Use of Mendelian Randomization for the Estimation of Marginal Health Care Costs of Obesity

Obesity is one of the major public health problems in Germany and worldwide. Many observational studies have shown that people who are overweight or obese have higher health care costs than normal weight individuals. However, the association between body mass index (BMI) and health care costs is probably highly biased/confounded by unmeasured characteristics. To address confounding, a previous study used genotype information of genes highly related to BMI as an instrument. An instrument is a variable external to the model of interest that is robustly associated with the risk factor, but is otherwise not associated with the outcome variable, other than through its effect on the risk factor.

Because genotypes are assigned randomly when passed from parents to offspring, the population genotype distribution should be unrelated to the confounders, making it ideal instruments. One challenge in using genetic instrumental variables is that many genetic variants are only modestly associated with the risk factor of interest, which limits the power and precision of a study. Weak instruments are invariably sensitive to very small unobserved biases, limiting the evidence of such studies, i.e. the probability that a study will reject a false null hypothesis when a specified magnitude of unobserved bias in the instrument is allowed for. Furthermore, even if a set of multiple instruments is valid, (i.e. they are not associated with confounding factors, have no direct effect on the outcome, and are at least weakly associated with the exposure) the two-stage least squares estimator can still be biased towards the conventional regression estimate. In consequence, strong instruments are an desirable aspect for strong evidence.

Analyses of this study are based on data of the population-based German KORA F4 (n=3080, year 2007) study. BMI is calculated using objectively measured height and weight and health care costs are calculated by multiplying self reported helth care utilization with respective unit costs. Mean age is 56 years and mean BMI of the sample is 27.6. We use 155 preselected single nucleotid polymorphisms (SNPs) of N=2922 individuals as instruments for BMI. Those SNPs have been found to be significantly associated with BMI in large genomewide association studies. To strengthen the instruments, we built a matched study (N=1477) in which very similar individuals were paired with very different BMIs, resulting in a strong instrument (weak instruments test p-value = 0.2 before matching, weak instruments test p-value = 0.002 after matching). The effect of BMI on health care costs was 7.32, on average, per one point increase in BMI in the unmatched weak instruments setting, but increased to 21.84, on average, in the matched study with strong instruments.

Our results support the conclusion that a smaller study with a strong instrument is preferable to a larger study with a weak instrument because of shorter confidence intervals and less sensitivity to unmeasured biases in the smaller but stronger matched comparison.