I feel like our impressions might be slightly thrown off by the fact that the two numbers are percentages. It's a difference of 0.4 percentage points, but that works out to a 4.2% increase in mortality, which seems a bit more substantial.

The preceding sentence says "If a heart attack patient is a woman and her emergency physician is a man, he says, her risk of death suddenly rises by about 12 percent."

The 11.9 percent mentioned in your quote refers to probability of death for the population (i.e. a random person where the gender of the patient and the doctor is unknown).

The 12.4 percent refers to probability of death for a woman given a male doctor. If that is 12 percent higher, as the quote above says, then the probability of death for a woman given a female doctor is about 11.07%

So its an increase of 1.3 percentage points. The article kind of obfuscates that though.

I am willing to bet once you account for other things, such as geography, the effect goes away.

Look at the map at the end. It clearly shows women being higher percentage in areas that have better mortality rates for heart disease which are both heavily influenced by access (response time) to medical care and other socioeconomic factors

this is not perfect, but it shows that other factors are probably more likely to be the reason other than jumping to conclusions about which sex is a better doctor.

https://www.kff.org/other/state-indicator/medical-school-gra...

> jumping to conclusions about which sex is a better doctor.

I don't believe that many people are even suggesting this conclusion.

Unfortunately, outside of more rational circles, I believe a significant number of people will in fact draw some kind of inaccurate and superficial conclusion from this data.

The other interpretation of those stats is that women with male doctors are 4% more likely to die (0.5/11.9), which looks like a pretty meaningful difference. And the sample size is pretty huge especially by medical study standards at over 500k patients.

A small difference can still be statistically significant.

0.5% difference seems a little questionable to draw conclusions. Agreed.

Why? With a sufficient sample size you can demonstrate even low power effects. The magnitude of the difference does not prevent good scientific analysis at all.

The discussion behind the discussion here is that nobody ever reports confidence intervals... When you don't have them you just have to guess what they are based on what's usual for the field. We're having this entire discussion here but unless the error bars show up it all ought to conclude nothing.

> nobody ever reports confidence intervals

But the article[0], in PNAS, has confidence intervals.

[0] http://www.pnas.org/content/early/2018/07/31/1800097115

They don't report it in their abstract, which is all the majority of HN has access to. As a result any conclusions reached will be unfounded. (Unless someone gets the paper and tells us what it said, which is what the linked article's authors were supposed to be doing...)

Edit: The thing is that in the abstract no form of statistical indicator was reported. That plus its absence from the linked article means that unless someone here can get access to the paper our discussion is in vain.

As much as people like to talk about how P values are not useful and debate what values we should use, I don't think there's an especially compelling reason to choose confidence intervals over P values, or complain that one is appropriate and the other is not. They both measure the relationship between statistical likelihood and parameter values. P values fix the parameter values and measure the statistical likelihood, confidence intervals fix the statistical likelihood and measure the parameter values. So if you ask for confidence intervals and they give you a P-value, well you have a confidence interval it just won't be a nice round number like 95% or 99%.

It's kind of like complaining that you ordered 1 kg of water but were delivered 1 l, and insisting that everyone measure water by weight rather than volume. Don't read too much into that analogy, but the relationship between P values and confidence intervals is of a broadly similar nature.

Knowing there are over 500k patients in the sample, you can calculate the error bars.

Well, ideally you would know more than just the number of patients. The roughest estimate would be to compute the expected variance of a binomial distribution with N=120e3 and P=0.12, which gives a standard deviation of 0.00094, so a difference of 0.5% is well over 5 standard deviations out. Not quite good enough for particle physics, but you're damn right it's good enough for medicine.

Now you just have to look at group sizes, possible confounding factors, etc...

Also a p-value would be nice.

Click on the link to the actual study, you will see P values right there in the abstract.

0.5% is not irrelevant when you talk about deaths. Statistically if you consider the sample size and significance (P = 0.001) it actually looks very non questionable. https://jamanetwork.com/journals/jamainternalmedicine/fullar...