Bryan Caplan  

Treatment: A Little Cost-Benefit Analysis is a Dangerous Thing

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Suppose you discover that a medical procedure genuinely reduces your risk of dying this year.  When you look further, however, you learn that your risk of dying only falls from 10-in-1000 to 9-in-1000.  Here are three reactions in order of sophistication.

1. Sheer innumeracy.  Many non-economists will say, "Eh, that's virtually the same.  Why bother?"

2. Elementary cost-benefit analysis.  Many economically literate people will rebuke to the innumerate with, "Dying is really bad.  Like, $10 million bad.  Multiply that $10M by 1-in-1000 - the change in the probability of dying - and you've got an expected benefit of $10,000.  As long as the treatment costs less than $10,000, do it!"

3. Sophisticated cost-benefit analysis.  Thoughtful analysts will realize this isn't just about quantity of life versus dollar cost.  Quality of life is also key.  Most medical treatments are unpleasant; many are downright ghastly.  Obvious issues include: How much pain does the treatment impose?  How much time does it take?  Will it prevent me from doing my favorite activities?  Limit my diet?  Once you monetize quality of life effects, they can readily swamp modest quantity of life effects.  Example: What would someone have to pay you to endure one day of extreme pain?  $1000?  Then even with free medical care,  the preceding treatment is a bad deal if it imposes 11 days of extreme pain.  And if the side effect lasts for the rest of your life, even a modest daily cost justifies inaction.

Observation: In most medical debates, elementary cost-benefit analysis contends against innumeracy.  Innumeracy ends up looking very stupid.  But this doesn't make the innumerate conclusion stupid.  Paying a large amount of money for a little extra quantity of life makes sense as long as quality of life stays the same.  Paying a large amount of money for a small increase in quantity of life paired with even a small decrease in quality of life is pretty foolish.  A little cost-benefit analysis is a dangerous thing.




COMMENTS (16 to date)
Jess Riedel writes:

One could say the same thing about a little classical economic reasoning. The unsophisticated view is that if people are getting paid too little we should just outlaw low pay. The elementary economic view is that this causes inefficiency and unemployment without benefiting many workers. The more sophisticated analysis often agrees with the unsophisticated one, citing various departures from ideal markets.

The fact that increasing sophistication of analysis often causes one to flip back and forth tells us that (1) we should be suspicious when our complicated tools allow us to return to what we wanted to believe anyways and (2) we should decrease our confidence in this process at all, since even at the highest levels of sophistication available we might expect yet higher levels to change our opinion.

konshtok writes:

actually I think the innumarates(sp?) are right with those specific odds. a change from 1/100 to 0.9/100 is just 10% gain(if that's the right way to put it. not really worth it unless the treatment is very cheap.

if otoh you used a change of 4/1000 to 3/1000 or 3/1000 to 2/1000 that would make the innumeracy much wronger

ThomasH writes:

Is it innumeracy or refusal to apply cost benefit analysis at all that leads the FDA to approve and doctors to prescribe expensive drugs, procedures, and treatments that have little impact on the quality adjusted life expectancy? I am forgiving of patients who are partially insulated from the financial expense who agree to roll the dice, but not those who should know better.

Jim writes:

How about number 4 - Consider the likelihood that a single study might have flaws and wait for corroborating evidence before changing established policies.

The history of medicine is filled with cases where a single study was used to justify a treatment plan or public policy. Years or decades later we learn that the study was flawed or incomplete and thousands of people were harmed needlessly.

People responsible for establishing public policy must pay heed to the reality that conducting a long-term medical study is incredibly difficult and the odds of making a mistake are greater than the odds of getting everything right.

The Original CC writes:

Jess wrote:

The more sophisticated analysis often agrees with the unsophisticated one, citing various departures from ideal markets.

And the even more sophisticated analysis would suggest that giving gov't officials the power to regulate this stuff would lead to a zillion principal-agent / public choice problems that have little to do with the problem you started with.

Daublin writes:

It's a good breakdown.

There's an even more innumerate argument that often shows up. Cancer is bad, so anything that can be done about it is a good thing.

I think you need a better name than "innumerate" for the first category. It's an accurate argument if the odds are really low. In large part, you don't even want to *think* about 1% events very much, or you will use your limited available mental time in life on things that aren't worth it.

ThomasH writes:

@Jess Riedel

The fact that increasing sophistication of analysis often causes one to flip back and forth tells us that (1) we should be suspicious when our complicated tools allow us to return to what we wanted to believe anyways

I agree. Part of my frustration with writers on this site is the frequency with which they refute the most naive arguments for the non-free-market policies they don't like (the minimum wage is their bête noire) without seeming to acknowledge that non-naive arguments exist.

Of course this applies to those making more sophisticated arguments in favor of specific government interventions in markets as well. Everyone needs to be suspicious of their own conclusions.

Ben writes:

I like Jess's point very much – and there's an obvious case in point here with Bryan's argument. Three levels of analysis are posited: "sheer innumeracy", "elementary cost-benefit analysis", and "sophisticated cost-benefit analysis". The "sophisticated" analysis discussed by Bryan includes quality-of-life effects – but only the negative ones associated with choosing the medical option are discussed. There are also negative quality-of-life effects to shunning the medical option, in addition to the possible quantity-of-life effect. Dying of a fatal disease (like the prostate cancer and breast cancer mentioned in Bryan two previous posts) is often a very unpleasant process, and can take quite a while to play out – it's not exactly a high-quality-of-life path. The probability of that happening, if medical tests/treatment are avoided, also needs to be factored in to the cost-benefit analysis. And if that is done, then as Jess points out, the evaluation might "flip" once again, back to the conclusion that the medical care is, in fact, worth it. So much for the "sophisticated" cost-benefit analysis. There is always a more "sophisticated" level of analysis; we haven't even started to delve into how the choice of treatment versus non-treatment might affect one's friends and family, how it might affect one's finances, and on and on. It's not a conclusion that I'm very happy with, as an advocate of rationalism, but I have found that all of the biggest decisions I have made in my life have, after weeks to months of careful deliberation, ended up feeling pretty much like random choices made on gut feel. There are just too many variables, too many unknowns, too many moving parts. (But I hope we can all agree that the "sheer innumeracy" option is dangerous, since it leads not only to personal decisions that might or might not be poor, but also to dangerous social movements like the anti-vaxxer movement.)

Njnnja writes:

I am sympathetic to the innumerate approach. If you really knew the exact theoretical probabilities then the more sophisticated approaches are better, but if you are getting your probabilities from the standard literature then you have to deal with all sorts of publication bias, "garden of forking paths," and other problems such that I wouldn't bet my life on a published 0.1% difference.

There is a lot of meta-research into how bad medical (and other) statistics are, even in peer reviewed published journals, that I think you have to be careful about making counterintuitive choices based on the results of a statistical study.

Mike W writes:

Paying a large amount of money for a small increase in quantity of life paired with even a small decrease in quality of life is pretty foolish.

Not if someone else is paying.

Mark Bahner writes:
And the even more sophisticated analysis would suggest that giving gov't officials the power to regulate this stuff would lead to a zillion principal-agent / public choice problems that have little to do with the problem you started with.

And a simple legal analysis would show that the Constitution doesn't give the *federal* government the power to set minimum wages.

Glenn writes:

A sophisticated economist drawing homogenous conclusions about the value of medical treatments based on a subject, undefined, and likely highly disparate assumption regarding general "quality of life" valuations, and how those valuations affect the cost-benefit analysis of medical treatment.

By simple observation of human behavior, we observe two basic facts: people value life tremendously; most people do not appear to place as much value on quality of life as they claim (every young men says they never want to grow old; most old people pursue continued existence over rapid demise).

Combined, the basic observed realities of pursuit of treatment versus costs of treatment do not appear prima facie unreasonable. Clearly, there are distortions created by the insurance markets. Even given those, however, it is quite a stretch to conclude that "paying a large amount of money for a small increase in quantity of life paired with even a small decrease in quality of life is pretty foolish".

This strikes me as surprisingly centralized, better-than-thee thinking for a sophisticated economist.

Phil writes:
And a simple legal analysis would show that the Constitution doesn't give the *federal* government the power to set minimum wages.

Just as simple CBAs are dangerous, so are simple legal analyses.

Andrew writes:

I would go through endless pain to have one more day with my children.

Scott Sumner writes:

Elsewhere I've argued that since humans can be replicated at low cost, we should err on the side of more pleasure and more risk, rather than the reverse. That would maximize the aggregate flow in utility. Of course you also need to account for the pain felt by your loved ones if you die.

Jesse writes:

Mark says:

And a simple legal analysis would show that the Constitution doesn't give the *federal* government the power to set minimum wages.
Thanks to ICC, the following template makes everyone a constitutional lawyer:
If X could even remotely and indirectly affect some person's ability to or decision whether to take some action that could (directly or indirectly) affect a financial transaction with a person or entity in another state, then X falls under the domain of federal law.

So minimum wage is almost explicitly a federal power.

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