Unbiased Analysis of Today's Healthcare Issues

The Intuition behind Bayes Theorem

Written By: Jason Shafrin - Apr• 03•16

Bayes Theorem is well-known in law of probability. Mathematically, you could write it as:
P(A|B)=P(A and B)/Pr(B) = P(B|A)*P(A)/P(B).

An interesting interview in Scientific American with Decision theorist Eliezer Yudkowsky explains Bayes Theorem more intuitively.

I might answer that Bayes’s Theorem is a kind of Second Law of Thermodynamics for cognition. If you obtain a well-calibrated posterior belief that some proposition is 99% probable, whether that proposition is milk being available at the supermarket or global warming being anthropogenic, then you must have processed some combination of sufficiently good priors and sufficiently strong evidence. That’s not a normative demand, it’s a law. In the same way that a car can’t run without dissipating entropy, you simply don’t get an accurate map of the world without a process that has Bayesian structure buried somewhere inside it, even if the process doesn’t explicitly represent probabilities or likelihood ratios. You had strong-enough evidence and a good-enough prior or you wouldn’t have gotten there.

On a personal level, I think the main inspiration Bayes has to offer us is just the fact that there are rules, that there are iron laws that govern whether a mode of thinking works to map reality. Mormons are told that they’ll know the truth of the Book of Mormon through feeling a burning sensation in their hearts. Let’s conservatively set the prior probability of the Book of Mormon at one to a billion (against). We then ask about the likelihood that, assuming the Book of Mormon is false, someone would feel a burning sensation in their heart after being told to expect one. If you understand Bayes’s Rule you can see at once that the improbability of the evidence is not commensurate with the improbability of the hypothesis it’s trying to lift.

To give some other examples. Let’s say that you are a kid and you are waiting for your mom to pick you up. Let’s say that your mom has picked you up from school every day for the past 2 years between 0 and 5 minutes after the school day has ended. If your mom is 1 minute late, what is the probability your mom is not going to pick you up? The answer is probably pretty low, given that your prior your expected probability (your prior) of your mom picking you up is so strong.

On the other hand, let’s say your mom is very irresponsible and over the past 2 years will pick you up between 0 and 5 minutes after the school day has ended half the time, and the other half of the time she forgets to show up and you have to walk home. In this case, a 1 minute delay in your mom’s arrival would be much more convincing evidence that your mom will not show up because your expected probability (your prior) was much lower.

Thus, with the same current data available (i.e., your mom is 1 minute late), Bayes Theorem tells you that you should not be worried if your mom has a great track record, but a bit more worried if over the past 2 years your mom has been a bit of a deadbeat.

Friday Links

Written By: Jason Shafrin - Mar• 31•16

Is Finland ending welfare?

Written By: Jason Shafrin - Mar• 29•16

Maybe yes.  According to City Journal:

This year, the Finnish government hopes to begin granting every adult citizen a monthly allowance of €800 (roughly $900). Whether rich or poor, each citizen will be free to use the money as he or she sees fit. The idea is that people are responsible for their actions. If someone decides to spend their €800 on vodka, that is their decision, and has nothing to do with the government. In return for the UBI, however, the public accepts the elimination of most welfare services. Currently, the Finnish government offers a variety of income-based assistance programs for everything from housing to children’s education to property insulation. Axing these programs should free up enough public resources to finance the UBI. The bureaucracy that currently governs welfare payments will disappear. There will no longer be any need to ask for government help, nor to fill out forms or wait for the competent authorities to examine each dossier to determine eligibility…

Remarkably, every major Finnish political party has signed on. The Left is cheered by the socialistic idea of government-assistance-for-all. The Right looks forward to the unprecedented drop in bureaucratic control over citizens, an unheard-of extension of freedom of choice, and an unconditional restitution of part of citizens’ taxes.

Could this form of a negative income tax be implementing in the U.S? Certainly. Should it? Clearly giving away money increases the risk of fraud and corruption, but giving individuals the choice of what to do with their money, reducing the cost of bureaucracy, while ensuring a minimum standard of living is clearly an attractive option.

On a side note, GiveDirectly uses a similar, cash-based approach to charity in the developing world.

How does cost sharing affect drug utilization?

Written By: Jason Shafrin - Mar• 28•16

Any economist knows that if you raise the price of a good, demand goes down.  Thus, one should not be surprised to find numerous studies that show that increased cost sharing decreases drug utilization.  But how does drug utilzation decrease?  Is it along the extensive margin (i.e., the decision to initiate the drug) or along the intensive margin (i.e., the decision to continue using the drug once it is initiated)?

Doshi et al. (2016) conduct a systematic literature review  examining the effect of cost sharing on specialty drug use finds the following:

Findings varied by disease, but generally indicated stronger effects for noninitiation or abandonment of a prescription at the pharmacy and somewhat smaller effects for refill behavior and drug spending once patients initiated therapy. Studies have not examined specialty tier cost sharing seen under Medicare Part D or health insurance exchanges, nor effects on medical utilization, spending, or health outcomes. 

The winner appears to be the extensive margin, although the results do vary by disease.

Is evidence-based policymaking in crisis?

Written By: Jason Shafrin - Mar• 27•16

A thought-provoking article from The Long+Short, make some interesting point on this topic:

…the problem seems to be caused by the use of the treatment-response model, in a context where the choice of how to analyse the data is made after collecting it. As Gelman details, if this is what you do, then it is very easy to put your finger on the scales – even without any bad faith and ignoring institutional pressure to produce statistically significant results, it is very hard for a researcher to avoid concluding that the ‘best’ way to analyse a collection of facts is the way which seems to give them a logical structure.

This is not what happens in pharmaceutical research. In drug tests, all details of methodology have to be filed and registered before the trial begins. It is a convention which has been adopted over the years precisely to avoid this kind of bias. Now here’s the bit that you’re not going to like. How expensive and time-consuming is it to get a new drug to market? How many initial ideas have to be generated in order to get a single robust result that can be confidently expected to perform better than a placebo without unacceptable side effects? This analogy is taking us in a pretty scary direction for a philosophy of policy-making that was meant to provide a quick and easy way to find out what works. So the real ‘reproducibility crisis’ for evidence-based policy making would be: if you’re serious about basing policy on evidence, how much are you prepared to spend on research, and how long are you prepared to wait for the answers?

Producing evidence can be quick and easy; producing high-quality, rigorous evidence, however is often time-consuming and expensive. The alternative–making policy based on no evidence–however, is far worse.

Friday Links

Written By: Jason Shafrin - Mar• 24•16

HWR is up

Written By: Jason Shafrin - Mar• 24•16

Charles Gaba makes his debut as host with a freshly posted Health Wonk Review: ACA Anniversary Edition! at ACASignups.net. Check it out.

Temptation Goods

Written By: Jason Shafrin - Mar• 23•16

Your annual salary clearly affects how much you spend on different goods and services.  However, does the frequency with which you are paid affect the composition of goods you purchase?  For instance, do individuals paid on a weekly basis differ than those paid on a monthly basis? If people are perfectly rational–ignoring any small differences due to interest rates or discount rates–one would believe that individuals paid weekly would behave the same as those paid monthly.

A paper by White and Basu (2016), however, finds that payment frequency does affect the composition of goods purchased.

We exploit a change in the payment schedule of Peru’s conditional cash transfer program to identify the impact of benefit receipt frequency on the purchase of temptation goods…Using a difference-in-differences estimation approach, we find that larger, less frequent payments increased the expenditure share of alcohol by 55–80% and sweets by 10–40%, although the absolute magnitudes of these effects are small. Our study suggests that less frequent benefits scheduling may lead cash recipients to make certain types of temptation purchases.

If you win the lottery, although financial advisors would recommend that you take the lump sum, regular payments may be better to reduce the incentive to spend money on temptation goods; then again, if you win the lottery, the majority of spending may be temptation goods regardless.

Precision acquires ACT Oncology

Written By: Jason Shafrin - Mar• 22•16

My employer, the Precision Medicine Group, recently made a new acquisition.  Details are in this press release and the excerpt below.

Precision for Medicine, part of the Precision Medicine Group, announced today that it has executed a binding agreement to acquire ACT Oncology, the leading contract research organization (CRO) specializing exclusively in the field of oncology. ACT Oncology provides drug development services focused on the design and execution of clinical trials on behalf of innovative life sciences companies and not-for-profit patient organizations.

ACT Oncology is an industry leader in oncology clinical trials with unparalleled experience conducting studies across all tumor types and hematology indications. ACT Oncology’s capabilities complement and significantly expand Precision’s strengths in biomarker-driven, precision drug development. Precision is an innovator in biomarker research with depth and expertise in genomics, bio-informatics, assay development, specialty lab services, global specimen logistics, and companion diagnostics. Together, Precision and ACT Oncology create the first comprehensive, fully integrated precision oncology clinical development solution, combining the highest standards in clinical trial management with the most advanced biomarker capabilities and processes.

Effect of publicly reported surgical quality measures and outcomes

Written By: Jason Shafrin - Mar• 21•16

There has been a shift towards making quality data publicly available for patients to examine when choosing physicians.  A commentary by Burns et al. (2016) finds that there is mixed evidence regarding whether making surgery-related mortality data publicly available improves patient outcomes (see table below).

Article Time Period Country Participants Key Findings
Hannan 1994 1989-1992 US NY State cardiac surgeons performing CABG Reduction in risk-adjusted mortality across all groups, with the groups that showed the highest initial mortality manifesting the most improvement
Bridgewater 2007 1997-2005 UK All patients undergoing CABG in northwest England Significant decline in observed to expected mortality ratio,
from 2.4 to 1.8, after UK mortality data published
Khan 2007 2000-2004 UK All patients undergoing CABG or aortic valuve or mitral valve surguries in a single hospital in England No change in overall mortality rate following publication of mortality rate data
Li 2010 2003-2006 US All CABG patients from California’s Outcomes Reporting Program Decline in observed mortality (2.22% from 2.90%)

However, the authors also note that even if reporting quality outcomes may improve quality in aggregate, identifying very high and very low quality surgeons from publicly reported data is very difficult. First, most surgeons perform a small number of each type of surgical procedures. Second, risk adjustment is typically insufficient and could penalize surgeons from taking more complex cases. Third, other outcomes–such as quality of life and patient satisfaction, typically are not included in the measure, but surgeons may have more control over the surgical experience than mortality if risk adjustment is imperfect.

I am completely in favor of making more data publicly available. The quality of the data-whether or not it is publicly released–must always be carefully scrutinized when attempting to answer any research question.