title: On models for binomial data with random numbers of trials.
abstract: A binomial outcome is a count s of the number of successes out of the total number of independent trials n=s+f, where f is a count of the failures. The n are random variables not fixed by design in many studies. Joint modeling of (s, f) can provide additional insight into the science and into the probability pi of success that cannot be directly incorporated by the logistic regression model. Observations where n= 0 are excluded from the binomial analysis yet may be important to understanding how pi is influenced by covariates. Correlation between s and f may exist and be of direct interest. We propose Bayesian multivariate Poisson models for the bivariate response (s, f), correlated through random effects. We extend our models to the analysis of longitudinal and multivariate longitudinal binomial outcomes. Our methodology was motivated by two disparate examples, one from teratology and one from an HIV tertiary intervention study.
authors: UCLA Center for Community Health, 10920 Wilshire Boulevard, Suite 350, Los Angeles, California 90024-6543, USA. scomulad@ucla.edu
authors: W Scott
authors: WS
authors: Comulada
authors: Robert E
authors: RE
authors: Weiss
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D001699:Biometry; D003627:Data Interpretation, Statistical; D003921:Diabetes Mellitus, Experimental / Q000150:complications; D005260:Female; D015658:HIV Infections / Q000517:prevention & control / Q000635:transmission; D006801:Humans; D016015:Logistic Models; D008297:Male; D051379:Mice; D015233:Models, Statistical; D015999:Multivariate Analysis; D009436:Neural Tube Defects / Q000209:etiology; D016012:Poisson Distribution; D011247:Pregnancy; D011254:Pregnancy in Diabetics; D018600:Teratology / Q000706:statistics & numerical data
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