LARS P. SYLL

Bradford Hill — comment trouver de la causalité dans des corrélations

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How to achieve ‘external validity’

There is a lot of discussion in the literature on beginning with experiments and then going on to check “external validity”. But to imagine that there is a scientific way to achieve external validity is, for the most part, a delusion … RCTs do not in themselves tell us anything about the traits of populations in other places and at other times. Hence, no matter how large the population from which we draw our random samples is, because it is impossible to draw samples from tomorrow’s population and all policies we craft today are for use tomorrow, there is no “scientific” way to go from RCTs to policy. En route from evidence and experience to policy, we have to rely on intuition, common sense and judgement. It is evidence coupled with intuition and judgement that gives us knowledge. To deny any role to intuition is to fall into total nihilism.

Kaushik Basu

Randomizations creating illusions of knowledge

The advantage of randomised experiments in describing populations creates an illusion of knowledge … This happens because of the propensity of scientific journals to value so-called causal findings and not to value findings where no (so-called) causality is found. In brief, it is arguable that we know less than we think we do.

To see this, suppose—as is indeed the case in reality—that thousands of researchers in thousands of places are conducting experiments to reveal some causal link. Let us in particular suppose that there are numerous researchers in numerous villages carrying out randomised experiments to see whether M causes P. Words being more transparent than symbols, let us assume they want to see whether medicine (M) improves the school participation (P) of school-going children. In each village, 10 randomly selected children are administered M and the school participation rates of those children and also children who were not given M are monitored. Suppose children without M go to school half the time and are out of school the other half. The question is: is there a systematic difference of behaviour among children given M?

I shall now deliberately construct an underlying model whereby there will be no causal link between M and P. Suppose Nature does the following. For each child, whether or not the child has had M, Nature tosses a coin. If it comes out tails the child does not go to school and if it comes out heads, the child goes to school regularly.

Consider a village and an RCT researcher in the village. What is the probability, p, that she will find that all 10 children given M will go to school regularly? The answer is clearly

p = (1/2)^10

because we have to get heads for each of the 10 tosses for the 10 children.

Now consider n researchers in n villages. What is the probability that in none of these villages will a researcher find that all the 10 children given M go to school regularly? Clearly, the answer is (1–p)^n.

Hence, if w(n) is used to denote the probability that among the n villages where the experiment is done, there is at least one village where all 10 tosses come out heads, we have:

w(n) = 1 – (1-p)^n.

It is easy to check the following are true:

w(100) = 0.0931,
w(1000) = 0.6236,
w(10 000) = 0.9999.

Therein lies the catch … If there are 1000 experimenters in 1000 villages doing this, the probability that there will exist one village where it will be found that all 10 children administered M will participate regularly in school is 0.6236. That is, it is more likely that such a village will exist than not. If the experiment is done in 10 000 villages, the probability of there being one village where M always leads to P is a virtual certainty (0.9999).

This is, of course, a specific example. But that this problem will invariably arise follows from the fact that

lim(n => infinity)w(n) = 1 – (1 -p)^n = 1.

Given that those who find such a compelling link between M and P will be able to publish their paper and others will not, we will get the impression that a true causal link has been found, though in this case (since we know the underlying process) we know that that is not the case. With 10 000 experiments, it is close to certainty that someone will find a firm link between M and P. Hence, the finding of such a link shows nothing but the laws of probability being intact. Yet, thanks to the propensity of journals to publish the presence rather than the absence of “causal” links, we get an illusion of knowledge and discovery where there are none.

Kaushik Basu

Why the idea of causation cannot be a purely statistical one

If contributions made by statisticians to the understanding of causation are to be taken over with advantage in any specific field of inquiry, then what is crucial is that the right relationship should exist between statistical and subject-matter concerns …

Where the ultimate aim of research is not prediction per se but rather causal explanation, an idea of causation that is expressed in terms of predictive power — as, for example, ‘Granger’ causation — is likely to be found wanting. Causal explanations cannot be arrived at through statistical methodology alone: a subject-matter input is also required in the form of background knowledge and, crucially, theory …

Likewise, the idea of causation as consequential manipulation is apt to research that can be undertaken primarily through experimental methods and, especially to ‘practical science’ where the central concern is indeed with ‘the consequences of performing particular acts’. The development of this idea in the context of medical and agricultural research is as understandable as the development of that of causation as robust dependence within applied econometrics. However, the extension of the manipulative approach into sociology would not appear promising, other than in rather special circumstances … The more fundamental difficulty is that, under the — highly anthropocentric — principle of ‘no causation without manipulation’, the recognition that can be given to the action of individuals as having causal force is in fact peculiarly limited.

John H. Goldthorpe

Causality in social sciences — and economics — can never solely be a question of statistical inference. Statistics and data often serve to suggest causal accounts, but causality entails more than predictability, and to really in depth explain social phenomena require theory. Analysis of variation — the foundation of all econometrics — can never in itself reveal how these variations are brought about. First, when we are able to tie actions, processes or structures to the statistical relations detected, can we say that we are getting at relevant explanations of causation.

Most facts have many different, possible, alternative explanations, but we want to find the best of all contrastive (since all real explanation takes place relative to a set of alternatives) explanations. So which is the best explanation? Many scientists, influenced by statistical reasoning, think that the likeliest explanation is the best explanation. But the likelihood of x is not in itself a strong argument for thinking it explains y. I would rather argue that what makes one explanation better than another are things like aiming for and finding powerful, deep, causal, features and mechanisms that we have warranted and justified reasons to believe in. Statistical — especially the variety based on a Bayesian epistemology — reasoning generally has no room for these kinds of explanatory considerations. The only thing that matters is the probabilistic relation between evidence and hypothesis. That is also one of the main reasons I find abduction — inference to the best explanation — a better description and account of what constitute actual scientific reasoning and inferences.

In the social sciences … regression is used to discover relationships or to disentangle cause and effect. However, investigators have only vague ideas as to the relevant variables and their causal order; functional forms are chosen on the basis of convenience or familiarity; serious problems of measurement are often encountered.

Regression may offer useful ways of summarizing the data and making predictions. Investigators may be able to use summaries and predictions to draw substantive conclusions. However, I see no cases in which regression equations, let alone the more complex methods, have succeeded as engines for discovering causal relationships.

David Freedman

Some statisticians and data scientists think that algorithmic formalisms somehow give them access to causality. That is, however, simply not true. Assuming ‘convenient’ things like faithfulness or stability is not to give proofs. It’s to assume what has to be proven. Deductive-axiomatic methods used in statistics do no produce evidence for causal inferences. The real causality we are searching for is the one existing in the real world around us. If there is no warranted connection between axiomatically derived theorems and the real-world, well, then we haven’t really obtained the causation we are looking for.