Aims: We will investigate the optimal methods for combining multiple genetic variants to estimate the causal effects of risk factors on outcomes. This is a methodological investigation, however as an example, we will investigate the associations of height and weight and IQ, behavioural problems (hyperactivity, emotional problems, conduct problems and peer problems) and academic achievement across childhood and adolescence.

Mendelian randomization uses genetic variants as instrumental variables for modifiable risk factors.5 It has been widely applied to investigate the effects of risk factors for disease such as weight, blood pressure, cholesterol, and behavioural risk factors such as alcohol and tobacco consumption on health and socio-economic outcomes.1-4 To be valid instruments, variants must be associated with risk factors of interest, and have no direct effect on the outcome of interest. The stronger the association between the instrument and the exposure, the more statistical power and precision a Mendelian randomization analysis can achieve. One challenge in using genetic instrumental variables is that many variants only have modest effects on the risk factor of interest.6 The use of multiple variants as instruments, thereby explaining more of the variability in the risk factor,7 could therefore increase the precision of the results, improving the likelihood of being able to draw inferences from any given dataset.

Researchers have used various approaches to construct instruments, including allele scores, weighted allele scores, using each genetic variant as an independent instrument, and using generalized method of moment estimators to efficiently weight each of the variants. However, we currently do know the optimal approach for aggregating this information for Mendelian randomization analysis. Thus in this project we will investigate the optimal methods for combining multiple variants to maximise statistical power.

We will examine the effects of anthropometry on cognitive and behavioural outcomes as a motivating example. However our major objective is to develop methodologies rather than investigating any single hypotheses.

Hypotheses: What is the most efficient method for combining multiple variants into a Mendelian randomization analysis?

Exposures: Height, weight and adiposity at age 8-13, genome-wide data.

Outcomes: Academic achievement, IQ score aged 8, measures at age 13 of hyperactivity, emotional problems, conduct problems, and peer problems (from SDQ).

Potential confounding variables or descriptive data: Age, birth weight, number of younger and older siblings, income, parents' education, social class and employment status. Index of multiple deprivation of families' neighbourhood. Mothers' characteristics during pregnancy: age, locus of control, EPDS, CCEI, and teaching score.