Robust Inference for Univariate Proportional Hazards Frailty Regression Models

By Michael R. Kosorok, Bee Leng Lee, Jason P. Fine. 2004

152 citations recorded by the source corpus.

We consider a class of semiparametric regression models which are one-parameter extensions of the Cox [J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220] model for right-censored univariate failure times. These models assume that the hazard given the covariates and a random frailty unique to each individual has the proportional hazards form multiplied by the frailty. The frailty is assumed to have mean 1 within a known one-parameter family of distributions. Inference is based on a nonparametric likelihood. The behavior of the likelihood maximizer is studied under general conditions where the fitted model may be misspecified. The joint estimator of the regression and frailty parameters as well as the baseline hazard is shown to be uniformly consistent for the pseudo-value maximizing the asymptotic limit of the likelihood. Appropriately standardized, the estimator converges weakly to a Gaussian process. When the model is correctly specified, the procedure is semiparametric efficient, achieving the semiparametric information bound for all parameter components. It is also proved that the bootstrap gives valid inferences for all parameters, even under misspecification. We demonstrate analytically the importance of the robust inference in several examples. In a randomized clinical trial, a valid test of the treatment effect is possible when other prognostic factors and the frailty distribution are both misspecified. Under certain conditions on the covariates, the ratios of the regression parameters are still identifiable. The practical utility of the procedure is illustrated on a non-Hodgkin's lymphoma dataset.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/808f7770e16e5a4b492c2e6f0cd4703965cec0f6

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Citations in the corpus

Bootstrap consistency for general semiparametric $M$-estimation (2009, methodology): “On the other hand, as a general data-resampling based statistical inference tool, the bootstrap method does not have the drawbacks of the profile sampler; see [6, 19, 21, 28, 37, 43] for its application in semiparametric models.”
Semiparametric Transformation Models With Random Effects for Recurrent Events (2007, unknown): “Our work can be viewed as a generalization of the transformation models for univariate survival data studied by Kosorok et al. (2004) to correlated recurrent event times. Our conditions on transformation are similar to those authors’ conditions D1 and D2; however, we do not assume their concavity of”
Maximum likelihood estimation in semiparametric regression models with censored data (2007, background): “Kosorok et al. (2004) studied the proportional hazards frailty model for univariate survival data.”
Efficient semiparametric estimators via modified profile likelihood (2005, unknown): “…class of models postulates, for the random lifetime of an individual with an observed d-dimensional vector Z of covariates, a conditional survival function Examples of different frailty distributions, also satisfying the assumptions, can be found in Kosorok et al. (2004) and references cited there.”
FURTHER DETAILS ON INFERENCE UNDER RIGHT CENSORING FOR TRANSFORMATION MODELS WITH A CHANGE-POINT BASED ON A COVARIATE THRESHOLD (2006, background): “Condition D2 is slightly weaker than conditions D2 and D3 of [17] who use the condition to obtain asymptotic theory for frailty regression models without a change-point.”