Conditional versus unconditional logistic regression in the medical literature

The study conducted by Bagley et al [1] is a timely article on the quality of logistic regression (LR) reporting in the medical literature. The authors included all the relevant issues related to proper use and reporting of LR models. We would like to add one more issue that is related to the appropriateness of using particular maximum likelihood (ML) approach (conditional versus unconditional) in a LR model for case-control studies. The use of a particular ML approach depends on the feature of data (matched or unmatched). It is already documented that unconditional LR analysis seriously overestimates the odds ratio when there are matching data [2]. The number of parameters in a LR model relative to the sample size in a study determines the type of ML approach needed for a particular data set [2]. The unconditional ML approach is preferred where the number of parameters is small relative to the number of subjects. On the other hand, the conditional ML approach is appropriate where the number of parameters is large relative to the total number of subjects. Thus, due to abundance in the number of parameters in a matched data set, the conditional ML approach is the appropriate method for analysis [2].

To examine the frequency of using unconditional LR for matched data, we searched the Medline database on 22 April 2002 with the key words “matching,” “matched,” “unmatched,” “conditional,” “unconditional,” “logistic regression,” and “case-control studies” to obtain relevant studies. Inclusion criteria were the following: articles published from 1991 to 2000, articles having “case-control studies” as a medical subject heading, and articles with information about matching and logistic regression analysis in the abstract. A total of 917 seventeen articles met these criteria. Among them, 507 articles had matched data and information about the ML approach in the abstracts, whereas 410 had no clear-cut information on those. Of the 507 articles, conditional and unconditional ML approaches were used in 459 (90.5%) and 48 articles (9.5%), respectively (Fig. 1).

View Large Image Download to PowerPoint

Fig. 1. Use of a ML approach in a LR model for matched case-control studies published from 1991 to 2000.

The finding that 10% of the case-control studies with matched data used an unconditional ML approach could vary because 410 out of 917 articles did not have enough information in their abstracts (Fig. 1). However, our study indicates that a good number of articles used an unconditional ML approached for matched data. Thus, the odds ratio generated in a matched case-control study with unconditional ML approach will have a biased estimate. Caution should be taken in interpreting the results of the matched case-control studies with unconditional LR analysis. Our results imply that authors, reviewers, and editors should pay attention to this, and consumers should take caution in interpreting the already published studies.