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In the context of time‐to‐event analysis, a primary objective is to model the risk of experiencing a particular event in relation to a set of observed predictors. The Concordance Index (C‐Index) is a statistic frequently used in practice to assess how well such models discriminate between various risk levels in a population. However, the properties of conventional C‐Index estimators when applied to left‐truncated time‐to‐event data have not been well studied, despite the fact that left‐truncation is commonly encountered in observational studies. We show that the limiting values of the conventional C‐Index estimators depend on the underlying distribution of truncation times, which is similar to the situation with right‐censoring as discussed in Uno et al. (2011) [On the C‐statistics for evaluating overall adequacy of risk prediction procedures with censored survival data. Statistics in Medicine 30(10), 1105–1117]. We develop a new C‐Index estimator based on inverse probability weighting (IPW) that corrects for this limitation, and we generalize this estimator to settings with left‐truncated and right‐censored data. The proposed IPW estimators are highly robust to the underlying truncation distribution and often outperform the conventional methods in terms of bias, mean squared error, and coverage probability. We apply these estimators to evaluate a predictive survival model for mortality among patients with end‐stage renal disease. [ABSTRACT FROM AUTHOR]

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right‐ and interval‐censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right‐ and interval‐censored data. [ABSTRACT FROM AUTHOR]

Screening mammography aims to identify breast cancer early and secondarily measures breast density to classify women at higher or lower than average risk for future breast cancer in the general population. Despite the strong association of individual mammography features to breast cancer risk, the statistical literature on mammogram imaging data is limited. While functional principal component analysis (FPCA) has been studied in the literature for extracting image‐based features, it is conducted independently of the time‐to‐event response variable. With the consideration of building a prognostic model for precision prevention, we present a set of flexible methods, supervised FPCA (sFPCA) and functional partial least squares (FPLS), to extract image‐based features associated with the failure time while accommodating the added complication from right censoring. Throughout the article, we hope to demonstrate that one method is favored over the other under different clinical setups. The proposed methods are applied to the motivating data set from the Joanne Knight Breast Health cohort at Siteman Cancer Center. Our approaches not only obtain the best prediction performance compared to the benchmark model, but also reveal different risk patterns within the mammograms. [ABSTRACT FROM AUTHOR]

With mammography being the primary breast cancer screening strategy, it is essential to make full use of the mammogram imaging data to better identify women who are at higher and lower than average risk. Our primary goal in this study is to extract mammogram-based features that augment the well-established breast cancer risk factors to improve prediction accuracy. In this article, we propose a supervised functional principal component analysis (sFPCA) over triangulations method for extracting features that are ordered by the magnitude of association with the failure time outcome. The proposed method accommodates the irregular boundary issue posed by the breast area within the mammogram imaging data with flexible bivariate splines over triangulations. We also provide an eigenvalue decomposition algorithm that is computationally efficient. Compared to the conventional unsupervised FPCA method, the proposed method results in a lower Brier Score and higher area under the ROC curve (AUC) in simulation studies. We apply our method to data from the Joanne Knight Breast Health Cohort at Siteman Cancer Center. Our approach not only obtains the best prediction performance comparing to unsupervised FPCA and benchmark models but also reveals important risk patterns within the mammogram images. This demonstrates the importance of utilizing additional supervised image-based features to clarify breast cancer risk. [ABSTRACT FROM AUTHOR]

In disease settings where study participants are at risk for death and a serious nonfatal event, composite endpoints defined as the time until the earliest of death or the nonfatal event are often used as the primary endpoint in clinical trials. In practice, if the nonfatal event can only be detected at clinic visits and the death time is known exactly, the resulting composite endpoint exhibits "component‐wise censoring." The standard method used to estimate event‐free survival in this setting fails to account for component‐wise censoring. We apply a kernel smoothing method previously proposed for a marker process in a novel way to produce a nonparametric estimator for event‐free survival that accounts for component‐wise censoring. The key insight that allows us to apply this kernel method is thinking of nonfatal event status as an intermittently observed binary time‐dependent variable rather than thinking of time to the nonfatal event as interval‐censored. We also propose estimators for the probability in state and restricted mean time in state for reversible or irreversible illness‐death models, under component‐wise censoring, and derive their large‐sample properties. We perform a simulation study to compare our method to existing multistate survival methods and apply the methods on data from a large randomized trial studying a multifactor intervention for reducing morbidity and mortality among men at above average risk of coronary heart disease. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Comparing areas under the ROC curve (AUCs) is a popular approach to compare prognostic biomarkers. The aim of this paper is to present an efficient method to control the family‐wise error rate when multiple comparisons are performed. We suggest to combine the max‐t test and the closed testing procedures. We build on previous work on asymptotic results for ROC curves and on general multiple testing methods to efficiently take into account both the correlations between the test statistics and the logical constraints between the null hypotheses. The proposed method results in an uniformly more powerful procedure than both the single‐step max‐t test procedure and popular stepwise extensions of the Bonferroni procedure, such as Bonferroni–Holm. As demonstrated in this paper, the method can be applied in most usual contexts, including the time‐dependent context with right censored data. We show how the method works in practice through a motivating example where we compare several psychometric scores to predict the t‐year risk of Alzheimer's disease. The example illustrates several multiple testing settings and demonstrates the advantage of using the proposed methods over common alternatives. R code has been made available to facilitate the use of the methods by others. [ABSTRACT FROM AUTHOR]

Survival analysis is a branch of statistics that deals with both the tracking of time and the survival status simultaneously as the dependent response. Current comparisons of survival model performance mostly center on clinical data with classic statistical survival models, with prediction accuracy often serving as the sole metric of model performance. Moreover, survival analysis approaches for censored omics data have not been thoroughly investigated. The common approach is to binarize the survival time and perform a classification analysis. Here, we develop a benchmarking design, SurvBenchmark, that evaluates a diverse collection of survival models for both clinical and omics data sets. SurvBenchmark not only focuses on classical approaches such as the Cox model but also evaluates state-of-the-art machine learning survival models. All approaches were assessed using multiple performance metrics; these include model predictability, stability, flexibility, and computational issues. Our systematic comparison design with 320 comparisons (20 methods over 16 data sets) shows that the performances of survival models vary in practice over real-world data sets and over the choice of the evaluation metric. In particular, we highlight that using multiple performance metrics is critical in providing a balanced assessment of various models. The results in our study will provide practical guidelines for translational scientists and clinicians, as well as define possible areas of investigation in both survival technique and benchmarking strategies. [ABSTRACT FROM AUTHOR]

In clinical and epidemiologic studies, hazard ratios are often applied to compare treatment effects between 2 groups for survival data. For competing-risks data, the corresponding quantities of interest are cause-specific hazard ratios and subdistribution hazard ratios. However, they both have some limitations related to model assumptions and clinical interpretation. Therefore, we recommend restricted mean time lost (RMTL) as an alternative measure that is easy to interpret in a competing-risks framework. Based on the difference in RMTL (RMTLd), we propose a new estimator, hypothetical test, and sample-size formula. Simulation results show that estimation of the RMTLd is accurate and that the RMTLd test has robust statistical performance (both type I error and statistical power). The results of 3 example analyses also verify the performance of the RMTLd test. From the perspectives of clinical interpretation, application conditions, and statistical performance, we recommend that the RMTLd be reported along with the hazard ratio in analyses of competing-risks data and that the RMTLd even be regarded as the primary outcome when the proportional hazards assumption fails. [ABSTRACT FROM AUTHOR]

Time is of the essence in evaluating potential drugs and biologics for the treatment and prevention of COVID‐19. There are currently 876 randomized clinical trials (phase 2 and 3) of treatments for COVID‐19 registered on clinicaltrials.gov. Covariate adjustment is a statistical analysis method with potential to improve precision and reduce the required sample size for a substantial number of these trials. Though covariate adjustment is recommended by the U.S. Food and Drug Administration and the European Medicines Agency, it is underutilized, especially for the types of outcomes (binary, ordinal, and time‐to‐event) that are common in COVID‐19 trials. To demonstrate the potential value added by covariate adjustment in this context, we simulated two‐arm, randomized trials comparing a hypothetical COVID‐19 treatment versus standard of care, where the primary outcome is binary, ordinal, or time‐to‐event. Our simulated distributions are derived from two sources: longitudinal data on over 500 patients hospitalized at Weill Cornell Medicine New York Presbyterian Hospital and a Centers for Disease Control and Prevention preliminary description of 2449 cases. In simulated trials with sample sizes ranging from 100 to 1000 participants, we found substantial precision gains from using covariate adjustment–equivalent to 4–18% reductions in the required sample size to achieve a desired power. This was the case for a variety of estimands (targets of inference). From these simulations, we conclude that covariate adjustment is a low‐risk, high‐reward approach to streamlining COVID‐19 treatment trials. We provide an R package and practical recommendations for implementation. [ABSTRACT FROM AUTHOR]

Phase IIb trials of tuberculosis therapy rely on early biomarkers of treatment effect. Despite limited predictive ability for clinical outcomes, culture conversion, the event in which an individual previously culture positive for Mycobacterium tuberculosis yields a negative culture after initiating treatment, is a commonly used endpoint. Lack of consensus on how to define the outcome and corresponding measure of treatment effect complicates interpretation and limits between-trial comparisons. We review common analytic approaches to measuring treatment effect and introduce difference in restricted mean survival times as an alternative to identify faster times to culture conversion and express magnitude of effect on the time scale. Findings from the PanACEA MAMS-TB trial are reanalyzed as an illustrative example. In a systematic review we demonstrate variability in analytic approaches, sampling strategies, and outcome definitions in phase IIb tuberculosis trials. Harmonization would allow for larger meta-analyses and may help expedite advancement of new tuberculosis therapeutics. [ABSTRACT FROM AUTHOR]

Immune checkpoint genes (ICGs) play critical roles in circumventing self-reactivity and represent a novel target to develop treatments for cancers. However, a comprehensive analysis for the expression profile of ICGs at a pan-cancer level and their correlation with patient response to immune checkpoint blockade (ICB) based therapy is still lacking. In this study, we defined three expression patterns of ICGs using a comprehensive survey of RNA-seq data of tumor and immune cells from the functional annotation of the mammalian genome (FANTOM5) project. The correlation between the expression patterns of ICGs and patients survival and response to ICB therapy was investigated. The expression patterns of ICGs were robust across cancers, and upregulation of ICGs was positively correlated with high lymphocyte infiltration and good prognosis. Furthermore, we built a model (ICGe) to predict the response of patients to ICB therapy using five features of ICG expression. A validation scenario of six independent datasets containing data of 261 patients with CTLA-4 and PD-1 blockade immunotherapies demonstrated that ICGe achieved area under the curves of 0.64–0.82 and showed a robust performance and outperformed other mRNA-based predictors. In conclusion, this work revealed expression patterns of ICGs and underlying correlations between ICGs and response to ICB, which helps to understand the mechanisms of ICGs in ICB signal pathways and other anticancer treatments. [ABSTRACT FROM AUTHOR]

Multi-omics data, that is, datasets containing different types of high-dimensional molecular variables, are increasingly often generated for the investigation of various diseases. Nevertheless, questions remain regarding the usefulness of multi-omics data for the prediction of disease outcomes such as survival time. It is also unclear which methods are most appropriate to derive such prediction models. We aim to give some answers to these questions through a large-scale benchmark study using real data. Different prediction methods from machine learning and statistics were applied on 18 multi-omics cancer datasets (35 to 1000 observations, up to 100 000 variables) from the database 'The Cancer Genome Atlas' (TCGA). The considered outcome was the (censored) survival time. Eleven methods based on boosting, penalized regression and random forest were compared, comprising both methods that do and that do not take the group structure of the omics variables into account. The Kaplan–Meier estimate and a Cox model using only clinical variables were used as reference methods. The methods were compared using several repetitions of 5-fold cross-validation. Uno's C-index and the integrated Brier score served as performance metrics. The results indicate that methods taking into account the multi-omics structure have a slightly better prediction performance. Taking this structure into account can protect the predictive information in low-dimensional groups—especially clinical variables—from not being exploited during prediction. Moreover, only the block forest method outperformed the Cox model on average, and only slightly. This indicates, as a by-product of our study, that in the considered TCGA studies the utility of multi-omics data for prediction purposes was limited. Contact:   moritz.herrmann@stat.uni-muenchen.de , +49 89 2180 3198 Supplementary information: Supplementary data are available at Briefings in Bioinformatics online. All analyses are reproducible using R code freely available on Github. [ABSTRACT FROM AUTHOR]

In randomized controlled trials (RCTs) with time-to-event outcomes, the difference in restricted mean survival times (RMSTD) offers an absolute measure of the treatment effect on the time scale. Computation of the RMSTD relies on the choice of a time horizon, $\tau$. In a meta-analysis, varying follow-up durations may lead to the exclusion of RCTs with follow-up shorter than $\tau$. We introduce an individual patient data multivariate meta-analysis model for RMSTD estimated at multiple time horizons. We derived the within-trial covariance for the RMSTD enabling the synthesis of all data by borrowing strength from multiple time points. In a simulation study covering 60 scenarios, we compared the statistical performance of the proposed method to that of two univariate meta-analysis models, based on available data at each time point and based on predictions from flexible parametric models. Our multivariate model yields smaller mean squared error over univariate methods at all time points. We illustrate the method with a meta-analysis of five RCTs comparing transcatheter aortic valve replacement (TAVR) with surgical replacement in patients with aortic stenosis. Over 12, 24, and 36 months of follow-up, those treated by TAVR live 0.28 [95% confidence interval (CI) 0.01 to 0.56], 0.46 (95% CI $-$0.08 to 1.01), and 0.79 (95% CI $-$0.43 to 2.02) months longer on average compared to those treated by surgery, respectively. [ABSTRACT FROM AUTHOR]

Asymptotic distributions under alternative hypotheses and their corresponding sample size and power equations are derived for nonparametric test statistics commonly used to compare two survival curves. Test statistics include the weighted log‐rank test and the Wald test for difference in (or ratio of) Kaplan‐Meier survival probability, percentile survival, and restricted mean survival time. Accrual, survival, and loss to follow‐up are allowed to follow any arbitrary continuous distribution. We show that Schoenfeld's equation—often used by practitioners to calculate the required number of events for the unweighted log‐rank test—can be inaccurate even when the proportional hazards (PH) assumption holds. In fact, it can mislead one to believe that 1:1 is the optimal randomization ratio (RR), when actually power can be gained by assigning more patients to the active arm. Meaningful improvements to Schoenfeld's equation are made. The present theory should be useful in designing clinical trials, particularly in immuno‐oncology where nonproportional hazards are frequently encountered. We illustrate the application of our theory with an example exploring optimal RR under PH and a second example examining the impact of delayed treatment effect. A companion R package npsurvSS is available for download on CRAN. [ABSTRACT FROM AUTHOR]

Summary: In comparing two treatments with the event time observations, the hazard ratio (HR) estimate is routinely used to quantify the treatment difference. However, this model dependent estimate may be difficult to interpret clinically especially when the proportional hazards (PH) assumption is violated. An alternative estimation procedure for treatment efficacy based on the restricted means survival time or t‐year mean survival time (t‐MST) has been discussed extensively in the statistical and clinical literature. On the other hand, a statistical test via the HR or its asymptotically equivalent counterpart, the logrank test, is asymptotically distribution‐free. In this article, we assess the relative efficiency of the hazard ratio and t‐MST tests with respect to the statistical power under various PH and non‐PH models theoretically and empirically. When the PH assumption is valid, the t‐MST test performs almost as well as the HR test. For non‐PH models, the t‐MST test can substantially outperform its HR counterpart. On the other hand, the HR test can be powerful when the true difference of two survival functions is quite large at end but not the beginning of the study. Unfortunately, for this case, the HR estimate may not have a simple clinical interpretation for the treatment effect due to the violation of the PH assumption. [ABSTRACT FROM AUTHOR]

Background. The restricted mean survival time (RMST) estimates life expectancy up to a given time horizon and can thus express the impact of a disease. The aim of this study was to estimate the 15-year RMST of a hypothetical cohort of incident patients starting renal replacement therapy (RRT), according to their age, gender and diabetes status, and to compare it with the expected RMST of the general population. Methods. Using data from 67 258 adult patients in the French Renal Epidemiology and Information Network (REIN) registry, we estimated the RMST of a hypothetical patient cohort (and its subgroups) for the first 15 years after starting RRT (cRMST) and used the general population mortality tables to estimate the expected RMST (pRMST). Results were expressed in three different ways: the cRMST, which calculates the years of life gained under the hypothesis of 100% death without RRT treatment, the difference between the pRMST and the cRMST (the years lost), and a ratio expressing the percentage reduction of the expected RMST: (pRMST – cRMST)/pRMST. Results. Over their first 15 years of RRT, the RMST of end-stage renal disease (ESRD) patients decreased with age, ranging from 14.3 years in patients without diabetes aged 18 years at ESRD to 1.8 years for those aged 90 years, and from 12.7 to 1.6 years, respectively, for those with diabetes; expected RMST varied from 15.0 to 4.1 years between 18 and 90 years. The number of years lost in all subgroups followed a bell curve that was highest for patients aged 70 years. After the age of 55 years in patients with and 70 years in patients without diabetes, the reduction of the expected RMST was>50%. Conclusion. While neither a clinician nor a survival curve can predict with absolute certainty how long a patient will live, providing estimates on years gained or lost, or percentage reduction of expected RMST, may improve the accuracy of the prognostic estimates that influence clinical decisions and information given to patients. [ABSTRACT FROM AUTHOR]

Long-term follow-up is common in many medical investigations where the interest lies in predicting patients' risks for a future adverse outcome using repeatedly measured predictors over time. A key quantity is the likelihood of developing an adverse outcome among individuals who survived up to time s given their covariate information up to time s. Simple, yet reliable, methodology for updating the predicted risk of disease progression using longitudinal markers remains elusive. Two main approaches have been considered in the literature. One approach, based on joint modeling (JM) of failure time and longitudinal covariate process (Tsiatis and Davidian, 2004), derives such longitudinal predictive probability from the joint probability of a longitudinal marker and an event at a given time. A second approach, the partly conditional (PC) modeling (Zheng and Heagerty, 2005), directly models the predictive probability conditional on survival up to a landmark time and information accrued by that time. In this article, we propose new PC models for longitudinal prediction that are more flexible than joint modeling and improve the prediction accuracy over existing PC models. We provide procedures for making inference regarding future risk for an individual with longitudinal measures up to a given time. In addition, we conduct simulations to evaluate both JM and PC approaches in order to provide practical guidance on modeling choices. We use standard measures of predictive accuracy adapted to our setting to explore the predictiveness of the two approaches. We illustrate the performance of the two approaches on a dataset from the End Stage Renal Disease Study (ESRDS). [ABSTRACT FROM AUTHOR]

Residual life is of great interest to patients with life threatening disease. It is also important for clinicians who estimate prognosis and make treatment decisions. Quantile residual life has emerged as a useful summary measure of the residual life. It has many desirable features, such as robustness and easy interpretation. In many situations, the longitudinally collected biomarkers during patients' follow-up visits carry important prognostic value. In this work, we study quantile regression methods that allow for dynamic predictions of the quantile residual life, by flexibly accommodating the post-baseline biomarker measurements in addition to the baseline covariates. We propose unbiased estimating equations that can be solved via existing L1-minimization algorithms. The resulting estimators have desirable asymptotic properties and satisfactory finite sample performance. We apply our method to a study of chronic myeloid leukaemia to demonstrate its usefulness as a dynamic prediction tool. [ABSTRACT FROM AUTHOR]

To evaluate a new therapy versus a control via a randomized, comparative clinical study or a series of trials, due to heterogeneity of the study patient population, a pre-specified, predictive enrichment procedure may be implemented to identify an 'enrichable' subpopulation. For patients in this subpopulation, the therapy is expected to have a desirable overall risk-benefit profile. To develop and validate such a 'therapy-diagnostic co-development' strategy, a three-step procedure may be conducted with three independent data sets from a series of similar studies or a single trial. At the first stage, we create various candidate scoring systems based on the baseline information of the patients via, for example, parametric models using the first data set. Each individual score reflects an anticipated average treatment difference for future patients who share similar baseline profiles. A large score indicates that these patients tend to benefit from the new therapy. At the second step, a potentially promising, enrichable subgroup is identified using the totality of evidence from these scoring systems. At the final stage, we validate such a selection via two-sample inference procedures for assessing the treatment effectiveness statistically and clinically with the third data set, the so-called holdout sample. When the study size is not large, one may combine the first two steps using a 'cross-training-evaluation' process. Comprehensive numerical studies are conducted to investigate the operational characteristics of the proposed method. The entire enrichment procedure is illustrated with the data from a cardiovascular trial to evaluate a beta-blocker versus a placebo for treating chronic heart failure patients. [ABSTRACT FROM AUTHOR]

In a typical randomized clinical study to compare a new treatment with a control, oftentimes each study subject may experience any of several distinct outcomes during the study period, which collectively define the “risk–benefit” profile. To assess the effect of treatment, it is desirable to utilize the entirety of such outcome information. The times to these events, however, may not be observed completely due to, for example, competing risks or administrative censoring. The standard analyses based on the time to the first event, or individual component analyses with respect to each event time, are not ideal. In this paper, we classify each patient's risk–benefit profile, by considering all event times during follow-up, into several clinically meaningful ordinal categories. We first show how to make inferences for the treatment difference in a two-sample setting where categorical data are incomplete due to censoring. We then present a systematic procedure to identify patients who would benefit from a specific treatment using baseline covariate information. To obtain a valid and efficient system for personalized medicine, we utilize a cross-validation method for model building and evaluation and then make inferences using the final selected prediction procedure with an independent data set. The proposal is illustrated with the data from a clinical trial to evaluate a beta-blocker for treating chronic heart failure patients. [ABSTRACT FROM PUBLISHER]

Recent developments in molecular biology have led to the massive discovery of new marker candidates for the prediction of patient survival. To evaluate the predictive value of these markers, statistical tools for measuring the performance of survival models are needed. We consider estimators of discrimination measures, which are a popular approach to evaluate survival predictions in biomarker studies. Estimators of discrimination measures are usually based on regularity assumptions such as the proportional hazards assumption. Based on two sets of molecular data and a simulation study, we show that violations of the regularity assumptions may lead to over-optimistic estimates of prediction accuracy and may therefore result in biased conclusions regarding the clinical utility of new biomarkers. In particular, we demonstrate that biased medical decision making is possible even if statistical checks indicate that all regularity assumptions are satisfied. [ABSTRACT FROM PUBLISHER]

Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai, Tonini, and Lin, 2011). In this article, we derive testing and prediction methods for KM regression under the accelerated failure time (AFT) model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer. [ABSTRACT FROM AUTHOR]

Recently meta-analysis has been widely utilized to combine information across multiple studies to evaluate a common effect. Integrating data from similar studies is particularly useful in genomic studies where the individual study sample sizes are not large relative to the number of parameters of interest. In this article, we are interested in developing robust prognostic rules for the prediction of -year survival based on multiple studies. We propose to construct a composite score for prediction by fitting a stratified semiparametric transformation model that allows the studies to have related but not identical outcomes. To evaluate the accuracy of the resulting score, we provide point and interval estimators for the commonly used accuracy measures including the time-specific receiver operating characteristic curves, and positive and negative predictive values. We apply the proposed procedures to develop prognostic rules for the 5-year survival of breast cancer patients based on five breast cancer genomic studies. [ABSTRACT FROM AUTHOR]

In clinical applications, the prediction error of survival models has to be taken into consideration to assess the practical suitability of conclusions drawn from these models. Different approaches to evaluate the predictive performance of survival models have been suggested in the literature. In this article, we analyze the properties of the estimator of prediction error developed by , Biometrics 56, 249-255), which quantifies the absolute distance between predicted and observed survival functions. We provide a formal proof that the estimator proposed by Schemper and Henderson is not robust against misspecification of the survival model, that is, the estimator will only be meaningful if the model family used for deriving predictions has been specified correctly. To remedy this problem, we construct a new estimator of the absolute distance between predicted and observed survival functions. We show that this modified Schemper-Henderson estimator is robust against model misspecification, allowing its practical application to a wide class of survival models. The properties of the Schemper-Henderson estimator and its new modification are illustrated by means of a simulation study and the analysis of two clinical data sets. [ABSTRACT FROM AUTHOR]

For modern evidence-based medicine, decisions on disease prevention or management strategies are often guided by a risk index system. For each individual, the system uses his/her baseline information to estimate the risk of experiencing a future disease-related clinical event. Such a risk scoring scheme is usually derived from an overly simplified parametric model. To validate a model-based procedure, one may perform a standard global evaluation via, for instance, a receiver operating characteristic analysis. In this article, we propose a method to calibrate the risk index system at a subject level. Specifically, we developed point and interval estimation procedures for t-year mortality rates conditional on the estimated parametric risk score. The proposals are illustrated with a dataset from a large clinical trial with post-myocardial infarction patients. [ABSTRACT FROM PUBLISHER]