Fitting Cox's proportional hazards models from survey data

The proportional hazards model makes a number of assumptions which may not always be completely satisfied. However, fitting such models can have both descriptive and analytical value. We discuss the implications of the survey design for large-scale studies. We propose a weighted estimator and derive a design-based estimator for the variance of the estimated parameters. The derivation requires using methods not previously used in the context of analysis of survey data. We conduct a small simulation study comparing the proposed method with others in the literature.