Ignorability conditions for frequentist non parametric analysis of conditional distributions with incomplete data

Rubin (1976 Rubin, D.B. (1976). Inference and missing data. Biometrika 63(3):581–592.[Crossref], [Web of Science ®] , [Google Scholar]) derived general conditions under which inferences that ignore missing data are valid. These conditions are sufficient but not generally necessary, and therefore may be relaxed in some special cases. We consider here the case of frequentist estimation of a conditional cdf subject to missing outcomes. We partition a set of data into outcome, conditioning, and latent variables, all of which potentially affect the probability of a missing response. We describe sufficient conditions under which a complete-case estimate of the conditional cdf of the outcome given the conditioning variable is unbiased. We use simulations on a renal transplant data set (Dienemann et al.) to illustrate the implications of these results.     

A Note on the Complementary Mixture Pareto II Distribution

We introduce a new survival distribution, of Pareto type, that arises from a cure-mixture frailty model. We describe its properties and demonstrate connections with familiar distributions including the Pareto and exponential. We derive its characteristic function and moments.     

Ignorability, Sufficiency and Ancillarity

This paper explores the relationship between ignorability, sufficiency and ancillarity in the coarse data model of Heitjan and Rubin. Bayes or likelihood ignorability has a natural relationship to sufficiency, and frequentist ignorability an analogous relationship to ancillarity. Weaker conditions, termed observed likelihood sufficiency, observed specific sufficiency and observed ancillarity, expand the concepts to models where the coarsening mechanism is sometimes, but not always, ignorable.     

Weibull prediction of event times in clinical trials

In clinical trials with interim analyses planned at pre-specified event counts, one may wish to predict the times of these landmark events as a tool for logistical planning. Currently available methods use either a parametric approach based on an exponential model for survival (Bagiella and Heitjan, Statistics in Medicine 2001; 20:2055) or a non-parametric approach based on the Kaplan-Meier estimate (Ying et al., Clinical Trials 2004; 1:352). Ying et al. (2004) demonstrated the trade-off between bias and variance in these models; the exponential method is highly efficient when its assumptions hold but potentially biased when they do not, whereas the non-parametric method has minimal bias and is well calibrated under a range of survival models but typically gives wider prediction intervals and may fail to produce useful predictions early in the trial. As a potential compromise, we propose here to make predictions under a Weibull survival model. Computations are somewhat more difficult than with the simpler exponential model, but Monte Carlo studies show that predictions are robust under a broader range of assumptions. We demonstrate the method using data from a trial of immunotherapy for chronic granulomatous disease.