Adjustment for sparse data bias in odds ratios: Significance to appraisal of risk of diabetes due to occupational trichlorfon insecticide exposure

Background

Bias away from the null in odds ratios (OR), aggravated by low power, is a well-known phenomenon in statistics (sparse data bias). Such bias increases in presence of selection of “significant” results on the basis of null hypothesis testing (effect size magnification, ESM).

Objectives

We seek to illustrate these issues and adjust for suspected sparse data bias in the context of a reported more than doubling of the odds of new onset type 2 diabetes in presence of occupational trichlorfon insecticide exposure reported in the Agricultural Health Study.

Methods

We performed ESM analysis on the crude ORs extracted from the contingency table in the published report, which is done by simulating selected OR given a posited true OR. Next, we applied easily accessible methods that adjust for sparse data bias to the extracted contingency tables, including data augmentation, bootstrap, Firth's regression, and Bayesian methods with weakly informative priors.

Results

During the ESM analysis, we observed that there was a reasonable chance that a “statistically significant” OR of around 2.5–2.6 would be observed for true OR of 1.2. Adjustment for sparse data bias revealed that Bayesian methods outperformed alternative approaches in terms of yielding more precise inference, while not making unjustified distributional assumptions about estimates of OR. The OR in the original paper of about 2.5–2.6 was reduced on average to OR of 1.9 to 2.2, with 95% (Bayesian) credible intervals that included the null.

Discussion

It is reasonable to adjust ORs for sparse data bias when the reported association has societal importance, because policy must be informed by the least biased estimates of the effect. We think that such adjustment would lead to a more appropriate evaluation of the extent of evidence on the contribution of occupational exposure to trichlorfon pesticide to risk of new onset diabetes.