Improving likelihood-based inference in control rate regression

TL;DR

This paper enhances likelihood-based inference in control rate regression for meta-analysis by using higher-order asymptotics, specifically Skovgaard's statistic, to improve accuracy in small samples with measurement error.

Contribution

It introduces the use of Skovgaard's statistic to improve inference accuracy in control rate regression, especially for small sample sizes and heterogeneity.

Findings

Skovgaard's statistic outperforms standard likelihood methods in accuracy.

Higher-order asymptotics significantly reduce inference errors.

The method is computationally efficient and validated through simulations and real data.

Abstract

Control rate regression is a diffuse approach to account for heterogeneity among studies in meta-analysis by including information about the outcome risk of patients in the control condition. Correcting for the presence of measurement error affecting risk information in the treated and in the control group has been recognized as a necessary step to derive reliable inferential conclusions. Within this framework, the paper considers the problem of small sample size as an additional source of misleading inference about the slope of the control rate regression. Likelihood procedures relying on first-order approximations are shown to be substantially inaccurate, especially when dealing with increasing heterogeneity and correlated measurement errors. We suggest to address the problem by relying on higher-order asymptotics. In particular, we derive Skovgaard's statistic as an instrument to improve the accuracy of the approximation of the signed profile log-likelihood ratio statistic to the standard normal distribution. The proposal is shown to provide much more accurate results than standard likelihood solutions, with no appreciable computational effort. The advantages of Skovgaard's statistic in control rate regression are shown in a series of simulation experiments and illustrated in a real data example. R code for applying first- and second-order statistic for inference on the slope on the control rate regression is provided.