Bring More Data!—A Good Advice? Removing Separation in Logistic Regression by Increasing Sample Size

Hana Šinkovec, Angelika Geroldinger and Georg Heinze
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Hana Šinkovec: Institute of Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems (CEMSIIS), Spitalgasse 23, 1090 Vienna, Austria
Angelika Geroldinger: Institute of Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems (CEMSIIS), Spitalgasse 23, 1090 Vienna, Austria
Georg Heinze: Institute of Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems (CEMSIIS), Spitalgasse 23, 1090 Vienna, Austria

IJERPH, 2019, vol. 16, issue 23, 1-12

Abstract: The parameters of logistic regression models are usually obtained by the method of maximum likelihood (ML). However, in analyses of small data sets or data sets with unbalanced outcomes or exposures, ML parameter estimates may not exist. This situation has been termed ‘separation’ as the two outcome groups are separated by the values of a covariate or a linear combination of covariates. To overcome the problem of non-existing ML parameter estimates, applying Firth’s correction (FC) was proposed. In practice, however, a principal investigator might be advised to ‘bring more data’ in order to solve a separation issue. We illustrate the problem by means of examples from colorectal cancer screening and ornithology. It is unclear if such an increasing sample size (ISS) strategy that keeps sampling new observations until separation is removed improves estimation compared to applying FC to the original data set. We performed an extensive simulation study where the main focus was to estimate the cost-adjusted relative efficiency of ML combined with ISS compared to FC. FC yielded reasonably small root mean squared errors and proved to be the more efficient estimator. Given our findings, we propose not to adapt the sample size when separation is encountered but to use FC as the default method of analysis whenever the number of observations or outcome events is critically low.

Keywords: maximum likelihood estimation; logistic regression; Firth’s correction; separation; penalized likelihood; bias (search for similar items in EconPapers)
JEL-codes: I I1 I3 Q Q5 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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