2021 FDA Science Forum
Adjusting Diagnostic Test Accuracy for Numerous Confounders: The Mantel-Haenszel Approach
- Authors:
- Center:
-
Contributing OfficeCenter for Devices and Radiological Health
Abstract
Background
Diagnostic test accuracy studies are typically observational and thus subject to confounding. Logistic regression could be used to adjust the odds ratio between test result and disease status for confounding strata, but the maximum likelihood (ML) estimator is inconsistent for the true value when the number of strata grows with sample size, i.e., the sparse data limiting model (SDLM). In contrast, the Mantel-Haenszel (MH) estimator of the odds ratio adjusted for stratum effects (Mantel, Haenszel, 1959) is consistent under SLDM. However, diagnostic tests are typically evaluated not with the odds ratio, but with pairs of measures such as specificity and sensitivity, negative and positive predictive value (NPV, PPV), and negative and positive likelihood ratio (NLR, PLR).
Purpose
To improve clinical evaluation of diagnostic test accuracy studies, we develop MH estimators of NLR and PLR that adjust for confounding stratum effects. Given disease prevalence, we convert MH estimators of NLR and PLR to NPV and PPV using Bayes Theorem.
Methodology: We derive MH estimators of PLR and NLR, which are consistent under SDLM. Confidence intervals are based on consistent estimators of the variances of the MH estimates. MH and ML estimators are compared on three hypothetical datasets: (1) data with the same PLR in each stratum yet a different marginal PLR (marginalization paradox), (2) matched pairs data with two observations per stratum, and (3) neonatal audiology test data.
Results
ML and MH estimates of PLR were identical for the first dataset. For the matched pairs data, ML and MH estimates of PLR diverged, indicating that the ML estimator of PLR is inconsistent under SDLM. For the neonatal audiology test data, MH and ML estimates of NLR diverged for very fine strata, suggesting that the ML estimator is inconsistent under SDLM. When adjusting for 973 subject strata, MH and ML estimates of PPV and NPV were worse than the marginal estimates based on collapsing data over strata, suggesting that subject strata are confounders.
Conclusion
MH estimators can be used to adjust diagnostic test accuracy for numerous confounding strata and are valid even in sparse data settings.
