Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure

Maximal oxygen consumption (VO₂max) is the standard measurement used to quantify cardiovascular functional capacity and aerobic fitness. Unfortunately, it is a costly, impractical and labour-intensive measure to obtain. The 6-min walk test (6MWT) also assesses cardiopulmonary function, but in contrast to the VO₂max test, it is inexpensive and can be performed almost anywhere. Various medical studies have addressed the correlation between VO₂max and 6MWT in patients with chronic heart failure. Of particular interest, from a medical point of view, is the conditional correlation between the two measures given the individual's height, weight, age and gender. In this paper, we have calculated the maximum likelihood estimate of the conditional correlation in patients with chronic heart failure under the assumption of skew normality. Data were recorded from 98 patients in the Operative Unit of Thoracic Surgery in Bari, Italy. The estimated conditional correlation was found to be much smaller than estimated marginal correlations reported in the medical literature.