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Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale.

ABSTRACT: Random intercept models are linear mixed models (LMM) including error and intercept random effects. Sometimes heteroscedasticity is included and the response variable is transformed into a logarithmic scale, while inference is required in the original scale; thus, the response variable has a log-normal distribution. Hence, correction terms should be included to predict the response in the original scale. These terms multiply the exponentiated predicted response variable, which subestimates the real values. We derive the correction terms, simulations and real data about the income of elderly are presented to show the importance of using them to obtain more accurate predictions. Generalizations for any LMM are also presented.

SUBMITTER: Ramirez-Aldana R

PROVIDER: S-EPMC8046211 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale.

Ramírez-Aldana Ricardo R Naranjo Lizbeth L

PloS one 20210414 4

Random intercept models are linear mixed models (LMM) including error and intercept random effects. Sometimes heteroscedasticity is included and the response variable is transformed into a logarithmic scale, while inference is required in the original scale; thus, the response variable has a log-normal distribution. Hence, correction terms should be included to predict the response in the original scale. These terms multiply the exponentiated predicted response variable, which subestimates the r ...[more]

PMID: 33852635

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Project description:BackgroundWhen 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.MethodsUsing 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.ResultsThe 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.ConclusionThe 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.

Dataset Information

Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale.

Publications

Random intercept and linear mixed models including heteroscedasticity in a logarithmic scale: Correction terms and prediction in the original scale.

Similar Datasets

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