Censored and truncated data frequently arise from HIV/AIDS related and other clinical trials and observational studies. Advanced nonparametric survival analysis techniques are required to handle these complicated incomplete data without sacrificing modeling principles. This project develops a usable software module based on recent advances in survival analysis that are routinely applicable to these incomplete data. The software module includes the following innovative estimation techniques: (1) nonparametric maximum likelihood estimator (NPMLE) for survival functions with interval censored, doubly censored and truncated data; (2) maximum profile likelihood approach to the proportional hazard model with interval censored and doubly censored data; and (3) implementation in a modern statistical computing environment. The software module complements its estimation techniques with the following inference procedures: (1) Nonparametric bootstrap, semiparametric likelihood ratio based confidence intervals and bands, (2) Rao, Wald and likelihood ratio tests and confidence sets in the proportional hazards model by profile likelihood. The feasibility of the project rests on several foundations, some of which consolidated and extended in the Phase I research: (1) a significantly faster hybrid algorithm for computing the NPMLE; (2) an effective maximization technique for computing the maximum profile likelihood estimates; (3) an object- oriented data analysis and graphics software environment S-PLUS to host these techniques.
The proposed product will have a ready market in extensive biomedical and public health researchers and practitioners because it provides advanced functionalities that are not found in other survival analysis products, and addresses non-traditional incomplete data commonly encountered in routine applications.
