Introduction

A study was conducted by UCLA which sought among other things to determine the suicide rate of transgender men (biologically female gender behavior male) and transgender women (biologically male gender behavior female, Transwomen). 
Suicide attempts among trans men (46%) and trans women (42%) were slightly higher than the full sample (41%).  Cross-dressers assigned male at birth have the lowest reported prevalence of suicide attempts among gender identity groups (21%). \cite{jd889a}.
 \cite{shapiro2016}  then argues that transgender healthcare is not helping on the basis of this statistic.   Ben Shapiro and others argue that transgender people should be given psychological treatment that dis-affirms their transgender behavior.  They argue that trans women in particular should not be treated with hormones or addressed with gender concordant pronouns and instead should be addressed by biological sex \cite{shapiro2016}.   
It will be shown in this paper that there are important and common misconceptions regarding statistics, in arguments like  \cite{shapiro2016} .   It is not the intention of this paper to single out Shapiro since these misconceptions are common, but to educate so discussion can flow from actual facts not misinterpretations of facts. 

Statistics 

There are two big misconceptions of statistics in this common argument which is not only made by Shapiro.  One regards sampling the other regards how a statistic will play out over time.  The sampling issue is simple to understand.  If one were to sample a glass of water from the ocean and see that it contains no fish; then conclude that there are no fish anywhere in the ocean, we would all know that is false.  Larger sample size can help, but there will be margins of error that must be considered, as often stated in political polls. 
 Another common misconception comes from thinking of a population as frozen in time.   If one says that half of group X does thing Y then in any given reasonable period of time, say a year, half the people in group X will really actually do thing Y.  If the number does not mean just exactly that then it is meaningless.    Consider that a coin can either be heads or tails so a single flip has a 50 50 chance of being heads or tails.   Flip 1000 coins,  one time and maybe 45% will be heads and 55% will be tails.  Do that 1000 times and average the percent that are heads and the percent that are tails and those averages will be close to 50-50.   \cite{lewis2012}  When one says that a coin flip will on average give heads 49.9% of the time that means that 49.9% of coin flips will be heads. 

Transgender Health

Contrary to a popular belief transgender health care is not simply blind affirmations.   There is a process of real life experience as the target gender, psychological counseling, medical and aesthetic treatments. This all takes years and happens before or instead of any surgical intervention.
A transgender person is one who starts out life as one gender and one biological sex (not anatomically intersexed) who then switches to another gender role as often shown by names and personal pronouns, clothing, employment choices, and in some cases hormones and surgeries.  A transgender woman is, in US and UK culture, one who is biologically male who lives in the gender role typical of a female.  A transgender man in this same culture is one who is biologically female who lives in the gender role of a male.  This excludes minor gender non conformity, bigender, agender, or non-binary people.  This definition of transgender may also include other gender expressions if they meet the definition of a transgender man or woman in most material ways.  
 
According to the World Professional Association for Transgender Health Standards of Care  (WPATH SOC's) psychological treatment is a very important part of the solution and is the first step.  Those standards recommend intensive psychological counseling, a long period of real life living as a transgender person in society, followed at the very end by surgery IF requested and with the approval of two PhD'd psychologist and the patients MD. \cite{wpath2001}  There are those  in the transgender who feel strongly that it is offensive to treat trangender people with psychology \cite{tcj0c6}, and there are those who feel it is a good and necessary step \cite{kininmonth2016}.  
However, Ben Shapiro and others who hold his views argue that if we treat transwomen like men and address them as men and don't accommodate them at all it will make them act like men and make them better.  Assuming a modicum of good faith on their part they use   \cite{jd889a}  and a few other studies to try and justify their views as coming from a place of wanting to help trans people.  
The math does not support their point of view. 

Numerical  Analysis

The point was made by a comment under a Ben Shapiro article on the Daily Wire which pointed out that the 45% statistic implies that the transgender population would crash to almost zero in a short amount of time.  They author of the current paper decided to examine how this number would play out over time.
Starting with the general population times the prevalence of transgender people of 380 per 100,000 \cite{Meerwijk2017}.  Times the population of the United States of America as of March 2018 of  approximately, G,  330 million \cite{us}.
\(P_0=Gt_p\)
Subsequent years are computed from this formula.  The transgender population in year y is equal to the product of one minus the product of the fraction of suicide attempts and suicide successes with the size of the transgender population the previous year.  Then add the number of people born times the percentage of births that will be someone who eventually comes out as transgender 0.01%.  Computed simply by dividing the number of transgender people by 50 and not meant to claim anything about the etiologies(s) or cause(s) of transgenderism. 
\(P_y=P_{y-1}\left(1-S_AS_S\right)+Bt_b\)
A summary of the spreadsheet calculation is here in figure 1.  The excel file is attached.