Dynamic prediction: A challenge for biostatisticians, but greatly needed by patients, physicians and the public

Time-varying effect in older patients with early-stage breast cancer: a model considering the competing risks based on a time scale

Background

Patients with early-stage breast cancer may have a higher risk of dying from other diseases, making a competing risks model more appropriate. Considering subdistribution hazard ratio, which is used often, limited to model assumptions and clinical interpretation, we aimed to quantify the effects of prognostic factors by an absolute indicator, the difference in restricted mean time lost (RMTL), which is more intuitive. Additionally, prognostic factors of breast cancer may have dynamic effects (time-varying effects) in long-term follow-up. However, existing competing risks regression models only provide a static view of covariate effects, leading to a distorted assessment of the prognostic factor.

Methods

To address this issue, we proposed a dynamic effect RMTL regression that can explore the between-group cumulative difference in mean life lost over a period of time and obtain the real-time effect by the speed of accumulation, as well as personalized predictions on a time scale.

Results

A simulation validated the accuracy of the coefficient estimates in the proposed regression. Applying this model to an older early-stage breast cancer cohort, it was found that 1) the protective effects of positive estrogen receptor and chemotherapy decreased over time; 2) the protective effect of breast-conserving surgery increased over time; and 3) the deleterious effects of stage T2, stage N2, and histologic grade II cancer increased over time. Moreover, from the view of prediction, the mean C-index in external validation reached 0.78.

Conclusion

Dynamic effect RMTL regression can analyze both dynamic cumulative effects and real-time effects of covariates, providing a more comprehensive prognosis and better prediction when competing risks exist.

Personalised follow-up and management schema for patients with screen-detected pulmonary nodules: A dynamic modelling study

BACKGROUND

Selecting the time target for follow-up testing in lung cancer screening is challenging. We aim to devise dynamic, personalized lung cancer screening schema for patients with pulmonary nodules detected through low-dose computed tomography.

METHODS

We developed and validated dynamic models using data of pulmonary nodule patients (aged 55-74 years) from the National Lung Screening Trial. We predicted patient-specific risk profiles at baseline (R0) and updated the risk evaluation results in repeated screening rounds (R1 and R2). We used risk cutoffs to optimize time-dependent sensitivity at an early decision point (3 months) and time-dependent specificity at a late decision point (1 year).

RESULTS

In validation, area under receiver operating characteristic curve for predicting 12-month lung cancer onset was 0.867 (95 % confidence interval: 0.827-0.894) and 0.807 (0.765-0.948) at R0 and R1-R2, respectively. The personalized schema, compared with National Comprehensive Cancer Network (NCCN) guideline and Lung-RADS, yielded lower rates of delayed diagnosis (1.7% vs. 1.7% vs. 6.9 %) and over-testing (4.9% vs. 5.6% vs. 5.6 %) at R0, and lower rates of delayed diagnosis (0.0% vs. 18.2% vs. 18.2 %) and over-testing (2.6% vs. 8.3% vs. 7.3 %) at R2. Earlier test recommendation among cancer patients was more frequent using the personalized schema (vs. NCCN: 29.8% vs. 20.9 %, p = 0.0065; vs. Lung-RADS: 33.2% vs. 22.8 %, p = 0.0025), especially for women, patients aged ≥65 years, and part-solid or non-solid nodules.

CONCLUSIONS

The personalized schema is easy-to-implement and more accurate compared with rule-based protocols. The results highlight value of personalized approaches in realizing efficient nodule management.

Blood biomarkers in dynamic prediction of conversion to Alzheimer's disease: An application of joint modeling

OBJECTIVES

To investigate the accuracy of longitudinal trajectories of blood biomarkers for predicting future onset of AD among MCI participants as well as to demonstrate dynamic prediction of the individual conversion risk applying joint modeling.

METHODS

A total of 446 participants with MCI at baseline from the Alzheimer's Disease Neuroimaging Initiative database were included. We introduced joint modeling to analyze the effects of the longitudinal blood biomarkers on the conversion risk to AD, and further to build individual-specific prediction risk model.

RESULTS

During the follow-up, 345 participants remained with MCI and 101 progressed to AD, and were categorized as non-progression and progression group, respectively. Longitudinally, the positive association of the concentration dynamics of plasma p-tau181 and NfL with the conversion risk to AD from MCI was also demonstrated, with Hazard Ratio (HR) = 5.83 and HR = 4.18, respectively. When incorporating plasma p-tau181 and NfL together to predict AD progression, we observed improved performance (AUC = 0.701, Brier Score = 0.119). Two participants were chosen to exemplify the individual-specific risk prediction at different follow-up time for comparative analysis.

CONCLUSIONS

Plasma p-tau181 and NfL could serve as biomarkers for the prediction of AD onset, and the individualized prediction opens up the possibility to provide clinical information at a personal level.

Dynamic effects of prognostic factors and individual survival prediction for amyotrophic lateral sclerosis disease

OBJECTIVE

Amyotrophic lateral sclerosis (ALS) is a neurodegenerative disease affecting motor neurons, with broad heterogeneity in disease progression and survival in different patients. Therefore, an accurate prediction model will be crucial to implement timely interventions and prolong patient survival time.

METHODS

A total of 1260 ALS patients from the PRO-ACT database were included in the analysis. Their demographics, clinical variables, and death reports were included. We constructed an ALS dynamic Cox model through the landmarking approach. The predictive performance of the model at different landmark time points was evaluated by calculating the area under the curve (AUC) and Brier score.

RESULTS

Three baseline covariates and seven time-dependent covariates were selected to construct the ALS dynamic Cox model. For better prognostic analysis, this model identified dynamic effects of treatment, albumin, creatinine, calcium, hematocrit, and hemoglobin. Its prediction performance (at all landmark time points, AUC ≥ 0.70 and Brier score ≤ 0.12) was better than that of the traditional Cox model, and it predicted the dynamic 6-month survival probability according to the longitudinal information of individual patients.

INTERPRETATION

We developed an ALS dynamic Cox model with ALS longitudinal clinical trial datasets as the inputs. This model can not only capture the dynamic prognostic effect of both baseline and longitudinal covariates but also make individual survival predictions in real time, which are valuable for improving the prognosis of ALS patients and providing a reference for clinicians to make clinical decisions.

Individual dynamic prediction and prognostic analysis for long-term allograft survival after kidney transplantation

Background

Predicting allograft survival is vital for efficient transplant success. With dynamic changes in patient conditions, clinical indicators may change longitudinally, and doctors’ judgments may be highly variable. It is necessary to establish a dynamic model to precisely predict the individual risk/survival of new allografts.

Methods

The follow-up data of 407 patients were obtained from a renal allograft failure study. We introduced a landmarking-based dynamic Cox model that incorporated baseline values (age at transplantation, sex, weight) and longitudinal changes (glomerular filtration rate, proteinuria, hematocrit). Model performance was evaluated using Harrell’s C-index and the Brier score.

Results

Six predictors were included in our analysis. The Kaplan–Meier estimates of survival at baseline showed an overall 5-year survival rate of 87.2%. The dynamic Cox model showed the individual survival prediction with more accuracy at different time points (for the 5-year survival prediction, the C-index = 0.789 and Brier score = 0.065 for the average of all time points) than the static Cox model at baseline (C-index = 0.558, Brier score = 0.095). Longitudinal covariate prognostic analysis (with time-varying effects) was performed.

Conclusions

The dynamic Cox model can utilize clinical follow-up data, including longitudinal patient information. Dynamic prediction and prognostic analysis can be used to provide evidence and a reference to better guide clinical decision-making for applying early treatment to patients at high risk.

An improved method for the effect estimation of the intermediate event on the outcome based on the susceptible pre-identification

Background

In follow-up studies, the occurrence of the intermediate event may influence the risk of the outcome of interest. Existing methods estimate the effect of the intermediate event by including a time-varying covariate in the outcome model. However, the insusceptible fraction to the intermediate event in the study population has not been considered in the literature, leading to effect estimation bias due to the inaccurate dataset.

Methods

In this paper, we propose a new effect estimation method, in which the susceptible subpopulation is identified firstly so that the estimation could be conducted in the right population. Then, the effect is estimated via the extended Cox regression and landmark methods in the identified susceptible subpopulation. For susceptibility identification, patients with observed intermediate event time are classified as susceptible. Based on the mixture cure model fitted the incidence and time of the intermediate event, the susceptibility of the patient with censored intermediate event time is predicted by the residual intermediate event time imputation. The effect estimation performance of the new method was investigated in various scenarios via Monte-Carlo simulations with the performance of existing methods serving as the comparison. The application of the proposed method to mycosis fungoides data has been reported as an example.

Results

The simulation results show that the estimation bias of the proposed method is smaller than that of the existing methods, especially in the case of a large insusceptible fraction. The results hold for small sample sizes. Besides, the estimation bias of the new method decreases with the increase of the covariates, especially continuous covariates, in the mixture cure model. The heterogeneity of the effect of covariates on the outcome in the insusceptible and susceptible subpopulation, as well as the landmark time, does not affect the estimation performance of the new method.

Conclusions

Based on the pre-identification of the susceptible, the proposed new method could improve the effect estimation accuracy of the intermediate event on the outcome when there is an insusceptible fraction to the intermediate event in the study population.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01378-8.

A predictive paradigm for COVID-19 prognosis based on the longitudinal measure of biomarkers

Novel coronavirus disease 2019 (COVID-19) is an emerging, rapidly evolving crisis, and the ability to predict prognosis for individual COVID-19 patient is important for guiding treatment. Laboratory examinations were repeatedly measured during hospitalization for COVID-19 patients, which provide the possibility for the individualized early prediction of prognosis. However, previous studies mainly focused on risk prediction based on laboratory measurements at one time point, ignoring disease progression and changes of biomarkers over time. By using historical regression trees (HTREEs), a novel machine learning method, and joint modeling technique, we modeled the longitudinal trajectories of laboratory biomarkers and made dynamically predictions on individual prognosis for 1997 COVID-19 patients. In the discovery phase, based on 358 COVID-19 patients admitted between 10 January and 18 February 2020 from Tongji Hospital, HTREE model identified a set of important variables including 14 prognostic biomarkers. With the trajectories of those biomarkers through 5-day, 10-day and 15-day, the joint model had a good performance in discriminating the survived and deceased COVID-19 patients (mean AUCs of 88.81, 84.81 and 85.62% for the discovery set). The predictive model was successfully validated in two independent datasets (mean AUCs of 87.61, 87.55 and 87.03% for validation the first dataset including 112 patients, 94.97, 95.78 and 94.63% for the second validation dataset including 1527 patients, respectively). In conclusion, our study identified important biomarkers associated with the prognosis of COVID-19 patients, characterized the time-to-event process and obtained dynamic predictions at the individual level.

Functional survival forests for multivariate longitudinal outcomes: Dynamic prediction of Alzheimer's disease progression

The random survival forest (RSF) is a non-parametric alternative to the Cox proportional hazards model in modeling time-to-event data. In this article, we developed a modeling framework to incorporate multivariate longitudinal data in the model building process to enhance the predictive performance of RSF. To extract the essential features of the multivariate longitudinal outcomes, two methods were adopted and compared: multivariate functional principal component analysis and multivariate fast covariance estimation for sparse functional data. These resulting features, which capture the trajectories of the multiple longitudinal outcomes, are then included as time-independent predictors in the subsequent RSF model. This non-parametric modeling framework, denoted as functional survival forests, is better at capturing the various trends in both the longitudinal outcomes and the survival model which may be difficult to model using only parametric approaches. These advantages are demonstrated through simulations and applications to the Alzheimer's Disease Neuroimaging Initiative.

Estimating cumulative incidence functions in competing risks data with dependent left-truncation

Both delayed study entry (left-truncation) and competing risks are common phenomena in observational time-to-event studies. For example, in studies conducted by Teratology Information Services (TIS) on adverse drug reactions during pregnancy, the natural time scale is gestational age, but women enter the study after time origin and upon contact with the service. Competing risks are present, because an elective termination may be precluded by a spontaneous abortion. If left-truncation is entirely random, the Aalen-Johansen estimator is the canonical estimator of the cumulative incidence functions of the competing events. If the assumption of random left-truncation is in doubt, we propose a new semiparametric estimator of the cumulative incidence function. The dependence between entry time and time-to-event is modeled using a cause-specific Cox proportional hazards model and the marginal (unconditional) estimates are derived via inverse probability weighting arguments. We apply the new estimator to data about coumarin usage during pregnancy. Here, the concern is that the cause-specific hazard of experiencing an induced abortion may depend on the time when seeking advice by a TIS, which also is the time of left-truncation or study entry. While the aims of counseling by a TIS are to reduce the rate of elective terminations based on irrational overestimation of drug risks and to lead to better and safer medical treatment of maternal disease, it is conceivable that women considering an induced abortion are more likely to seek counseling. The new estimator is also evaluated in extensive simulation studies and found preferable compared to the Aalen-Johansen estimator in non-misspecified scenarios and to at least provide for a sensitivity analysis otherwise.

A comparison of the beta-geometric model with landmarking for dynamic prediction of time to pregnancy

We conducted a simulation study to compare two methods that have been recently used in clinical literature for the dynamic prediction of time to pregnancy. The first is landmarking, a semi-parametric method where predictions are updated as time progresses using the patient subset still at risk at that time point. The second is the beta-geometric model that updates predictions over time from a parametric model estimated on all data and is specific to applications with a discrete time to event outcome. The beta-geometric model introduces unobserved heterogeneity by modelling the chance of an event per discrete time unit according to a beta distribution. Due to selection of patients with lower chances as time progresses, the predicted probability of an event decreases over time. Both methods were recently used to develop models predicting the chance to conceive naturally. The advantages, disadvantages and accuracy of these two methods are unknown. We simulated time-to-pregnancy data according to different scenarios. We then compared the two methods by the following out-of-sample metrics: bias and root mean squared error in the average prediction, root mean squared error in individual predictions, Brier score and c statistic. We consider different scenarios including data-generating mechanisms for which the models are misspecified. We applied the two methods on a clinical dataset comprising 4999 couples. Finally, we discuss the pros and cons of the two methods based on our results and present recommendations for use of either of the methods in different settings and (effective) sample sizes.