topic Re: Relative Risk in Statistical Procedures

Relative Risk

corbinLA — Fri, 13 Nov 2020 22:13:46 GMT

Hello All! I have been computing relative risk for cohort data with the Proc freq Tables command and have been a little confused by the meaning of the two different risk values. When I get the relative risk (Column 1) I understand that this refers to the intersection of the first row and the first column. But what does the column 2 risk refer to? Is this the intersection of the first row and the second column or the second row and the second column? Any help is much appreciated!

Re: Relative Risk

FreelanceReinh — Sat, 14 Nov 2020 10:27:18 GMT

Hello @corbinLA and welcome to the SAS Support Communities!

The relative risk estimates of PROC FREQ are ratios of row proportions ("Row Pct / 100") in the 2x2 table with the first row in the numerator and the second row in the denominator. If you denote these proportions for the first column with p₁ (row 1) and p₂ (row 2) and for the second column with q₁ (row 1) and q₂ (row 2), then p₁/p₂ is the (estimated) "Relative Risk (Column 1)" and q₁/q₂ = (1-p₁)/(1-p₂) is the (estimated) "Relative Risk (Column 2)."

Example:

Fictitious "cohort study" with 100,000 smokers and 100,000 non-smokers, who (by the end of the study) develop some sort of condition (cond=1) with probabilities 0.25+0.45=0.7 and 0.25, respectively.

data have;
call streaminit(27182818);
do smoker='Y','n';
  do _n_=1 to 100000;
    cond=rand('table',0.25+0.45*(smoker='Y'));
    output;
  end;
end;
run;

proc freq data=have;
tables smoker*cond / relrisk;
run;

Result:

Table of smoker by cond smoker cond Frequency| Percent | Row Pct | Col Pct | 1| 2| Total ---------+--------+--------+ Y | 69938 | 30062 | 100000 | 34.97 | 15.03 | 50.00 | 69.94 | 30.06 | | 73.73 | 28.59 | ---------+--------+--------+ n | 24918 | 75082 | 100000 | 12.46 | 37.54 | 50.00 | 24.92 | 75.08 | | 26.27 | 71.41 | ---------+--------+--------+ Total 94856 105144 200000 47.43 52.57 100.00 Statistics for Table of smoker by cond Odds Ratio and Relative Risks Statistic Value 95% Confidence Limits ------------------------------------------------------------------ Odds Ratio 7.0100 6.8733 7.1495 Relative Risk (Column 1) 2.8067 2.7746 2.8392 Relative Risk (Column 2) 0.4004 0.3964 0.4045 Sample Size = 200000

SAS doesn't know if cond=1 or cond=2 is the condition of interest, so it estimates the relative risks (true values: 0.7/0.25=2.8, (1-0.7)/(1-0.25)=0.4, estimates: 0.69938/0.24918=2.8067, 0.30062/0.75082=0.4004) for both.

Re: Relative Risk

corbinLA — Sat, 14 Nov 2020 16:51:28 GMT

Thank you this is an excellent explanation!

Re: Relative Risk

Watts — Sat, 14 Nov 2020 17:08:26 GMT

Thanks @FreelanceReinh

Also -- if you want to display the relative risk for only one column, you can use the RELRISK COLUMN= option to specify which column. For example, this displays the column 1 relative risk together with score confidence limits.

tables smoker * cond / relrisk(column=1 cl=score);