On the estimation of the median odds ratio for measuring contextual effects in multilevel binary data from complex survey designs

Shafayet Khan Shafee; M. Shafiqur Rahman

Home/Archive/arXiv

arXiv · 2606.15145

On the estimation of the median odds ratio for measuring contextual effects in multilevel binary data from complex survey designs

Shafayet Khan Shafee·M. Shafiqur Rahman

View original source ↗Read source document ↗Export metadata ↓

Abstract

In studies with clustered or hierarchical data structures, quantifying between-cluster heterogeneity, referred to as contextual effects, is crucial for valid cluster-level inference. The median odds ratio (MOR), derived from random effects (RE) logistic regression models for clustered binary data, provides an intuitive assessment of contextual effects. Most existing research focuses on point estimation of the MOR for two-level models, with limited exploration of its statistical properties under complex multilevel structures. However, the development of corresponding interval estimators is essential for statistical inference. Moreover, many real-world datasets, particularly those from multistage surveys, involve hierarchical structures beyond two levels, where contextual effects at each level are of interest. This paper discusses the estimation of MOR for both the two-and three-level binary data, with particular emphasis on interval estimation. Since the MOR is a post-estimation measure based on variance components of the RE logit model, its confidence interval is derived using the Delta method, treating the log-transformed MOR as asymptotically normal. The approach is demonstrated across different model specifications in two-and three-level settings. An extensive simulation study evaluated the performance of the MOR estimators across diverse scenarios in hierarchical data settings. The results showed that the estimators exhibited negligible bias and satisfactory coverage probability of a 95% confidence interval for moderate to large samples, with small-sample bias mainly due to variance component estimation. An application of the methods for estimating the contextual effect on C-section delivery demonstrated that the proposed framework enhances interpretability and supports more informed statistical and policy-oriented analyses.

Explore related subjects

stat.ME

Keep this discovery

BibTeX RIS

Shafayet Khan Shafee, M. Shafiqur Rahman. 2026-06-13. On the estimation of the median odds ratio for measuring contextual effects in multilevel binary data from complex survey designs. https://arxiv.org/abs/2606.15145

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Surprise Reduction and Nullification in Bayesian and Inverse Bayesian Inference under Ambiguous Prediction-Error Attribution

In non-stationary environments, prediction errors may signal environmental change or transient outliers, and adaptive systems must track such changes without overreacting to outliers. We distinguish surprise reduction, which updates beliefs to fit observations, from surprise nullification, which weakens constraints imposed by the predictive structure, and formalize both within Bayesian and inverse Bayesian (BIB) inference. Belief and likelihood updates are derived from variational objectives sharing a nullification strength, determined endogenously by minimizing surprise under the candidate post-update predictive distribution. In the Gaussian case, nullification expands belief and likelihood variances by a common factor relative to standard Bayesian updating, leaving the ratio unchanged. BIB thus defers attribution of the prediction error, committing to neither latent-state change nor observation-process uncertainty. The nullification strength is carried over as a candidate and is maintained or released according to the predictive surprise of the next observation. In a mean estimation task with outliers and changepoints, no scanned parameter setting of a Sage-Husa-type adaptive Kalman filter, fixed-strength BIB variant, or belief-forgetting-only variant outperforms BIB in both changepoint tracking and post-outlier stability. An oracle-informed reduced Bayesian model tracks changepoints better but is less stable after outliers. Although BIB maintains no explicit hypotheses about changepoints or outliers, it generates event-dependent dynamics. The learning rate increases after changepoints, whereas after outliers, nullification is released, and this increase is suppressed. Deferring attribution and letting subsequent observations differentiate the responses may constitute a principle of adaptive inference in non-stationary environments.

stat.ME↗

arXiv2026

Generalized Ridge Refitting for the Lasso and Prediction Improvement Bounds

We study a class of Lasso based estimators obtained by applying a quadratic correction on the Lasso equicorrelation set. The penalty matrix determines both the magnitude and geometry of the correction and contains, among other cases, the isotropic Lasso--Ridge correction, least squares refitting, Gram proportional interpolation between the Lasso and least squares, and coordinate specific penalties. We first derive a closed form representation and isolate the positive gain component of the resulting prediction improvement. We then control the remaining stochastic linear term in expectation by localizing the random signed equicorrelation model around a deterministic reference support. This yields a finite sample expectation bound that explicitly accounts for the randomness induced by Lasso model selection. The resulting decomposition provides a unified framework for understanding when Lasso based quadratic corrections can improve prediction.

stat.ME↗

arXiv2026

Discretization in covariate-adaptive randomization: gains and losses

Covariate-adaptive randomization(CAR) is widely implemented in clinical trials to balance prognostic covariates across treatment arms. Continuous covariates are often discretized into strata in practice, yet their consequences are not clearly understood. This paper provides a comprehensive study of the impact of discretization on both the CAR design process and the inferential results thereafter. We establish the asymptotic properties of both imbalance measures and treatment effect estimators under discretized and non-discretized settings. Practical recommendations are given on when and how discretization should be employed. We show that discretization in design is generally recommended, as it enhances robustness against model misspecification. However, if the true model is known, the most efficient strategy is to balance covariates according to that model in the design. The theoretical results are corroborated by extensive simulation studies and an empirical application to a diabetes trial dataset. Together, the results clarify the gains and losses of discretization in CAR and pave the way for learning impact of discretization to other designs and beyond.

stat.ME↗