Multivariate continuation ratio models: connections and caveats. (English) Zbl 1060.62559
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 [D. G. Clayton, Biometrika 65, 141–151 (1978; Zbl 0394.92021); D. Oakes, J. Am. Stat. Assoc. 84, No. 406, 487–493 (1989; Zbl 0677.62094)]. These models have recently been proposed by J. H. Shih [Biometrics 54, 1115–1128 (1998; Zbl 1058.62562)]. We relate the discrete survival models to multivariate multinomial models presented in P. J. Heagerty and S. L. Zeger [J. Am. Stat. Assoc. 91, No. 435, 1024–1036 (1996; Zbl 0882.62061)] and derive a paired estimating equations procedure that is computationally feasible for moderate and large clusters. We extend the work of S. W. Guo and D. Y. Lin [Biometrics 50, No. 3, 632–639 (1994; Zbl 0825.62780)] and J. H. 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 T. R. T. Have and D. H. Uttal [J. R. Stat. Soc., Ser. C 43, 371–384 (1994; Zbl 0825.62923)] and Guo and Lin (loc. cit.).
MSC:
| 62N02 | Estimation in survival analysis and censored data |
| 62H12 | Estimation in multivariate analysis |
| 62G08 | Nonparametric regression and quantile regression |
| 62P15 | Applications of statistics to psychology |
Citations:
Zbl 1058.62562; Zbl 0394.92021; Zbl 0677.62094; Zbl 0882.62061; Zbl 0825.62780; Zbl 0825.62923References:
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