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The main purpose of this paper is to survey the statistical inference for covariate-specific time-dependent receiver operating characteristic (ROC) curves with nonignorable missing continuous biomarker values. To construct time-dependent ROC curves, we consider a joint model which assumes that the failure time depends on the continuous biomarker and the covariates through a Cox proportional hazards model and that the continuous biomarker depends on the covariates through a semiparametric location model. Assuming a purely parametric model on the propensity score, we utilize instrumental variables to deal with the identifiable issue and estimate the unknown parameters of the propensity score by a simple and efficient method. In addition, when the propensity score is estimated, we develop HT and AIPW approaches to estimate our interested quantities. In the presence of nonignorable missing biomarker, our AIPW estimators of the interested quantities are still doubly robust when the true propensity score is a special parametric logistic model. At last, simulation studies are conducted to assess the performance of our proposed approaches, and a real data analysis is also carried out to illustrate its application. [ABSTRACT FROM AUTHOR]

Concordance refers to the probability that subjects with high values on one variable also have high values on another variable. This index has wide application in practice, as a measure of effect size in group-comparison studies, an index of accuracy in diagnostic studies, and a discrimination index for prediction models. Herein, we provide a unified framework for statistical inference involving concordance indices for standard variables of binary, ordinal, and continuous types. In particular, we develop confidence interval procedures for a single concordance index and differences between two correlated indices. Simulation results show that procedures based on logit-transformation for a single index and Fisher's z -transformation for a difference between indices perform very well in terms of coverage and tail errors even when the sample size is as small as 30, unless the concordance is high and the standard is a binary variable for which at least 50 subjects are needed. We illustrate the procedures for a variety of standard variables with previously published data. Illustrative SAS code is provided. [ABSTRACT FROM AUTHOR]

The novel mechanism of action of immunotherapy agents, in treatment of various types of cancer, poses unique challenges during the designing of clinical trials. It is important to account for possibility of a delayed treatment effect and adjust sample size accordingly. This paper provides an analytical approach for computing sample size in the presence of a delayed effect using a piece-wise proportional hazards model. Failing to account for an anticipated treatment delay may result in considerable loss in power. The overall hazard ratio (HR), which now represents the average HR across the entire treatment period, can remain a meaningful measure of average benefit to patients in the trial. We show that, special consideration needs to be given for the designing of interim analyses related to futility, so as not to increase the probability of incorrectly stopping an effective agent. It is shown that the weighted log-rank test, using the Fleming-Harrington class of weights, can be used as supportive analysis to better reflect the impact of a delayed effect and possible long-term benefit in a subset of the overall population. [ABSTRACT FROM AUTHOR]

Recently, an increasing number of researchers propose to use restricted mean survival time (RMST) to evaluate medical treatment outcomes when the proportional hazards assumption is in doubt. Using the empirical likelihood ratio for the Kaplan-Meier mean, we show how the statistical analysis for the RMST and difference/ratio of two RMSTs can be obtained. Examples are given using R software and package emplik. We argue that the confidence intervals produced with this new method has several intrinsic advantages over the current method implemented in R package survRM2. A simulation is also included. [ABSTRACT FROM AUTHOR]

In a comparative longitudinal clinical study, multiple clinical events of interest are typically collected in timing and occurrence during the follow-up period. These clinical events are often indicative of disease burden over the study period and provide overall evidence of benefit/risk of one treatment relative to another. While these clinical events are usually used to form a composite endpoint, only the first occurrence of the composite endpoint event is considered in primary efficacy analysis. This type of analysis is commonly performed but it may not be ideal. Most of the existing methods for analyzing multiple event-time data were developed, relying on certain model assumptions. However, the assumptions may greatly affect the inferences for treatment effect. In this paper, we propose a simple, non-parametric estimator of conditional mean survival time for multiple events to quantify treatment effect which has clinically meaningful interpretation. We use simulation studies to evaluate the performance of the new method. Further, we apply this method to analyze the data from a cardiovascular clinical trial as an illustration. [ABSTRACT FROM AUTHOR]

The win ratio method has received much attention in methodological research, ad hoc analyses, and designs of prospective studies. As the primary analysis, it supported the approval of tafamidis for the treatment of cardiomyopathy to reduce cardiovascular mortality and cardiovascular-related hospitalization. However, its dependence on censoring is a potential shortcoming. In this article, we propose the inverse-probability-of-censoring weighting (IPCW) adjusted win ratio statistic (i.e., the IPCW-adjusted win ratio statistic) to overcome censoring issues. We consider independent censoring, common censoring across endpoints, and right censoring. We develop an asymptotic variance estimator for the logarithm of the IPCW-adjusted win ratio statistic and evaluate it via simulation. Our simulation studies show that, as the amount of censoring increases, the unadjusted win proportions may decrease greatly. Consequently, the bias of the unadjusted win ratio estimate may increase greatly, producing either an overestimate or an underestimate. We demonstrate theoretically and through simulation that the IPCW-adjusted win ratio statistic gives an unbiased estimate of treatment effect. [ABSTRACT FROM AUTHOR]

In traditional survival analyses, hazard ratio (HR) is commonly used to evaluate treatment effects. However, HR may not be easy to interpret. Restricted mean survival time is a viable alternative to HR, particularly when the proportional hazards assumption is not satisfied. We developed a conditional restricted mean survival time (CRMST) estimator for a time interval of interest using counting process. The variance of CRMST was estimated using a perturbation re-sampling method for asymptotic normality. The utility of our CRMST seems promising based on comprehensive simulation studies and a real data case study. [ABSTRACT FROM AUTHOR]

We review the design, data monitoring, and analyses of clinical trials with co-primary endpoints. Recently developed methods for fixed-sample and group-sequential settings are described. Practical considerations are discussed, and guidance for the application of these methods is provided. [ABSTRACT FROM PUBLISHER]

The Cox proportional hazards cure model is a survival model incorporating a cure rate with the assumption that the population contains both uncured and cured individuals. It contains a logistic regression for the cure rate, and a Cox regression to estimate the hazard for uncured patients. A single predictive model for both the cure and hazard can be developed by using a cure model that simultaneously predicts the cure rate and hazards for uncured patients; however, model selection is a challenge because of the lack of a measure for quantifying the predictive accuracy of a cure model. Recently, we developed an area under the receiver operating characteristic curve (AUC) for determining the cure rate in a cure model (Asano et al., 2014), but the hazards measure for uncured patients was not resolved. In this article, we propose novel C-statistics that are weighted by the patients’ cure status (i.e., cured, uncured, or censored cases) for the cure model. The operating characteristics of the proposed C-statistics and their confidence interval were examined by simulation analyses. We also illustrate methods for predictive model selection and for further interpretation of variables using the proposed AUCs and C-statistics via application to breast cancer data. [ABSTRACT FROM PUBLISHER]

Biomarkers play an important role to predict the time to event of interest. To evaluate the prediction performance of biomarkers, Cox proportional hazards model and Harrell’s C-index have been widely used. However, when some of the biomarker measurements are not fully observed due to detection limits of given instrument, evaluation may become complicated. We estimate the Cox model and concordance probability in the presence of censored biomarker data. Simulation study demonstrates that the proposed method outperforms over the simple ad hoc method. Our approach is especially useful to evaluate discrimination potential of the biomarker regardless of variant detection limits. [ABSTRACT FROM PUBLISHER]