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A simple non-parametric approach is developed to simultaneously estimate net incidence and morbidity time from specific AIDS illnesses in populations at high risk for death from these illnesses and other causes. The disease-death process has four-stages that can be recast as two sandwiching three-state multiple decrement processes. Non-parametric estimation of net incidence and morbidity time with error bounds are achieved from these sandwiching models through modification of methods from Aalen and Greenwood, and bootstrapping. An application to immunosuppressed HIV-1 infected homosexual men reveals that cytomegalovirus disease, Kaposi's sarcoma and Pneumocystis pneumonia are likely to occur and cause significant morbidity time.

Methods are developed to estimate and test for the impact of intervention use on a population's survival function (time to AIDS). Each participant's history is divided into J + 1 components: omega 0 occurring before the intervention is available and omega 1 to omega J occurring later, as the intervention becomes successively more available. Distribution free truncated Kaplan-Meier models based on time since exposure fit separately to the risk sets/outcomes in omega 0 to omega J directly show the changing patterns of survival. Multivariate proportional hazards models can be used to adjust for covariates. Application of these methods indicates that availability of proven anti-AIDS interventions may have delayed time to AIDS by 8 months in an educated HIV-1 infected homosexual cohort with good access to medical care.

In natural history studies of human immunodeficiency virus type 1 (HIV-1) infection a substantial proportion of participants are seropositive at time of enrollment in the study. These participants form a prevalent subcohort. Estimation of the unknown times since exposure to HIV-1 in the prevalent subcohort is of primary importance for estimation of the incubation time of AIDS. The subset of the cohort that tested negative for antibody to HIV-1 at study entry and was observed to seroconvert forms the incident subcohort that provides longitudinal data on markers of maturity (that is, duration) of infection. We use parametric life table regression models incorporating truncation to describe the conditional distribution (imputing model) of the times since seroconversion given a vector of the markers of maturity. Using the fitted model and the values of the markers of maturity of infection provided by the seroprevalent subcohort at entry into the study, we can impute the unknown times since seroconversion for the prevalent subcohort. We implement multiple imputation based on a model-robust estimate of the covariance matrix of parameters of the imputing model to provide confidence intervals for the geometric mean of the time since seroconversion in the prevalent subcohort, and to compare maturity of infection of cohorts recruited in different cities. The accuracy of imputation is further validated by comparisons of imputation-based estimates of AIDS incubation distribution in the seroprevalent subcohort with more direct estimates obtained from the seroincident subcohort.