A solution to the problem of separation in logistic regression
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...It is a well-known phenomenon that low cell counts or empty cells can cause numerical instability of the maximum-likelihood estimation.(34) When logistic-regression analysis was applied to collapsed variants or to the CMC method, type I error was well controlled; however, this might not be the case if after collapsing the total allele frequency is still very low....
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"A solution to the problem of separa..." refers background or methods in this paper
...By using this modi cation Firth [19] showed that the O(n−1) bias of maximum likelihood...
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...order to reduce the small sample bias of these estimates Firth [19] suggested basing estimation on modi ed score equations...
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...Estimation of standard errors can be based on the roots of the diagonal elements of I(̂)−1, which is a rst-order approximation to {−92 log L∗=(9 )2}−1 (see Firth, reference [19], p....
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...In the following section we rst review some principal ideas of Firth [19], then deal with their implementation in logistic regression (FL), and, nally, suggest con dence intervals based on the pro le penalized likelihood....
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