by What does randomisation guarantee? Nothing! Does not randomization somehow or other guarantee (or perhaps, much more plausibly, provide the nearest thing that we can have to a guarantee) that any possible links to … outcome, aside from the link to treatment …, are broken? Although he does not explicitly make this claim, and although there are issues about how well it sits with his own technical programme, this seems to me the only way in which Pearl could, in the end, ground his argument for randomizing. Notice, first, however, that even if the claim works then it would provide a justification, on the basis of his account of cause, only for randomizing after we have deliberately matched for known possible confounders … Once it is accepted that for any
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What does randomisation guarantee? Nothing!
Does not randomization somehow or other guarantee (or perhaps, much more plausibly, provide the nearest thing that we can have to a guarantee) that any possible links to … outcome, aside from the link to treatment …, are broken?
Although he does not explicitly make this claim, and although there are issues about how well it sits with his own technical programme, this seems to me the only way in which Pearl could, in the end, ground his argument for randomizing. Notice, first, however, that even if the claim works then it would provide a justification, on the basis of his account of cause, only for randomizing after we have deliberately matched for known possible confounders … Once it is accepted that for any real randomized allocation known factors might be unbalanced — and more sensible defenders of randomization do accept this (though curiously, as we saw earlier, they recommend rerandomizing until the known factors are balanced rather than deliberately balancing them!) — then it seems difficult to deny that a properly matched experimental and control group is better, so far as preventing known confounders from producing a misleading outcome, than leaving it to the happenstance of the tosses …
The random allocation may ‘sever the link’ with this unknown factor or it may not (since we are talking about an unknown factor, then, by definition, we will not and cannot know which). Pearl’s claim that Fisher’s method ‘guarantees’ that the link with the possible confounders is broken is then, in practical terms, pure bluster.
The point of making a randomized experiment is often said to be that it ‘ensures’ that any correlation between a supposed cause and effect indicates a causal relation. This is believed to hold since randomization (allegedly) ensures that a supposed causal variable does not correlate with other variables that may influence the effect.
The problem with that (rather simplistic) view on randomization is that the claims made are both exaggerated and strictly seen false:
• Even if you manage to do the assignment to treatment and control groups ideally random, the sample selection certainly is — except in extremely rare cases — not random. Even if we make a proper randomized assignment, if we apply the results to a biased sample, there is always the risk that the experimental findings will not apply. What works ‘there,’ does not work ‘here.’ Randomization hence does not ‘guarantee ‘ or ‘ensure’ making the right causal claim. Although randomization may help us rule out certain possible causal claims, randomization per se does not guarantee anything!
• Even if both sampling and assignment are made in an ideal random way, performing standard randomized experiments only give you averages. The problem here is that although we may get an estimate of the ‘true’ average causal effect, this may ‘mask’ important heterogeneous effects of a causal nature. Although we get the right answer of the average causal effect being 0, those who are ‘treated’ may have causal effects equal to -100 and those ‘not treated’ may have causal effects equal to 100. Contemplating being treated or not, most people would probably be interested in knowing about this underlying heterogeneity and would not consider the average effect particularly enlightening.
• There is almost always a trade-off between bias and precision. In real-world settings, a little bias often does not overtrump greater precision. And — most importantly — in case we have a population with sizeable heterogeneity, the average treatment effect of the sample may differ substantially from the average treatment effect in the population. If so, the value of any extrapolating inferences made from trial samples to other populations is highly questionable.
• Since most real-world experiments and trials build on performing a single randomization, what would happen if you kept on randomizing forever, does not help you to ‘ensure’ or ‘guarantee’ that you do not make false causal conclusions in the one particular randomized experiment you actually do perform. It is indeed difficult to see why thinking about what you know you will never do, would make you happy about what you actually do.
The problem many ‘randomistas’ end up with when underestimating heterogeneity and interaction is not only an external validity problem when trying to ‘export’ regression results to different times or different target populations. It is also often an internal problem to the millions of regression estimates that economists produce every year.
‘Ideally controlled experiments’ tell us with certainty what causes what effects — but only given the right ‘closures.’ Making appropriate extrapolations from (ideal, accidental, natural, or quasi) experiments to different settings, populations, or target systems, is not easy. And since trials usually are not repeated, unbiasedness and balance on average over repeated trials say nothing about anyone trial. ‘It works there’ is no evidence for ‘it will work here.’ Causes deduced in an experimental setting still have to show that they come with an export-warrant to the target population/system. The causal background assumptions made have to be justified, and without licenses to export, the value of ‘rigorous’ and ‘precise’ methods — and ‘on-average-knowledge’ — is despairingly small.
RCTs have very little reach beyond giving descriptions of what has happened in the past. From the perspective of the future and for policy purposes they are as a rule of limited value since they cannot tell us what background factors were held constant when the trial intervention was being made.
RCTs usually do not provide evidence that the results are exportable to other target systems. RCTs cannot be taken for granted to give generalisable results. That something works somewhere for someone is no warranty for us to believe it to work for us here or even that it works generally.
Randomisation may often — in the right contexts — help us to draw causal conclusions. But it certainly is not necessary to secure scientific validity or establish causality. Randomisation guarantees nothing. Just as observational studies may be subject to different biases, so are randomised studies and trials.