Time-Dependent Confounding in the Study of the Effects of Regular Physical Activity in Chronic Obstructive Pulmonary Disease: An Application of the Marginal Structural Model
Introduction
The regular practice of physical activity has been related to a reduced risk of premature mortality and several chronic diseases and conditions, including cardiovascular diseases, diabetes, or colon cancer (1). Despite the large amount of research on the benefits of physical activity, its effects on respiratory health have hardly been studied (1). Chronic obstructive pulmonary disease (COPD) is one of the main causes of morbidity and mortality worldwide (2); it has been recently reported that the regular practice of physical activity may reduce the risk of developing this disease (3) and improve its prognosis 4, 5.
A limitation of the studies alluded to above is that they could not have sufficiently accounted for confounding. Standard methods of analysis model the probability of the outcome as a function of exposure and covariates. In the study of the effects of physical activity in COPD, as in many other settings, both exposure (physical activity) and many of the covariates (nutritional status, respiratory symptoms, or quality of life) are time varying. When both exposure and covariates change over time, and covariates are confounders that are also affected by prior exposure, standard methods of analysis may be biased (6). This situation has been labeled as time-dependent confounding (7). To appreciate how time-dependent confounding may lead to biased results, consider the role of obesity in a longitudinal study of the association between physical activity and mortality, with repeated measures over time of physical activity and obesity. Physical activity (at time t) is a behavior that reduces the risk of mortality (1). Previous obesity (at t-1) is a covariate that relates to a reduced level of physical activity (at t) and it is also associated with higher risk of mortality (8). Therefore, obesity at t−1 is a confounder. Additionally, subjects practicing higher levels of physical activity (at t) have a reduced risk of obesity (at t+1) (8), so obesity (at each tn) is also affected by prior exposure (physical activity at tn-1). In this example, the crude association between physical activity (at t) and mortality (at t+1) will be biased because subjects with lower level of physical activity (at t) will tend to be those with higher obesity (at t−1) and higher risk of mortality (at t+1). The estimate obtained after adjusting for obesity at time t−1 will be biased because it ignores the fact that, after the start of the study (at t), the level of physical activity may change according to changes in obesity (at t or t+1). The control for repeated measures of obesity will also give biased estimates in part because obesity is on the pathway between exposure and outcome 9, 10, 11.
Since standard methods for longitudinal analysis do not properly account for the problems derived from time-dependent confounding, marginal structural models (MSMs) have been developed (6). Although these models are relatively easy to implement in common statistical software, their use in applied epidemiology is still scarce. It is interesting to note that several of the studies using MSMs have reported differences between the estimates obtained with MSMs and estimates obtained with standard methods, which in some cases meant even a change in the direction of the association under study 12, 13, 14, 15. As a result, all these studies recommend the use of MSMs when time-dependent confounding is likely. In the study of the health effects of physical activity, to our knowledge only two papers have used MSMs 16, 17. These studies pointed to the need to consider repeated measurements of physical activity and body composition to appropriately assess their role as determinants of functional limitations in the elderly, since the changing nature of physical activity and body composition over time could produce the mentioned time-dependent confounding.
In the present study, we used the population-based cohort Copenhagen City Heart Study to assess the presence of time-dependent confounding in the association between physical activity and (i) COPD development, and (ii) COPD course, by comparing standard statistical methods with MSMs.
Section snippets
Subjects
The Copenhagen City Heart Study (CCHS) involves the study of an ongoing prospective cohort of adults recruited from the general population, with repeated examinations every 5 to 10 years. A random age-stratified sample of the general population aged 20 years or more was drawn from the Copenhagen Population Register as of January 1, 1976, and an initial examination (n = 14,223, 74% of the eligible) took place in 1976–1978. At the second examination 5 years later (1981–1983), the cohort was
Physical Activity and COPD Development
A total of 6,568 subjects from the general population were included (41% men; mean age at baseline, 49 years) (Table 1). In the standard (adjusted) analysis, higher physical activity levels showed an improved FEV1 decline by gaining +6.5 and +10.2 mL/yr in the moderate and high physical activity groups, respectively, as compared with the low physical activity group. Corresponding figures in the marginal structural (weighted) approach were very similar: +7.4 and +10.3 (Table 2, a). Similarly,
Discussion
We have used MSMs to estimate the effects of physical activity on COPD development and COPD course because standard methods are not appropriate when there are confounders that are affected by previous levels of physical activity. This is the first study assessing time-dependent confounding in the study of the effects of physical activity on respiratory outcomes. The inclusion of several outcomes allowed to test whether the magnitude of this confounding could vary from one outcome to another. It
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