From the cross-sectional observational studies, the direction of the relationship is not clear.
It was to set the direction of observational cosmology for 40 years, ruling out the Steady State and the Big Crunch and culminating in the surprise discovery in 1998 that the expansion is not slowing down at all but speeding up.
The effectiveness of influenza vaccination in the elderly has long been a topic of debate, fueled by the absence of direct evidence from randomized trials on its effect on mortality and the methodological limitations of observational studies pointing this direction.
In the meantime, data from observational cohorts provide valuable direction.
They showed slight bias in the direction of the observational estimate, consistent with that predicted by weak instrument bias.
In addition, as noted above, this would be a stronger argument than the modified probabilities arising from the observational data, which have no direction of likelihood.
This may be due to the slight residual bias in the direction of the observational estimate in the subsample case and in the direction of the null in the 2-sample case.
Although causal inferences from these observational studies are limited, the direction and strength of association are all consistent and also might suggest that the duration of hypocapnia required to induce significant injury to a vulnerable brain is very short.
IV estimates using weak instruments are biased in the direction of the observational estimate, and the distribution of the IV estimate is poorly approximated by a normal distribution [Burgess and Thompson, 2011].
In the subsample setting, the bias towards the null and the bias in the direction of the observational association (which is usually in the same direction as the causal effect when this is present) can balance each other out, as demonstrated in the left-hand panel of Figure 3 when the ratio n X: n Y is 0.5.
If the same set of individuals is used for estimating both the gene-risk factor and gene-outcome associations, then bias of the causal effect estimate will be in the direction of the observational association between the risk factor and the outcome.
