title: Bayesian random-effect model for predicting outcome fraught with heterogeneity--an illustration with episodes of 44 patients with intractable epilepsy.
abstract: OBJECTIVE
  The study aimed to develop a predictive model to deal with data fraught with heterogeneity that cannot be explained by sampling variation or measured covariates.
  
  
  METHODS
  The random-effect Poisson regression model was first proposed to deal with over-dispersion for data fraught with heterogeneity after making allowance for measured covariates. Bayesian acyclic graphic model in conjunction with Markov Chain Monte Carlo (MCMC) technique was then applied to estimate the parameters of both relevant covariates and random effect. Predictive distribution was then generated to compare the predicted with the observed for the Bayesian model with and without random effect. Data from repeated measurement of episodes among 44 patients with intractable epilepsy were used as an illustration.
  
  
  RESULTS
  The application of Poisson regression without taking heterogeneity into account to epilepsy data yielded a large value of heterogeneity (heterogeneity factor = 17.90, deviance = 1485, degree of freedom (df) = 83). After taking the random effect into account, the value of heterogeneity factor was greatly reduced (heterogeneity factor = 0.52, deviance = 42.5, df = 81). The Pearson chi2 for the comparison between the expected seizure frequencies and the observed ones at two and three months of the model with and without random effect were 34.27 (p = 1.00) and 1799.90 (p < 0.0001), respectively.
  
  
  CONCLUSIONS
  The Bayesian acyclic model using the MCMC method was demonstrated to have great potential for disease prediction while data show over-dispersion attributed either to correlated property or to subject-to-subject variability.
authors.affiliation: Institute of Preventive Medicine, College of Public Health, National Taiwan University, Taipei, 100, Taiwan.
authors.forename: A M-F
authors.initials: AM
authors.lastname: Yen
authors.forename: H-H
authors.initials: HH
authors.lastname: Liou
authors.forename: H-L
authors.initials: HL
authors.lastname: Lin
authors.forename: T H-H
authors.initials: TH
authors.lastname: Chen
mesh_terms: D000293:Adolescent; D000328:Adult; D001499:Bayes Theorem; D004827:Epilepsy / Q000628:therapy*; D017050:Episode of Care; D005260:Female; D006801:Humans; D008297:Male; D008390:Markov Chains; D008875:Middle Aged; D015233:Models, Statistical; D009010:Monte Carlo Method; D016012:Poisson Distribution; D016896:Treatment Outcome