Performance of prior and weighting bias correction methods for rare event logistic regression under the influence of sampling bias

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The problem of classifying events to binary classes has been popularly addressed by Logistic Regression Analysis. However, there may be situations where the most interested class of event is rare such as an infectious disease, earthquake, financial crisis etc. The model of such events tends to focus on the majority class, resulting in the underestimation of probabilities for the rare class. Additionally, the model may incorporate sampling bias if the rare class of the sample is not representative of its population. It is therefore important to investigate whether such rareness is genuine or caused by an improperly drawn sample. We conducted a simulation study by creating three populations with different rarity levels and drawing samples from each of those which are either compatible or incompatible with the actual rare classes of the population. Then, the effect of sampling bias is discussed under the two correction methods of bias due to rareness as suggested by King and Zeng.