures of model discrimination and calibration based on what summary measure is employed for the response variable.

Scaling and interpreting treatment effects in clinical trials using restricted mean survival time

BACKGROUND

Restricted mean survival time is the expected duration of survival up to a chosen time of restriction τ . For comparison studies, the difference in restricted mean survival times between two groups provides a summary measure of the treatment effect that is free of assumptions regarding the relative shape of the two survival curves, such as proportional hazards. However, it can be difficult to judge the magnitude of the effect from a comparison of restricted means due to the truncation of observation at time τ .

METHODS

In this article, we describe additional ways of expressing the treatment effect based on restricted means that can be helpful in this regard. These include the ratio of restricted means, the ratio of life-years (or time) lost, and the average integrated difference between the survival curves, equal to the difference in restricted means divided by τ . These alternative metrics are straightforward to calculate and provide a means for scaling the effect size as an aid to interpretation. Examples from two randomized, multicenter clinical trials in prostate cancer, NRG/RTOG 0521 and NRG/RTOG 0534, with primary endpoints of overall survival and biochemical/radiological progression-free survival, respectively, are presented to illustrate the ideas.

RESULTS

The four effect measures (restricted mean survival time difference, restricted mean survival time ratio, time lost ratio, and average survival rate difference) were 0.45 years, 1.05, 0.81, and 0.038 for RTOG 0521 and 1.36 years, 1.17, 0.56, and 0.12 for RTOG 0534 with τ  = 12 and 11 years, respectively. Thus, for example, the 0.45-year difference in the first trial translates into a 19% reduction in time lost and a 3.8% average absolute difference between the survival curves over the 12-year horizon, a modest effect size, whereas the 1.36-year difference in the second trial corresponds to a 44% reduction in time lost and a 12% absolute survival difference, a rather large effect.

CONCLUSIONS

In addition to the difference in restricted mean survival times, these alternative measures can be helpful in determining whether the magnitude of the treatment effect is clinically meaningful.

Temporal trends in mortality in patients with rheumatoid arthritis: a Danish population-based matched cohort study

OBJECTIVES

To investigate the 5-year all-cause mortality in patients with RA compared with the general population.

METHODS

This was a nationwide population-based matched cohort study. RA patients diagnosed between 1996 and the end of 2015 were identified using administrative heath registries and followed until the end of 2020 allowing 5 years of follow-up. Patients with incident RA were matched 1:5 on year of birth and sex with non-RA individuals from the Danish general population. Time-to-event analyses were performed using the pseudo-observation approach.

RESULTS

Compared with matched controls in 1996-2000, the risk difference for RA patients ranged from 3.5% (95% CI 2.7%, 4.4%) in 1996-2000 to -1.6% (95% CI -2.3%, -1.0%) in 2011-15, and the relative risk from 1.3 (95% CI 1.2, 1.4) in 1996-2000 to 0.9 (95% CI 0.8, 0.9) in 2011-15. The age-adjusted 5-year cumulative incidence proportion of death for a 60-year-old RA patient decreased from 8.1% (95% CI 7.3%, 8.9%) when diagnosed in 1996-2000 to 2.9% (95% CI 2.3%, 3.5%) in 2011-15, and for matched controls from 4.6% (95% CI 4.2%, 4.9%) to 2.1% (95% CI 1.9%, 2.4%). Excess mortality persisted in women with RA throughout the study period, while the mortality risk for men with RA in 2011-15 was similar to their matched controls.

CONCLUSIONS

Enhanced improvement in mortality was found in RA patients compared with matched controls, but for sex-specific differences excess mortality was only persistent in women with RA.

Incidence of type 2 diabetes, cardiovascular disease and chronic kidney disease in patients with multiple sclerosis initiating disease-modifying therapies: Retrospective cohort study using a frequentist model averaging statistical framework

Researchers are increasingly using insights derived from large-scale, electronic healthcare data to inform drug development and provide human validation of novel treatment pathways and aid in drug repurposing/repositioning. The objective of this study was to determine whether treatment of patients with multiple sclerosis with dimethyl fumarate, an activator of the nuclear factor erythroid 2-related factor 2 (Nrf2) pathway, results in a change in incidence of type 2 diabetes and its complications. This retrospective cohort study used administrative claims data to derive four cohorts of adults with multiple sclerosis initiating dimethyl fumarate, teriflunomide, glatiramer acetate or fingolimod between January 2013 and December 2018. A causal inference frequentist model averaging framework based on machine learning was used to compare the time to first occurrence of a composite endpoint of type 2 diabetes, cardiovascular disease or chronic kidney disease, as well as each individual outcome, across the four treatment cohorts. There was a statistically significantly lower risk of incidence for dimethyl fumarate versus teriflunomide for the composite endpoint (restricted hazard ratio [95% confidence interval] 0.70 [0.55, 0.90]) and type 2 diabetes (0.65 [0.49, 0.98]), myocardial infarction (0.59 [0.35, 0.97]) and chronic kidney disease (0.52 [0.28, 0.86]). No differences for other individual outcomes or for dimethyl fumarate versus the other two cohorts were observed. This study effectively demonstrated the use of an innovative statistical methodology to test a clinical hypothesis using real-world data to perform early target validation for drug discovery. Although there was a trend among patients treated with dimethyl fumarate towards a decreased incidence of type 2 diabetes, cardiovascular disease and chronic kidney disease relative to other disease-modifying therapies-which was statistically significant for the comparison with teriflunomide-this study did not definitively support the hypothesis that Nrf2 activation provided additional metabolic disease benefit in patients with multiple sclerosis.

τ $$ \tau $$ -Inflated beta regression model for censored recurrent events

This research introduces a multivariateτ $$ \tau $$ -inflated beta regression (τ $$ \tau $$ -IBR) modeling approach for the analysis of censored recurrent event data that is particularly useful when there is a mixture of (a) individuals who are generally less susceptible to recurrent events and (b) heterogeneity in duration of event-free periods amongst those who experience events. The modeling approach is applied to a restructured version of the recurrent event data that consists of censored longitudinal times-to-first-event inτ $$ \tau $$ length follow-up windows that potentially overlap. Multiple imputation (MI) and expectation-solution (ES) approaches appropriate for censored data are developed as part of the model fitting process. A suite of useful analysis outputs are provided from theτ $$ \tau $$ -IBR model that include parameter estimates to help interpret the (a) and (b) mixture of event times in the data, estimates of meanτ $$ \tau $$ -restricted event-free duration in aτ $$ \tau $$ -length follow-up window based on a patient's covariate profile, and heat maps of rawτ $$ \tau $$ -restricted event-free durations observed in the data with censored observations augmented via averages across MI datasets. Simulations indicate good statistical performance of the proposedτ $$ \tau $$ -IBR approach to modeling censored recurrent event data. An example is given based on the Azithromycin for Prevention of COPD Exacerbations Trial.

Comparison of baseline covariate adjustment methods for restricted mean survival time

The restricted mean survival time provides a straightforward clinical measure that dispenses with the need for proportional hazards assumptions. We focus on two strategies to directly model the survival time and adjust covariates. Firstly, pseudo-survival time is calculated for each subject using a leave-one-out approach, followed by a model analysis that adjusts for covariates using all pseudo-values. This method is used to reflect information of censored subjects in the model analysis. The second approach adjusts for covariates for those subjects with observed time-to-event while incorporating censored subjects using inverse probability of censoring weighting (IPCW). This paper evaluates these methods' power to detect group differences through computer simulations. We find the interpretation of pseudo-values challenging with the pseudo-survival time method and confirm that pseudo-survival times deviate from actual data in a primary biliary cholangitis clinical trial, mainly due to extensive censoring. Simulations reveal that the IPCW method is more robust, unaffected by the balance of censors, whereas pseudo-survival time is influenced by this balance. The IPCW method retains a nominal significance level for the type-1 error rate, even amidst group differences concerning censor incidence rates and covariates. Our study concludes that IPCW and pseudo-survival time methods differ significantly in handling censored data, impacting parameter estimations. Our findings suggest that the IPCW method provides more robust results than pseudo-survival time and is recommended, even when censor probabilities vary between treatment groups. However, pseudo-survival time remains a suitable choice when censoring probabilities are balanced.

Dynamic increase in myoglobin level is associated with poor prognosis in critically ill patients: a retrospective cohort study

Background

Myoglobin is an important biomarker for monitoring critically ill patients. However, the relationship between its dynamic changes and prognosis remains unclear.

Methods

We retrospectively enrolled 11,218 critically ill patients from a general and surgical intensive care unit (ICU) of a tertiary hospital between June 2016 and May 2020. Patients with acute cardiovascular events, cardiac and major vascular surgeries, and rhabdomyolysis were excluded. To investigate the early myoglobin distribution, the critically ill patients were stratified according to the highest myoglobin level within 48 h after ICU admission. Based on this, the critically ill patients with more than three measurements within 1 week after ICU admission were included, and latent class trajectory modeling was used to classify the patients. The characteristics and outcomes were compared among groups. Sensitivity analysis was performed to exclude patients who had died within 72 h after ICU admission. Restricted mean survival time regression model based on pseudo values was used to determine the 28-day relative changes in survival time among latent classes. The primary outcome was evaluated with comparison of in-hospital mortality among each Trajectory group, and the secondary outcome was 28-day mortality.

Results

Of 6,872 critically ill patients, 3,886 (56.5%) had an elevated myoglobin level (≥150 ng/mL) at admission to ICU, and the in-hospital mortality significantly increased when myoglobin level exceeded 1,000 μg/mL. In LCTM, 2,448 patients were unsupervisedly divided into four groups, including the steady group (n = 1,606, 65.6%), the gradually decreasing group (n = 523, 21.4%), the slowly rising group (n = 272, 11.1%), and the rapidly rising group (n = 47, 1.9%). The rapidly rising group had the largest proportion of sepsis (59.6%), the highest median Sequential Organ Failure Assessment (SOFA) score (10), and the highest in-hospital mortality (74.5%). Sensitivity analysis confirmed that 98.2% of the patients were classified into the same group as in the original model. Compared with the steady group, the rapidly rising group and the slowly rising group were significantly related to the reduction in 28-day survival time (β = -12.08; 95% CI -15.30 to -8.86; β = -4.25, 95% CI -5.54 to -2.97, respectively).

Conclusion

Elevated myoglobin level is common in critically ill patients admitted to the ICU. Dynamic monitoring of myoglobin levels offers benefit for the prognosis assessment of critically ill patients.

Analysis of survival data with nonproportional hazards: A comparison of propensity-score-weighted methods

One of the most common ways researchers compare cancer survival outcomes across treatments from observational data is using Cox regression. This model depends on its underlying assumption of proportional hazards, but in some real-world cases, such as when comparing different classes of cancer therapies, substantial violations may occur. In this situation, researchers have several alternative methods to choose from, including Cox models with time-varying hazard ratios; parametric accelerated failure time models; Kaplan-Meier curves; and pseudo-observations. It is unclear which of these models are likely to perform best in practice. To fill this gap in the literature, we perform a neutral comparison study of candidate approaches. We examine clinically meaningful outcome measures that can be computed and directly compared across each method, namely, survival probability at time T, median survival, and restricted mean survival. To adjust for differences between treatment groups, we use inverse probability of treatment weighting based on the propensity score. We conduct simulation studies under a range of scenarios, and determine the biases, coverages, and standard errors of the average treatment effects for each method. We then demonstrate the use of these approaches using two published observational studies of survival after cancer treatment. The first examines chemotherapy in sarcoma, which has a late treatment effect (i.e., similar survival initially, but after 2 years the chemotherapy group shows a benefit). The other study is a comparison of surgical techniques for kidney cancer, where survival differences are attenuated over time.

Semiparametric estimation of restricted mean survival time as a function of restriction time

The restricted mean survival time (RMST) is an appealing measurement in clinical or epidemiological studies with censored survival outcome and receives a lot of attention in the past decades. It provides a useful alternative to the Cox model for evaluating the covariate effect on survival time. The covariate effect on RMST usually varies with the restriction time. However, existing methods cannot address this problem properly. In this article, we propose a semiparametric framework that directly models RMST as a function of the restriction time. Our proposed model adopts a widely-used proportional form, enabling the estimation of RMST predictions across an interval using a unified model. Furthermore, the covariate effect for multiple restriction time points can be derived simultaneously. We develop estimators based on estimating equations theories and establish the asymptotic properties of the proposed estimators. The finite sample properties of the estimators are evaluated through extensive simulation studies. We further illustrate the application of our proposed method through the analysis of two real data examples. Supplementary Material are available online.

Analysis of dynamic restricted mean survival time based on pseudo-observations

In clinical follow-up studies with a time-to-event end point, the difference in the restricted mean survival time (RMST) is a suitable substitute for the hazard ratio (HR). However, the RMST only measures the survival of patients over a period of time from the baseline and cannot reflect changes in life expectancy over time. Based on the RMST, we study the conditional restricted mean survival time (cRMST) by estimating life expectancy in the future according to the time that patients have survived, reflecting the dynamic survival status of patients during follow-up. In this paper, we introduce the estimation method of cRMST based on pseudo-observations, the statistical inference concerning the difference between two cRMSTs (cRMSTd), and the establishment of the robust dynamic prediction model using the landmark method. Simulation studies are conducted to evaluate the statistical properties of these methods. The results indicate that the estimation of the cRMST is accurate, and the dynamic RMST model has high accuracy in coefficient estimation and good predictive performance. In addition, an example of patients with chronic kidney disease who received renal transplantations is employed to illustrate that the dynamic RMST model can predict patients' expected survival times from any prediction time, considering the time-dependent covariates and time-varying effects of covariates.

Multiply robust causal inference of the restricted mean survival time difference

The hazard ratio (HR) remains the most frequently employed metric in assessing treatment effects on survival times. However, the difference in restricted mean survival time (RMST) has become a popular alternative to the HR when the proportional hazards assumption is considered untenable. Moreover, independent of the proportional hazards assumption, many comparative effectiveness studies aim to base contrasts on survival probability rather than on the hazard function. Causal effects based on RMST are often estimated via inverse probability of treatment weighting (IPTW). However, this approach generally results in biased results when the assumed propensity score model is misspecified. Motivated by the need for more robust techniques, we propose an empirical likelihood-based weighting approach that allows for specifying a set of propensity score models. The resulting estimator is consistent when the postulated model set contains a correct model; this property has been termed multiple robustness. In this report, we derive and evaluate a multiply robust estimator of the causal between-treatment difference in RMST. Simulation results confirm its robustness. Compared with the IPTW estimator from a correct model, the proposed estimator tends to be less biased and more efficient in finite samples. Additional simulations reveal biased results from a direct application of machine learning estimation of propensity scores. Finally, we apply the proposed method to evaluate the impact of intrapartum group B streptococcus antibiotic prophylaxis on the risk of childhood allergic disorders using data derived from electronic medical records from the Children's Hospital of Philadelphia and census data from the American Community Survey.

Variable selection using inverse probability of censoring weighting

In this article, we propose two variable selection methods for adjusting the censoring information for survival times, such as the restricted mean survival time. To adjust for the influence of censoring, we consider an inverse probability of censoring weighted for subjects with events. We derive a least absolute shrinkage and selection operator (lasso)-type variable selection method, which considers an inverse weighting for of the squared losses, and an information criterion-type variable selection method, which applies an inverse weighting of the survival probability to the power of each density function in the likelihood function. We prove the consistency of the inverse probability of censoring weighted lasso estimator and the maximum inverse probability of censoring weighted likelihood estimator. The performance of the inverse probability of censoring weighted lasso and inverse probability of censoring weighted information criterion are evaluated via a simulation study with six scenarios, and then their variable selection ability is demonstrated using data from two clinical studies. The results confirm that inverse probability of censoring weighted lasso and the inverse probability of censoring weighted likelihood function produce good estimation accuracy and consistent variable selection. We conclude that our two proposed methods are useful variable selection tools for adjusting the censoring information for survival time analyses.

Restricted mean survival time to estimate an intervention effect in a cluster randomized trial

For time-to-event outcomes, the difference in restricted mean survival time is a measure of the intervention effect, an alternative to the hazard ratio, corresponding to the expected survival duration gain due to the intervention up to a predefined time t*. We extended two existing approaches of restricted mean survival time estimation for independent data to clustered data in the framework of cluster randomized trials: one based on the direct integration of Kaplan-Meier curves and the other based on pseudo-values regression. Then, we conducted a simulation study to assess and compare the statistical performance of the proposed methods, varying the number and size of clusters, the degree of clustering, and the magnitude of the intervention effect under proportional and non-proportional hazards assumption. We found that the extended methods well estimated the variance and controlled the type I error if there was a sufficient number of clusters (≥ 50) under both proportional and non-proportional hazards assumption. For cluster randomized trials with a limited number of clusters (< 50), a permutation test for pseudo-values regression was implemented and corrected the type I error. We also provided a procedure to estimate permutation-based confidence intervals which produced adequate coverage. All the extended methods performed similarly, but the pseudo-values regression offered the possibility to adjust for covariates. Finally, we illustrated each considered method with a cluster randomized trial evaluating the effectiveness of an asthma-control education program.

Simultaneous hypothesis testing for multiple competing risks in comparative clinical trials

Competing risks data are commonly encountered in randomized clinical trials or observational studies. Ignoring competing risks in survival analysis leads to biased risk estimates and improper conclusions. Often, one of the competing events is of primary interest and the rest competing events are handled as nuisances. These approaches can be inadequate when multiple competing events have important clinical interpretations and thus of equal interest. For example, in COVID-19 in-patient treatment trials, the outcomes of COVID-19 related hospitalization are either death or discharge from hospital, which have completely different clinical implications and are of equal interest, especially during the pandemic. In this paper we develop nonparametric estimation and simultaneous inferential methods for multiple cumulative incidence functions (CIFs) and corresponding restricted mean times. Based on Monte Carlo simulations and a data analysis of COVID-19 in-patient treatment clinical trial, we demonstrate that the proposed method provides global insights of the treatment effects across multiple endpoints.

Survival After Implementation of a Decision Support Tool to Facilitate Evidence-Based Cancer Treatment

PURPOSE

Decision support tools (DSTs) to facilitate evidence-based cancer treatment are increasingly common in care delivery organizations. Implementation of these tools may improve process outcomes, but little is known about effects on patient outcomes such as survival. We aimed to evaluate the effect of implementing a DST for cancer treatment on overall survival (OS) among patients with breast, colorectal, and lung cancer.

METHODS

We used institutional cancer registry data to identify adults treated for first primary breast, colorectal, or lung cancer between December 2013 and December 2017. Our intervention of interest was implementation of a commercial DST for cancer treatment, and outcome of interest was OS. We emulated a single-arm trial with historical comparison and used a flexible parametric model to estimate standardized 3-year restricted mean survival time (RMST) difference and mortality risk ratio (RR) with 95% confidence limits (CLs).

RESULTS

Our study population comprised 1,059 patients with cancer (323 breast, 318 colorectal, and 418 lung). Depending on cancer type, median age was 55-60 years, 45%-67% were racial/ethnic minorities, and 49%-69% were uninsured. DST implementation had little effect on survival at 3 years. The largest effect was observed among patients with lung cancer (RMST difference, 1.7 months; 95% CL, -0.26 to 3.7; mortality RR, 0.95; 95% CL, 0.88 to 1.0). Adherence with tool-based treatment recommendations was >70% before and >90% across cancers.

CONCLUSION

Our results suggest that implementation of a DST for cancer treatment has nominal effect on OS, which may be partially attributable to high adherence with evidence-based treatment recommendations before tool implementation in our setting. Our results raise awareness that improved process outcomes may not translate to improved patient outcomes in some care delivery settings.

Regression models for censored time-to-event data using infinitesimal jack-knife pseudo-observations, with applications to left-truncation

Jack-knife pseudo-observations have in recent decades gained popularity in regression analysis for various aspects of time-to-event data. A limitation of the jack-knife pseudo-observations is that their computation is time consuming, as the base estimate needs to be recalculated when leaving out each observation. We show that jack-knife pseudo-observations can be closely approximated using the idea of the infinitesimal jack-knife residuals. The infinitesimal jack-knife pseudo-observations are much faster to compute than jack-knife pseudo-observations. A key assumption of the unbiasedness of the jack-knife pseudo-observation approach is on the influence function of the base estimate. We reiterate why the condition on the influence function is needed for unbiased inference and show that the condition is not satisfied for the Kaplan-Meier base estimate in a left-truncated cohort. We present a modification of the infinitesimal jack-knife pseudo-observations that provide unbiased estimates in a left-truncated cohort. The computational speed and medium and large sample properties of the jack-knife pseudo-observations and infinitesimal jack-knife pseudo-observation are compared and we present an application of the modified infinitesimal jack-knife pseudo-observations in a left-truncated cohort of Danish patients with diabetes.

Disease-free survival as a predictor of overall survival in localized renal cell carcinoma following initial nephrectomy: A retrospective analysis of Surveillance, Epidemiology and End Results-Medicare datac

OBJECTIVES

This study aimed to assess whether disease-free survival (DFS) may serve as a predictor for long-term survival among patients with intermediate-high risk or high risk renal cell carcinoma (RCC) post-nephrectomy when overall survival (OS) is unavailable.

METHODS

The Surveillance, Epidemiology and End Results-Medicare database (2007-2016) was used to identify patients with non-metastatic intermediate-high risk and high risk RCC post-nephrectomy. Landmark analysis and Kendall's τ were used to evaluate the correlation between DFS and OS. Multivariable regression models were used to quantify the incremental OS post-nephrectomy associated with increased time to recurrence among patients with recurrence, adjusting for baseline covariates.

RESULTS

A total of 643 patients were analyzed; mean age of 75 years; >95% of patients had intermediate-high risk RCC at diagnosis; 269 patients had recurrence post-nephrectomy. For patients with versus without recurrence at the landmark points of 1, 3, and 5 years post-nephrectomy, the 5-year OS were 37.0% versus 70.1%, 42.3% versus 72.8%, and 53.2% versus 78.6%, respectively. The Kendall's τ between DFS and OS post-nephrectomy was 0.70 (95% CI: 0.65, 0.74; p < 0.001). After adjusting for baseline covariates, patients with one additional year of time to recurrence were associated with 0.73 years longer OS post-nephrectomy (95% CI: 0.40, 1.05; p < 0.001).

CONCLUSION

The significant positive association of DFS and OS among patients with intermediate-high risk and high risk RCC post-nephrectomy from this study supports the use of DFS as a potential predictor of OS for these patients when OS data are immature.

Confirmatory prediction-driven RCTs in comparative effectiveness settings for cancer treatment

BACKGROUND

Medical advances in the treatment of cancer have allowed the development of multiple approved treatments and prognostic and predictive biomarkers for many types of cancer. Identifying improved treatment strategies among approved treatment options, the study of which is termed comparative effectiveness, using predictive biomarkers is becoming more common. RCTs that incorporate predictive biomarkers into the study design, called prediction-driven RCTs, are needed to rigorously evaluate these treatment strategies. Although researched extensively in the experimental treatment setting, literature is lacking in providing guidance about prediction-driven RCTs in the comparative effectiveness setting.

METHODS

Realistic simulations with time-to-event endpoints are used to compare contrasts of clinical utility and provide examples of simulated prediction-driven RCTs in the comparative effectiveness setting.

RESULTS

Our proposed contrast for clinical utility accurately estimates the true clinical utility in the comparative effectiveness setting while in some scenarios, the contrast used in current literature does not.

DISCUSSION

It is important to properly define contrasts of interest according to the treatment setting. Realistic simulations should be used to choose and evaluate the RCT design(s) able to directly estimate that contrast. In the comparative effectiveness setting, our proposed contrast for clinical utility should be used.

Propensity score matching and stratification using multiparty data without pooling

Matching and stratification based on confounding factors or propensity scores (PS) are powerful approaches for reducing confounding bias in indirect treatment comparisons. However, implementing these approaches requires pooled individual patient data (IPD). The research presented here was motivated by an indirect comparison between a single-armed trial in acute myeloid leukemia (AML), and two external AML registries with current treatments for a control. For confidentiality reasons, IPD cannot be pooled. Common approaches to adjusting confounding bias, such as PS matching or stratification, cannot be applied as 1) a model for PS, for example, a logistic model, cannot be fitted without pooling covariate data; 2) pooling response data may be necessary for some statistical inference (e.g., estimating the SE of mean difference of matched pairs) after PS matching. We propose a set of approaches that do not require pooling IPD, using a combination of methods including a linear discriminant for matching and stratification, and secure multiparty computation for estimation of within-pair sample variance and for calculations involving multiple control sources. The approaches only need to share aggregated data offline, rather than real-time secure data transfer, as required by typical secure multiparty computation for model fitting. For survival analysis, we propose an approach using restricted mean survival time. A simulation study was conducted to evaluate this approach in several scenarios, in particular, with a mixture of continuous and binary covariates. The results confirmed the robustness and efficiency of the proposed approach. A real data example is also provided for illustration.

External validation of a CT-based radiomics signature in oropharyngeal cancer: Assessing sources of variation

BACKGROUND AND PURPOSE

Radiomics is a high-throughput approach that allows for quantitative analysis of imaging data for prognostic applications. Medical images are used in oropharyngeal cancer (OPC) diagnosis and treatment planning and these images may contain prognostic information allowing for treatment personalization. However, the lack of validated models has been a barrier to the translation of radiomic research to the clinic. We hypothesize that a previously developed radiomics model for risk stratification in OPC can be validated in a local dataset.

MATERIALS AND METHODS

The radiomics signature predicting overall survival incorporates features derived from the primary gross tumor volume of OPC patients treated with radiation +/- chemotherapy at a single institution (n = 343). Model fit, calibration, discrimination, and utility were evaluated. The signature was compared with a clinical model using overall stage and a model incorporating both radiomics and clinical data. A model detecting dental artifacts on computed tomography images was also validated.

RESULTS

The radiomics signature had a Concordance index (C-index) of 0.66 comparable to the clinical model's C-index of 0.65. The combined model significantly outperformed (C-index of 0.69, p = 0.024) the clinical model, suggesting that radiomics provides added value. The dental artifact model demonstrated strong ability in detecting dental artifacts with an area under the curve of 0.87.

CONCLUSION

This work demonstrates model performance comparable to previous validation work and provides a framework for future independent and multi-center validation efforts. With sufficient validation, radiomic models have the potential to improve traditional systems of risk stratification, treatment personalization and patient outcomes.

Performance of Restricted Mean Survival Time Based Methods and Traditional Survival Methods: An Application in an Oncological Data

Objective

To compare restricted mean survival time- (RMST-) based methods with traditional survival methods when multiple covariates are of interest.

Methods

4405 osteosarcomas were captured from Surveillance, Epidemiology, and End Results Program Database. RMST-based methods included group comparison using Kaplan-Meier (KM) method, pseudovalue (PV) regression, and inverse probability of censoring probability (IPCW) regressions with group-specific and individual weights. Log-rank test, Wilcoxon test, Cox regression, and its extension with time-dependent variables were selected as traditional methods. Proportional hazard (PH) assumption and homogeneity of censoring mechanism assumption were assessed. We estimated hazard ratio (HR) and difference in RMST and explored their relationships.

Results

When covariate violated PH assumption, time-varying HR was inconvenient to report as a single value but PH assumption-free RMST allowed to report a single value of difference in RMST. In univariable analyses, using the difference in RMST calculated by KM method as reference, PV regressions (slope = 1.02 and R ² = 0.98) and IPCW regressions with group-specific weights (slope = 0.98 and R ² = 0.99) gave more consistent estimation than IPCW with individual weights (slope = 0.31 and R ² = 0.06), moreover, PV regressions presented more robust statistical power than IPCW regressions with group-specific weights. In multivariable analyses, IPCW regression with group-specific weights was limited when multiple covariates violated homogeneity of censoring mechanism assumption. For covariates met PH assumption, well-fitted logarithmic relationships between HR and difference in RMST estimated by PV regression were observed in both univariable and multivariable analyses (R ² = 0.97 and R ² = 0.94, respectively), which supported the robustness of PV regression and possible conversion between the two effect measures.

Conclusions

Difference in RMST is more interpretable than time-varying HR. The performance supports KM method and PV regression to be the preferred ones in RMST-based methods. IPCW regression can be an alternative sensitivity analysis. We encourage adoption of both traditional methods and RMST-based methods to present effects of covariates comprehensively.

The Association between Exposures and Disease Characteristics in Familial Pulmonary Fibrosis

Rationale: Heterogeneous characteristics are observed in familial pulmonary fibrosis (FPF), suggesting that nongenetic factors contribute to disease manifestations. Objectives: To determine the relationship between environmental exposures and disease characteristics of FPF, including the morphological characteristics on chest computed tomography (CT) scan, and timing of FPF symptom onset, lung transplantation, or death. Methods: Subjects with FPF with an exposure questionnaire and chest CT were selected from a prospective cohort at Vanderbilt. Disease characteristics were defined by lung parenchymal findings on chest CT associated with fibrotic hypersensitivity pneumonitis (fHP) or usual interstitial pneumonia (UIP) and by time from birth to symptom onset or a composite of lung transplantation or death. After assessing the potential for confounding by sex or smoking, adjusted logistic or Cox proportional hazards regression models identified exposures associated with fHP or UIP CT findings. Findings were validated in a cohort of patients with sporadic pulmonary fibrosis enrolled in the LTRC (Lung Tissue Research Consortium) study. Results: Among 159 subjects with FPF, 98 (61.6%) were males and 96 (60.4%) were ever-smokers. Males were less likely to have CT features of fHP, including mosaic attenuation (FPF: adjusted [for sex and smoking] odds ratio [aOR], 0.27; 95% confidence interval [CI], 0.09-0.76; P = 0.01; LTRC: aOR, 0.35; 95% CI, 0.21-0.61; P = 0.0002). Organic exposures, however, were not consistently associated with fHP features in either cohort. Smoking was a risk factor for honeycombing in both cohorts (FPF: aOR, 2.19; 95% CI, 1.12-4.28; P = 0.02; LTRC: aOR, 1.69; 95% CI, 1.22-2.33; P = 0.002). Rock dust exposure may also be associated with honeycombing, although the association was not statistically-significant when accounting for sex and smoking (FPF: aOR, 2.27; 95% CI, 0.997-5.15; P = 0.051; LTRC: aOR, 1.51; 95% CI, 0.97-2.33; P = 0.07). In the FPF cohort, ever-smokers experienced a shorter transplant-free survival (adjusted hazard ratio, 1.64; 95% CI, 1.07-2.52; P = 0.02), whereas sex was not associated with differential survival (male adjusted hazard ratio, 0.75; 95% CI, 0.50-1.14; P = 0.18). Conclusions: In FPF, smoking contributes to shortened transplant-free survival and development of honeycombing, a finding that is also likely applicable to sporadic pulmonary fibrosis. Females are more likely to manifest CT features of fHP (mosaic attenuation), a finding that was incompletely explained by sex differences in exposures. These findings may have implications for pulmonary fibrosis classification and management.

Contemporary trends in PGD incidence, outcomes, and therapies

BACKGROUND

We sought to describe trends in extracorporeal membrane oxygenation (ECMO) use, and define the impact on PGD incidence and early mortality in lung transplantation.

METHODS

Patients were enrolled from August 2011 to June 2018 at 10 transplant centers in the multi-center Lung Transplant Outcomes Group prospective cohort study. PGD was defined as Grade 3 at 48 or 72 hours, based on the 2016 PGD ISHLT guidelines. Logistic regression and survival models were used to contrast between group effects for event (i.e., PGD and Death) and time-to-event (i.e., death, extubation, discharge) outcomes respectively. Both modeling frameworks accommodate the inclusion of potential confounders.

RESULTS

A total of 1,528 subjects were enrolled with a 25.7% incidence of PGD. Annual PGD incidence (14.3%-38.2%, p = .0002), median LAS (38.0-47.7 p = .009) and the use of ECMO salvage for PGD (5.7%-20.9%, p = .007) increased over the course of the study. PGD was associated with increased 1 year mortality (OR 1.7 [95% C.I. 1.2, 2.3], p = .0001). Bridging strategies were not associated with increased mortality compared to non-bridged patients (p = .66); however, salvage ECMO for PGD was significantly associated with increased mortality (OR 1.9 [1.3, 2.7], p = .0007). Restricted mean survival time comparison at 1-year demonstrated 84.1 days lost in venoarterial salvaged recipients with PGD when compared to those without PGD (ratio 1.3 [1.1, 1.5]) and 27.2 days for venovenous with PGD (ratio 1.1 [1.0, 1.4]).

CONCLUSIONS

PGD incidence continues to rise in modern transplant practice paralleled by significant increases in recipient severity of illness. Bridging strategies have increased but did not affect PGD incidence or mortality. PGD remains highly associated with mortality and is increasingly treated with salvage ECMO.

Outcome disparities in patients with atrial fibrillation based on insurance plan and educational attainment: a nationwide, multicenter and prospective cohort trial

BACKGROUND

Atrial fibrillation (AF) is a complex disease. The management of AF requires continuous patient engagement and integrative healthcare.

OBJECTIVES

To explore the association between adverse AF-related clinical outcomes and the following two sociodemographic factors: educational attainment and insurance plan.

DESIGN

A nationwide, prospective, multicenter, cohort trial.

SETTING

National registry of 3402 patients with non-valvular AF in Thailand.

PARTICIPANTS

All patients enrolled in the registry, except those with missing information on educational attainment or insurance plan. Finally, data from 3026 patients (mean age 67 years, SD 11.3; 59% male sex) were analysed.

PRIMARY OUTCOMES

Incidences of all-cause mortality, ischaemic stroke and major bleeding during the 36-month follow-up period. Survival analysis was performed using restricted mean survival time (RMST) and adjusted for multiple covariates. The levels of the educational attainment were as follows: no formal education, elementary (grade 1-6), secondary (grade 7-12) and higher education (tertiary education).

RESULTS

The educational attainment of the majority of patients was elementary (N=1739, 57.4%). The predominant health insurance plans were the Civil Servant Medical Benefit Scheme (N=1397, 46.2%) and the Universal Coverage Scheme (N=1333, 44.1%). After 36 months of follow-up, 248 patients died (8.2%), 95 had ischaemic stroke (3.1%) and 136 had major bleeding (4.5%). Patients without formal education died 1.78 months earlier (adjusted RMST difference -1.78; 95% CI, -3.25 to -0.30; p=0.02) and developed ischaemic stroke 1.04 months sooner (adjusted RMST difference -1.04; 95% CI, -2.03 to -0.04; p=0.04) than those attained a level of higher education. There were no significant differences in RMSTs for all three clinical outcomes when considering the type of health insurance plan.

CONCLUSION

Educational attainment was independently associated with all-cause mortality and ischaemic stroke in patients with AF, but adverse clinical outcomes were not related to the types of health insurance in Thailand.

TRIAL REGISTRATION NUMBER

Thai Clinical Trial Registration; Study ID: TCTR20160113002.

Adjuvant immunotherapy in patients with high-risk muscle-invasive urothelial carcinoma: The potential impact of informative censoring

BACKGROUND

The results of 2 studies exploring adjuvant immune checkpoint inhibition (aCPI) in high-risk muscle-invasive urothelial cancer have yielded conflicting results. A trial employing placebo as the control arm demonstrated a significant prolongation in disease-free survival (DFS) whereas a trial employing observation as the control arm (IMvigor010) demonstrated no prolongation in DFS with CPI. Here, the authors aimed to estimate the aCPI benefit and to model the potential impact of informative censoring on trial results.

METHODS

Survival data from 1518 patients was reconstructed from Kaplan-Meier curves. A network meta-analysis approach was used to estimate aCPI benefit through the restricted mean disease-free survival time (RMDFST). To estimate the potential impact of informative censoring on IMvigor010, a simulation was performed. The minimum proportion of informative censoring on the observation arm that could account for the lack of observed improvement in DFS was estimated. Random variability from the time of censoring to progression was modeled using the exponential distribution.

RESULTS

Patients receiving aCPI had better DFS: ΔRMDFST at 36 months of 2.2 (95% CI, 0.6-3.7, P = .006) months relative to observation/placebo. In IMvigor010, in the observation arm, 20.5% of patients were censored due to consent withdrawal, protocol violation and/or noncompliance, or lost to follow-up versus 8.2% in the treatment arm. On simulation, it was found that the lack of observed improvement in DFS could have resulted from as few as 14% of the censored patients on observation arm not being censored at random (simulated DFS with 14% informative censoring hazard ratio, 0.83; 95% CI, 0.69-0.99; P = .049).

CONCLUSIONS

Phase 3 trials comparing adjuvant therapies to observation are at risk for informative censoring that could potentially impact interpretation of study results.

A Review of Causal Inference for External Comparator Arm Studies

Randomized controlled trials (RCTs) are the gold standard design to establish the efficacy of new drugs and to support regulatory decision making. However, a marked increase in the submission of single-arm trials (SATs) has been observed in recent years, especially in the field of oncology due to the trend towards precision medicine contributing to the rise of new therapeutic interventions for rare diseases. SATs lack results for control patients, and information from external sources can be compiled to provide context for better interpretability of study results. External comparator arm (ECA) studies are defined as a clinical trial (most commonly a SAT) and an ECA of a comparable cohort of patients-commonly derived from real-world settings including registries, natural history studies, or medical records of routine care. This publication aims to provide a methodological overview, to sketch emergent best practice recommendations and to identify future methodological research topics. Specifically, existing scientific and regulatory guidance for ECA studies is reviewed and appropriate causal inference methods are discussed. Further topics include sample size considerations, use of estimands, handling of different data sources regarding differential baseline covariate definitions, differential endpoint measurements and timings. In addition, unique features of ECA studies are highlighted, specifically the opportunity to address bias caused by unmeasured ECA covariates, which are available in the SAT.

Regression modeling of restricted mean survival time for left-truncated right-censored data

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. The pseudo-observation (PO) approach has been used in regression modeling of RMST for right-censored data and competing-risks data. For left-truncated right-censored data, we propose to directly model RMST as a function of baseline covariates based on POs under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from surveillance, epidemiology, and end results-medicare linked database.

CondiS: A conditional survival distribution-based method for censored data imputation overcoming the hurdle in machine learning-based survival analysis

Data analyses by machine learning (ML) algorithms are gaining popularity in biomedical research. When time-to-event data are of interest, censoring is common and needs to be properly addressed. Most ML methods cannot conveniently and appropriately take the censoring information into consideration, potentially leading to inaccurate or biased results. We aim to develop a general-purpose method for imputing censored survival data, facilitating downstream ML analysis. In this study, we propose a novel method of imputing the survival times for censored observations. The proposal is based on their conditional survival distributions (CondiS) derived from Kaplan-Meier estimators. CondiS can replace censored observations with their best approximations from the statistical model, allowing for direct application of ML methods. When covariates are available, we extend CondiS by incorporating the covariate information through ML modeling (CondiS-X), which further improves the accuracy of the imputed survival time. Compared with existing methods with similar purposes, the proposed methods achieved smaller prediction errors and higher concordance with the underlying true survival times in extensive simulation studies. We also demonstrated the usage and advantages of the proposed methods through two real-world cancer datasets. The major advantage of CondiS is that it allows for the direct application of standard ML techniques for analysis once the censored survival times are imputed. We present a user-friendly R package to implement our method, which is a useful tool for ML-based biomedical research in this era of big data.

Restricted mean survival time regression model with time-dependent covariates

In clinical or epidemiological follow‐up studies, methods based on time scale indicators such as the restricted mean survival time (RMST) have been developed to some extent. Compared with traditional hazard rate indicator system methods, the RMST is easier to interpret and does not require the proportional hazard assumption. To date, regression models based on the RMST are indirect or direct models of the RMST and baseline covariates. However, time‐dependent covariates are becoming increasingly common in follow‐up studies. Based on the inverse probability of censoring weighting (IPCW) method, we developed a regression model of the RMST and time‐dependent covariates. Through Monte Carlo simulation, we verified the estimation performance of the regression parameters of the proposed model. Compared with the time‐dependent Cox model and the fixed (baseline) covariate RMST model, the time‐dependent RMST model has a better prediction ability. Finally, an example of heart transplantation was used to verify the above conclusions.

Doubly-robust estimator of the difference in restricted mean times lost with competing risks data

In the context of competing risks data, the subdistribution hazard ratio has limited clinical interpretability to measure treatment effects. An alternative is the difference in restricted mean times lost (RMTL), which gives the mean time lost to a specific cause of failure between treatment groups. In non-randomized studies, the average causal effect is conventionally used for decision-making about treatment and public health policies. We show how the difference in RMTL can be estimated by contrasting the integrated cumulative incidence functions from a Fine-Gray model. We also show how the difference in RMTL can be estimated by using inverse probability of treatment weighting and contrasts between weighted non-parametric estimators of the area below the cumulative incidence. We use pseudo-observation approaches to estimate both component models and we integrate them into a doubly-robust estimator. We demonstrate that this estimator is consistent when either component is correctly specified. We conduct simulation studies to assess its finite-sample performance and demonstrate its inherited consistency property from its component models. We also examine the performance of this estimator under varying degrees of covariate overlap and under a model misspecification of nonlinearity. We apply the proposed method to assess biomarker-treatment interaction in subpopulations of the POPLAR and OAK randomized controlled trials of second-line therapy for advanced non-small-cell lung cancer.

Clustered restricted mean survival time regression

For multicenter randomized trials or multilevel observational studies, the Cox regression model has long been the primary approach to study the effects of covariates on time-to-event outcomes. A critical assumption of the Cox model is the proportionality of the hazard functions for modeled covariates, violations of which can result in ambiguous interpretations of the hazard ratio estimates. To address this issue, the restricted mean survival time (RMST), defined as the mean survival time up to a fixed time in a target population, has been recommended as a model-free target parameter. In this article, we generalize the RMST regression model to clustered data by directly modeling the RMST as a continuous function of restriction times with covariates while properly accounting for within-cluster correlations to achieve valid inference. The proposed method estimates regression coefficients via weighted generalized estimating equations, coupled with a cluster-robust sandwich variance estimator to achieve asymptotically valid inference with a sufficient number of clusters. In small-sample scenarios where a limited number of clusters are available, however, the proposed sandwich variance estimator can exhibit negative bias in capturing the variability of regression coefficient estimates. To overcome this limitation, we further propose and examine bias-corrected sandwich variance estimators to reduce the negative bias of the cluster-robust sandwich variance estimator. We study the finite-sample operating characteristics of proposed methods through simulations and reanalyze two multicenter randomized trials.

Analyzing differences between restricted mean survival time curves using pseudo-values

Hazard ratios are ubiquitously used in time to event analysis to quantify treatment effects. Although hazard ratios are invaluable for hypothesis testing, other measures of association, both relative and absolute, may be used to fully elucidate study results. Restricted mean survival time (RMST) differences between groups have been advocated as useful measures of association. Recent work focused on model-free estimates of the difference in restricted mean survival through follow-up times, instead of focusing on a single time horizon. The resulting curve can be used to quantify the association in time units with a simultaneous confidence band. In this work a model-based estimate of the curve is proposed using pseudo-values allowing for possible covariate adjustment. The method is easily implementable with available software and makes possible to compute a simultaneous confidence region for the curve. The pseudo-values regression using multiple restriction times is in good agreement with the estimates obtained by standard direct regression models fixing a single restriction time. Moreover, the proposed method is flexible enough to reproduce the results of the non-parametric approach when no covariates are considered. Examples where it is important to adjust for baseline covariates will be used to illustrate the different methods together with some simulations.

Gini's mean difference and the long-term prognostic value of nodal quanta classes after pre-operative chemotherapy in advanced breast cancer

Gini's mean difference (GMD, mean absolute difference between any two distinct quantities) of the restricted mean survival times (RMSTs, expectation of life at a given time limit) has been proposed as a new metric where higher GMD indicates better prognostic value. GMD is applied to the RMSTs at 25 years time-horizon to evaluate the long-term overall survival of women with breast cancer who received neoadjuvant chemotherapy, comparing a classification based on the number (pN) versus a classification based on the ratio (LNRc) of positive nodes found at axillary surgery. A total of 233 patients treated in 1980–2009 with documented number of positive nodes (npos) and number of nodes examined (ntot) were identified. The numbers were categorized into pN0, npos = 0; pN1, npos = [1,3]; pN2, npos = [4,9]; pN3, npos ≥ 10. The ratios npnx = npos/ntot were categorized into Lnr0, npnx = 0; Lnr1, npnx = (0,0.20]; Lnr2, npnx = (0.20,0.65]; Lnr3, npnx > 0.65. The GMD for pN-classification was 5.5 (standard error: ± 0.9) years, not much improved over a simple node-negative vs. node-positive that showed a GMD of 5.0 (± 1.4) years. The GMD for LNRc-classification was larger, 6.7 (± 0.8) years. Among other conventional metrics, Cox-model LNRc's c-index was 0.668 vs. pN's c = 0.641, indicating commensurate superiority of LNRc-classification. The usability of GMD-RMSTs warrants further investigation.

Direct modeling of the crude probability of cancer death and the number of life years lost due to cancer without the need of cause of death: a pseudo-observation approach in the relative survival setting

In population-based cancer studies, net survival is a crucial measure for population comparison purposes. However, alternative measures, namely the crude probability of death (CPr) and the number of life years lost (LYL) due to death according to different causes, are useful as complementary measures for reflecting different dimensions in terms of prognosis, treatment choice, or development of a control strategy. When the cause of death (COD) information is available, both measures can be estimated in competing risks setting using either cause-specific or subdistribution hazard regression models or with the pseudo-observation approach through direct modeling. We extended the pseudo-observation approach in order to model the CPr and the LYL due to different causes when information on COD is unavailable or unreliable (i.e., in relative survival setting). In a simulation study, we assessed the performance of the proposed approach in estimating regression parameters and examined models with different link functions that can provide an easier interpretation of the parameters. We showed that the pseudo-observation approach performs well for both measures and we illustrated their use on cervical cancer data from the England population-based cancer registry. A tutorial showing how to implement the method in R software is also provided.

Nonparametric inference in the accelerated failure time model using restricted means

We propose a nonparametric estimate of the scale-change parameter for characterizing the difference between two survival functions under the accelerated failure time model using an estimating equation based on restricted means. Advantages of our restricted means based approach compared to current nonparametric procedures is the strictly monotone nature of the estimating equation as a function of the scale-change parameter, leading to a unique root, as well as the availability of a direct standard error estimate, avoiding the need for hazard function estimation or re-sampling to conduct inference. We derive the asymptotic properties of the proposed estimator for fixed and for random point of restriction. In a simulation study, we compare the performance of the proposed estimator with parametric and nonparametric competitors in terms of bias, efficiency, and accuracy of coverage probabilities. The restricted means based approach provides unbiased estimates and accurate confidence interval coverage rates with efficiency ranging from 81% to 95% relative to fitting the correct parametric model. An example from a randomized clinical trial in head and neck cancer is provided to illustrate an application of the methodology in practice.

Stratified Restricted Mean Survival Time Model for Marginal Causal Effect in Observational Survival Data

Time to event outcomes is commonly encountered in epidemiologic research. Multiple papers have discussed the inadequacy of using the hazard ratio as a causal effect measure due to its noncollapsibility and the time-varying nature. In this paper, we further clarified that the hazard ratio might be used as a conditional causal effect measure, but it is generally not a valid marginal effect measure, even under randomized design. We proposed to use the restricted mean survival time (RMST) difference as a causal effect measure, since it essentially measures the mean difference over a specified time horizon and has a simple interpretation as the area under survival curves. For observational studies, propensity score adjustment can be implemented with RMST estimation to remove observed confounding bias. We proposed a propensity score stratified RMST estimation strategy, which performs well in our simulation evaluation and is relatively easy to implement for epidemiologists in practice. Our stratified RMST estimation includes two different versions of implementation, depending on whether researchers want to involve regression modeling adjustment, which provides a powerful tool to examine the marginal causal effect with observational survival data.

Value of Lymphadenectomy in Patients Receiving Neoadjuvant Therapy for Esophageal Adenocarcinoma

OBJECTIVE

The aim of this study was to assess the effect on survival of extent of lymphadenectomy during esophagectomy for patients undergoing multimodality (neoadjuvant) therapy for adenocarcinoma of the esophagus and esophagogastric junction using Worldwide Esophageal Cancer Collaboration data.

SUMMARY BACKGROUND DATA

Previous worldwide data demonstrated that optimum lymphadenectomy during esophagectomy alone for esophageal cancer provides accurate staging and maximum survival. However, for patients undergoing neoadjuvant therapy for locally advanced adenocarcinoma, its value is unclear, leading to wide practice variability.

METHODS

A total of 3859 patients with adenocarcinoma of the esophagus or esophagogastric junction received neoadjuvant therapy. The endpoint was all-cause mortality, reported as gain or loss of lifetime within 10 years. Lifetime predicted for each regional lymph node resected used quantile survival random forest methodology.

RESULTS

Across all post-neoadjuvant ypTNM cancer categories, some degree of lymphadenectomy was associated with longer lifetime, but in a nonlinear fashion. For patients with ypN0 cancers, there was a modest gain in lifetime up to 25 lymph nodes resected and an incremental loss in lifetime as >25 were resected. For patients with ypN+ cancers, there was a robust gain in lifetime up to 30 lymph nodes resected and then an incremental loss in lifetime.

CONCLUSIONS

Worldwide data for adenocarcinoma of the esophagus and esophagogastric junction demonstrate that lymphadenectomy during esophagectomy is a valuable component of neoadjuvant therapy. Survival is maximized when an optimum range of nodes is resected.

Dynamic prediction and analysis based on restricted mean survival time in survival analysis with nonproportional hazards

BACKGROUND AND OBJECTIVE

In the process of clinical diagnosis and treatment, the restricted mean survival time (RMST), which reflects the life expectancy of patients up to a specified time, can be used as an appropriate outcome measure. However, the RMST only calculates the mean survival time of patients within a period of time after the start of follow-up and may not accurately portray the change in a patient's life expectancy over time.

METHODS

The life expectancy can be adjusted for the time the patient has already survived and defined as the conditional restricted mean survival time (cRMST). A dynamic RMST model based on the cRMST can be established by incorporating time-dependent covariates and covariates with time-varying effects. We analyzed data from a study of primary biliary cirrhosis (PBC) to illustrate the use of the dynamic RMST model, and a simulation study was designed to test the advantages of the proposed approach. The predictive performance was evaluated using the C-index and the prediction error.

RESULTS

Considering both the example results and the simulation results, the proposed dynamic RMST model, which can explore the dynamic effects of prognostic factors on survival time, has better predictive performance than the RMST model. Three PBC patient examples were used to illustrate how the predicted cRMST changed at different prediction times during follow-up.

CONCLUSIONS

The use of the dynamic RMST model based on the cRMST allows for the optimization of evidence-based decision-making by updating personalized dynamic life expectancy for patients.

Radiographic Graft Surveillance in Lung Transplantation: Prognostic Role of Parametric Response Mapping

RATIONALE

Chronic lung allograft dysfunction (CLAD) results in significant morbidity following lung transplantation. Potential CLAD occurs when lung function declines to 80-90% of baseline. Better non-invasive tools to prognosticate at potential CLAD are needed.

OBJECTIVES

To determine if parametric response mapping (PRM), a CT voxel-wise methodology, applied to high resolution CT scans can identify patients at risk of progression to CLAD or death.

METHODS

Radiographic features and PRM-based CT metrics quantifying functional small airways disease (PRMfSAD) and parenchymal disease (PRMPD) were studied at potential CLAD (n=61). High PRMfSAD and high PRMPD were defined as ≥ 30%. Restricted mean modeling was performed to compare CLAD-free survival among groups.

MEASUREMENTS AND MAIN RESULTS

PRM metrics identified 3 unique signatures: high PRMfSAD (11.5%), high PRMPD (41%) and neither (PRMNormal; 47.5%). Patients with high PRMfSAD or PRMPD had shorter CLAD-free median survival times (0.46 years and 0.50 years) compared to patients with predominantly PRMNormal (2.03 years; p=0.004 and 0.007 compared to PRMfSAD and PRMPD groups, respectively). In multivariate modeling adjusting for single versus double lung transplant, age at transplant, BMI at potential CLAD, and time from transplant to CT, PRMfSAD or PRMPD ≥ 30% continue to be statistically significant predictors of shorter CLAD-free survival. Air trapping by radiologist interpretation was common (66%), similar across PRM groups, and was not predictive of CLAD-free survival. Ground glass opacities by radiologist read occurred in 16% of cases and was associated with decreased CLAD-free survival (p<0.001).

CONCLUSIONS

PRM analysis offers valuable prognostic information at potential CLAD, identifying patients most at risk of developing CLAD or death.

Adjusting for covariates in analysis based on restricted mean survival times

We summarize extensions to the analysis of restricted mean survival time (RMST) in the context of time-to-event outcomes. The RMST estimate and its inference are based on the classical Kaplan-Meier curves. When covariate effects are considered, an adjusted RMST (ARMST) estimate can be derived analogously based on adjusted Kaplan-Meier curves. The adjusted Kaplan-Meier Estimator (AKME) was developed to reduce confounding by the method of inverse probability of treatment weighting. We will show how the ARMST method combines the concepts of the RMST and AKME to make inferences. Two regression based methods to adjust for potential covariate effect on the RMST estimates will be compared with the ARMST approach. Simulation studies are performed to compare the different methods with and without covariate adjustments. In addition, we will summarize the extension of RMST and ARMST to the setting with competing risks. The restricted mean time lost (RMTL) and adjusted RMTL (ARMTL) are estimates of interest from cumulative incidence curves. A phase 3 oncology clinical trial example is provided to demonstrate the applications of these methods.

Estimation and modeling of the restricted mean time lost in the presence of competing risks

Survival data with competing or semi-competing risks are common in observational studies. As an alternative to cause-specific and subdistribution hazard ratios, the between-group difference in cause-specific restricted mean times lost (RMTL) gives the mean difference in life expectancy lost to a specific cause of death or in disease-free time lost, in the case of a nonfatal outcome, over a prespecified period. To adjust for covariates, we introduce an inverse probability weighted estimator and its variance for the marginal difference in RMTL. We also introduce an inverse probability of censoring weighted regression model for the RMTL. In simulation studies, we examined the finite sample performance of the proposed methods under proportional and nonproportional subdistribution hazards scenarios. We illustrated both methods with competing risks data from the Framingham Heart Study. We estimated sex differences in atrial fibrillation (AF)-free times lost over 40 years. We also estimated sex differences in mean lifetime lost to cardiovascular disease (CVD) and non-CVD death over 10 years among individuals with AF.

Deep Neural Networks For Predicting Restricted Mean Survival Times

 

Restricted mean survival time (RMST) is a useful summary measurement of the time-to-event data, and it has attracted great attention for its straightforward clinical interpretation. In this article, I propose a deep neural network model that directly relates the RMST to its baseline covariates for simultaneous prediction of RSMT at multiple times. Each subject's survival time is transformed into a series of jackknife pseudo observations and then used as quantitative response variables in a deep neural network model. By using the pseudo values, a complex survival analysis is reduced to a standard regression problem, which greatly simplifies the neural network construction. By jointly modelling RMST at multiple times, the neural network model gains prediction accuracy by information sharing across times. The proposed network model was evaluated by extensive simulation studies and was further illustrated on three real datasets. In real data analyses, I also used methods to open the blackbox by identifying subject-specific predictors and their importance in contributing to the risk prediction.

AVAILABILITY AND IMPLEMENTATION

The source code is freely available at http://github.com/lilizhaoUM/DnnRMST.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Restricted mean survival time as a function of restriction time

Restricted mean survival time (RMST) is a clinically interpretable and meaningful survival metric that has gained popularity in recent years. Several methods are available for regression modeling of RMST, most based on pseudo-observations or what is essentially an inverse-weighted complete-case analysis. No existing RMST regression method allows for the covariate effects to be expressed as functions over time. This is a considerable limitation, in light of the many hazard regression methods that do accommodate such effects. To address this void in the literature, we propose RMST methods that permit estimating time-varying effects. In particular, we propose an inference framework for directly modeling RMST as a continuous function of L. Large-sample properties are derived. Simulation studies are performed to evaluate the performance of the methods in finite sample sizes. The proposed framework is applied to kidney transplant data obtained from the Scientific Registry of Transplant Recipients.

Deep Neural Networks for Survival Analysis Using Pseudo Values

There has been increasing interest in modelling survival data using deep learning methods in medical research. Current approaches have focused on designing special cost functions to handle censored survival data. We propose a very different method with two simple steps. In the first step, we transform each subject's survival time into a series of jackknife pseudo conditional survival probabilities and then use these pseudo probabilities as a quantitative response variable in the deep neural network model. By using the pseudo values, we reduce a complex survival analysis to a standard regression problem, which greatly simplifies the neural network construction. Our two-step approach is simple, yet very flexible in making risk predictions for survival data, which is very appealing from the practice point of view. The source code is freely available at http://github.com/lilizhaoUM/DNNSurv.

Cumulative risk regression in case-cohort studies using pseudo-observations

Case-cohort studies are useful when information on certain risk factors is difficult or costly to ascertain. Particularly, a case-cohort study may be well suited in situations where several case series are of interest, e.g. in studies with competing risks, because the same sub-cohort may serve as a comparison group for all case series. Previous analyses of this kind of sampled cohort data most often involved estimation of rate ratios based on a Cox regression model. However, with competing risks this method will not provide parameters that directly describe the association between covariates and cumulative risks. In this paper, we study regression analysis of cause-specific cumulative risks in case-cohort studies using pseudo-observations. We focus mainly on the situation with competing risks. However, as a by-product, we also develop a method by which absolute mortality risks may be analyzed directly from case-cohort survival data. We adjust for the case-cohort sampling by inverse sampling probabilities applied to a generalized estimation equation. The large-sample properties of the proposed estimator are developed and small-sample properties are evaluated in a simulation study. We apply the methodology to study the effect of a specific diet component and a specific gene on the absolute risk of atrial fibrillation.

The effect of insurance status on overall survival among children and adolescents with cancer

Background

Differences in access, delivery and utilisation of health care may impact childhood and adolescent cancer survival. We evaluated whether insurance coverage impacts survival among US children and adolescents with cancer diagnoses, overall and by age group, and explored potential mechanisms.

Methods

Data from 58 421 children (aged ≤14 years) and adolescents (15–19 years), diagnosed with cancer from 2004 to 2010, were obtained from the National Cancer Database. We examined associations between insurance status at initial diagnosis or treatment and diagnosis stage; any treatment received; and mortality using logistic regression, Cox proportional hazards (PH) regression, restricted mean survival time (RMST) and mediation analyses.

Results

Relative to privately insured individuals, the hazard of death (all-cause) was increased and survival months were decreased in those with Medicaid [hazard ratio (HR) = 1.27, 95% confidence interval (CI): 1.22 to 1.33; and −1.73 months, 95% CI: −2.07 to −1.38] and no insurance (HR = 1.32, 95% CI: 1.20 to 1.46; and −2.13 months, 95% CI: −2.91 to −1.34). The HR for Medicaid vs. private insurance was larger (pinteraction &lt;0.001) in adolescents (HR = 1.52, 95% CI: 1.41 to 1.64) than children (HR = 1.16, 95% CI: 1.10 to 1.23). Despite statistical evidence of PH assumption violation, RMST results supported all interpretations. Earlier diagnosis for staged cancers in the Medicaid and uninsured populations accounted for an estimated 13% and 19% of the survival deficit, respectively, vs. the privately insured population. Any treatment received did not account for insurance-associated survival differences in children and adolescents with cancer.

Conclusions

Children and adolescents without private insurance had a higher risk of death and shorter survival within 5 years following cancer diagnosis. Additional research is needed to understand underlying mechanisms.

On permutation tests for comparing restricted mean survival time with small sample from randomized trials

Between-group comparison based on the restricted mean survival time (RMST) is getting attention as an alternative to the conventional logrank/hazard ratio approach for time-to-event outcomes in randomized controlled trials (RCTs). The validity of the commonly used nonparametric inference procedure for RMST has been well supported by large sample theories. However, we sometimes encounter cases with a small sample size in practice, where we cannot rely on the large sample properties. Generally, the permutation approach can be useful to handle these situations in RCTs. However, a numerical issue arises when implementing permutation tests for difference or ratio of RMST from two groups. In this article, we discuss the numerical issue and consider six permutation methods for comparing survival time distributions between two groups using RMST in RCTs setting. We conducted extensive numerical studies and assessed type I error rates of these methods. Our numerical studies demonstrated that the inflation of the type I error rate of the asymptotic methods is not negligible when sample size is small, and that all of the six permutation methods are workable solutions. Although some permutation methods became a little conservative, no remarkable inflation of the type I error rates were observed. We recommend using permutation tests instead of the asymptotic tests, especially when the sample size is less than 50 per arm.