Page 233 - Special Topic Session (STS) - Volume 4

STS582 Mariza de A.

Figure 2: DAG for the effect of circulating levels of C-reactive protein on insulin resistance
determined using CRP as an instrumental variable. XRP, c-Reactive protein genetic variant, the
IV; E: CRP, circulating c-reactive protein levels, the modifiable exposure of interest; Y: HOMA-R,
homeostasis model assessment of insulin resistance, the outcome of interest; M: (unmeasured
or measured with error) confounders.

The three assumptions are sufficient for the simple case of statistical
testing, i.e., using genotype as an IV to test the null hypothesis that the
modifiable exposure X is not associated with outcome Y. To avoid incorrect
inference due to type II errors, the usual aim of MR studies is to provide an
estimate of effect with reliable confidence intervals (7). Additional assumptions
are needed to estimate a causal effect with IV analysis, i.e., one should
assumed the following:
4. All of the associations depicted in Figure 1 are linear and unaffected
by statistical interactions. (8)
This assumption is problematic for binary outcomes since the effect
estimates are represented as an odds ratio or risk ratio. In the case the one
needs to estimate causal effects using IV methods using linear associations
and a continuous outcome Y, the IV estimate of the regression coefficient for
̂
̂
̂
the effect of exposure (E) on Y is ̂ = / , where is the coefficient

for the regression of outcome (Y) on the IV (Z), and is the coefficient for
̂

the regression of exposure (X) on the IV.
The IV estimator provides an estimate of the causal effect of
̂

exposure on outcome, even in the presence of mediators of the
exposure=outcome association. Several methods of IV estimation are
available where more than one IV and the outcome Y is a numerical variable
and associations between variables are linear. The most common used
estimator is the two-stage least squares (2SLS) where can be derived by first
perform the least-squares regression of the exposure X on the IV(s) Z; then
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