Some Methodological Considerations in Mendelian Randomization Studies Eric J. Tchetgen Tchetgen Depts of Epidemiology and Biostatistics

What is Mendelian Randomization Use genotypes as instrumental variables (IVs) to estimate the causal health effects of phenotypes influenced by those genotypes MR methodology relies on strong assumptions Consider a recent study by Kivimaki et al AJE 2011 Causal DAG of Valid IV FTOBMIMD Unmeasured trait ? INTUITION behind IV estimand:“FTO->MD”=“FTO->BMI”x”BMI->MD”One can solve for ”BMI->MD”

More formal interpretation Suppose all variables are binary “Average effect in the compliers “ Suppose all variables are binary and the following monotonicity assumption holds: “FTO -> BMI” same direction for all individuals. Then the IV estimand of ”BMI->MD” =“FTO->MD” / “FTO->BMI” =The causal effect of BMI on MD in the subpopulation of individuals for whom “FTO -> BMI” is not zero “ Average effect in the exposed” If the causal effect ”BMI->MD” is the same for individuals with a high BMI regardless of their FTO status, Then the IV estimand of ”BMI->MD” =“FTO->MD” / “FTO->BMI” =The causal effect of BMI on MD among individuals with high BMI

More formal interpretation Suppose all variables are binary “Population Average effect ” If in subpopulation with a given BMI, the causal effect ”BMI->MD” is independent of their FTO status, Then the IV estimand of ”BMI->MD” =“FTO->MD” / “FTO->BMI” =The average causal effect of BMI on MD in the entire population

Is the IV the causal gene? Suppose all variables are binary “Average effect in the compliers “ Provided monoticity of causal gene and relation of FTO with (BMI,MD) only through KIAA1005 ”BMI->MD” =“FTO->MD” / “FTO->BMI” =The causal effect of BMI on MD amongst the subpopulation of individuals for whom “KIAA1005 -> BMI” is not zero “Average effect in the compliers and population Average effect “ equal to IV estimand as long as respective homogeneity assumption hold for the causal gene FTO BMIMD Unmeasured trait ? Gene in LD KIAA1005

Most GWAS are case-control studies Over sampling of cases introduces selection bias which induces violation of the IV assumption This connects to recent interest into methods for repurposing case-control samples Simple solution is to reweight sample to break the link between Diabetes and selection into case control sampling Matched density sampling, i.e. within risk sets, more complicated weighting scheme but can be done (Walter et al, 2012, in progress) FTOBMIMD Unmeasured trait ? DIABETES Case-control sample

Timing may be everything BMI is a lifecourse exposure, do we measure BMI at a time where it matters for MD. This is generally more severe than classical measurement error If we use either BMI(1) or BMI(2) alone, FTO is no longer be a valid IV, so –called exclusion restriction may not hold. Sometimes, people use the average of BMI(1) and BMI(2), this implicitly assumes that the effects are of the same magnitude Can use Robins Structural Nested models for average effect (Glymour et al, 2012, in progress) FTOBMI(1)MD Unmeasured trait ? BMI(2) ?

Survival analysis should be more powerful than binary regression Modeling time to MD should generally be more powerful than cumulative risk analysis Robins’ Structural nested AFT model an option, but can be difficult to implement with administrative censoring Structural Cox regression can be used to obtain a “compliers “ hazards ratio. (Tchetgen Tchetgen, 2012, in progress) Alternatively Structural nested additive hazards model can be used. (Tchetgen Tchetgen and Glymour, 2012, in progress) FTOBMIMD Unmeasured trait ?

Credible Mendelian Randomization The strong assumptions needed to identify the causal effects of a phenotype on a disease via MR will often not hold exactly These assumptions are not routinely systematically evaluated in MR applications, although such evaluation could add to the credibility of MR Approaches to Falsify an IV (Glymour, Tchetgen Tchetgen, Robins, AJE,2012): – Leverage prior causal assumption such as the known direction of confounding – Identify modifying subgroups – Instrumental inequality tests – Overidentification tests

MR Collaborators Maria Glymour Liming Liang Laura Kubzansky, Stefan Walter James Robins Shun-Chiao Chang Eric Rimm Marilyn Cornelis, Karestan Koenen Ichiro Kawachi Stijn Vansteelandt