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Background: According to long-term follow-up data of malignant tumor patients, assessing treatment effects requires careful consideration of competing risks. The commonly used cause-specific hazard ratio (CHR) and sub-distribution hazard ratio (SHR) are relative indicators and may present challenges in terms of proportional hazards assumption and clinical interpretation. Recently, the restricted mean time lost (RMTL) has been recommended as a supplementary measure for better clinical interpretation. Moreover, for observational study data in epidemiological and clinical settings, due to the influence of confounding factors, covariate adjustment is crucial for determining the causal effect of treatment. Methods: We construct an RMTL estimator after adjusting for covariates based on the inverse probability weighting method, and derive the variance to construct interval estimates based on the large sample properties. We use simulation studies to study the statistical performance of this estimator in various scenarios. In addition, we further consider the changes in treatment effects over time, constructing a dynamic RMTL difference curve and corresponding confidence bands for the curve. Results: The simulation results demonstrate that the adjusted RMTL estimator exhibits smaller biases compared with unadjusted RMTL and provides robust interval estimates in all scenarios. This method was applied to a real-world cervical cancer patient data, revealing improvements in the prognosis of patients with small cell carcinoma of the cervix. The results showed that the protective effect of surgery was significant only in the first 20 months, but the long-term effect was not obvious. Radiotherapy significantly improved patient outcomes during the follow-up period from 17 to 57 months, while radiotherapy combined with chemotherapy significantly improved patient outcomes throughout the entire period. Conclusions: We propose the approach that is easy to interpret and implement for assessing treatment effects in observational competing risk data. [ABSTRACT FROM AUTHOR]

Background: Pocock-Simon's minimisation method has been widely used to balance treatment assignments across prognostic factors in randomised controlled trials (RCTs). Previous studies focusing on the survival outcomes have demonstrated that the conservativeness of asymptotic tests without adjusting for stratification factors, as well as the inflated type I error rate of adjusted asymptotic tests conducted in a small sample of patients, can be relaxed using re-randomisation tests. Although several RCTs using minimisation have suggested the presence of non-proportional hazards (non-PH) effects, the application of re-randomisation tests has been limited to the log-rank test and Cox PH models, which may result in diminished statistical power when confronted with non-PH scenarios. To address this issue, we proposed two re-randomisation tests based on a maximum combination of weighted log-rank tests (MaxCombo test) and the difference in restricted mean survival time (dRMST) up to a fixed time point τ , both of which can be extended to adjust for randomisation stratification factors. Methods: We compared the performance of asymptotic and re-randomisation tests using the MaxCombo test, dRMST, log-rank test, and Cox PH models, assuming various non-PH situations for RCTs using minimisation, with total sample sizes of 50, 100, and 500 at a 1:1 allocation ratio. We mainly considered null, and alternative scenarios featuring delayed, crossing, and diminishing treatment effects. Results: Across all examined null scenarios, re-randomisation tests maintained the type I error rates at the nominal level. Conversely, unadjusted asymptotic tests indicated excessive conservatism, while adjusted asymptotic tests in both the Cox PH models and dRMST indicated inflated type I error rates for total sample sizes of 50. The stratified MaxCombo-based re-randomisation test consistently exhibited robust power across all examined scenarios. Conclusions: The re-randomisation test is a useful alternative in non-PH situations for RCTs with minimisation using the stratified MaxCombo test, suggesting its robust power in various scenarios. [ABSTRACT FROM AUTHOR]

Background: Advancements in linking publicly available census records with vital and administrative records have enabled novel investigations in epidemiology and social history. However, in the absence of unique identifiers, the linkage of the records may be uncertain or only be successful for a subset of the census cohort, resulting in missing data. For survival analysis, differential ascertainment of event times can impact inference on risk associations and median survival. Methods: We modify some existing approaches that are commonly used to handle missing survival times to accommodate this imperfect linkage situation including complete case analysis, censoring, weighting, and several multiple imputation methods. We then conduct simulation studies to compare the performance of the proposed approaches in estimating the associations of a risk factor or exposure in terms of hazard ratio (HR) and median survival times in the presence of missing survival times. The effects of different missing data mechanisms and exposure-survival associations on their performance are also explored. The approaches are applied to a historic cohort of residents in Ambler, PA, established using the 1930 US census, from which only 2,440 out of 4,514 individuals (54%) had death records retrievable from publicly available data sources and death certificates. Using this cohort, we examine the effects of occupational and paraoccupational asbestos exposure on survival and disparities in mortality by race and gender. Results: We show that imputation based on conditional survival results in less bias and greater efficiency relative to a complete case analysis when estimating log-hazard ratios and median survival times. When the approaches are applied to the Ambler cohort, we find a significant association between occupational exposure and mortality, particularly among black individuals and males, but not between paraoccupational exposure and mortality. Discussion: This investigation illustrates the strengths and weaknesses of different imputation methods for missing survival times due to imperfect linkage of the administrative or registry data. The performance of the methods may depend on the missingness process as well as the parameter being estimated and models of interest, and such factors should be considered when choosing the methods to address the missing event times. [ABSTRACT FROM AUTHOR]

Background: The residual life of a patient with human immunodeficiency virus (HIV) is of major interest to patients and their physicians. While existing analyses of HIV patient survival focus mostly on data collected at baseline, residual life analysis allows for dynamic analysis based on additional data collected over a period of time. As survival times typically exhibit a right-skewed distribution, the median provides a more useful summary of the underlying distribution than the mean. In this paper, we propose an efficient inference procedure that fits a semiparametric quantile regression model assessing the effect of longitudinal biomarkers on the residual life of HIV patients until the development of dyslipidemia, a disease becoming more prevalent among those with HIV. Methods: For estimation of model parameters, we propose an induced smoothing method that smooths nonsmooth estimating functions based on check functions. For variance estimation, we propose an efficient resampling-based estimator. The proposed estimators are theoretically justified. Simulation studies are used to evaluate their finite sample performances, including their prediction accuracy. We analyze the Korea HIV/AIDS cohort study data to examine the effects of CD4 (cluster of differentiation 4) cell count on the residual life of HIV patients to the onset of dyslipidemia. Results: The proposed estimator is shown to be consistent and normally distributed asymptotically. Under various simulation settings, our estimates are approximately unbiased. Their variances estimates are close to the empirical variances and their computational efficiency is superior to that of the nonsmooth counterparts. Two measures of prediction performance indicate that our method adequately reflects the dynamic character of longitudinal biomarkers and residual life. The analysis of the Korea HIV/AIDS cohort study data shows that CD4 cell count is positively associated with residual life to the onset of dyslipidemia but the effect is not statistically significant. Conclusions: Our method enables direct prediction of residual lifetimes with a dynamic feature that accommodates data accumulated at different times. Our estimator significantly improves computational efficiency in variance estimation compared to the existing nonsmooth estimator. Analysis of the HIV/AIDS cohort study data reveals dynamic effects of CD4 cell count on the residual life to the onset of dyslipidemia. [ABSTRACT FROM AUTHOR]

Background: Multivariate longitudinal data are under-utilized for survival analysis compared to cross-sectional data (CS - data collected once across cohort). Particularly in cardiovascular risk prediction, despite available methods of longitudinal data analysis, the value of longitudinal information has not been established in terms of improved predictive accuracy and clinical applicability. Methods: We investigated the value of longitudinal data over and above the use of cross-sectional data via 6 distinct modeling strategies from statistics, machine learning, and deep learning that incorporate repeated measures for survival analysis of the time-to-cardiovascular event in the Coronary Artery Risk Development in Young Adults (CARDIA) cohort. We then examined and compared the use of model-specific interpretability methods (Random Survival Forest Variable Importance) and model-agnostic methods (SHapley Additive exPlanation (SHAP) and Temporal Importance Model Explanation (TIME)) in cardiovascular risk prediction using the top-performing models. Results: In a cohort of 3539 participants, longitudinal information from 35 variables that were repeatedly collected in 6 exam visits over 15 years improved subsequent long-term (17 years after) risk prediction by up to 8.3% in C-index compared to using baseline data (0.78 vs. 0.72), and up to approximately 4% compared to using the last observed CS data (0.75). Time-varying AUC was also higher in models using longitudinal data (0.86–0.87 at 5 years, 0.79–0.81 at 10 years) than using baseline or last observed CS data (0.80–0.86 at 5 years, 0.73–0.77 at 10 years). Comparative model interpretability analysis revealed the impact of longitudinal variables on model prediction on both the individual and global scales among different modeling strategies, as well as identifying the best time windows and best timing within that window for event prediction. The best strategy to incorporate longitudinal data for accuracy was time series massive feature extraction, and the easiest interpretable strategy was trajectory clustering. Conclusion: Our analysis demonstrates the added value of longitudinal data in predictive accuracy and epidemiological utility in cardiovascular risk survival analysis in young adults via a unified, scalable framework that compares model performance and explainability. The framework can be extended to a larger number of variables and other longitudinal modeling methods. Trial registration: ClinicalTrials.gov Identifier: NCT00005130, Registration Date: 26/05/2000. [ABSTRACT FROM AUTHOR]

Background: The Pooled Cohort Equations (PCEs) are race- and sex-specific Cox proportional hazards (PH)-based models used for 10-year atherosclerotic cardiovascular disease (ASCVD) risk prediction with acceptable discrimination. In recent years, neural network models have gained increasing popularity with their success in image recognition and text classification. Various survival neural network models have been proposed by combining survival analysis and neural network architecture to take advantage of the strengths from both. However, the performance of these survival neural network models compared to each other and to PCEs in ASCVD prediction is unknown. Methods: In this study, we used 6 cohorts from the Lifetime Risk Pooling Project (with 5 cohorts as training/internal validation and one cohort as external validation) and compared the performance of the PCEs in 10-year ASCVD risk prediction with an all two-way interactions Cox PH model (Cox PH-TWI) and three state-of-the-art neural network survival models including Nnet-survival, Deepsurv, and Cox-nnet. For all the models, we used the same 7 covariates as used in the PCEs. We fitted each of the aforementioned models in white females, white males, black females, and black males, respectively. We evaluated models' internal and external discrimination power and calibration. Results: The training/internal validation sample comprised 23216 individuals. The average age at baseline was 57.8 years old (SD = 9.6); 16% developed ASCVD during average follow-up of 10.50 (SD = 3.02) years. Based on 10 × 10 cross-validation, the method that had the highest C-statistics was Deepsurv (0.7371) for white males, Deepsurv and Cox PH-TWI (0.7972) for white females, PCE (0.6981) for black males, and Deepsurv (0.7886) for black females. In the external validation dataset, Deepsurv (0.7032), Cox-nnet (0.7282), PCE (0.6811), and Deepsurv (0.7316) had the highest C-statistics for white male, white female, black male, and black female population, respectively. Calibration plots showed that in 10 × 10 validation, all models had good calibration in all race and sex groups. In external validation, all models overestimated the risk for 10-year ASCVD. Conclusions: We demonstrated the use of the state-of-the-art neural network survival models in ASCVD risk prediction. Neural network survival models had similar if not superior discrimination and calibration compared to PCEs. [ABSTRACT FROM AUTHOR]

Background: In the older general population, neurodegenerative diseases (NDs) are associated with increased disability, decreased physical and cognitive function. Detecting risk factors can help implement prevention measures. Using deep neural networks (DNNs), a machine-learning algorithm could be an alternative to Cox regression in tabular datasets with many predictive features. We aimed to compare the performance of different types of DNNs with regularized Cox proportional hazards models to predict NDs in the older general population. Methods: We performed a longitudinal analysis with participants of the English Longitudinal Study of Ageing. We included men and women with no NDs at baseline, aged 60 years and older, assessed every 2 years from 2004 to 2005 (wave2) to 2016–2017 (wave 8). The features were a set of 91 epidemiological and clinical baseline variables. The outcome was new events of Parkinson's, Alzheimer or dementia. After applying multiple imputations, we trained three DNN algorithms: Feedforward, TabTransformer, and Dense Convolutional (Densenet). In addition, we trained two algorithms based on Cox models: Elastic Net regularization (CoxEn) and selected features (CoxSf). Results: 5433 participants were included in wave 2. During follow-up, 12.7% participants developed NDs. Although the five models predicted NDs events, the discriminative ability was superior using TabTransformer (Uno's C-statistic (coefficient (95% confidence intervals)) 0.757 (0.702, 0.805). TabTransformer showed superior time-dependent balanced accuracy (0.834 (0.779, 0.889)) and specificity (0.855 (0.0.773, 0.909)) than the other models. With the CoxSf (hazard ratio (95% confidence intervals)), age (10.0 (6.9, 14.7)), poor hearing (1.3 (1.1, 1.5)) and weight loss 1.3 (1.1, 1.6)) were associated with a higher DNN risk. In contrast, executive function (0.3 (0.2, 0.6)), memory (0, 0, 0.1)), increased gait speed (0.2, (0.1, 0.4)), vigorous physical activity (0.7, 0.6, 0.9)) and higher BMI (0.4 (0.2, 0.8)) were associated with a lower DNN risk. Conclusion: TabTransformer is promising for prediction of NDs with heterogeneous tabular datasets with numerous features. Moreover, it can handle censored data. However, Cox models perform well and are easier to interpret than DNNs. Therefore, they are still a good choice for NDs. [ABSTRACT FROM AUTHOR]

Background: Precision medicine is an emerging field that involves the selection of treatments based on patients' individual prognostic data. It is formalized through the identification of individualized treatment rules (ITRs) that maximize a clinical outcome. When the type of outcome is time-to-event, the correct handling of censoring is crucial for estimating reliable optimal ITRs. Methods: We propose a jackknife estimator of the value function to allow for right-censored data for a binary treatment. The jackknife estimator or leave-one-out-cross-validation approach can be used to estimate the value function and select optimal ITRs using existing machine learning methods. We address the issue of censoring in survival data by introducing an inverse probability of censoring weighted (IPCW) adjustment in the expression of the jackknife estimator of the value function. In this paper, we estimate the optimal ITR by using random survival forest (RSF) and Cox proportional hazards model (COX). We use a Z-test to compare the optimal ITRs learned by RSF and COX with the zero-order model (or one-size-fits-all). Through simulation studies, we investigate the asymptotic properties and the performance of our proposed estimator under different censoring rates. We illustrate our proposed method on a phase III clinical trial of non-small cell lung cancer data. Results: Our simulations show that COX outperforms RSF for small sample sizes. As sample sizes increase, the performance of RSF improves, in particular when the expected log failure time is not linear in the covariates. The estimator is fairly normally distributed across different combinations of simulation scenarios and censoring rates. When applied to a non-small-cell lung cancer data set, our method determines the zero-order model (ZOM) as the best performing model. This finding highlights the possibility that tailoring may not be needed for this cancer data set. Conclusion: The jackknife approach for estimating the value function in the presence of right-censored data shows satisfactory performance when there is small to moderate censoring. Winsorizing the upper and lower percentiles of the estimated survival weights for computing the IPCWs stabilizes the estimator. [ABSTRACT FROM AUTHOR]

Background: Clinical prediction models are often not evaluated properly in specific settings or updated, for instance, with information from new markers. These key steps are needed such that models are fit for purpose and remain relevant in the long-term. We aimed to present an overview of methodological guidance for the evaluation (i.e., validation and impact assessment) and updating of clinical prediction models. Methods: We systematically searched nine databases from January 2000 to January 2022 for articles in English with methodological recommendations for the post-derivation stages of interest. Qualitative analysis was used to summarize the 70 selected guidance papers. Results: Key aspects for validation are the assessment of statistical performance using measures for discrimination (e.g., C-statistic) and calibration (e.g., calibration-in-the-large and calibration slope). For assessing impact or usefulness in clinical decision-making, recent papers advise using decision-analytic measures (e.g., the Net Benefit) over simplistic classification measures that ignore clinical consequences (e.g., accuracy, overall Net Reclassification Index). Commonly recommended methods for model updating are recalibration (i.e., adjustment of intercept or baseline hazard and/or slope), revision (i.e., re-estimation of individual predictor effects), and extension (i.e., addition of new markers). Additional methodological guidance is needed for newer types of updating (e.g., meta-model and dynamic updating) and machine learning-based models. Conclusion: Substantial guidance was found for model evaluation and more conventional updating of regression-based models. An important development in model evaluation is the introduction of a decision-analytic framework for assessing clinical usefulness. Consensus is emerging on methods for model updating. [ABSTRACT FROM AUTHOR]

Background: The occurrence and timing of mycobacterial culture conversion is used as a proxy for tuberculosis treatment response. When researchers serially sample sputum during tuberculosis studies, contamination or missed visits leads to missing data points. Traditionally, this is managed by ignoring missing data or simple carry-forward techniques. Statistically advanced multiple imputation methods potentially decrease bias and retain sample size and statistical power.Methods: We analyzed data from 261 participants who provided weekly sputa for the first 12 weeks of tuberculosis treatment. We compared methods for handling missing data points in a longitudinal study with a time-to-event outcome. Our primary outcome was time to culture conversion, defined as two consecutive weeks with no Mycobacterium tuberculosis growth. Methods used to address missing data included: 1) available case analysis, 2) last observation carried forward, and 3) multiple imputation by fully conditional specification. For each method, we calculated the proportion culture converted and used survival analysis to estimate Kaplan-Meier curves, hazard ratios, and restricted mean survival times. We compared methods based on point estimates, confidence intervals, and conclusions to specific research questions.Results: The three missing data methods lead to differences in the number of participants achieving conversion; 78 (32.8%) participants converted with available case analysis, 154 (64.7%) converted with last observation carried forward, and 184 (77.1%) converted with multiple imputation. Multiple imputation resulted in smaller point estimates than simple approaches with narrower confidence intervals. The adjusted hazard ratio for smear negative participants was 3.4 (95% CI 2.3, 5.1) using multiple imputation compared to 5.2 (95% CI 3.1, 8.7) using last observation carried forward and 5.0 (95% CI 2.4, 10.6) using available case analysis.Conclusion: We showed that accounting for missing sputum data through multiple imputation, a statistically valid approach under certain conditions, can lead to different conclusions than naïve methods. Careful consideration for how to handle missing data must be taken and be pre-specified prior to analysis. We used data from a TB study to demonstrate these concepts, however, the methods we described are broadly applicable to longitudinal missing data. We provide valuable statistical guidance and code for researchers to appropriately handle missing data in longitudinal studies. [ABSTRACT FROM AUTHOR]

Background: Although there are discussions regarding standards of the analysis of patient-reported outcomes and quality of life (QOL) in oncology clinical trials, that of QOL with death events is not within their scope. For example, ignoring death can lead to bias in the QOL analysis for patients with moderate or high mortality rates in the palliative care setting. This is discussed in the estimand framework but is controversial. Information loss by summary measures under the estimand framework may make it challenging for clinicians to interpret the QOL analysis results. This study illustrated the use of graphical displays in the framework. They can be helpful for discussions between clinicians and statisticians and decision-making by stakeholders.Methods: We reviewed the time-to-deterioration analysis, prioritized composite outcome approach, semi-competing risk analysis, survivor analysis, linear mixed model for repeated measures, and principal stratification approach. We summarized attributes of estimands and graphs in the statistical analysis and evaluated them in various hypothetical randomized controlled trials.Results: Graphs for each analysis method provide different information and impressions. In the time-to-deterioration analysis, it was not easy to interpret the difference in the curves as an effect on QOL. The prioritized composite outcome approach provided new insights for QOL considering death by defining better conditions based on the distinction of OS and QOL. The semi-competing risk analysis provided different insights compared with the time-to-deterioration analysis and prioritized composite outcome approach. Due to the missing assumption, graphs by the linear mixed model for repeated measures should be carefully interpreted, even for descriptive purposes. The principal stratification approach provided pure comparison, but the interpretation was difficult because the target population was unknown.Conclusions: Graphical displays can capture different aspects of treatment effects that should be described in the estimand framework. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: The exchange of knowledge between statisticians developing new methodology and clinicians, reviewers or authors applying them is fundamental. This is specifically true for clinical trials with time-to-event endpoints. Thereby, one of the most commonly arising questions is that of equal survival distributions in two-armed trial. The log-rank test is still the gold-standard to infer this question. However, in case of non-proportional hazards, its power can become poor and multiple extensions have been developed to overcome this issue. We aim to facilitate the choice of a test for the detection of survival differences in the case of crossing hazards.Methods: We restricted the review to the most recent two-armed clinical oncology trials with crossing survival curves. Each data set was reconstructed using a state-of-the-art reconstruction algorithm. To ensure reproduction quality, only publications with published number at risk at multiple time points, sufficient printing quality and a non-informative censoring pattern were included. This article depicts the p-values of the log-rank and Peto-Peto test as references and compares them with nine different tests developed for detection of survival differences in the presence of non-proportional or crossing hazards.Results: We reviewed 1400 recent phase III clinical oncology trials and selected fifteen studies that met our eligibility criteria for data reconstruction. After including further three individual patient data sets, for nine out of eighteen studies significant differences in survival were found using the investigated tests. An important point that reviewers should pay attention to is that 28% of the studies with published survival curves did not report the number at risk. This makes reconstruction and plausibility checks almost impossible.Conclusions: The evaluation shows that inference methods constructed to detect differences in survival in presence of non-proportional hazards are beneficial and help to provide guidance in choosing a sensible alternative to the standard log-rank test. [ABSTRACT FROM AUTHOR]

Introduction: Extrapolation of time-to-event data from clinical trials is commonly used in decision models for health technology assessment (HTA). The objective of this study was to assess performance of standard parametric survival analysis techniques for extrapolation of time-to-event data for a single event from clinical trials with limited data due to small samples or short follow-up.Methods: Simulated populations with 50,000 individuals were generated with an exponential hazard rate for the event of interest. A scenario consisted of 5000 repetitions with six sample size groups (30-500 patients) artificially censored after every 10% of events observed. Goodness-of-fit statistics (AIC, BIC) were used to determine the best-fitting among standard parametric distributions (exponential, Weibull, log-normal, log-logistic, generalized gamma, Gompertz). Median survival, one-year survival probability, time horizon (1% survival time, or 99th percentile of survival distribution) and restricted mean survival time (RMST) were compared to population values to assess coverage and error (e.g., mean absolute percentage error).Results: The true exponential distribution was correctly identified using goodness-of-fit according to BIC more frequently compared to AIC (average 92% vs 68%). Under-coverage and large errors were observed for all outcomes when distributions were specified by AIC and for time horizon and RMST with BIC. Error in point estimates were found to be strongly associated with sample size and completeness of follow-up. Small samples produced larger average error, even with complete follow-up, than large samples with short follow-up. Correctly specifying the event distribution reduced magnitude of error in larger samples but not in smaller samples.Conclusions: Limited clinical data from small samples, or short follow-up of large samples, produce large error in estimates relevant to HTA regardless of whether the correct distribution is specified. The associated uncertainty in estimated parameters may not capture the true population values. Decision models that base lifetime time horizon on the model's extrapolated output are not likely to reliably estimate mean survival or its uncertainty. For data with an exponential event distribution, BIC more reliably identified the true distribution than AIC. These findings have important implications for health decision modelling and HTA of novel therapies seeking approval with limited evidence. [ABSTRACT FROM AUTHOR]