Estimation of overall survival in an 'illness-death' model with application to the vertical transmission of HIV-1.

We derive a nonparametric maximum likelihood estimate of the overall survival distribution in an illness-death model from interval censored observations with unknown status of the nonfatal event. This expanded model is applied to the re-analysis of data from a randomized trial where infants, born to women infected with HIV-1 that were randomly assigned to breastfeeding or counseling for formula feeding, were followed for 24 months for HIV-1 positivity, HIV-1-free survival, and overall survival. HIV-1 positivity, assessed by postpartum venous blood tests, is the interval censored nonfatal event, and HIV-1 positivity status is unknown for a subset of infants due to periodic assessment. The analysis demonstrates that estimation of the overall and the pre- and post-nonfatal event survival distributions with the proposed methods provide novel insights into how overall survival is influenced by the occurrence of the nonfatal event. More generally, it suggests the usefulness of this expanded illness-death model when evaluating composite endpoints as potential surrogates for overall survival in a given disease setting.