Analysis of covariance with incomplete data via semiparametric model transformations

We propose a method for fitting semiparametric models such as the proportio nal hazards (PH), additive risks (AR), and proportional odds (PO) models. E ach of these semiparametric models implies that some transformation of the conditional cumulative hazard function (at each t) depends linearly on the covariates. The proposed method is based on nonparametric estimation of the conditional cumulative hazard function, forming a weighted average over a range of t-values, and subsequent use of least squares to estimate the para meters suggested by each model. An approximation to the optimal weight func tion is given. This allows semiparametric models to be fitted even in incom plete data cases where the partial likelihood fails (e.g., left censoring, right truncation). However, the main advantage of this method rests in the fact that neither the interpretation of the parameters nor the validity of the analysis depend on the appropriateness of the PH or any of the other se miparametric models. In fact, we propose an integrated method for data anal ysis where the role of the various semiparametric models is to suggest the best fitting transformation. A single continuous covariate and several cate gorical covariates (factors) are allowed. Simulation studies indicate that the test statistics and confidence intervals have good small-sample perform ance. A real data set is analyzed.