Using Mendelian Randomization for Cost-Effectiveness Analyses

We have a new paper out on the preprint server MedRXiv, with the intimidating name of:

I don’t think this is as terrifying or dull as the title makes it sound.

The Aim

The aim of the paper is to go through a (new?) method of estimating whether an intervention might be cost-effective, i.e. save more money than it costs, accounting for how much extra life it might give people.

The method uses Mendelian randomization to estimate the effect of an exposure (body mass index [BMI] in the paper, defined as weight in kilograms divided by height in metres squared) on healthcare costs and quality-adjusted life years, then using those results to estimate whether an intervention that affects that exposure by a known amount and costing another amount (laparoscopic bariatric surgery and a policy on high fat, sugar and salt foods in the paper) is therefore cost-effective, when valuing a year of full life at yet another amount.

I imagine there may be new terms in that last paragraph, so I’ll explain.

Mendelian randomization

Mendelian randomization is a technique that uses genetic information to reduce the risk of bias from confounding and reverse causation in observational research, at the cost of much less statistical power (so you need a whole lot of participants to see anything) and the possibility of different biases, though these are probably less severe than straight observational research.

Want to know how much an increase in BMI across a population will cost healthcare providers? You could measure the BMI and healthcare costs of loads of people and see how healthcare costs change with BMI, but that might be confounded by things like health conditions, smoking, diet, exercise etc. If you measure people’s genetics too (specifically the ones that cause changes in BMI), then you can get a less biased results, because genetics are not affected by health conditions, smoking, diet or exercise.

We have a “” guide coming out soon, written for non-statisticians/geneticists. It’s not out just yet, but I’ll link to it when it’s available. Also, there’s that’s pretty good. I wrote a post about using Mendelian randomization previously too (that was accepted for publication last week, so that was nice).

Of course, randomization controlled trials (RCTs) can be used to estimate the cost effectiveness of interventions too – these are fantastic and usually the best evidence, but a) RCTs tend to be small, so estimates of cost-effectiveness may be imprecise (plus there are generalisability estimates), and short (so not long-term estimates available), b) don’t help if you’re trying to measure the cost of a change in an exposure, rather than in an intervention, and c) cost a lot. So, people tend to use observational methods for exposures like BMI, either following cohorts or using simulation models that rely on observational data. We talk about these types of studies in the paper (mostly in the supplement due to word constraints), but we have this figure too that tries to explain the differences between each method:


Caption: Schematic representation of different methods of estimating cost effectiveness of bariatric surgery. The intervention or exposure for each analysis is in the blue box with bold text. Blue arrows represent what is estimated in each study, while green arrows represent estimates from previous studies used to inform the study. In panel a, the estimate of cost-effectiveness is not confounded as the intervention is randomised. In panel b, the estimate of cost-effectiveness could be confounded as receiving bariatric surgery is not randomly assigned. In panel c, the estimate of cost-effectiveness could be confounded, as could be the estimates from previous studies, there may be effects of bariatric surgery on QALYs and healthcare costs that don’t go through BMI, and there may be effects of BMI on QALYs and healthcare costs that do not go through the modelled health conditions. In panel d, the estimate of cost-effectiveness is less likely to be affected by confounding, as genetic variants are randomly distributed within families at conception, though there may be effects of bariatric surgery on QALYs and healthcare costs that don’t go through BMI.

Healthcare costs

For this work, we used UK Biobank, which recruited about 500,000 participants between 2006 and 2010. The data has been linked to hospital episode statistics (HES), which are a record of any stay in hospital, however short (not necessarily an overnight stay). About half of participants have also been linked to primary care data, which is really detailed. Like, properly detailed, it’s great.

Using those two sources of data, we estimated, for everyone in UK Biobank, how much their healthcare cost, including all hospital stays, all GP appointments and the cost of all drugs prescribed in primary care. Even for people without primary care data, we estimated their primary care costs using multiple imputation, which estimates the costs but allows for as much error as necessary so you don’t over-interpret the data.

All in all, we cover a sizeable chunk of healthcare costs from recruitment up to March 2017 (or March 2015 for secondary care costs – they were tricky) – we’ll be underestimating costs a little, as some sources of NHS costs aren’t accounted for, and we don’t account for private healthcare costs at all.

Quality-adjusted life years

Quality-adjusted life years (QALYs) are a tool used to assess the quality and quantity of life people have. A full year at perfect health is 1 QALY. Any time at all while dead is 0 QALYs. If someone lives for 50 years at perfect health, then 30 years at half health, that’s a sum total of 50 + 30*0.5 = 65 QALYs. One morbid curiosity of this is that you can have negative QALYs, i.e. life worse than death. This is a pretty potent reminder that quality of life is as important as quantity of life.

QALYs are estimated in various ways. We just used health as an indicator for QALYs: there was that estimated by how much each of 240 chronic health conditions reduced QALYs. Some conditions (conjunctivitis, allergies) barely reduced QALYs, and some reduced QALYs by a LOT (paralytic syndromes, nervous system disorders, muscular dystrophy). We used the linked medical data to estimate the average QALYs people had over follow up, based on how many of the 240 chronic health conditions the participant had.

This is certainly not a perfect way to estimate quality of life (though quantity is pretty sound), as it doesn’t include any non-health quality of life indicators (e.g. just general happiness with life). However, so long as we interpret the results as being health-related QALYs, I think this method is reasonably good.

In cost-effectiveness analyses, a QALY is set to be worth a certain amount, allowing you to make comparisons between interventions: if one intervention is hugely costly, and saves only a bit of extra life, then you’d probably be better off funding the latter intervention given limited resources. Also, smoking may be considered cost-effective if you don’t account for QALYs, given smokers tend to consume less healthcare resources over their (on average shorter) lives.

The current amount in the UK is about £20,000 per QALY, but can be higher depending on the intervention.

Laparoscopic bariatric surgery

The “gold standard” of surgery for weight loss. A surgeon literally makes your stomach smaller, meaning you feel fuller quicker and reducing absorption of food eaten.

Evidently, it’s pretty effective: a followed-up people who had the surgery for 20 years, and found about a 25% reduction in weight after 10 and 20 years.

The Method

Here’s what we did, in numbered points because I wouldn’t be allowed to do this in an academic paper:

  1. Estimated the average healthcare costs and QALYs per year for all white British people in UK Biobank (note: we restricted to white British people because otherwise the genetics get difficult/impossible to work with)
  2. Used Mendelian randomization to estimate the effect of BMI on those healthcare costs and QALYs per year
  3. Estimated how much BMI would change due to an intervention for BMI, on average across the UK in 2017 for people aged 40 to 69 years
  4. Multiplied the estimated change in BMI by the effect of BMI on healthcare costs and QALYs, to estimate for either a person (on average) or a population, the total effect of an intervention
  5. Also estimates cost-effectiveness, taking into account the cost of the intervention itself and giving a value of £20,000 to each QALY

In the supplement, we go through (in detail, and hopefully in simple terms) how to use this method to estimate the total cost of being overweight and obese in the population of England and Wales aged 40-69 years in 2017 (results below).

Main Analysis Results

The headline figure is that we estimated each 1 kg/m2 increase in BMI leads to an increase in annual healthcare costs of about £42 (95% confidence interval [CI], i.e. we are 95% sure the estimate is in the range of: £33 to £52), and decrease in QALYs by 0.65% of a QALY (95% CI: 0.49% to 0.81%), which I’m interpreting as a reduction in the quality and/or quantity of life of 0.65% in total over an entire life, per 1 kg/m2 increase in BMI. These estimates are specific to UK Biobank, which has a particular age and BMI profile.

A 1 kg/m2 increase in BMI has different effects depending on whether you are in the normal weight range (a BMI of 18.5 kg/m2 to 25 kg/m2) or overweight or obese (a BMI of more than 25 kg/m2): if you’re in the normal weight range, there’s very limited evidence a 1 kg/m2 increase will do anything, but if you’re overweight or obese the effect is larger, and, interestingly, pretty stable. That is, gaining or losing 1 kg/m2 when obese (a BMI of more than 30 kg/m2) has roughly the same effect on healthcare costs and QALYs as gaining or losing 1 kg/m2 when overweight. There is also some evidence that gaining weight is beneficial if underweight (BMI less than 18.5 kg/m2): there were too few people with low BMI values in UK Biobank to get the necessary statistical power for this, but it looks that way for now.

Age is also important: the estimated effects are larger in older age groups. This is expected: older people use more healthcare and are more likely to have chronic health conditions. But having an effect that varies by age and BMI means we need to account for them when estimating the effect of an intervention for BMI.

Here’s some graphs: the first two show the estimated effect of BMI on average QALYs and total healthcare costs per year, split by sex (males and females show about the same effect sizes), BMI category, and age category. The “main analysis MR” results in blue are the Mendelian randomization results, whereas the “multivariable adjusted” results in red are the results you get from the same analysis without using genetics – you’ll notice they’re much more precise.


Caption: Forest plot showing the estimated effect of a unit increase in BMI on average QALYs per year for the main Mendelian randomization, sex-specific, BMI categorical (where “Normal” is a BMI below 25 kg/m2, “Overweight” is a BMI between 25 kg/m2 and 30 kg/m2, and “Obese” is a BMI of above 30 kg/m2) and age categorical analyses.


Caption: Forest plot showing the estimated effect of a unit increase in BMI on average total healthcare costs per year for the main Mendelian randomization, sex-specific, BMI categorical (where “Normal” is a BMI below 25 kg/m2, “Overweight” is a BMI between 25 kg/m2 and 30 kg/m2, and “Obese” is a BMI of above 30 kg/m2) and age categorical analyses.

The second two graphs show the effect of adding 1 kg/m2 BMI across BMI levels: these are a bit unintuitive, but they both show that increasing BMI while underweight may be beneficial, whereas increasing BMI while overweight/obese is bad, and increasing BMI while a normal weight could be either.


Caption: The estimated effect of one kg/m2 increase in BMI on QALYs per year, across BMI levels. A positive value indicates an increase in BMI would increase QALYs, and vice versa. An increase in BMI is beneficial to QALYs up to around 22 kg/m2, then becomes increasingly detrimental until the effect plateaus in overweight and remains steady relatively in obesity.


Caption: The effect of one kg/m2 increase in BMI on total healthcare costs per year, across BMI levels. A positive value indicates an increase in BMI would increase total healthcare costs, and vice versa. Due to the uncertainty in the estimates, there is little statistical evidence of non-linearity in the effect of BMI on total healthcare costs, though descriptively it appears a one kg/m2 increase in BMI has a smaller effect on costs in the normal weight category, and a larger effect in overweight and obesity.

Sensitivity Analysis Results

We did a lot of sensitivity analyses to check the results make sense. We think they do – the supplement of the paper is filled with this stuff if you’re interested.

One important sensitivity analysis was in estimating the effect of BMI on QALYs using only the health conditions usually associated with obesity: cancer, cardiovascular disease, cerebrovascular disease and type 2 diabetes. This is what happens in many simulation studies, since they can’t model the effect of BMI on every health condition, they pick the ones most associated with obesity.

Predicting QALYs using only the limited set of health conditions drastically reduced the estimated effect of BMI on QALYs, from a reduction of 0.65% (95% CI: 0.49% to 0.81%) of a QALY to a reduction of 0.16% of a QALY per one kg/m2 increase in BMI (95% CI: 0.10% to 0.22%). This indicates BMI affects more health conditions than just cancer, cardiovascular disease, cerebrovascular disease and type 2 diabetes, and these other conditions have a considerable impact on health-related quality of life.

We didn’t do the same with healthcare costs, just because of the way healthcare costs are estimated using HES data.

Policy Analyses Results

Ok, here’s where things get (more?) interesting.

We estimated the effect of each of the following on QALYs and healthcare costs for the population aged 40-69 years of England and Wales in 2017 (21.7 million adults):

  1. The effect of laparoscopic bariatric surgery in people with a BMI above 35 kg/m2
  2. The effect of restricting volume promotions for high fat, sugar, and salt (HFSS) foods
  3. The effect of the increase in BMI between 1993 and 2017
  4. The effect of having the BMI profile of England and Wales in 2017 versus a hypothetical profile where no one has a BMI above 25 kg/m2

We used data from the office of national statistics and the health survey for England for all these analyses, so we could estimate the total number of people aged 40-69 years, and roughly what their BMI looked like in 2017 (and 1993).

a. Cost-Effectiveness of laparoscopic bariatric surgery

In this example, we estimated the average effect of laparoscopic bariatric surgery on someone aged 40-69 years, assuming it reduced BMI by 25% over 20 years (with some uncertainty). We restricted the analysis to people with high BMI levels (over 35 kg/m2) as per NHS recommendations.

We estimated that just over 2.7 million people in England and Wales had a BMI above 35 kg/m2 in 2017. Compared to no intervention, over 20 years for each person receiving laparoscopic bariatric surgery we estimated that QALYs would increase by 0.92 (95% CI: 0.66 to 1.17), i.e. almost a full extra year of perfect health, total healthcare costs would decrease by £5,096 (95% CI: £3,459 to £6,852), and the net monetary benefit (at £20,000 per QALY and £9,549 per surgery) would be £13,936 (95% CI: £8,112 to £20,658). A positive net monetary benefit means the intervention is cost-effective at the specified value of a QALY.

b. Cost-Effectiveness of restricting volume promotions for high fat, sugar, and salt (HFSS) products

This is a government policy type example, which would restrict volume promotions (“buy two chocolate bars for £1” type deals) for “high fat, sugar and salt (HFSS) products”. These tend to be tasty foods, sadly.

The government estimates that this would reduce daily Calorie intake by between 11 and 14 Calories per person, depending on age and sex. The government also believes each Calorie consumed per day sustains 42 grams of body weight, so if a person eats 10 Calories less per day (or does 10 Calories worth of exercise more per day), they should lose approximately 420 grams of body weight and keep it off over the long term.

Given this, we estimated that restricting volume promotions for HFSS products would, across everyone aged 40 to 69 years in England and Wales, increase QALYs by 20,551 per year (95% CI: 15,335 to 25,301), decrease total healthcare costs by £137 million per year (95% CI: £106 million to £170 million), and would have a net monetary benefit (at £20,000 per QALY and no intervention cost) of £546 million per year (95% CI: £435 million to £671 million).

c. Estimation of the Effect of the Population Change in BMI Between 1993 and 2017

The mean BMI increased from 26.7 kg/m2 to 28.6 kg/m2 between 1993 and 2017 in people aged between 40 and 69 years in England and Wales. The rise in BMI was more pronounced in people with obesity than people with a normal weight, but there were increases in all parts of the BMI distribution.

Given this increase in BMI, we estimated that between 1993 and 2017, the increase in BMI led to an average decrease in QALYs of 1.13% per person per year (95% CI: 0.90% to 1.38%), or a decrease of 246,390 QALYs in total per year (95% CI: 196,231 to 300,481) and an increase in total healthcare costs of £69 per person per year (95% CI: £53 to £84), or £1.50 billion in total per year (95% CI: £1.15 billion to £1.82 billion).

d. The Cost of Being Overweight and Obese in 2017

Just over 70% of people aged 40 to 69 years in England and Wales had a BMI above 25 kg/m2 in 2017. We estimated the cost to healthcare and QALYs of people being overweight or obese, and therefore the expected reduction in costs and increase in QALYs if everyone with a BMI above 25 kg/m2 reduced their BMI to 25 kg/m2.

We estimated that, compared to if all people with a BMI above 25 kg/m2 aged 40 to 69 years in England and Wales in 2017 had a BMI of 25 kg/m2, QALYs are decreased by 3.73% per person (with a BMI above 25 kg/m2) per year (95% CI: 2.94% to 4.61%), or a decrease of 580,494 QALYs in total per year (95% CI: 457,907 to 717,691), and an increase in total healthcare costs of £230 per person on average per year (95% CI: £176 to £279), or £3.58 billion in total per year (95% CI: £2.75 billion to £4.34 billion).

I feel at this point I should make it clear that these estimates should not be used as ammunition against people with high BMIs. The purpose of this work was to a) show that Mendelian randomization can be used for this purpose, and b) allow people to estimate the likely cost effectiveness of interventions targeting BMI, based on the expected cost of the intervention and its effect on BMI. I’d say that the mean BMI in England and Wales increasing by almost 2 kg/m2 in 24 years is a strong indication that there are systemic reasons why people may have larger BMI values, and therefore systemic change is likely necessary.


Mendelian randomization has several limitations, though we limited and tested for what we could. We think we reduced the chance of bias compared to straight observational research, but it’s impossible to know by how much, and how much remains, though we saw no evidence of big problems.

Using genetics also means we estimated the lifetime effect of BMI on healthcare costs and QALYs, assuming someone with a larger BMI at 50 or 60 years old, on average, always had a larger BMI. This means the translation to interventions is tricky – the estimates will be best for interventions that affect BMI over a long time-frame, preferably the whole life course. There’s likely little applicability to interventions that only reduce BMI for a few months, though it’s probably pretty good for systemic changes.

UK Biobank is also not completely representative of the UK population, the participants tend to be healthier and wealthier. Though that likely means we underestimated our effects, which is safer than overestimating them.

So What?

Well, Mendelian randomization is usually a good bet for analyses that can’t be conducted using RCTs, and where you’re worried about confounding/reverse causation in observational studies. So this approach could be especially useful where it is difficult, unethical or impossible to randomise participants to an exposure such as obesity or for prevalent behaviours with adverse health impacts such as smoking or alcohol use, or where RCT evidence is rare for an intervention. Results from these types of studies will hopefully be of benefit to both policy and the NHS.

As for the BMI estimates: I was surprised by a) how much BMI has increased over time in England, and b) how much additional cost this is likely to be for the NHS. Previous estimates of how much obesity affects healthcare costs may be subject to confounding and reverse causation because they all use observational data: for example, by estimating the cost of obesity-related health conditions, then estimating the proportion of those conditions resulting from obesity: does that, though the  minimum cost was assumed to be at 21 kg/m2.

That paper’s estimate of the healthcare costs of obesity was £5.1 billion in 2006-7 pounds, equating to about £7.4 billion in 2019 after inflation. Using the method above, I estimated just now in people aged just 40 to 69 years a healthcare cost of £5.7 billion for having BMI values higher than 21 kg/m2. If anything, my estimate seems more extreme than the paper’s, given the costs will be higher in older age groups (which I didn’t include), and we underestimated costs a little anyway. In fairness though, the BMI profile was probably lower in 2006 than in 2017, so costs would have been less.