/**** Calculates Logit of probability of cancer ****/

 -- Cancer is the treatment.  It is also response/dependent variable in analysis.  
 -- Death is the outcome and this routine does not examine it.

DROP TABLE #Prob
SELECT SUM(CAST(Cancer as Float))/Cast(Count(distinct [column 0]) as float) AS Prob  
, count(distinct [column 0]) as n 
,[I305 1] ,[I309 81] ,[I311 ] ,[IE849 7] ,[I150 9] ,[I276 1] ,[I276 8]  ,[I530 81] 
,[I263 9] ,[I276 51] ,[IV15 82] ,[I511 9] ,[I401 9]  ,[I787 20] ,[I564 00] ,[I272 4] ,[I280 9] ,[I285 9] ,[I496 ] ,[I458 9]  ,[I486 ] ,[IV58 61] ,[I197 7] ,[I578 9] ,[I584 9] ,[IV66 7] ,[I244 9]  ,[I414 01] ,[I599 0] ,[I414 00] ,[I585 9] ,[I600 00] ,[I428 0]  
,[I427 31] ,[I403 90]    
INTO #PROB    
FROM [Cancer].[dbo].[StomachCancer]   
GROUP BY [I305 1] ,[I309 81] ,[I311 ] ,[IE849 7] ,[I150 9] ,[I276 1] ,[I276 8]  ,[I530 81] ,[I263 9] ,[I276 51] ,[IV15 82] ,[I511 9] ,[I401 9]  ,[I787 20] ,[I564 00] ,[I272 4] ,[I280 9] ,[I285 9] ,[I496 ] ,[I458 9]  ,[I486 ] ,[IV58 61] ,[I197 7] ,[I578 9] ,[I584 9] ,[IV66 7] ,[I244 9]  ,[I414 01] ,[I599 0] ,[I414 00] ,[I585 9] ,[I600 00] ,[I428 0]  ,[I427 31] ,[I403 90]  
HAVING Count(distinct [column 0])>9
 
-- Next we calculate the logit
-- Logit cannot be calculated for probability 0 or 1.  
-- We want the approximation of logit to show how confident we are about these numbers
-- We want the estimates to be in order of confidence, de facto in order of sample size

SELECT 
	CASE 
		 WHEN Prob=0 THEN log(1/(cast(n as FLOAT)+1.) )
		 WHEN Prob=1 Then Log(Cast(n as FLOAT)+1.)
		 ELSE log(Prob/(1-prob)) 
		 END AS Logit
	 , * -- gets the remaining values  
FROM #Prob