Comparison of state occupation, entry, exit and waiting times in two or more groups based on current status data in a multistate model

Lan and Datta have a paper in Statistics in Medicine. This complements their previous work on non-parametric estimation of current status data multi-state models. Specifically, they develop a K-sample test to compare state occupation probabilities, entry time distribution or state waiting time distributions between groups. The test statistic is based on the integrated L1 distance between the quantities of interest. A p-value for the test is found by bootstrap resampling. This is computationally feasible because of the relative simplicity of the estimator requiring only pool-adjacent-violator algorithm and kernel smoothing. While no Markov assumption is required for the state occupation probabilities, entry and waiting time distributions require a Markov assumption.

The method is demonstrated using a 5-state progressive model on data relating to pubertal development in children. They confirm that there is a significant difference in pubertal development between girls and boys, with boys reaching stages of development later.

Cause-specific cumulative incidence estimation and the Fine and Gray model under both left truncation and right censoring

Ronald Geskus has a new paper in Biometrics. This extends the Fine and Gray model, for regression of the subdistribution hazards for competing risks models, to the case of left truncated (and right censored) data. Essentially it is shown that the standard estimator of the cumulative incidence function (CIF) can be derived as a inverse-probability-weighting estimator. Thus the Fine-Gray model for left-truncated and right-censored data can be obtained as a weighted Cox-model where individuals who are censored or experience a competing risk at time s, have weights at time t>s given by where G(t) is the empirical CDF of the censoring distribution and H(t) is the empirical survivor distribution of the truncation distribution. This form appears to imply that independence is assumed between the censoring and truncation distributions. However, the equivalence of estimates of the CIF in the no-covariates case holds regardless of the relationship between censoring and truncation - only independence with failure times is required.

Experimenting with the Coxian Phase-Type distribution to uncover suitable fits

Marshall and Zenga have a new paper in Methodology and Computing in Applied Probability. This considers the best approach to fitting Coxian phase-type distributions to fully observed survival or duration data. Several previous studies have shown that the EM algorithm, Nelder-Mead and quasi-Newton approaches give estimates that are highly dependent on initial values. In a series of simulations it is shown that the quasi-Newton algorithm is preferable to Nelder-Mead in converging to values closer to the true parameters. However, in the absence of a criterion for global convergence it still seems wise to consider several starting values to try to ensure a global rather than local optimum is obtained.