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A comparative study of the bias corrected estimates in logistic regression

¹ Department of Statistics, Iowa State University, IA, USA
² Cytel Inc., Cambridge, MA, USA

^* To whom correspondence should be addressed.

	Abstract

Logistic regression is frequently used in many areas of applied statistics. The maximumlikelihood estimates (MLE) of the logistic regression parameters are usually computed usingthe iterative Newton-Raphson method. It is well known that these estimates are biased.Several methods are proposed to correct the bias of these estimates. Among them Firth(1993) and Cordeiro and McCullagh (1991) proposed two promising methods. Theconditional exact method (CMLE) is popular for small-sample estimates, and is available inmany software packages. In this article we compare these methods in terms of their bias. Ingeneral, our extensive simulations show that the methods proposed by Cordeiro andMcCullagh and by Firth work well, though Cordeiro and McCullagh is slightly better in oursimulations. In case of separation, Firth or CMLE can be used; however, a judiciousapproach is required when there is a wide variation in results. Two real data analyses aregiven exhibiting these properties. The data analysis also includes bootstrap results.

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