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Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure a
Corrado Crocetta & Nicola Loperfido
b
a
DSEMS, Università degli Studi di Foggia, L.go Papa Giovanni Paolo II, Foggia, Italy b
Dipartimento di Economia e Metodi Quantitativi, Università di Urbino ‘Carlo Bo’, Urbino, Italy Version of record first published: 24 Sep 2009.
To cite this article: Corrado Crocetta & Nicola Loperfido (2009): Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure, Journal of Applied Statistics, 36:10, 1101-1108 To link to this article: http://dx.doi.org/10.1080/02664760802653545
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Journal of Applied Statistics Vol. 36, No. 10, October 2009, 1101–1108
Downloaded by [Nicola Loperfido] at 10:06 27 November 2012
Maximum likelihood estimation of correlation between maximal oxygen consumption and the 6-min walk test in patients with chronic heart failure Corrado Crocettaa∗ and Nicola Loperfidob a Università
degli Studi di Foggia, DSEMS, L.go Papa Giovanni Paolo II, Foggia, Italy; b Dipartimento di Economia e Metodi Quantitativi, Università di Urbino ‘Carlo Bo’, Urbino, Italy (Received 21 May 2008; final version received 27 November 2008)
Maximal oxygen consumption (VO2 max) 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 VO2 max test, it is inexpensive and can be performed almost anywhere. Various medical studies have addressed the correlation between VO2 max 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. Keywords: cardiopulmonary exercise testing; correlation; maximal oxygen consumption; 6-min walk test; skew-normal distribution
1.
Introduction
The maximal oxygen consumption test (VO2 max) measures the energetic expenditure of any physical activity. It is performed using a treadmill or cycle ergometer, during which the cardiopulmonary response is measured and respiratory gases are analysed. It is the criterion measure of cardiorespiratory fitness [7], the ‘benchmark’ measurement for quantifying cardiovascular functional capacity [15] and one of the most important predictors of prognosis in chronic heart failure [8]. ∗ Corresponding
author. Email:
[email protected]
ISSN 0266-4763 print/ISSN 1360-0532 online © 2009 Taylor & Francis DOI: 10.1080/02664760802653545 http://www.informaworld.com
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The VO2 max test is frequently performed by cardiovascular patients. Standard situations where this test is often used include: prescribing exercise therapy intensities for patients with long-standing myocardial infarction; the evaluation of drug effects [21]; determination of the appropriateness and timing of cardiac transplantation [5]. It can also be used to predict long-term post-operative lung function [19]. In sports medicine, it is used for assessing endurance exercise capacity and the prevention of overtraining syndrome [21]. Unfortunately, VO2 max is a costly and labour-intensive measure to obtain, since it requires sophisticated equipment and specially trained personnel [5]. Moreover, some patients might find the VO2 max procedure difficult, when they are not used to physical activity [16]. For these reasons, functional walk tests are used to measure cardiopulmonary functional status or capacity – mainly patients’ abilities to undertake physically demanding activities that constitute daily life. Compared with traditional laboratory indices of exercise capacity, walk tests require less technical expertise and equipment, making them inexpensive and easy to administer [20]. Solway et al. [25] has presented a qualitative and comprehensive overview of the measurement properties of the most commonly utilized walk tests in the cardiorespiratory domain: the 2-min walk test, 6-min walk test (6MWT), 12-min walk test, self-paced walk test and shuttle walk test. They concluded that the 6MWT should be chosen when using a functional walk test for clinical or research purposes. This test measures the distance that a patient can quickly walk on a flat, hard surface over a time-scale of 6 min. It is a practical and simple test that requires a 100-ft hallway but no exercise equipments nor advanced training for the technicians, making it suitable for large investigations and prevention campaigns [6]. Several researchers have observed highly significant correlations between the 6MWT distance measure and VO2 max in patients with heart failure. Sample correlations range from 0.54 [13] to 0.90 [23]. The distance walked has been shown to be strongly correlated with VO2 max in patients who walked
