Doximity Physician Pay Survey Raises More Questions Than It Answers

I recently got into it on Twitter with Leah Houston, M.D. regarding physician pay scales, and an alleged gender pay gap:

Serious question: what do you think of the looming physician-hours crisis? It seems to me this comes in (at least) two dimensions:

1) Insane levels of “paperwork”.
2) The feminization of the field. As of last year, a majority of incoming med school students were women. >

— Rob McMillin (@scareduck) April 11, 2019

Then, this:

Seriously? A “pay gap” that compares aggregate wages of male versus female doctors that fails to control for hours worked, continuity of employment, and specialization? For shame. This has been multiply debunked in the broad economy. No reason to think doctors are any different.

— Rob McMillin (@scareduck) April 11, 2019

(I was wrong about the control for hours, but see below.) The principal argument here comes from the 2019 Doximity physician pay report (PDF), but when you skip down to their methodology (p. 16), you see this:

Doximity’s study is drawn from self-reported compensation surveys completed by approximately 90,000 full-time, licensed U.S. physicians who practice at least 40 hours per week. Responses were mapped across metropolitan statistical areas, and the top 50 were ranked by the number of respondents in the data.

To control for differences in specialty, geography, and other provider-specific factors that might influence spending, we estimated a multivariate regression with fixed effects for provider specialty and MSA. We also controlled for how long each provider has practiced medicine and their self-reported average hours worked per week. This regression was estimated using a generalized linear model with a log link and gamma distribution. For the geographic and specialty rankings, we used the predicted values from this regression.

So, some questions:

1. Why does this not take into consideration interruptions in service years? Or, does "how long each provider has practiced medicine" refer to actual service time (opposite time since receiving certification)?
2. Was sex used for the multivariate analysis? If not, why not?
3. Why are self-reported hours not mentioned in the results? Considering the fracas of Relative Value Units, this would be valuable to know.
4. How many hours does an average male full-time physician work? How many for females?
5. When you say you queried "approximately 90,000 full-time, licensed U.S. physicians who practice at least 40 hours per week", is that physician-patient face time, or overall compensated time?

Overall, it does not seem to me that this looks closely enough at the data (and likely, does not ask the right questions) to arrive at any substantive conclusions as to whether there is a gender pay gap for physicians, even in the same specialty and market.