Bias in Penalized Quasi-Likelihood Estimation in Random Effects Logistic Regression Models When the Random Effects Are not Normally Distributed
Bibliographic record
Abstract
Regression models incorporating random effects are being used with increasing frequency to examine variations in outcomes following the provision of medical care across providers. These models frequently assume a normal distribution for the provider-specific random effects. However, the validity of this assumption is rarely explicitly tested. We used Monte Carlo simulation methods to examine the impact of misspecifying the distribution of the random effects on estimation of and inference about both the fixed effects and the random effects in hierarchical logistic regression models. We demonstrated that estimation and inferences concerning the fixed effects was insensitive to misspecification of the distribution of the random effects. However, estimation and inferences concerning the provider-specific random effects was affected by model misspecification. In particular, estimation of cluster-specific random effects and the coverage of the associated 95% confidence intervals were particularly poor for individual random effects that came from the extreme tails of t-distributions with low degrees of freedom. These findings have important implications for those using hierarchical logistic regression models to identify health care providers with either exceptionally high or low rates of an outcome.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.157 | 0.531 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".