Regression analysis of a future state entry time distribution conditional on a past state occupation in a progressive multistate model

We present a nonparametric method for estimating the conditional future state entry probabilities and distributions of state entry time conditional on a past state visit when data are subject to dependent censorings in a progressive multistate model where Markovianity of the system is not assumed. These estimators are constructed using the competing risk techniques with risk sets consisting of fractional observations and inverse probability of censoring weights. The fractional observations correspond to estimates of the number of persons who ultimately enter a state from which the future state in question can be reached in one step. We then address the corresponding regression problem by combining these marginal estimators with the pseudo-value approach. The performance of our regression scheme is studied using a comprehensive simulation study. An analysis of existing data on graft-versus-host disease for bone marrow transplant individuals is presented using our novel methodology. A second analysis of another well-known data set on burn patients is also included.

Pseudo-value approach for comparing survival medians for dependent data

Survival median is commonly used to compare treatment groups in cancer-related research. The current literature focuses on developing tests for independent survival data. However, researchers often encounter dependent survival data such as matched pair data or clustered data. We propose a pseudo-value approach to test the equality of survival medians for both independent and dependent survival data. We investigate the type I error and power of the proposed method by a simulation study, in which we examine independent and dependent data. The simulation study shows that the proposed method performs equivalently to the existing methods for independent survival data and performs better for dependent survival data. A study comparing survival median times for bone marrow transplants illustrates the proposed method.

Analyzing survival curves at a fixed point in time for paired and clustered right-censored data

In clinical trials, information about certain time points may be of interest in making decisions about treatment effectiveness. Rather than comparing entire survival curves, researchers can focus on the comparison at fixed time points that may have a clinical utility for patients. For two independent samples of right-censored data, Klein et al. (2007) compared survival probabilities at a fixed time point by studying a number of tests based on some transformations of the Kaplan-Meier estimators of the survival function. However, to compare the survival probabilities at a fixed time point for paired right-censored data or clustered right-censored data, their approach would need to be modified. In this paper, we extend the statistics to accommodate the possible within-paired correlation and within-clustered correlation, respectively. We use simulation studies to present comparative results. Finally, we illustrate the implementation of these methods using two real data sets.