Multivariate continuation ratio models: Connections and caveats

We develop semiparametric estimation methods for a pair of regressions that characterize the first and second moments of clustered discrete survival t imes. In the first regression, we represent discrete survival times through univariate continuation indicators whose expectations are modeled using a generalized linear model. In the second regression, we model the marginal p airwise association of survival times using the Clayton-Oakes cross-product ratio (Clayton, 1978, Biometrika 65, 141-151; Cakes, 1989, Journal of the American Statistical Association 84, 487-493). These models have recently b een proposed by Shih (1998, Biometrics 54, 1115-1128). We relate the discre te survival models to multivariate multinomial models presented in Heagerty and Zeger (1996, Journal of the American Statistical Society 91, 1024-1036 ) and derive a paired estimating equations procedure that is computationall y feasible for moderate and large clusters. We extend the work of Guo and L in (1994, Biometrics 50, 632-639) and Shih (1998) to allow covariance weigh ted estimating equations and investigate the impact of weighting in terms o f asymptotic relative efficiency. We demonstrate that the multinomial struc ture must be acknowledged when adopting weighted estimating equations and s how that a naive use of GEE methods can lead to inconsistent parameter esti mates. Finally, we illustrate the proposed methodology by analyzing psychol ogical testing data previously summarized by TenHave and Uttal (1994, Appli ed Statistics 43, 371-384) and Guo and Lin (1994).