How do I obtain the standard deviation of statistics calculated using SQL aggregate functions such as count().

[SasUser324]

Hello all,    

I can’t seem to wrap my mind around this and was wondering if anyone could help clarify things.  How do I calculate the standard deviation of calculations of SQL count data that was collapsed across observations and then how do I carry that through the calculations I’m executing in SQL?  This is hard to explain so I made an illustrative example and tried to describe clearly the calculation I’m doing and the standard deviation I’m looking for.  I have a hunch I’m overlooking some fundamental concept here. 

Let’s assume I have a cohort of 20 people (8 exposed, 12 unexposed) and I am interested in determining the proportion of people that had each of three procedures, stratified by exposure status.  I can only see claims for 13 people here, 7 had no procedure and so don’t appear in this data table. My eventual goal is to generate the usual Table 1 comparing exposed to unexposed and including a standardized difference (of procedure rates).  Unfortunately, I can't accomplish the first step of generating standard deviation estimates. 

My data is in the following format:

TABLE 1. DATA_SET_A

Procedure	Exposed	Subject
1	1	Person 1
1	1	Person 2
1	1	Person 3
1	1	Person 4
1	0	Person 5
1	0	Person 6
1	0	Person 7
1	0	Person 8
2	1	Person 1
2	1	Person 3
2	0	Person 6
2	0	Person 8
2	1	Person 9
2	1	Person 10
2	0	Person 11
2	1	Person 12
2	0	Person 13
3	0	Person 5
3	0	Person 8
3	1	Person 10
3	0	Person 11
3	0	Person 13

1. First, I use PROC SQL to pull population counts (stratified by exposure) from my source population, which contains records for all people [STEP 1].
2. Next, I use PROC SQL to collapse DATA_SET_A so each procedure is listed, for each exposure status, with the count [STEP 2].
3. Finally, I use LEFT JOIN to link procedure/exposure numerators with their appropriate denominators and perform the proportion calculation [STEP 3].

Please refer to the SAS code I've pasted at the bottom of this post.

This code generates Table 2 (see below).  How do obtain the standard deviations for these proportion estimates (see ? in the table below)? I don’t know how to obtain the standard deviation of a count that I’ve collapsed in SQL.  I tried using aggregate functions such as std(count(*)) AS StdDev, but SAS didn’t like that.  Do I have to obtain the standard deviation during the count step and then carry it forward or can I somehow obtain it during my proportion step?  I know how to calculate the standard deviation if I transform my dataset such that each procedure is a variable instead of having a procedure variable that aligns with the counts.  The problem is that my real problem involves hundreds of procedures so I can't switch them all over manually.

TABLE 2. DATA_SET_B

Procedure	Exposed	Count	Denominator	Proportion		Std. Dev.
1	1	4	8	4/8	0.50	?
1	0	4	12	4/12	0.33	?
2	1	5	8	5/8	0.63	?
2	0	4	12	4/12	0.33	?
3	1	1	8	1/8	0.13	?
3	0	4	12	4/12	0.33	?

Thanks for your help. Please be blunt if I’m missing something obvious. 

CODE BELOW:

*CALCULATING THE PROPORTION OF PATIENTS THAT WERE CODED FOR EACH PROCEDURE AT LEAST ONCE IN THE FOLLOW-UP PERIOD*;

STEP 1

      *COUNTS FOR DENOMENATORS*;

                        *COUNT UNIQUE PATIENTS*;

PROC SQL;

CREATE TABLE work.Denominators AS

      SELECT DISTINCT exposed, count(*) AS Denominator

      FROM (SELECT DISTINCT exposed, subject FROM work.SourcePopn)           

GROUP BY exposed;

QUIT;

STEP 2

*COUNT UP PROCEDURS FOR NUMERATOR*;

PROC SQL;

      CREATE TABLE work.Numerators AS

      SELECT DISTINCT exposed, procedure, count(*) AS count

      FROM (SELECT DISTINCT subject, procedure, exposed FROM work.DATA_SET_A)

      GROUP BY exposed, procedure

      ORDER BY exposed DESC, count DESC;

QUIT;

STEP 3

*THIS CODE ATTACHES THE DENOMENATOR AND DOES PROPORTION CALCULATION*;

PROC SQL;

      CREATE TABLE work.DATA_SET_B AS

SELECT a.procedure, a.exposed, a.count, b.denominator,

(a.count/b.denominator) AS Proportion

      FROM work.Numerators AS a LEFT JOIN work.Denominators as b

      ON a.exposed=b.exposed

      ORDER BY exposed DESC, count DESC;

RUN;

[PaigeMiller · Accepted solution]

The standard deviation of a proportion is sqrt(p*(1-p)/n), where p is the estimated proportion; should be easy enough to compute from PROC SQL or otherwise.