Assessing the Lognormal Distribution Assumption For the Crude Odds Ratio: Implications For Point and Interval Estimation
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The assumption that the sampling distribution of the crude odds ratio (ORcrude) is a log-normal distribution with parameters mu and sigma leads to the incorrect conclusion that the expectation of the log of ORcrude is equal to the parameter mu. In fact, mu is the median of the lognormal distribution, not the mean. If a different parameter is obtained as the expected value of the lognormal distribution, then this quantity can be used to obtain a new estimate of the true odds ratio (ORtrue). Here, simulations are conducted based on a simple randomized clinical trial study design. The simulations demonstrate that the new estimate of ORtrue (based on the expectation of the lognormal distribution function) yields interval estimates that are more statistically valid than the standard method. These interval estimates are obtained by both a parametric bootstrap method and a calculated percentile method. The statistical conclusion validity of the estimated confidence intervals are based on the intended coverage probability (ie the probability the confidence interval contains ORtrue). Additionally, an interval based hypothesis test based on the improved confidence interval estimate has higher power to reject the null hypothesis that ORtrue is equal to one when the alternative hypothesis is true (ie ORtrue is not equal to one) than the standard hypothesis test when the intervention is protective.
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