Background: Consider a meta-analysis where a ‘head-to-head’ comparison of diagnostic tests for a disease of interest is intended. Assume there are two or more tests available for the disease, where each test has been studied in one or more papers. Some of the papers may have studied more than one test, hence the results are not independent. Also the collection of tests studied may change from one paper to the other, hence incomplete matched groups.

Methods: We propose a model, the proportional odds ratio (POR) model, which makes no assumptions about the shape of OR₀, a baseline function capturing the way OR changes across papers. The POR model does not assume homogeneity of ORs, but merely specifies a relationship between the ORs of the two tests.

One may expand the domain of the POR model to cover dependent studies, multiple outcomes, multiple thresholds, multi-category or continuous tests, and individual-level data.

Results: In the paper we demonstrate how to formulate the model for a few real examples, and how to use widely available or popular statistical software (like SAS, R or S-Plus, and Stata) to fit the models, and estimate the discrimination accuracy of tests. Furthermore, we provide code for converting ORs into other measures of test performance like predictive values, post-test probabilities, and likelihood ratios, under mild conditions. Also we provide code to convert numerical results into graphical ones, like forest plots, heterogeneous ROC curves, and post test probability difference graphs.

Conclusion: The flexibility of POR model and its generalized applicability, coupled with ease with which it can be estimated in familiar software, suits the daily practice of meta-analysis and improves clinical decision-making.

Keywords
Meta-analysis, diagnostic test, proportional odds ratio model, odds ratio homogeneity, marginal model, mixed effects model, logistic regression, generalized estimating equations, grouped binary data, heterogeneous ROC curve, deviation-from-means parameterization, repeated measures, SAS, R.

Formulation
Consider a meta-analysis where a comparison of diagnostic tests for a disease of interest is intended. Assume there are two or more tests available for the disease, where each test has been studied in one or more papers. Some of the papers may have studied more than one test; hence the results are not independent. Also the collection of tests studied may change from one paper to the other, hence incomplete matched groups.

Using odds ratio (OR) as measure of diagnostic discrimination accuracy, consider the model
OR_i(Paper) = OR₀(Paper) * e ^bi   ,  i = 1, 2, …, k

where i is an index for the k diagnostic tests, and Paper is a categorical variable representing the studies included in the analysis. OR₀ is a function capturing the way OR changes across papers. Then to compare two diagnostic tests

OR_i(Paper) / OR_j(Paper) = e ^{(bi - bj)}

where the ratio of the two ORs depends only on the difference between the effect estimates of the two tests, and is independent of the underlying OR₀ and Paper. Thus the model makes no assumptions about the shape of OR₀ (and in particular homogeneity of ORs) but merely specifies a relationship between the ORs of the two tests.