Calculates modified form of Cochran's Q statistic measuring heterogeneity in causal effect estimates obtained using each genetic variant. Observed heterogeneity is indicative of a violation of the exclusion restriction assumption in MR (validity), which can result in biased effect estimates.
The function takes a formatted dataframe as an input, obtained using the function format_mvmr(). Additionally, covariance matrices
for estimated effects of individual genetic variants on each exposure can also be provided. These can be estimated using external data by
applying the snpcov_mvmr() or phenocov_mvmr() functions, are input manually. The function returns a dataframe including the conditional
Q-statistic for instrument validity, and a corresponding P-value.
Usage
pleiotropy_mvmr(r_input, gencov = 0, estimator = c("ivw", "qmin"))Arguments
- r_input
A formatted data frame using the
format_mvmr()function or an object of classMRMVInputfromMendelianRandomization::mr_mvinput()- gencov
Calculating heterogeneity statistics requires the covariance between the effect of the genetic variants on each exposure to be known. This can either be estimated from individual level data, be assumed to be zero, or fixed at zero using non-overlapping samples of each exposure GWAS. A value of
0is used by default.- estimator
The causal effect estimates at which the Q-statistic is evaluated:
"ivw"(the default) for the inverse variance weighted estimates, or"qmin"for the estimates that minimise the Q-statistic.
Details
By default the Q-statistic is evaluated at the inverse variance weighted (IVW) estimates of the causal effects and compared with a
chi-squared distribution on L - K degrees of freedom, where L is the number of genetic variants and K the number of exposures.
This is the Q-statistic for heterogeneity in MVMR described in Sanderson, Spiller and Bowden (2021). It is not robust to weak
instruments and will be inflated when the instruments are conditionally weak, so instrument strength should first be assessed
with strength_mvmr(); if the instruments are weak the results should not be interpreted.
Setting estimator = "qmin" instead evaluates the Q-statistic at the causal effect estimates that minimise it, which are
robust to weak instruments, as discussed in Section 3.2 of Sanderson, Spiller and Bowden (2021).
References
Sanderson, E., et al., An examination of multivariable Mendelian randomization in the single-sample and two-sample summary data settings. International Journal of Epidemiology, 2019, 48, 3, 713–727. doi:10.1093/ije/dyy262
Sanderson, E., Spiller, W., and Bowden, J., Testing and correcting for weak and pleiotropic instruments in two-sample multivariable Mendelian randomization. Statistics in Medicine, 2021, 40, 25, 5434–5452. doi:10.1002/sim.9133