Abstract
BackgroundThe odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. In the process of dichotomizing the data, however, information is lost about the underlying counts which can reduce the precision of inferences on the OR.MethodsWe propose analyzing the count data directly using regression models with the log odds link function. With this approach, the parameter estimates in the model have the exact same interpretation as in a logistic regression of the dichotomized data, yielding comparable estimates of the OR. We prove analytically, using the Fisher information matrix, that our approach produces more precise estimates of the OR than logistic regression of the dichotomized data. We also show the gains in precision using simulation studies and real-world datasets. We focus on three related distributions for count data: geometric, Poisson, and negative binomial.ResultsIn simulation studies, confidence intervals for the OR were 56–65% as wide (geometric model), 75–79% as wide (Poisson model), and 61–69% as wide (negative binomial model) as the corresponding interval from a logistic regression produced by dichotomizing the data. When we analyzed existing datasets using our approach, we found that confidence intervals for the OR could be up to 64% shorter (36% as wide) compared to if the data had been dichotomized and analyzed using logistic regression.ConclusionsMore precise estimates of the OR can be obtained directly from the count data by using the log odds link function. This analytic approach is easy to implement in software packages that are capable of fitting generalized linear models or of maximizing user-defined likelihood functions.
Highlights
The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence
From a survey of dietary behaviors among Canadian youth, Vanderlee et al [1] dichotomized the number of sugar-sweetened beverages consumed and compared the odds of consuming at least one beverage based on gender, age group, and physical activity
The percent bias is smaller for the geometric model than the logistic regression of the dichotomized data, and the percent bias decreases as the sample size increases (Additional file 1: Table S.1)
Summary
The odds ratio (OR) is used as an important metric of comparison of two or more groups in many biomedical applications when the data measure the presence or absence of an event or represent the frequency of its occurrence. In the latter case, researchers often dichotomize the count data into binary form and apply the well-known logistic regression technique to estimate the OR. Count data arise naturally in many biomedical applications These data are often converted to binary values and commonly analyzed using logistic regression methods. A similar approach was used to estimate the odds of one or more motor vehicle collisions by elderly drivers based on the frequency of falls [2] and the odds of one or more dental caries in children based on diet and obesity [3]
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