Estimating correlation between alternative measures of disease progression in a longitudinal study. Modification of...

A primary outcome variable in longitudinal studies is often the rate of change of a continuous measurement over time. Examples include the one-second forced expiratory volume (FEV1) in pulmonary studies or glomerular filtration rate (GFR) in renal studies. An individual patient's least-squares estimate of slope obtained from a linear regression is an imprecise measure of the true slope for that patient, and correlations involving the estimated slopes will be biased due to this measurement error. This paper presents methods for estimating the true correlation between these imprecise slope estimates, or between slope estimates and other variables measured with error. In addition to providing a simple consistent estimator of the correlation, we show how the maximum likelihood estimate of the correlation coefficient and a 100(1 - alpha) per cent confidence interval can be obtained. An example estimating the correlation between GFR and inverse serum creatinine slopes in patients with chronic renal disease is given.