title: Analyzing hospitalization data: potential limitations of Poisson regression.
abstract: BACKGROUND
  Poisson regression is commonly used to analyze hospitalization data when outcomes are expressed as counts (e.g. number of days in hospital). However, data often violate the assumptions on which Poisson regression is based. More appropriate extensions of this model, while available, are rarely used.
  
  
  METHODS
  We compared hospitalization data between 206 patients treated with hemodialysis (HD) and 107 treated with peritoneal dialysis (PD) using Poisson regression and compared results from standard Poisson regression with those obtained using three other approaches for modeling count data: negative binomial (NB) regression, zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression. We examined the appropriateness of each model and compared the results obtained with each approach.
  
  
  RESULTS
  During a mean 1.9 years of follow-up, 183 of 313 patients (58%) were never hospitalized (indicating an excess of 'zeros'). The data also displayed overdispersion (variance greater than mean), violating another assumption of the Poisson model. Using four criteria, we determined that the NB and ZINB models performed best. According to these two models, patients treated with HD experienced similar hospitalization rates as those receiving PD {NB rate ratio (RR): 1.04 [bootstrapped 95% confidence interval (CI): 0.49-2.20]; ZINB summary RR: 1.21 (bootstrapped 95% CI 0.60-2.46)}. Poisson and ZIP models fit the data poorly and had much larger point estimates than the NB and ZINB models [Poisson RR: 1.93 (bootstrapped 95% CI 0.88-4.23); ZIP summary RR: 1.84 (bootstrapped 95% CI 0.88-3.84)].
  
  
  CONCLUSIONS
  We found substantially different results when modeling hospitalization data, depending on the approach used. Our results argue strongly for a sound model selection process and improved reporting around statistical methods used for modeling count data.
authors: Department of Community Health Sciences, University of Calgary, Calgary, Alberta, Canada.
authors: Colin G
authors: CG
authors: Weaver
authors: Department of Community Health Sciences, University of Calgary, Calgary, Alberta, Canada Department of Medicine, University of Calgary, Calgary, Alberta, Canada.
authors: Pietro
authors: P
authors: Ravani
authors: Department of Medicine, University of Toronto, Toronto, Ontario, Canada Sunnybrook Health Sciences Centre, Toronto, Ontario, Canada.
authors: Matthew J
authors: MJ
authors: Oliver
authors: Institute for Clinical Evaluative Sciences, University of Toronto, Toronto, Ontario, Canada Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Ontario, Canada.
authors: Peter C
authors: PC
authors: Austin
authors: Department of Community Health Sciences, University of Calgary, Calgary, Alberta, Canada Department of Medicine, University of Calgary, Calgary, Alberta, Canada.
authors: Robert R
authors: RR
authors: Quinn
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D005260:Female; D006760:Hospitalization / Q000706:statistics & numerical data*; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D010530:Peritoneal Dialysis; D016012:Poisson Distribution; D006435:Renal Dialysis; D055815:Young Adult
keywords: Poisson; hospitalization; negative binomial; zero-inflated Poisson; zero-inflated negative binomial