title: Prediction models for clustered data: comparison of a random intercept and standard regression model.
abstract: BACKGROUND
  When study data are clustered, standard regression analysis is considered inappropriate and analytical techniques for clustered data need to be used. For prediction research in which the interest of predictor effects is on the patient level, random effect regression models are probably preferred over standard regression analysis. It is well known that the random effect parameter estimates and the standard logistic regression parameter estimates are different. Here, we compared random effect and standard logistic regression models for their ability to provide accurate predictions.
  
  
  METHODS
  Using an empirical study on 1642 surgical patients at risk of postoperative nausea and vomiting, who were treated by one of 19 anesthesiologists (clusters), we developed prognostic models either with standard or random intercept logistic regression. External validity of these models was assessed in new patients from other anesthesiologists. We supported our results with simulation studies using intra-class correlation coefficients (ICC) of 5%, 15%, or 30%. Standard performance measures and measures adapted for the clustered data structure were estimated.
  
  
  RESULTS
  The model developed with random effect analysis showed better discrimination than the standard approach, if the cluster effects were used for risk prediction (standard c-index of 0.69 versus 0.66). In the external validation set, both models showed similar discrimination (standard c-index 0.68 versus 0.67). The simulation study confirmed these results. For datasets with a high ICC (≥15%), model calibration was only adequate in external subjects, if the used performance measure assumed the same data structure as the model development method: standard calibration measures showed good calibration for the standard developed model, calibration measures adapting the clustered data structure showed good calibration for the prediction model with random intercept.
  
  
  CONCLUSIONS
  The models with random intercept discriminate better than the standard model only if the cluster effect is used for predictions. The prediction model with random intercept had good calibration within clusters.
authors: Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Utrecht, The Netherlands. bouwmeester.w@kpnmail.nl
authors: Walter
authors: W
authors: Bouwmeester
authors: Jos W R
authors: JW
authors: Twisk
authors: Teus H
authors: TH
authors: Kappen
authors: Wilton A
authors: WA
authors: van Klei
authors: Karel G M
authors: KG
authors: Moons
authors: Yvonne
authors: Y
authors: Vergouwe
mesh_terms: D000328:Adult; D000368:Aged; D000701:Analgesics, Opioid / Q000009:adverse effects; D002138:Calibration / Q000592:standards*; D016000:Cluster Analysis; D005260:Female; D006801:Humans; D016015:Logistic Models; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D020250:Postoperative Nausea and Vomiting / Q000209:etiology; D011237:Predictive Value of Tests; D015203:Reproducibility of Results; D018570:Risk Assessment / Q000379:methods* / Q000592:standards*; D013514:Surgical Procedures, Operative / Q000009:adverse effects; D016896:Treatment Outcome
chemical_list: D000701:Analgesics, Opioid