Weighted kappa coefficients are commonly used to quantify inter- or intra-rater reliability or test-retest reliability of ordinal ratings in clinical and epidemiologic applications. In this paper, we assess the dependence of weighted kappa coefficients on the number of categories and the type of weighting scheme, which vary between applications. The most commonly used weights are weights that are proportional to the deviation of individual ratings ("linear weights") or to the square of the deviation of individual ratings ("quadratic weights"). Quadratically weighted kappa coefficients are equivalent to the intraclass correlation coefficient and to the product-moment correlation coefficient under certain conditions. We illustrate that an increase of quadratically weighted kappa coefficients with the number of categories is expected under a broad variety of conditions, whereas linearly weighted kappa coefficients appear to be less sensitive to the number of categories. Number of categories and type of weighting scheme therefore require careful consideration in the interpretation of weighted kappa coefficients.
We conducted a retrospective cohort study to evaluate the relation between the level of total trihalomethanes in drinking water and adverse birth outcomes. The study population comprised women residing in an area with municipal surface water who had a singleton birth in Nova Scotia between January 1, 1988, and December 31, 1995, or a pregnancy termination for a major fetal anomaly. We found little association between trihalomethane level and the outcomes related to fetal weight or gestational age, but we found an elevated relative risk for stillbirths for average trihalomethane levels during pregnancy of 100 microg/liter or greater (adjusted relative risk = 1.66; 95% confidence interval = 1.09-2.52) relative to women exposed to trihalomethane levels of 0-49 microg/liter. We saw little evidence of an elevated prevalence or dose-response pattern for congenital anomalies, with the possible exception of chromosomal abnormalities (adjusted prevalence ratio = 1.38 and 95% confidence interval = 0.73-2.59 for women exposed to trihalomethane levels of 100 microg/liter or greater).
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