Binary methods for continuous outcomes: a parametric alternative.

Abstract

Often a "disease" or "state of disease" is defined by a subdomain of a continuous outcome variable. For example, the subdomain of diastolic blood pressure greater than 90 mmHg has been used to define hypertension. The classical method of estimating the risk (or prevalence) of such defined disease states is to dichotomize the outcome variable according to the cutoff value. The standard statistical analysis of such risk of disease then exploits methods developed specifically for binary data, usually based on the binomial distribution. We present a method, based on the assumption of a Gaussian (normal) distribution for the continuous outcome, which does not resort to dichotomization. Specifically, the estimation of risk and its variance is presented for the one- and two-sample situations, with the latter focusing on risk differences and ratios, and odds ratios. The binomial approach applied to the dichotomized data is found to be less efficient than the proposed method by 67% or less. The latter is found to be very accurate, even for small sample sizes, although rather sensitive to substitutions of the underlying distribution by thicker tailed distributions. Canadian total cholesterol data are used to illustrate the problem. For the one-sample case, the approach is illustrated using data from a study of the arterial oxygenation of 20 patients during one-lung anesthesia for thoracic surgery. For the two-sample case, data from a prognostic study of the renal function of 87 lupus nephritic patients are used.