Failure Time Outcome Research Articles

Application of the Time‐Dependent ROC Curves for Prognostic Accuracy with Multiple Biomarkers

The rapid advancement in molecule technology has led to the discovery of many markers that have potential applications in disease diagnosis and prognosis. In a prospective cohort study, information on a panel of biomarkers as well as the disease status for a patient are routinely collected over time. Such information is useful to predict patients' prognosis and select patients for targeted therapy. In this article, we develop procedures for constructing a composite test with optimal discrimination power when there are multiple markers available to assist in prediction and characterize the accuracy of the resulting test by extending the time-dependent receiver operating characteristic (ROC) curve methodology. We employ a modified logistic regression model to derive optimal linear composite scores such that their corresponding ROC curves are maximized at every false positive rate. We provide theoretical justification for using such a model for prognostic accuracy. The proposed method allows for time-varying marker effects and accommodates censored failure time outcome. When the effects of markers are approximately constant over time, we propose a more efficient estimating procedure under such models. We conduct numerical studies to evaluate the performance of the proposed procedures. Our results indicate the proposed methods are both flexible and efficient. We contrast these methods with an application concerning the prognostic accuracies of expression levels of six genes.

Nonparametric prediction of event times in randomized clinical trials

In clinical trials with planned interim analysis, it can be valuable for logistical reasons to predict the times of landmark events such as the 50th and 100th event. Bagiella and Heitjan (Stat Med 2001; 20: 2055-63) proposed a parametric prediction model for failure-time outcomes assuming exponential survival and Poisson enrollment. When little is known about the distributions of interest, there is concern that parametric prediction methods may be biased and inefficient if their underlying distributional assumptions are invalid. We propose nonparametric approaches to make point and interval predictions for landmark dates during the course of the trial. We obtain point predictions using the Kaplan-Meier estimator to extrapolate the survival probability into the future, selecting the time when the expected number of events is equal to the landmark number. To construct prediction intervals, we use a simulation strategy based on the Bayesian bootstrap. Monte Carlo results demonstrate the superiority of the nonparametric method when the assumptions underlying the parametric model are incorrect. We demonstrate the methods using data from a trial of immunotherapy of chronic granulomatous disease.

A Flexible Stochastic Curtailing Procedure for the Log-Rank Test

For safety and ethical reasons, a data monitoring committee of a clinical trial may wish to assess the futility of continuing a trial if the currently available data at an interim look show no beneficial effect due to treatment, especially when accompanied by mounting evidence of treatment emergent adverse effects. Stochastic curtailing whereby conditional power is evaluated given currently observed data is one way of evaluating futility. In clinical trials that look at “time-to-event” as the primary outcome, difference between treatment groups with respect to the primary outcome is commonly evaluated using the log-rank test. Although the unconditional power function for the log-rank test has been described previously, its conditional power has not been widely investigated. We describe a method for evaluating conditional power when the log-rank test is used to assess the difference between the survival distributions of two treatment groups with respect to some failure-time outcome. The method is useful under a wide range of assumptions regarding the underlying survival distribution, patient entry distribution, losses to follow-up, and (if applicable) noncompliance, drop-ins, lag in treatment effect, and stratification. This level of applicability is attained by generalizing a flexible Markov chain approach to unconditional power computation, described previously, to compute conditional power. Control Clin Trials 2000;21:428–439

Power considerations for testing an interaction in a 2 × k factorial design with a failure time outcome

We examine the power and sample size requirements for testing an interaction in the situation of a 2 × k factorial design with time to failure as the outcome of interest. Using the distribution of a general test statistic, based on a weighted residual sum of squares for testing a general interaction in a 2 × k factorial experiment, we describe the relationship between the power of the test and the size of the sample. In a Simulation study, we evaluate the behavior of three commonly used estimators as methods for estimating the parameters of the test statistic. These are the Mantel-Haenszel (MH) method, a method (O/E) based on the ratio of the observed to expected number of events, and the maximum likelihood (MLE) method. We show that in most cases nominal test sizes and appropriate powers are attained using the MLE and MH methods, whereas the O/E method yielded test sizes and powers less than expected. With both large baseline hazard rates and large differences in relative hazard rates, the difference between the simulated and asymptotic powers for all three methods become larger; however, the size of this difference is small and unlikely to seriously affect the use of either the MLE or MH methods. The proposed methods could also be used to calculate the power and sample size for testing a treatment-covariate interaction in a stratified data analysis.

Using Surrogate Failure Time Data to Increase Cost Effectiveness in Clinical Trials

In clinical trials with failure time, outcomes, the cost of follow-up for the endpoint of primary interest is sometimes expensive. In many of these settings, one or more secondary or surrogate failure time outcomes are also available which either occur much earlier or are much less expensive to follow than the primary outcome. This paper presents a method for using these secondary outcomes to increase the power of detecting a treatment effect on the primary outcome only, without introducing bias. The proposed method requires that patients be randomized to either extended or limited follow-up. A test statistic is constructed by forming a minimum variance linear combination of a linear rank statistic based on the primary outcome and a mean zero weighted sum of linear rank statistics based on secondary outcomes from both follow-up arms. Large-sample distribution theory for this statistic is developed while moderate sample behaviour is explored through a simulation study.

Using surrogate failure time data to increase cost effectiveness in clinical trials

SUMMARY In clinical trials with failure time outcomes, the cost of follow-up for the endpoint of primary interest is sometimes expensive. In many of these settings, one or more secondary or surrogate failure time outcomes are also available which either occur much earlier or are much less expensive to follow than the primary outcome. This paper presents a method for using these secondary outcomes to increase the power of detecting a treatment effect on the primary outcome only, without introducing bias. The proposed method requires that patients be randomized to either extended or limited follow-up. A test statistic is constructed by forming a minimum variance linear combination of a linear rank statistic based on the primary outcome and a mean zero weighted sum of linear rank statistics based on secondary outcomes from both follow-up arms. Large-sample distribution theory for this statistic is developed while moderate sample behaviour is explored through a simulation study.