Hi Ilya,
I am giving this talk. If you want, I can send you the slides when they are ready. However, since you were the teaching assistant for the course where I learned this material, I very much doubt I will cover anything you aren’t already very familiar with…
Does anyone have any opinions on this paper? [http://arxiv.org/pdf/1207.4913.pdf]
It is a proof of Bell’s Inequality using counterfactual language. The idea is to explore links between counterfactual causal reasoning and quantum mechanics. Since these are both central topics on Less Wrong, I’m guessing there are people on this website who might be interested.
I don’t have any background in Quantum Mechanics, so I cannot evaluate the paper myself, but I know two of the authors and have very high regard for their intelligence.
Last week, I gave a presentation at the Boston meetup, about using causal graphs to understand bias in the medical literature. Some of you requested the slides, so I have uploaded them at http://scholar.harvard.edu/files/huitfeldt/files/using_causal_graphs_to_understand_bias_in_the_medical_literature.pptx
Note that this is intended as a “Causality for non-majors” type presentation. If you need a higher level of precision, and are able the follow the maths, you would be much better off reading Pearl’s book.
(Edited to change file location)
I understand your skepticism about associational studies. Clearly, the likelihood ratio from seeing a positive result in such a study should be tiny in most cases. But just out of curiosity, if you automatically discount all cohort studies, where do you expect evidence on the causal effects of lifestyle interventions to come from?
Nobody questions that doing a randomized controlled trial would provide much stronger evidence, but a RCT with a lifestyle intervention as the exposure and mortality as the outcome would take decades to complete, would require a very large sample size, and would have several potential threats to its validity, including low adherence to treatment assignment and loss to followup. Furthermore, you would need a separate arm for every possible variation of the intervention, and you would need to do one of these trials for every possible lifestyle intervention
In the absence of an RCT, the best we can do is a properly designed and properly analyzed cohort study.
As far as I know, instrumental variables are the only other option that is seriously considered, but there are very few perfect instruments, and in most realistic epidemiologic settings, using a weak instrument is probably worse than doing a cohort study. If you want to go into a further discussion on this, as a starting point, see the article “Instruments for Causal Inference: An Epidemiologist’s Dream?” by Miguel Hernan and Jamie Robins, and focus on the section on how minor violations of unverifiable assumptions can blow up the bias.
I am not suggesting that cohort studies are the answer, but rather that we only have four options:
Either (1) Conduct a lot of very expensive randomized controlled trials on every possible lifestyle intervention and wait a couple of decades for the results, or (2) do associational studies, or (3) Postulate that we understand physiology and biochemistry well enough that we can learn about the effects of lifestyle intervention simply by reasoning, or (4) accept that we are unable to learn about the effects on lifestyle interventions on longevity
Personally, I am leaning towards option 4, but I am willing to accept properly conducted cohort studies as weak evidence, at least to give us some idea about what randomized trials would be most promising.
What really confuses me about your comment, is that you doubt the rest of his post simply because he cited a cohort study, when it was obvious from just reading the title of the post that the only evidence he could possibly have on the effect of lifestyle interventions, would necessarily come from associational studies.
Your workaround is correct, and not as unwieldy as it may appear at first glance. A lot of people have been using causal diagrams with this structure very successfully in situations where the data generating mechanism has loops. As a starting point, see the literature on inverse probability weighting and marginal structural models.
Processes with feedback loops are, in fact, a primary motivation for using causal directed acyclic graphs. If there are no feedback loops, reasoning about causality is relatively simple even without graphs; whereas if there are loops, even very smart people will get it wrong unless they are able to analyze the situation in terms of the graphical concept of ‘collider stratification bias’.
It is certainly true that you can get any results you want if you pick control variables based on how it changes the effect estimates. This is a major problem with almost all observational research, and greatly reduces its reliability. People have suggested getting around it by requiring all investigators to publish their protocols before data collection begins, so that they have to specify at that time exactly what variables they will control for. This would be a good start, but it does not appear to be on the horizon.
The only way to obtain a valid estimate of a causal effect, is to run a randomized controlled trial. However, this is not always feasible, and in situations where we really need information on causal effects but are unable to perform the experiment, the only thing we can do is to assume that nature ran a randomized controlled trial for us. This might have been a complicated trial where “nature” used one loaded dice in men with high GPA, another loaded dice in men with low GPA, a third dice in women with high GPA and a fourth dice in women with low GPA etc.
If the data came from such a trial, it will be possible to recover an estimate of the causal effect. In a simple situation, a linear regression model that controls for sex and GPA may be sufficient; but in most realistic settings, you will need models that are able to account for the fact that “exposure” varies with time. The important thing to note is that the validity of the estimate is only as valid as your belief in the untestable assumption that the data came from a randomized trial run by nature.
What Pearl’s causal framework gives you, is a very powerful language for reasoning about whether it is reasonable to interpret observational data as if it came from a randomized controlled trial run by nature. Pearl’s students will be able to tell you whether the framework has been applied correctly, but this is not sufficient to assess the trustworthiness of the result: For that, you need someone with subject matter expertise, ie, someone who is willing to make untestable claims about whether the map (the DAG model) matches the territory (the data generating mechanism)
My main point is that you shouldn’t just automatically discount observational studies, but instead use DAG models to reason carefully about what level of confidence you assign to the investigators’ implicit claim that the data came from a natural experiment where exposure was assigned by loaded dice that differed between the groups defined by the control variables.
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Edited to add that if you believe the main problem with observational studies is that investigators choose their set of control variables in order to get the results they want, one solution to this is to use Don Rubin’s propensity score matching method, which specifically avoids this problem. See this paper. The only problem with the propensity score method, is that it does not generalize to situations where exposure varies with time; in fact, students who are trained in the Rubin Causal Model (which competes with Pearl’s graphical model) often become blind to a range of biases that arise because exposure varies with time.
I don’t disagree with anything you are saying: There is nothing in the propensity score estimation method itself that makes the results less prone to bias, compared to other methods
I should have been more specific, my point was rather that the specific implementation of propensity score matching which Rubin recommends in the paper I linked to, allows the investigator to blind themselves to the outcome while assessing whether they have been able to create balanced groups. It is possible that you can do something similar with other estimation methods, but I haven’t heard anyone talk much about it, and it is not immediately obvious to me how you would go about it
If you use the propensity score matching method, you begin by estimating the propensity score, then you match on the propensity score to create exposed and unexposed groups within levels of the propensity score. After you create those groups, there is a step where you can look at the matched groups without the outcome data, and assess whether you have achieved balance on the baseline covariates. If I understand Rubin’s students correctly, they see this as a major advantage of the estimation method.
You can obviously blind yourself to the outcome using any estimation method, but I am not sure if there is a step in the process where you look at the data without the outcome to evaluate how confident you are in your work.
Good question! “Untestable assumption” can actually mean two different things:
In this context, you are correct to point out that I am talking about assumptions that are not testable by the data we are analyzing. I would be able to falsify my unconfoundedness assumption if I run an experiment where I first observe what value the treatment variable would take naturally in all individuals, then intervene so that everyone are treated, and look at whether the distribution of the outcome differs between the group who naturally would have had treatment, and the group who naturally would not have had treatment
In other contexts, there are other types of untestable assumptions, which are unfalsifiable even in principle. These relate to independences between counterfactual variables from different “worlds”. Basically, they assume that certain columns in your ideal dataset are independent of each other, when it is impossible even in theory to observe those two columns in the whole population at the same time.
If you refuse to make assumptions of the second type, you will still be able to estimate the effect of any intervention that is identifiable in Pearl’s causal framework NPSEM, but you will not be able to analyze mediation or causal pathways. This is the difference between Pearl’s model NPSEM and Robins’ model FFRCISTG. The refusal to make unfalsifiable assumptions about independences between cross-world counterfactuals is also the primary motivation behind the “Single World Intervention Graph” paper by Robins and Richardson, which Ilya linked to in another comment in this thread.
This approach might work sometimes, but I think it is problematic in most cases for the following reason:
Health care spending can only affect health through medical interventions (unless it is possible to extend someone’s life by signalling that you care enough to spend money on health care).
If the study is designed to estimate the effect of some medical intervention, that intervention will be in the regression model. If you want to interpret the coefficient for health care spending causally, you have a major problem in that the primary causal pathway has been blocked by conditioning on whether the patient got the intervention. In such situations, the coefficient of health care spending would be expected to be zero even if it has a causal effect through the intervention.
How is it surprising that an individual’s ethical code sometimes prevents them from maximizing their utility function? If this was never the case, ethics would be redundant, because there would never be a need for ethical constraints on choice.
Humans evolved to have utility functions that value the taste of meat. This fact does not prevent us from reaching the ethical conclusion that killing an animal for consumption is wrong. The best way to maximize the utility function under this constraint, may be to find a close substitute for meat.
I was vegetarian for twelve years for ethical reasons: both to avoid killing sentient beings, and because I was concerned about the environmental externalities associated with meat production. My utility function definitely always valued the taste of meat very strongly.
Maybe I incorrectly extrapolated too much from myself in my model of other vegetarians, but I always assumed that most of them had similar reasons. I think it is likely that a lot of them lie to themselves about not liking meat, in order to make it easier to live within their ethical constraints. There is a widespread belief among vegetarians that, after several years of not eating meat, your body adapts such that eating meat may make you physically ill. I don’t know whether this is true, it certainly never happened to me, and I suspect it may be a meme that is retained because it helps keep people in the fold.
Smoking is not “accused” of being strongly correlated with negative outcomes. It is strongly correlated with negative outcomes, as a simple empirical fact. This is a statement about the joint distribution of the observed variables “smoking” and “negative outcomes”, and it has nothing to do with causal inference. I cannot even imagine a scenario where the statement “Smoking is strongly correlated with lung cancer” is false, short of a vast conspiracy among scientists and doctors
A slightly more interesting question is whether the correlation between smoking and cancer is due to causation. It is theoretically possible that an unmeasured confounder is responsible for the observed correlation. In fact, R.A. Fisher believed such a confounder was probably at work . One of the first uses of sensitivity analysis was to show how unrealistic Fisher’s claim was. A sensitivity analysis is essentially a thought experiment that lets you play around with how “strong” a confounder has to be, in order to account for the observed correlation if the causal null hypothesis were true. See http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2755131/.
In this case, I think any reasonable investigator who looks at the data and does some basic reasoning about possible confounders, will come away with a very strong posterior in favor of smoking causing lung cancer. However, the relationship between smoking and certain other negative outcomes is in some cases much more questionable, and it would not surprise me if publication bias accounts for many of the negative outcomes smoking has been connected to
This is the opposite conclusion of the first citation I provided.
Sorry, can you be more specific? Where does anybody claim that smoking is not strongly correlated with life expectancy?
And the second “in house” LW link asserts that in terms of decision making about smoking in light of whether or not it’s linked to cancer is about a 50⁄50 proposition.
The second “in house” link is a very simple thought experiment to explain the concept of confounding. It is meant as an example where evidential decision theory fails. In this situation, causal decision theory gives the right answer, it is certainly not a 50-50 proposition. Moreover, the correct answer within the thought experiment is that smoking does not cause cancer. This is because they postulated the existence of a deterministic confounder. This has no implications for whether or not such a confounder exists in the real world.
I ’m asking why the correlations are thought of as causes by reports on the relationship.
Because the confounders, ie the “smoking lesions”, would have to be unrealistically strong to fully explain the observed correlation between smoking and lung cancer. This is the part where I showed you the sensitivity analysis.
Furthermore, ccording to Hume, causal inferences are THEMSELVES observed by constant conjunction, implying we have know sure way of knowing what the relationship between causes and correlations is.
Of course we don’t have a “sure” way of knowing about causal relationships. But if you adopt “certainty” as your epistemic standard, you wouldn’t even be able to tell whether parachutes save lives in people who are falling from airplanes.
The Japanese smoke more (if not the most) than most cultures yet are also one of the most healthy cultures.
This is called an “ecologic” argument, and it is considered very weak. Note that your sample size is essentially 2, as the units you are making inferences about are countries, not individuals.
A further problem is that “negative outcomes” are normatively tied to cultural standards.
Now you’re just trolling… We’re talking about life expectancy, lung cancer, heart attacks etc here.
As someone who gave up a career in medicine in order get a doctoral degree in Causal Inference, I am half-upvoting this, because I really want it to be true :-)
I originally trained as a medical doctor, but came to the conclusion that what I was doing had almost no value on utilitarian grounds. Sure, once in a while you feel good about helping a patient, but really, if you weren’t working that day, somebody else would have done the same thing. I decided I would rather have my one-in-a-thousand chance of coming up with an original idea with real impact, instead of spending the rest of my career as a doctor, where my utilitarian impact would almost certainly be negligible.
I came to the Harvard School of Public Health intent on going into academic Global Health, but after I took an introductory course on applied causal inference with some basic DAG theory, that all changed. Partly, this was because I recognized the importance of Causal DAGs from reading Less Wrong. I ended up staying at HSPH to get a doctoral degree with some of the leading researchers in the field; this even allowed me to take a course that Ilya was a Teaching Assistant for (I ended up being a TA for the same course the following year)
Currently, my career plan is to get a faculty job at some school of public health, where I see my mission as taking part in a “reboot” of epidemiology and comparative effectiveness research, to cleanse it of the cargo cult science and magical thinking that is currently all too common, and train investigators in rigorous causal reasoning. I honestly believe that this could have a major utilitarian impact, because in the absence of randomized trials, proper causal reasoning about observational data is the only way we can learn how to make better clinical decisions that optimize patient outcomes,
( Hopefully, if I play my cards right, this career choice will also have the added benefit of giving me sufficient status in the medical community to get a real discussion started on some of the most horrific things that doctors do to patients)
This is true, but I think a key difference is the time aspect. I am not really a causal inference researcher, I am more of a dragon slayer. The particular dragon I am engaging in battle is called cargo cult science . When fighting dragons, time is always essential; history will ask us how we allowed this dragon to terrorize us for so long. ( There are obviously more fiercesome creatures out there, but I don’t really have any insight on how to defeat them, so starting with cargo cult science could at least be useful as target practice )
With this particular dragon, I believe the proper strategy is to train all scientists in causal reasoning. This is analogous to telling engineers that they can build more solid bridges if they learn calculus. The earlier you get this message out, the fewer bridges collapse. And importantly, the engineers themselves don’t have to worry about the underlying mathematical theory and proofs, but it is really important that there are real mathematicians who work on that. This is why the work of people like Ilya, Pearl, Robins, Glymour, Richardson, etc is so important.
Why should a myth about Zeus change anyone’s belief by “orders of magnitude”?
Because the probability of there being a myth about Zeus, given that Zeus exists, is orders of magnitude higher than the probability of there being a myth about Zeus, given that he does not exist?
Neither. Obviously, the average excellence of “doctors, masters and bachelors” of the most renowned universities is higher than the average excellence of people who are self-taught. Nobody suggests that being self-taught correlates positively with excellence.
The quotation is still undoubtedly true, because there are many more individuals who are self-taught than individuals who have these credentials. It is also plausible that the variance in excellence among the self-taught is much higher. Therefore, it is trivial to identify self-taught individuals who are more knowledgeable than most highly credentialed university graduates.
In fact, as a doctoral student in applied causal inference at a fairly renowned university, I can identify several self-taught Less Wrong community members who understand causality theory better than I do.
I agree with this comment, but I want to point out that there may be a problem with equating the natural language concept “strength of evidence” with the likelihood ratio.
You can compare two probabilities on either an additive or multiplicative scale. When applying a likelihood ratio of 1000, your prior changes by a multiplicative factor of 1000 (this actually applies to odds rather than probabilities, but for low probability events, the two approximate each other). However, on an additive scale, a change from 10^{-18} to 10^{-15} is really just a change of less than 10^{-15} , which is negligible.
The multiplicative scale is great for several reasons: The likelihood ratio is suggested by Bayes’ theorem, it is easy to reason with, it does not depend on the priors, several likelihood ratios can easily be applied sequentially, and it is suitable for comparing the strength of different pieces of evidence for the same hypothesis.
The additive scale does not have those nice properties, but it may still correspond more closely to the natural language concept of “strength of evidence”
My name is Anders. I have been lurking for a long time, and have attended meetups in Boston for the last three years. I recently began commenting more frequently. This is a new account; after discussing Ben’s name change with him at the meetup today, I decided to switch to something closer to my real name, sacrificing my 20 karma points in the process.
I am 31 years old. I am a doctoral candidate in Epidemiology at the Harvard School of Public Health, where I work on some new implementations of causal models for comparative effectiveness research, particularly for screening interventions. I am originally from Norway. I attended medical school in Ireland, and worked for 18 months as a junior doctor in western Norway before moving to Boston.
On Less Wrong, I am particularly interested in the material on causality and decision theory. I am also interested in epistemic rationality and cognitive bias in general, and in the extent to which our actions are explained by signaling. In terms of mainstream philosophy, I see myself as formalist, falsificationist and prioritarian consequentialist. The “formalist” part is due to spending a year as an undergraduate student in mathematics; 12 years later, the only thing I retain from that year is a persistent belief that mainstream philosophy is underrating the importance of David Hilbert.