Using Historical Controls to Adjust for Covariates in Trend Tests for Binary Data

Abstract Historical data often play an important role in helping interpret the results of a current study. This article is motivated primarily by one specific application: the analysis of data from rodent carcinogenicity studies. By proposing a suitable informative prior distribution on the relationship between control outcome data and covariates, we derive modified trend test statistics that incorporate historical control information to adjust for covariate effects. Frequentist and fully Bayesian methods are presented, and novel computational techniques are developed to compute the test statistics. Several attractive theoretical and computational properties of the proposed priors are derived. In addition, a semiautomatic elicitation scheme for the priors is developed. Our approach is used to modify a widely used prevalence test for carcinogenicity studies. The proposed methodology is applied to data from a National Toxicology Program carcinogenicity experiment and is shown to provide helpful insight on t...

[1]  R. O'Neill.  Algorithm AS 47: Function Minimization Using a Simplex Procedure , 1971 .

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

[3]  R. Tarone,et al.  The Use of Historical Control Information in Testing for a Trend in Proportions , 1982 .

[4]  Gregg E. Dinse,et al.  Regression Analysis of Tumour Prevalence Data , 1983 .

[5]  Peter E. Rossi,et al.  Bayesian analysis of dichotomous quantal response models , 1984 .

[6]  Joseph K. Haseman,et al.  Use of Historical Control Data in Carcinogenicity Studies in Rodents , 1984, Toxicologic pathology.

[7]  M. West,et al.  Dynamic Generalized Linear Models and Bayesian Forecasting , 1985 .

[8]  Chan‐Fu Chen.  On Asymptotic Normality of Limiting Density Functions with Bayesian Implications , 1985 .

[9]  Samuel D. Oman,et al.  Specifying a Prior Distribution in Structured Regression Problems , 1985 .

[10]  Bailer Aj,et al.  Effects of treatment-induced mortality and tumor-induced mortality on tests for carcinogenicity in small samples. , 1988 .

[11]  J. Albert.  Computational methods using a Bayesian hierarchical generalized linear model , 1988 .

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

[13]  Scott L. Zeger,et al.  Generalized linear models with random e ects: a Gibbs sampling approach , 1991 .

[14]  D. Gaylor,et al.  Analysis of trinomial responses from reproductive and developmental toxicity experiments. , 1991, Biometrics.

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

[16]  Adrian F. M. Smith,et al.  Bayesian Inference for Generalized Linear and Proportional Hazards Models Via Gibbs Sampling , 1993 .

[17]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[18]  Ming-Hui Chen.  Importance-Weighted Marginal Bayesian Posterior Density Estimation , 1994 .

[19]  Purushottam W. Laud,et al.  A Predictive Approach to the Analysis of Designed Experiments , 1994 .

[20]  M. Schervish.  Theory of Statistics , 1995 .

[21]  Flaws in Risk Assessments , 1995, Science.

[22]  Purushottam W. Laud,et al.  Predictive Model Selection , 1995 .

[23]  Seymour Geisser,et al.  8. Predictive Inference: An Introduction , 1995 .

[24]  S. Seilkop.  The Effect of Body Weight on Tumor Incidence and Carcinogenicity Testing in B6C3F1 Mice and F344 Rats , 1995 .

[25]  Xiao-Li Meng,et al.  SIMULATING RATIOS OF NORMALIZING CONSTANTS VIA A SIMPLE IDENTITY: A THEORETICAL EXPLORATION , 1996 .

[26]  A. Gelfand,et al.  Efficient parametrizations for generalized linear mixed models, (with discussion). , 1996 .

[27]  Edward I. George,et al.  Two Approaches to Bayesian Model Selection with Applications , 1996 .

[28]  R. Christensen,et al.  A New Perspective on Priors for Generalized Linear Models , 1996 .

[29]  J G Ibrahim,et al.  Use of historical controls in time-adjusted trend tests for carcinogenicity. , 1996, Biometrics.

[30]  Joseph G. Ibrahim,et al.  Predictive specification of prior model probabilities in variable selection , 1996 .

[31]  Ming-Hui Chen,et al.  On Monte Carlo methods for estimating ratios of normalizing constants , 1997 .