Abstract
Multivariate frailty models have been used for clustered survival data to characterize the relationship between the hazard of correlated failures/events and exposure variables and covariates. However, these models can introduce serious biases of the estimation for failures from complex surveys that may depend on the sampling design (informative or noninformative). In order to consistently estimate parameters, this paper considers weighting the multivariate frailty model by the inverse of the probability of selection at each stage of sampling. This follows the principle of the pseudolikelihood approach. The estimation is carried out by maximizing the penalized partial and marginal pseudolikelihood functions. The performance of the proposed estimator is assessed through a Monte Carlo simulation study and the 4 waves of data from the 1998–1999 Early Childhood Longitudinal Study. Results show that the weighted estimator is consistent and approximately unbiased.
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References
Andersen PK, Borgan O, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York
Binder CJ (1983) On the variances of asymptotically normal estimators from complex surveys. Int Stat Rev 51:279–292
Breslow NE, Clayton DG (1993) Approximate inference in generalized linear mixed models. J Am Stat Assoc 88:9–25
Cox DR (1972) Regression models and life tables. J R Stat Soc Ser B 20:187–220 with discussion
Cox DR (1975) Partial likelihood. Biometrika 62:269–276
Green PJ (1987) Penalized likelihood for general semi- parametric regression model. Int Stat Rev 55:245–259
Hougaard P (2000) Shared frailty models. In: Hougaard P (ed) Analysis of multivariate survival data. Statistics for Biology and Health. Springer, New York
Klein JP (1992) Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics 48:795–806
McGilchrist CA (1993) REML estimation for survival models with frailty. Biometrics 49:221–225
Ripatti S, Palmgren J (2000) Estimation of multivariate frailty models using penalized partial likelihood. Biometrics 56:1016–1022
Skinner CJ (1983) Domain means, regression and multivariate analysis. In: Skinner CJ, Holt D, Smith TMF (eds) Analysis of complex surveys. Wiley, Chichester, pp 59–87
Therneau TM, Grambsch PM (2000) Modeling survival data: extending the Cox model. Springer, New York
Vaupel JW, Manton KG, Stallard E (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16:439–454
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Wang, J. Weighted estimation for multivariate shared frailty models for complex surveys. Lifetime Data Anal 25, 469–479 (2019). https://doi.org/10.1007/s10985-019-09469-x
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DOI: https://doi.org/10.1007/s10985-019-09469-x