Regression analysis of data with correlated errors: an example from the NHLBI twin study

Epidemiologic studies often involve genetically related individuals, spouses, or repeat observations on the same individual. When regression analysis is required in such studies, significant correlation of the residuals may affect the estimates of the standard errors of the regression coefficients. Ordinary least squares may not provide the best (minimum variance) estimates of the regression coefficients. Generalized least squares (weighted least squares) is more appropriate when the covariance matrix of the errors is known or can be estimated with some degree of confidence. Data from a twin study of pulmonary function were analyzed by three different regression techniques and comparisons of the coefficients and standard errors are made to illustrate the potential effects of correlated errors.