IngentaConnect Multivariate Continuation Ratio Models: Connections and Caveats

Abstract:

Summary.

We develop semiparametric estimation methods for a pair of regressions that characterize the first and second moments of clustered discrete survival times. 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 pairwise association of survival times using the Clayton-Oakes cross-product ratio (Clayton, 1978, Biometrika65, 141-151; Oakes, 1989, Journal of the American Statistical Association84, 487-493). These models have recently been proposed by Shih (1998, Biometrics54, 1115-1128). We relate the discrete survival models to multivariate multinomial models presented in Heagerty and Zeger (1996, Journal of the American Statistical Society91, 1024-1036) and derive a paired estimating equations procedure that is computationally feasible for moderate and large clusters. We extend the work of Guo and Lin (1994, Biometrics50, 632-639) and Shih (1998) to allow covariance weighted estimating equations and investigate the impact of weighting in terms of asymptotic relative efficiency. We demonstrate that the multinomial structure must be acknowledged when adopting weighted estimating equations and show that a naive use of GEE methods can lead to inconsistent parameter estimates. Finally, we illustrate the proposed methodology by analyzing psychological testing data previously summarized by TenHave and Uttal (1994, Applied Statistics43, 371-384) and Guo and Lin (1994).

Keywords: Cross-product ratio; Discrete survival; Estimating equation; Proportional hazards

Document Type: Research article

DOI: 10.1111/j.0006-341X.2000.00719.x

Affiliations: 1: Department of Biostatistics, University of Washington, Seattle, Washington 98195, U.S.A., Email: heagerty@biostat.washington.edu 2: Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205, U.S.A.

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