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    Firth’s logistic regression for separation problem : Comparing between R-logistf and SAS-LOGISTIC = 분리 문제에 대한 Firth의 로지스틱 회귀분석: R-logistf와 SAS-LOGISTIC의 비교

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    https://www.riss.kr/link?id=T15525536

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    The phenomenon of separation or monotone likelihood commonly occurs in fitting logistic regression model. Separation problems usually occur for small sample sizes with a highly imbalanced independent variable, or for large sample sizes with rare events. In this case the logistic regression model causes serious bias problem in the maximum likelihood (Firth D 1993, King, G. and Zeng, L 2001). To solve this bias, Firth proposed a penalized maximum likelihood estimation method. It produces finite parameter estimates with a simple modification of the score function.
    We can use the Firth’s method through several software packages such as R and SAS. But the motivating example showed differences in the output. For example, R-logistf and SAS-LOGISTIC gave different conclusions about the significance of variables even though they referred to the same Firth’s method paper (Heinze G, Schemper M 2002). Therefore the purpose of this study is to investigate the performance of Firth’s logistic regression in R (version 3.6.0) and SAS (version 9.4). We conducted a simulation study under various scenarios to compare standardized bias of estimates, mean standard error, coverage rate and convergence issue.
    According to the results of simulation study, in the case of separation problem caused by continuous variables, SAS has less bias of estimates and convergence problem than R. However in the case of separation problem caused by binomial variables, R and SAS has similar performance. Therefore we recommend using SAS software when analyzing Firth’s logistic regression.
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    The phenomenon of separation or monotone likelihood commonly occurs in fitting logistic regression model. Separation problems usually occur for small sample sizes with a highly imbalanced independent variable, or for large sample sizes with rare event...

    The phenomenon of separation or monotone likelihood commonly occurs in fitting logistic regression model. Separation problems usually occur for small sample sizes with a highly imbalanced independent variable, or for large sample sizes with rare events. In this case the logistic regression model causes serious bias problem in the maximum likelihood (Firth D 1993, King, G. and Zeng, L 2001). To solve this bias, Firth proposed a penalized maximum likelihood estimation method. It produces finite parameter estimates with a simple modification of the score function.
    We can use the Firth’s method through several software packages such as R and SAS. But the motivating example showed differences in the output. For example, R-logistf and SAS-LOGISTIC gave different conclusions about the significance of variables even though they referred to the same Firth’s method paper (Heinze G, Schemper M 2002). Therefore the purpose of this study is to investigate the performance of Firth’s logistic regression in R (version 3.6.0) and SAS (version 9.4). We conducted a simulation study under various scenarios to compare standardized bias of estimates, mean standard error, coverage rate and convergence issue.
    According to the results of simulation study, in the case of separation problem caused by continuous variables, SAS has less bias of estimates and convergence problem than R. However in the case of separation problem caused by binomial variables, R and SAS has similar performance. Therefore we recommend using SAS software when analyzing Firth’s logistic regression.

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