Proc FREQ producing strange Relative Risk values

[Jim_from_Canada]

For a simple estimate of a risk ratio in a 2x2 table, FREQ is giving a value that is too large. In the example below, the Experimental group has 4 out of 336 subjects with the attribute (1.19%), and the Control group has 7 out of 355 (1.97%). That produces an estimated RR of 0.6037. Simple, right?

However, FREQ gives RR=0.8042. I can't figure how FREQ got that value!!!

I think this is a glitch, but I don't see a FIX for this. I'm running SAS 9.4 TS Level 1M4 on a X64_10PRO platform.

proc freq data=test;
   table Outcome * Treatment / relrisk ;
   run;

The FREQ Procedure

348 50.36 51.18 98.03	332 48.05 48.82 98.81	680 98.41
7 1.01 63.64 1.97	4 0.58 36.36 1.19	11 1.59
355 51.37	336 48.63	691 100.00

Statistics for Table of Outcome by tmt

Odds Ratio and Relative Risks Statistic Value

Odds Ratio 0.5990

Relative Risk (Col 1) 0.8042

Relative Risk (Col 2) 1.3426

95% Confidence Limits:

0.1737	2.0649
0.5114	1.2647
0.6121	2.9452

[Rick_SAS]

The documentation section "Odds Ratio and Relative Risks for 2x2 tables" defines the RELRISK computation.

"The relative risk is the ratio of the row 1 risk to the row 2 risk in a 2x2 table. The column 1 risk in row 1 is the proportion of row 1 observations that are classified in column 1, which can be expressed as"

p1 = n11 / n1 which for your table is 348/680

p2 = n21 / n2 which for your table is 7/11

The column 1 relative risk is computed as

R = p1/p2 which for your data is 0.8042, as reported.

[Jim_from_Canada]

Thanks for the reply. Probably worth a caution to users.

[Jim_from_Canada]

---

@Rick_SAS wrote:

The documentation section "Odds Ratio and Relative Risks for 2x2 tables" defines the RELRISK computation.

"The relative risk is the ratio of the row 1 risk to the row 2 risk in a 2x2 table. The column 1 risk in row 1 is the proportion of row 1 observations that are classified in column 1, which can be expressed as"

p1 = n11 / n1 which for your table is 348/680

p2 = n21 / n2 which for your table is 7/11

The column 1 relative risk is computed as

R = p1/p2 which for your data is 0.8042, as reported.

---

Thanks for the reply. It's probably worth a caution to users who prefer the RR to the OR.

[Jim_from_Canada]

If you want the correct answer for a risk ratio in SAS for a 2x2 table or a stratified 2x2 table using the FREQ procedure, you need to be careful with the configuration and the coding. We found this out the hard way!

For example, for a generic 2x2 table where the RR is the ratio of the Experimental to the Control proportion:

		Outcome
		Yes	No
Tmt	Experimental	4	332
	Control	7	348

It is extremely important on the “order” of both the Treatment and Outcome label values.

For example, the data coding below for “tmt” and “outcome” will not give you what you want!

DATA tab2x2 ;
input tmt $ outcome $ freq ;
datalines ;
Exp Yes 4
Exp No  332
Ctl Yes 7
Ctl No  348
;

However, if you “order” the label values correctly, as shown below, for example:

		Outcome
		Yes	No
Tmt	Experimental	1, 1	1, 2
	Control	2, 1	2, 2

DATA tab2x2;
input tmt $ outcome $ freq;
datalines;
1Exp 1Yes 4
1Exp 2No  332
2Ctl 1Yes 7
2Ctl 2No  348
;

This will give you the correct RR estimate.

Also, in the TABLE statement, the “tmt” factor must be listed before the “outcome” variable. For stratified tables, the stratum factor must be the first variable (e.g. stratum*tmt*outcome):

proc FREQ data=tab2x2 ;
TABLE tmt*outcome / relrisk ;
Weight freq ;
run ;

The output is shown below.

WRONG answers!

Frequency Percent Row Pct Col Pct

Table of tmt by outcome tmt outcome No Yes Total Ctl 348 50.36 98.03 51.18 7 1.01 1.97 63.64 355 51.37 Exp 332 48.05 98.81 48.82 4 0.58 1.19 36.36 336 48.63 Total 680 98.41 11 1.59 691 100.00

Odds Ratio and Relative Risks
Statistic	Value	95% Confidence Limits
Odds Ratio	0.5990	0.1737	2.0649
Relative Risk (Column 1)	0.9921	0.9736	1.0110
Relative Risk (Column 2)	1.6563	0.4893	5.6069

RIGHT answer!

Frequency Percent Row Pct Col Pct

Table of tmt by outcome tmt outcome 1Yes 2No Total 1Exp 4 0.58 1.19 36.36 332 48.05 98.81 48.82 336 48.63 2Ctl 7 1.01 1.97 63.64 348 50.36 98.03 51.18 355 51.37 Total 11 1.59 680 98.41 691 100.00

Odds Ratio and Relative Risks
Statistic	Value	95% Confidence Limits
Odds Ratio	0.5990	0.1737	2.0649
Relative Risk (Column 1)	0.6037	0.1784	2.0437
Relative Risk (Column 2)	1.0080	0.9891	1.0272