see this: https://raceandconflicts.home.blog/2021/03/30/vaush-response-2/ (see header "Sex Reassignment Surgery").

The first study (Cornell) you link is not a meta-analysis

Meta-analysis give effect sizes like Cohen’s d, Pearson’s r or something else, but the Cornell article did not do this. Instead, it’s just a systematic review of the literature, not a meta-analysis. That’s just a nitpick, but these studies still suffer from the same issues as the actual meta-analysis up above.

Of the 52 studies finding a positive effect, one of them have to be excluded due its nature. Padula, Heru, and Campbell (2015) was simply an attempt to model the mathematical cost/ benefit of gender transitioning, not anything that actually provides original research on the effects of SRS. This leaves us with 51 studies, which is still a lot, but the rest still have problems. 5 of the largest studies cited by Cornell suffer from problems. Bailey, Ellis, and Mcneil (2014) was a narrative analysis that utilized an online survey and that was promoted by LGBT groups and support organizations. The method of getting there sample was not random, and is guilty of non-response bias. Due to the nature of their self-selected survey, it offers nothing to make a generalized claim since it is not a random sample. St. Amand et al. (2011) got their sample from “online groups and discussion forums that were dedicated to FTM [female-to-male] members…” Again, not a random sample, suffers from non-response bias, and thus can not be used to make a generalized claim. Ironically enough, Vaush criticized a study for using a internet survey and for going on sites that were biased for their sample, and thus would lead to skewed results.

The second study you link ("Hormonal therapy and sex reassignment: a systematic review and meta-analysis of quality of life and psychosocial outcomes" Murad et al. (2010)) has flaws due how bad the underlying studies are

Murad et al. (2010) looked at 28 studies with a sample size of 1833 participants and found that SRS had a positive effect. Even without knowing how many studies were looked at and the sample size, Vaush’s summary of it lets readers know that SRS does work — but he leaves out how badly done these studies were.

None of the studies were RCT and only 3 of them had a control group, but one of those 3 studies had a control group in which the control group did not fit the criteria for those with Gender Identity Disorder. The exposure to hormone therapy in some of the studies looked at were self-reported, and “the details of treatments were in general not reported.” 23 of the studies reported SRS as a whole (hormone therapy + SRS), so it was hard to separate the effects of hormones and SRS. 21 of the studies assessed outcomes via a structured interview or clinical exam, 7 studies used a questionnaire, and 1 used an internet survey.

Looking at Table 1 of the study shows that a large portion of these studies had high dropout percentages. Many of these studies had small sample sizes, and the authors do not tell us the type of sampling used, so it’s hard to know if the samples were representative or biased. Regardless, the authors note that “In most of the included studies, at least two thirds of individuals with GID reported improvement in some aspects of their quality of life such as more stable relationships, better adjustment, satisfaction with sex reassignment, and overall happiness and contentness.” Furthermore, even the authors admit these studies were poorly done: