A modification of the redistribution to the right algorithm using disease markers

Disease markers are time-dependent covariates which describeprogression towards development of disease. Traditional methodsin survival analysis do not make use of available data on thesemarkers to recover additional information from censored individuals.Using a heuristic modification of the redistribution to theright algorithm (Efron, 1967), a new approach for recoveringinformation for censored individuals using disease markers isproposed. Additionally, the statistical properties of the proposedmethod are examined. There are two possible advantages to thismodification: (i) bias reduction when censoring is informative,and (ii) an increase in efficiency in the case of truly noninformativecensoring.     

Semiparametric analysis of survival data with left truncation and dependent right censoring

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Because mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left-truncated and right-censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. First, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed-form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.     

A note on P-values under group sequential testing and nonproportional hazards

Summary .   Group sequential designs are often used for periodically assessing treatment efficacy during the course of a clinical trial. Following a group sequential test, P -values computed under the assumption that the data were gathered according to a fixed sample design are no longer uniformly distributed under the null hypothesis of no treatment effect. Various sample space orderings have been proposed for computing proper P -values following a group sequential test. Although many of the proposed orderings have been compared in the setting of time-invariant treatment effects, little attention has been given to their performance when the effect of treatment within an individual varies over time. Our interest here is to compare two of the most commonly used methods for computing proper P -values following a group sequential test, based upon the analysis time (AT) and Z -statistic orderings, with respect to resulting power functions when treatment effects on survival are delayed. Power under the AT ordering is shown to be heavily influenced by the presence of a delayed treatment effect, while power functions corresponding to the Z -statistic ordering remain robust under time-varying treatment effects.