Design and analysis of two-phase studies with binary outcome applied to Wilms tumour prognosis

Two-phase stratified sampling is used to select subjects for the collection of additional data, e.g. validation data in measurement error problems. St ratification jointly by outcome and covariates, with sampling fractions cho sen to achieve approximately equal numbers per stratum at the second phase of sampling, enhances efficiency compared with stratification based on the outcome or covariates alone. Nonparametric maximum likelihood may result in substantially more efficient estimates of logistic regression coefficients than weighted or pseudolikelihood procedures. Software to implement all th ree procedures is available. We demonstrate the practical importance of the se design and analysis principles by an analysis of, and simulations based on, data from the US National Wilms Tumor Study.