Why no serious researchers conduct "per protocol" analyses

All observational data must be adjusted in order to correct biases. But our science teems with irresponsible statistical adjustments - throwing a bunch of variables into a regression model, and declaring that all known biases have been satisfactorily resolved is all too common.

In the medical literature, publishing one's adjustment model is rarely done. I don't trust any adjusted models unless the researcher discloses the equations, the coefficients and goodness of fit statistics. Even better, the researcher should compare the adjusted to unadjusted results, note how the adjustments affected the outcome, and explain why these adjustments make sense.

Handwaving about the structure of the adjustment model, referencing other papers that supposedly use similar methods, etc. suggest that the researchers lack confidence in their methods.

In this blog post, I demonstrate how to evaluate statistical adjustments, using the recently released, highly controversial results from the colonoscopy clinical trial. (See my related writeup here.) It took a lot of work to put this together, because the disclosure of details in the paper is scarce (this is the norm rather than the exception, unfortunately.)

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The colonoscopy trial was the first randomized clinical trial (RCT) conducted to measure the effect of colonoscopy screening on risks of diagnoses or deaths from colon cancer. The trial enrolled two groups of participants: those invited to screening, and the "usual care" group which means no screening (as is the practice in Poland, Norway and Sweden, where the trial took place).

For this post, I focus only on risk of colon cancer diagnoses (i.e. cases). That's because the disclosure on mortality outcomes is even worse, making it impossible to judge the adjustment procedure. The trial specifies an intent-to-screen analysis (more generally known as intent-to-treat, ITT), The ITT analysis shows that 0.93% of the invited group were diagnosed during the 10-year follow-up window, compared to 1.13% of the usual-care group. This result is described as a 18% reduction in risk of colon cancer, even though the difference in diagnosis rate is only 0.2%, that is to say, out of 1,000 people invited to colonoscopy, only two fewer cases will be detected relative to usual care.

As discussed in the previous blog, the medical profession was none too happy with this outcome because doctors, esp. American ones, have convinced themselves that colonoscopy could reduce both cases and deaths by 70% or more. Neither did the authors of the paper disclosing the trial results - in the section of the paper in which they discussed the findings, they did not mention the primary endpoint, but only talked about an "adjusted per-protocol" analysis, which moved the reported result from 18% reduction in risk to 31%. Still far from the 70% previously believed, but deemed more palatable.

The media then mis-reported this analysis as "per-protocol" analysis, dropping the all-important word "adjusted". By the end of this post, you'll understand why I say this.

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Intent-to-treat vs per-protocol is a long-running debate but any serious researcher goes with the former, which is exactly what the designers of the colonoscopy trial did. Let's look at this debate using a marketing example.

Let's say Target is running a Black Friday promotion in which online customers get an extra 30% discount if they type the code SAVE30 when checking out. In order to measure the effectiveness of this promotion, Target data scientists design an A/B test in which shoppers are randomly divided into the exposed group and the non-exposed group upon visiting Target's website. They intend to analyze the results of this experiment by looking at metrics such as proportion of visitors who made a purchase, and average purchase amount, comparing the two groups. This analysis is known as an intent-to-treat (ITT) analysis.

Ouch! The ITT analysis showed that the additional sales generated by exposure to the SAVE30 promotion failed to cover the cost of giving out these extra discounts. Inevitably, there will be at least one business manager who complains that the wrong analysis was done. They argue that we should not include people who did not notice the promotion. Being exposed to the promotion just means Target shows notifications while the customers browse around but some fraction of customers did not pay attention. So, what do they think is the right analysis? We should only analyze those people for whom we know for sure they noticed the promotion - in other words, we only analyze those people who entered the promotion code on checkout (or other variants, such as only those who clicked on a promotion banner). This style of analysis is "per protocol".

Why would all serious researchers shy away from per-protocol analyses? In this example, everyone in the exposed group who subsequently entered the promotion code on checkout is someone who is surely, or almost surely, making a purchase. In the non-exposed group, there is no such thing as entering the promotion code, thus we effectively narrowed the exposed group to almost sure shoppers against the unexposed group that contains the average online shopper. Which group will show better metrics? Will the better results on the exposed group be due to the promotion or inherent differences in the group composition?

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Back to the colonoscopy trial. In the per-protocol analysis, the data analyst threw out roughly half of the invited-to-screen group because they did not "comply". The reasoning is that they could not have benefited from the screening (read: SAVE30) and thus, they drag down the efficacy. But the "compliers" typically have different characteristics than the "non-compliers", and so per-protocol destroys the randomization aspect of the "randomized" controlled trial. In other words, the complier subset is different from the usual-care group not just in being screened but in unknowable dimensions. We've turned the RCT into an observational study.

People who advocate PP analysis say not to worry - they will throw a bunch of demographic variables into a regression model, and all biases will disappear. I find this quite fascinating. If such adjustment strategies indeed can cure all biases, then why would the community embrace RCTs as the gold standard? It would appear that observational data blended in a mixer known as regression modeling is equally as good as a randomized experiment!

In fact, the colonoscopy controversy clearly shows the opposite. Prior observational studies have consistently shown extremely positive results of 70% or so, and the first time a research team conducts an RCT, the outcome is below 20%. If anything, this proves that carefully analyzed observational studies cannot replace the gold-standard RCT.

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Even if all biases are cured, and we are able to believe the PP analysis, the real-world results are guaranteed to disappoint.

Let's go back to the Target example. Let's say the PP analysis showed that customers who used the SAVE30 promotion were 80% more likely to complete the transaction than the customers who were not shown the promotion. So now, the head of marketing tells everyone if all shoppers are shown the promotion, then the experiment proves that they should see an 80% jump in number of transactions.

Of course, reality bites. The problem is that the 80% incremental sales apply only to the subset who used the promotion code. If only 10% of those exposed used the code during the A/B test, then only about 10% would contribute an 80% jump in sales. The other 90% are exposed but would not be using the code.

If half the trial population elect not to take the colonoscopy screening during the trial, it is likely the case that half the population would make this decision if colonoscopy was rolled out to all. The 30% reduction in colon cancer risk would still only apply to the subset choosing to be screened, and would not make a dent on those who chose to forego it.

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It looks like I have to defer showing you my analysis till the next post. The plan is to compare the ITT analysis and the "adjusted PP analysis", pointing out how the adjustments affected the outcomes. Come back tomorrow.

(By the way, all Covid-19 vaccine trials were per-protocol analyses as well, even though such analyses are problematic.)

 

 

 

Comments

[Antonio]

"The 30% reduction in colon cancer risk" Maybe did you confuse with the marketing example?
I'm wondering how to solve this problem.
Order the law enforcement to take people randomized to experimental group to hospital and force them to have the colonoscopy?
Randomize people getting the colonoscopy and submitting half of them to a "placebo" colonoscopy?
(obviously, not two feasible options)

[Kaiser]

Antonio: The 30% reduction is the "adjusted per-protocol analysis"; the intent-to-screen which respects randomization shows 18%.
There is nothing to solve - if the experiment is used to find a practical solution. In practice, a proportion of people will ignore guidance to do a colonoscopy so the current setup mimics that. (Analogously, even something non-invasive like "wear a mask" is shunned by a large proportion of Americans.)
Put differently, an intervention may fail because it is not effective but it can also fail despite being effective if adoption rate is low.
Here's a design that measures only the effect on people who choose to do a colonosopy: invite everybody, then randomize those who accept the invite, so that half of those people are held out of the intervention. The problem of course is that this measures the effect on those who choose to do it but the overall effect will be muted by the subset who refuses the treatment.

[Ken]

Inviting everyone, and then only randomising the ones who accept the invite is perfectly reasonable. All our population now is people who want to be screened and now we are doing a randomised control on them. The main worry with doing this type of trial is that the people who are randomised to usual care may decide to have a colonoscopy because they are now aware of them.

The reason the observational studies showed an effect would be that people who had colonoscopies are inherently different from ones that don't. They are probably more careful about their health, for example diet, and may be more likely to see a doctor if minor symptoms occur. It is similar to the problem with Covid, where people who wear masks are more likely to adopt other measures to reduce the risk of Covid, like spending the last couple of years at home.

[Kaiser]

Ken: Good point. In the current study, because in those countries, colonoscopy is not the usual care, they were sure (and they verified) that the usual-care group didn't get colonoscopies on their own. In the randomize on accepting invitation setup, there is higher risk that someone violates the treatment protocol; but that is a risk with every RCT, including the Covid-19 vaccine trials. In fact, as I have pointed out here, the fact that close to 100% of all placebo participants in those vaccine trials almost immediately took up the vaccine when they were offered one actually proved the point that those trials had incredibly biased populations.