| Participants in prospective studies are often evaluated for the occurrence of an absorbing event of interest (e.g., HIV seroconversion) at baseline and a set of pre-specified visit times. Since participants often miss visits, the visit of first detection may be interval censored, or more generally, coarsened.; Interval-censored data are usually analyzed assuming coarsening at random (CAR), a generalization of non-informative censoring. However, this assumption may not be valid. To examine the sensitivity of inference to assumptions about the visit-compliance mechanism, a class of models that express deviations from CAR is posited assuming discrete time. We define these departures from CAR by assuming relationships between the event process and visit compliance process. Plausible ranges for these assumed relationships require eliciting information from scientific experts. For each model, the EM algorithm is used to estimate group-specific survival functions and proportional hazards regression parameters. Also, test statistics for the equality of survival functions are proposed. In addition, Bayesian Markov Chain Monte Carlo (MCMC) methods are developed that average over an elicited distribution of assumptions about the visit compliance mechanism. These methods are analogs to proposed frequentist methods. The regression procedure is extended to allow covariate model selection using the criterion of highest posterior probability. The performance of the frequentist methods is assessed via simulation studies. In general, when the correct assumptions are made, the method performs well. However, when incorrect assumptions are made, the results are biased. The mean posterior parameter estimates and credible intervals for the Bayesian analyses are computed assuming elicited prior distributions and assuming diffuse prior distributions. The results are compared to those from the EM algorithm. For all procedures, CAR-based results are compared to those from the proposed methods. Data analyses from two studies are also presented: AIDS Clinical Trial Group (ACTG) 181, a natural history study of cytomegalovirus (CMV) shedding among AIDS patients, and AIDS Link to the Intravenous Experience (ALIVE), an observational study of HIV infection among injection drug users. Analysis is performed using information elicited from substantive experts affiliated with ACTG 181 or ALIVE and additional scientists. |
