Frailty models with missing covariates.

We present a method for estimating the parameters in random effects models for survival data when covariates are subject to missingness. Our method is more general than the usual frailty model as it accommodates a wide range of distributions for the random effects, which are included as an offset in the linear predictor in a manner analogous to that used in generalized linear mixed models. We propose using a Monte Carlo EM algorithm along with the Gibbs sampler to obtain parameter estimates. This method is useful in reducing the bias that may be incurred using complete-case methods in this setting. The methodology is applied to data from Eastern Cooperative Oncology Group melanoma clinical trials in which observations were believed to be clustered and several tumor characteristics were not always observed.

[1]  D J Sargent,et al.  A general framework for random effects survival analysis in the Cox proportional hazards setting. , 1998, Biometrics.

[2]  J. Ibrahim.  Incomplete Data in Generalized Linear Models , 1990 .

[3]  J G Ibrahim,et al.  Monte Carlo EM for Missing Covariates in Parametric Regression Models , 1999, Biometrics.

[4]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[5]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  J P Klein,et al.  Semiparametric estimation of random effects using the Cox model based on the EM algorithm. , 1992, Biometrics.

[7]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[8]  L Ryan,et al.  Semiparametric Regression Analysis of Interval‐Censored Data , 2000, Biometrics.

[9]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[10]  Joseph G. Ibrahim,et al.  A conditional model for incomplete covariates in parametric regression models , 1996 .

[11]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[12]  J G Ibrahim,et al.  Using the EM-algorithm for survival data with incomplete categorical covariates , 1996, Lifetime data analysis.

[13]  H Li,et al.  Semiparametric estimation of major gene and family-specific random effects for age of onset. , 1997, Biometrics.

[14]  W. Tsai,et al.  On using the Cox proportional hazards model with missing covariates , 1997 .

[15]  S. Johansen.  An Extension of Cox's Regression Model , 1983 .

[16]  D. Cox.  Regression Models and Life-Tables , 1972 .

[17]  D B Rubin,et al.  Multiple imputation in health-care databases: an overview and some applications. , 1991, Statistics in medicine.

[18]  Daniel W. Schafer,et al.  Covariate measurement error in generalized linear models , 1987 .

[19]  R. Gray.  Some diagnostic methods for Cox regression models through hazard smoothing. , 1990, Biometrics.

[20]  V. Sondak,et al.  High- and low-dose interferon alfa-2b in high-risk melanoma: first analysis of intergroup trial E1690/S9111/C9190. , 2000, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[21]  N. Breslow.  Covariance analysis of censored survival data. , 1974, Biometrics.

[22]  Scott L. Zeger,et al.  Some recent developments for regression analysis of multivariate failure time data , 1995, Lifetime data analysis.

[23]  G. C. Wei,et al.  A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms , 1990 .

[24]  Wayne Nelson,et al.  Hazard Plotting for Incomplete Failure Data , 1969 .

[25]  P. Hougaard.  Survival models for heterogeneous populations derived from stable distributions , 1986 .

[26]  D. Rubin.  Multiple imputation for nonresponse in surveys , 1989 .

[27]  J. Kirkwood,et al.  Interferon alfa-2b adjuvant therapy of high-risk resected cutaneous melanoma: the Eastern Cooperative Oncology Group Trial EST 1684. , 1996, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[28]  Ron Brookmeyer,et al.  Bivariate frailty model for the analysis of multivariate survival time , 1996, Lifetime data analysis.

[29]  T. Louis.  Finding the Observed Information Matrix When Using the EM Algorithm , 1982 .

[30]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[31]  R. Gray.  A Bayesian analysis of institutional effects in a multicenter cancer clinical trial. , 1994, Biometrics.

[32]  Joseph G. Ibrahim,et al.  Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable , 1999 .