topic Re: Proc FREQ producing strange Relative Risk values in SAS Programming

Proc FREQ producing strange Relative Risk values

Jim_from_Canada — Mon, 23 Jan 2017 04:45:11 GMT

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

1.01

63.64

1.97

0.58

36.36

1.19

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

Re: Proc FREQ producing strange Relative Risk values

Rick_SAS — Mon, 23 Jan 2017 14:49:31 GMT

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.

Re: Proc FREQ producing strange Relative Risk values

Jim_from_Canada — Mon, 23 Jan 2017 14:55:04 GMT

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

Re: Proc FREQ producing strange Relative Risk values

Jim_from_Canada — Mon, 23 Jan 2017 14:58:29 GMT

@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.

Re: Proc FREQ producing strange Relative Risk values

Jim_from_Canada — Wed, 25 Jan 2017 15:56:27 GMT

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

Yes

Total

Ctl

348

50.36

98.03

51.18

1.01

1.97

63.64

355

51.37

Exp

332

48.05

98.81

48.82

0.58

1.19

36.36

336

48.63

Total

680

98.41

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

0.58

1.19

36.36

332

48.05

98.81

48.82

336

48.63

2Ctl

1.01

1.97

63.64

348

50.36

98.03

51.18

355

51.37

Total

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