# Statistics and alternate reality: one more mince pie can’t hurt, can it?

December 6, 2018

Sarah Lay-Flurrie is a senior statistician within the Nuffield Department of Primary care Health Sciences and deputy co-ordinator of the Big Data Epidemiology module.

It’s that time of year again when temptations abound: Christmas lunches, dinners and drinks and a seemingly never-ending supply of chocolate, cake and the all-important mince pies. In my case there is even a Christmas breakfast to attend! So today I imagine that at least a few people are eyeing up the office biscuit tin thinking “Just the one won’t hurt” or nursing a sore head and musing “If only I’d stopped at 3 pints last night”.

The problem is, we can never know for certain what would have happened in that alternate reality where you dodged the biscuit in favour of fruit, or left the drinks party at a reasonable hour. In medical research, the alternate realities we commonly consider are arguably a little more serious: what are the benefits and harms of taking a particular drug compared to not? What are the chances of developing cancer if you smoke compared to not? The good news is that by conducting well designed research studies and applying appropriate statistical methods, such as those taught on our Essential Medical Statistics module, we can at least estimate what might have been.

In the absence of evidence from randomised controlled trials, one of the simplest ways of estimating what might have been is through regression modelling combined with a technique known as “adjustment”. Consider a recently published analysis of The Atherosclerosis Risk in Communities Study, where the authors wanted to find out whether having children affects your chances of developing cardiovascular disease (CVD).[1] The authors found that women who had 5 or more children were 26% more likely to develop CVD compared to women who had only 1 or 2 children. These results were “adjusted” for a range of factors including age, race, smoking status and deprivation. But what does this actually mean?

Essentially, this tells us that if you compare two women who are similar in terms of all of these factors (including age, race, smoking status etc.), and only differ in terms of the number of children they have, the woman with more children is more likely to develop CVD. The more factors that can be adjusted for, the more similar the two women become and (generally speaking) the more accurately we can estimate the effect of having children on the chance of developing CVD.

Taking this to the extreme, imagine that we can measure and adjust for an infinite number of factors, including all genetic and environmental factors. What we end up with is an estimate of each woman’s alternate reality: what is the chance of CVD in a woman who has 5 children compared to an entirely identical woman with only 1 child? Practically such an approach is impossible. However, with good knowledge of the key factors that may affect both the exposure (number of children) and the outcome (CVD), so-called “confounding” factors, we can get a pretty good estimate of what might have been. More advanced statistical approaches can be used, such as those covered in our Big Data Epidemiology module, but the simplest approach is often a good place to start.

And for those of you still wondering whether that extra mince pie will really make a difference or not, I refer you to a review published last year by Diaz-Zavala and colleagues.[2] They found that adults, including those trying to lose weight, gain between 0.4 and 0.9 kg on average over the festive season. Thankfully, it’s not clear from existing studies whether this gain is maintained in the long-term!

1 Oliver-Williams C, Vladutiu CJ, Loehr LR, et al. The Association Between Parity and Subsequent Cardiovascular Disease in Women: The Atherosclerosis Risk in Communities Study. J Women’s Heal 2018;:jwh.2018.7161. doi:10.1089/jwh.2018.7161

2 Díaz-Zavala RG, Castro-Cantú MF, Valencia ME, et al. Effect of the Holiday Season on Weight Gain: A Narrative Review. J Obes 2017;2017:1–13. doi:10.1155/2017/2085136