  Two-phase design can reduce the cost of epidemiological studies by limiting
the ascertainment of expensive covariates or/and exposures to an efficiently
selected subset (phase-II) of a larger (phase-I) study. Efficient analysis of
the resulting dataset combining disparate information from phase-I and
phase-II, however, can be complex. Most of the existing methods including
semiparametric maximum-likelihood estimator, require the information in phase-I
to be summarized into a fixed number of strata. In this paper, we describe a
novel method for analysis of two-phase studies where information from phase-I
is summarized by parameters associated with a reduced logistic regression model
of the disease outcome on available covariates. We then setup estimating
equations for parameters associated with the desired extended logistic
regression model, based on information on the reduced model parameters from
phase-I and complete data available at phase-II after accounting for non-random
sampling design at phase-II. We use the generalized method of moments to solve
overly identified estimating equations and develop the resulting asymptotic
theory for the proposed estimator. Simulation studies show that the use of
reduced parametric models, as opposed to summarizing data into strata, can lead
to more efficient utilization of phase-I data. An application of the proposed
method is illustrated using the US National Wilms Tumor study data.
