Estimating and Testing Significance of Change in Prevalence of a Trait When Some Change may be Attributable to Regression to the Mean

When the prevalence of a disease-related trait rises to a level that causes public health concern, a typical course of action is to investigate population level interventions aimed at reducing the amount of existing disease in the population. Suppose a characteristic of interest [e.g., body mass index (BMI)] is measured on a continuous scale and the collection of all values of the trait (BMI’s) in the population has a distribution that is symmetric and bell shaped so that it is well approximated by a normal distribution. Further, suppose there is a specific value (cut-point) such that values that exceed that cut-point are considered to be unhealthy in the context of disease or risk of disease. The aim is to estimate and test significance of change in prevalence of unhealthy status following intervention when a portion of the change may be attributable to that intervention with a second portion attributable to regression to the mean. Key considerations are the nature of the underlying unrestricted bivariate distribution of pre- and post-intervention responses, the strength of correlation between these observed responses, and the choice of cut-point used to define the unhealthy status. The motivation for analytical methods discussed is a weight loss intervention for lowering the prevalence of obesity in adults where individuals with BMI ≥ 30 mg/kg² are classified as obese.