| Summary: | Assuming a binary outcome, Logistic Regression is the most common approach to
estimating odds ratio corresponding to continous predictor. We revisit a method termed
the discriminant Function Approach, which leads to closed-form estimators and
coresponding standard errors. In its most appealing implication, we show that the
approach suggests a multiple linier regression of the continuous predictor of interest on
the outcome and other covariates, in place of the traditional logistic regression model. If
standard diagnostic support the assumptions (including normality of errors)
accompanying this linier regression model, the resulting estimator has demonstrable
advantages over the usual maximum likelihood estimator via logistic regression. The
include improvements in term of bias and efficiency based on unbiased estimator of the
log odds ratio, as well as the availability of an estimate when logistic regression fails to
converge due to a separation of data point. Use of the discriminant Function approach as
described here for multivariable analysis requiresless stringent assumptions than those for
which it was historically criticized, and is worth considering when odds ratio associated
with particular continous predictor is of primary interest. Case studies illustrate these
points.
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