Generalizations of Current Status Data With Applications

In estimation of a survival function, current status data arises when the only information available on individuals is their survival status at a single monitoring time. Here we briefly review extensions of this form of data structure in two directions: (i) doubly censored current status data, where there is incomplete information on the origin of the failure time random variable, and (ii) current status information on more complicated stochastic processes. Simple examples of these data forms are presented for motivation.

Uncertainty About the Incubation Period of AIDS and its Impact on Backcalculation

We analyze three sets of doubly-censored cohort data on incubation times, estimating incubation distributions using semi-parametric methods and assessing the comparability of the estimates. Weibull models appear to be inappropriate for at least one of the cohorts, and the estimates for the different cohorts are substantially different. We use these estimates as inputs for backcalculation, using a nonparametric method based on maximum penalized likelihood. The different incubations all produce fits to the reported AIDS counts that are as good as the fit from a nonstationary incubation distribution that models treatment effects, but the estimated infection curves are very different. We also develop a method for estimating nonstationarity as part of the backcalculation procedure and find that such estimates also depend very heavily on the assumed incubation distribution. We conclude that incubation distributions are so uncertain that meaningful error bounds are difficult to place on backcalculated estimates and that backcalculation may be too unreliable to be used without being supplemented by other sources of information in HIV prevalence and incidence.

Causal Inference in Observational Studies with Outcome-Dependent Sampling

In this paper, we consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals are drawn from a population. On these individuals, information is obtained on treatment, outcome, and a few low-dimensional confounders. These individuals are then stratified according to these factors. In the second phase, a random sub-sample of individuals are drawn from each stratum, with known, stratum-specific selection probabilities. On these individuals, a rich set of confounding factors are collected. In this setting, we introduce four estimators: (1) simple inverse weighted, (2) locally efficient, (3) doubly robust and (4)enriched inverse weighted. We evaluate the finite-sample performance of these estimators in a simulation study. We also use our methodology to estimate the causal effect of trauma care on in-hospital mortality using data from the National Study of Cost and Outcomes of Trauma.