Bayesian Random-effect Model for Predicting Outcome Fraught with Heterogeneity

A. M. -F. Yen; H.-H. Liou; H.-L. Lin; T. H.-H. Chen

doi:10.1055/s-0038-1634127

Methods of Information in Medicine, Inhaltsverzeichnis

Methods Inf Med 2006; 45(06): 631-637
DOI: 10.1055/s-0038-1634127

Original Article

Schattauer GmbH

Bayesian Random-effect Model for Predicting Outcome Fraught with Heterogeneity

An Illustration with Episodes of 44 Patients with Intractable Epilepsy

A. M. -F. Yen

¹Institute of Preventive Medicine, College of Public Health, National Taiwan University, Taipei, Taiwan

,

H.-H. Liou

²Department of Pharmacology, College of Medicine, National Taiwan University, Taipei, Taiwan

,

H.-L. Lin

¹Institute of Preventive Medicine, College of Public Health, National Taiwan University, Taipei, Taiwan

,

T. H.-H. Chen

¹Institute of Preventive Medicine, College of Public Health, National Taiwan University, Taipei, Taiwan

³Division of Biostatistics, Graduate Institute of Epidemiology, College of Public Health, National Taiwan University, Taipei, Taiwan

› Institutsangaben

Abstract

Summary

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 χ² 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.

Conclusion: 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.

Keywords

Heterogeneity - random effect - Bayesian acyclic graphic model - Markov Chain Monte Carlo (MCMC) - predictive model

Volltext

Referenzen

References
1 Fabbri A, Servadei F, Marchesini G, Morselli-Labate AM, Dente M, Iervese T, Spada M, Vandelli A. Prospective validation of a proposal for diagnosis and management of patients attending the emergency department for mild head injury. J Neurol Neurosurg Psychiatry 2004; 75: 410-6.
2 Wong DT, Crofts SL, Gomez M, McGuire GP, Byrick RJ. Evaluation of predictive ability of APACHE II system and hospital outcome in Canadian intensive care unit patients. Crit Care Med 1995; 23: 1177-83.
3 Stevens TA, Carroll MA, Promecene PA, Seibel M, Monga M. Utility of Acute Physiology, Age, and Chronic Health Evaluatoin (APACHE III) score in maternal admissions to the intensive care unit. Am J Obstet Gynecol 2006; 194: e13-5.
4 Zimmerman JE, Kramer AA, McNair DS, Malila FM. Acute Physiology and Chronic Health Evalu- ation (APACHE) IV: hospital mortality assessment for today’s critically ill patients. Crit Care Med 2006; 34: 1297-310.
5 Selker HP, Griffith JL, D’Agostino RB. A tool for judging coronary care unit admission appropriateness, valid for both real-time and retrospective use. A time-insensitive predictive instrument (TIPI) for acute cardiac ischemia: a multicenter study. Med Care 1991; 29: 610-27.
6 Shroyer AL, Plomondon ME, Grover FL, Edwards FH. The 1996 coronary artery bypass risk model: the Society of Thoracic Surgeons Adult Cardiac National Database. Ann Thorac Surg 1999; 67: 1205-8.
7 Cuckle HS, Wald NJ, Thompson SG. Estimating a woman’s risk of having a pregnancy associated with Down’s syndrome using her age and serum alpha-fetoprotein level. Br J Obstet Gynaecol 1987; 94: 387-402.
8 Cuckle H. Risk estimation in Down’s syndrome screening policy and practice. In Grudzinskas JG, Chard T, Chapman M, Cuckle H. (eds) Screening for Down’s Syndrome, Cambridge: Cambridge University Press 1994; pp 31-46.
9 Collett D. Modelling Binary Data. London: Chapman & Hall/CRC Press 1991
10 Chang CM, Kuo HS, Chang SH, Chang HJ, Liou DM, Laszlo T, Chen THH. Computer-aided disease prediction system: development of application software with SAS component language. J Eval Clin Pract 2005; 11: 139-59.
11 De la Cruz-Mesia R, Marshall G. Non-linear random effects models with continuous time autoregressive errors: a Bayesian approach. Stat Med 2006; 25: 1471-84.
12 Bohning D. Meta-analysis: a unifying metalikelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality. Methods Inf Med 2005; 44: 127-35.
13 Minelli C, Thompson JR, Abrams KR, Lambert PC. Bayesian implementation of a genetic modelfree approach to the meta-analysis of genetic association studies. Stat Med 2005; 24: 3845-61.
14 Higgins JP, Spiegelhalter DJ. Being sceptical about meta-analyses: a Bayesian perspective on magnesium trials in myocardial infarction. Int J Epidemiol 2002; 31: 96-104.
15 Held L, Ranyimbo AO. A Bayesian approach to estimate and validate the false negative fraction in a two-stage multiple screening test. Methods Inf Med 2004; 43: 461-4.
16 Boyd HA, Flanders WD, Addiss DG, Waller LA. Residual spatial correlation between geographically referenced observations: a Bayesian hierarchical modeling approach. Epidemiology 2005; 16: 532-41.
17 Gilks WR, Richardson S, Spiegelhalter DJ. Markov Chain Monte Carlo in Practice. London: Chapman & Hall; 1996
18 Gamerman D. Markov Chain Monte Carlo: stochastic simulation for Bayesian inference. London: Chapman & Hall; 1997
19 Spiegelhalter DJ, Thomas A, Best NG. Computation on Bayesian graphical models. In Bernardo JM, Berger JO, Dawid AP, Smith AFM. (eds). Bayesian Statistics 5. pp 407-25. Oxford University Press; 1996
20 Dobson AJ. Introduction to Generalized Linear Models. Second Edition. London: Chapman and Hall/CRC; 2001
21 Geman D, Geman S. Bayesian image-restoration, with 2 applications in spatial statistics - discussion. Ann Inst Statist Math 1991; 43: 21-2.
22 Joseph L, Gyorkos TW, Coupal L. Bayesian estimation of disease prevalence and the parameters of diagnostic tests in the absence of a gold standard. Am J Epidemiol 1995; 141: 263-72.
23 Zhou X, Liu KY, Wong ST. Cancer classification and prediction using logistic regression with Bayesian gene selection. J Biomed Inform 2004; 37: 249-59.
24 Batterham MJ. Investigating heterogeneity in studies of resting energy expenditure in persons with HIV/AIDS: a meta-analysis. Am J Clin Nutr 2005; 81: 702-13.
25 Chen RC, Chang YC, Chen TH, Wu HM, Liou HH. Mortality in adult patients with epilepsy in Taiwan. Epileptic Disord 2005; 7: 213-9.