Methods for epidemiologic analyses of multiple exposures: a review and comparative study of maximum-likelihood, preliminary-testing, and empirical-Bayes regression.

Many epidemiologic investigations are designed to study the effects of multiple exposures. Most of these studies are analysed either by fitting a risk-regression model with all exposures forced in the model, or by using a preliminary-testing algorithm, such as stepwise regression, to produce a smaller model. Research indicates that hierarchical modelling methods can outperform these conventional approaches. I here review these methods and compare two hierarchical methods, empirical-Bayes regression and a variant I call 'semi-Bayes' regression, to full-model maximum likelihood and to model reduction by preliminary testing. I then present a simulation study of logistic-regression analysis of weak exposure effects to illustrate the type of accuracy gains one may expect from hierarchical methods. Finally, I compare the performance of the methods in a problem of predicting neonatal mortality rates. Based on the literature to date, I suggest that hierarchical methods should become part of the standard approaches to multiple-exposure studies.

[1]  W. Wong,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[2]  S. Cessie,et al.  Ridge Estimators in Logistic Regression , 1992 .

[3]  J Cornfield,et al.  Bayesian estimation for higher order cross-classifications. , 1970, The Milbank Memorial Fund quarterly.

[4]  J Siemiatycki,et al.  The problem of multiple inference in studies designed to generate hypotheses. , 1985, American journal of epidemiology.

[5]  C. Morris.  Parametric Empirical Bayes Inference: Theory and Applications , 1983 .

[6]  K J Rothman,et al.  No Adjustments Are Needed for Multiple Comparisons , 1990, Epidemiology.

[7]  T. A. Louis,et al.  Using empirical Bayes methods in biopharmaceutical research. , 1991, Statistics in medicine.

[8]  Thomas A. Louis,et al.  Empirical Bayes Ranking Methods , 1989 .

[9]  C. Morris,et al.  Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution , 1972 .

[10]  Nicholas G. Polson,et al.  Inference for nonconjugate Bayesian Models using the Gibbs sampler , 1991 .

[11]  R. Kass,et al.  Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models) , 1989 .

[12]  J. Geweke,et al.  Antithetic acceleration of Monte Carlo integration in Bayesian inference , 1988 .

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

[14]  S Greenland,et al.  Effect of fetal monitoring on neonatal death rates. , 1978, The New England journal of medicine.

[15]  S Greenland,et al.  A semi-Bayes approach to the analysis of correlated multiple associations, with an application to an occupational cancer-mortality study. , 1992, Statistics in medicine.

[16]  N. Wermuth,et al.  A Simulation Study of Alternatives to Ordinary Least Squares , 1977 .

[17]  T. Louis,et al.  Empirical Bayes Confidence Intervals Based on Bootstrap Samples , 1987 .

[18]  P. McCullagh,et al.  Bias Correction in Generalized Linear Models , 1991 .

[19]  L Bernardinelli,et al.  Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk. , 1992, Statistics in medicine.

[20]  A. F. M. Smith,et al.  Progress with numerical and graphical methods for practical Bayesian statistics , 1987 .

[21]  J M Robins,et al.  Analysis of proportionate mortality data using logistic regression models. , 1987, American journal of epidemiology.

[22]  B. Efron.  Logistic Regression, Survival Analysis, and the Kaplan-Meier Curve , 1988 .

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

[24]  David Lindley,et al.  Bayes Empirical Bayes , 1981 .

[25]  Clifford M. Hurvich,et al.  The impact of model selection on inference in linear regression , 1990 .

[26]  B. Efron,et al.  Data Analysis Using Stein's Estimator and its Generalizations , 1975 .

[27]  J M Robins,et al.  Empirical‐Bayes Adjustments for Multiple Comparisons Are Sometimes Useful , 1991, Epidemiology.

[28]  N. Breslow,et al.  Statistical methods in cancer research. Volume II--The design and analysis of cohort studies. , 1987, IARC scientific publications.

[29]  J. Copas.  Regression, Prediction and Shrinkage , 1983 .

[30]  S Greenland,et al.  The impact of confounder selection criteria on effect estimation. , 1989, American journal of epidemiology.