With great (statistical) power comes great responsibility

Tessa Strain and Søren Brage

We are all familiar with studies that investigate the associations between physical activity and outcomes such as death or cardiovascular disease. However, we rarely focus on the length of time over which these study participants are followed up to see if one of the outcomes occurs.

There are now several very large cohort studies, such as the UK Biobank, China Kadoorie Biobank and the Million Women Study, that each have more than 500,000 participants. With such large sample sizes, the numbers of deaths, cardiovascular events or other outcomes of scientific interest that occur in the first few years after the baseline assessment are higher than the numbers seen in traditionally smaller studies. These larger numbers can be sufficient to power the analyses in a statistical sense, whereas, previously, we would have had to wait much longer for a sufficient number of events to occur. What we don’t know is whether analysing data at these much earlier time points, compared with the traditionally longer follow-up periods, makes a difference to the nature of the associations reported.

In our study, recently published in the IJE, we analysed data from 96,476 UK Biobank participants in a variety of different ways, artificially shortening the time over which they were followed up. We found that the shorter this time was, the stronger the association between physical activity and death or cardiovascular disease — that is, at shorter follow-ups, there was a greater difference in risk of death and cardiovascular disease between participants with low and high physical activity levels.

These findings might be caused, in part, by ‘reverse-causality bias’. This is the concept that those who die or have a cardiovascular event soon after their baseline measurement might have had an underlying health condition when they reported their physical activity. This health condition, whether it was diagnosed or not, may have caused the participants to have lower physical activity levels. This potentially means that, instead of isolating the effect of physical activity, low physical activity levels might be partly acting as an indicator of poor health.   

To investigate this hypothesis, we re-analysed the same data using different strategies to try to minimise the risk of reverse-causality bias. This included statistical adjustment for whether participants had diagnosed cardiovascular disease or cancer at baseline and excluding those participants from the analyses. We also tried excluding those who died or had a cardiovascular event in the first 1 or 2 years after baseline assessment, regardless of whether they had reported a health condition previously.

We found that the more we accounted for underlying health conditions, the weaker the associations between physical activity and mortality or cardiovascular disease became. This was particularly apparent when participants were only followed up for 1 to 2 years. This finding supported our hypothesis that reverse-causality bias may, at least in part, explain why stronger associations are seen over shorter time periods.

It may not, however, be the only reason. We also expect that participants will change their physical activity levels over time. The longer the time since the initial measurement, the greater the chance that people would be ranked differently if we were to remeasure their activity levels. This is a form of ‘regression dilution bias’, which means that it is harder to detect an association (i.e. the associations will be weaker).

Overall, these findings have implications for decisions about when to analyse data from these large cohort studies. It is a timely reminder that just because we could analyse the data at an early time point, it doesn’t mean we should. It is also important to consider these factors when comparing the results of different studies, whether informally as a reader or in a systematic review or meta-analysis. Studies with different lengths of observation time, or with different methods for accounting for the effect of disease on activity levels, may not be directly comparable, and we should be aware of why.

Read more:

Strain T, Wijndaele K, Sharp SJ, et al. Impact of follow-up time and analytical approaches to account for reverse causality on the association between physical activity and health outcomes in UK Biobank. Int J Epidemiol 2019; Oct XX. doi: 10.1093/ije/dyz212.


Dr Tessa Strain is an MRC Postdoctoral Fellow at the MRC Epidemiology Unit at the University of Cambridge. Her research focuses on the measurement of physical activity.

Dr Søren Brage leads the Physical Activity Epidemiology program at the MRC Epidemiology Unit at the University of Cambridge. His research interests include developing and evaluating assessment methods for physical activity and characterising the relationship between physical activity and metabolic disease.

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