Download A SAS/IML Routine to Calculate SPMR Relative Risk Confidence Bounds

A SAS lml Routine to Calculate SPMR Relative Risk
Confidenc e Bounds
Statistics
2 71
Jimmy Thomas Efird
Applied Statistics Corporation
1430 Mass. Ave., Suite 306-51
Cambridge, MA 02138
In Medical research the relative the Relative Risk (RR) of dying from an agent or compound
with respect to a specified health condition may be calculated by dividing the Relative
Standardized Mortality Ratio (RSMR) for exposure versus non-exposure. In practice, since
Population at Risk (PAR) information is seldom available, RSMR's are estimated by Standarized
Proportional Mortality Ratio's (SPMR), with confidence bounds on the individual SPMR's
readily calculated using the formula of Kupper, et al. (1978). Assuming the worst case
scenario, a confidence interval for Relative Risk may be obtained by dividing the lower
numerator RSMR bound by the upper denominator RSMR bound, yieldinp a lower RSMR bound,
and vice versa for the upper RSMR bound. Alph levels (Aic) for the RSMR interval estimate
should be set using Demorgan-Bonferroni's inequality, i.e.
(1.1)
Simple put, (1.1) implies that the probability for each event A;, Ai+1• ... , An simultaneously
holding true is less than the sum of the individual probababilities. For example, setting SPMR
alpha levels at 0.025 yields a Relative Risk alpha level of 0.05.
Following the convention of Kupper, let ddotj, ddotdot, didot, whatj and aij denote SAS data sets
containing respective statistics d.j. d .. , di·· Wj, and aij· Attachment 1 provides a SAS-IML
procedure to calculate SPMR's and confidence bounds for RMSR's and RR statistics. Typical
output is given in Table 1. Here Relative Risks for various disease groups are calculated with
respect to oral contraceptive use. Risks are relative to unity, wherein a RR-1 implies that the
given agent does not increase nor decrease the risk of the disease under consideration. For
example, the condition "Suicide" has a RR of 1.04, while the RR for "Breast Cancer" is 1.72.
Clearly, the risk of "Breast Cancer" is far greater than for "Suicide", or for that matter
"Accidents" (RR=1.05), which are logically independent of oral contraceptive use, and thus
have a RR close to 1.
Table 1 : Confidence Bounds tor Relative Risk by Disease Group
LowerCI
1.22
1.44
1.06
0.84
0.86
0.76
0.78
0.77
0.76
1.28
0.86
Relative Risk
Upoer Cl
1.41
1.72
1.19
1.61
2.02
1.12
1.00
1.35
1.48
1.13
0.91
1.08
1.00
1.26
1.43
1.42
2.20
1.37
1.05
1.04
1.70
1.09
Disease
All Malig. Neoplasms (3)
Breast Cancer (17)
Cervix (19)
Malig. Melanoma (25)
Cerebrovascular Disease (38)
All Hean (39)
Ischemic Heart Disease (41)
Accidents and Violent (56)
Suicides (60)
Endometrial Ca. (63)
Ovarium Cancer (64)
NESUG '91 Proceedings
272
Statistics
Attachment 1: SAS·IML Routine to Calculate Confidence Bounds for RMSR
Statistics
%macro main(alpha,rc);
proc iml worksize=1 00;
s:an mainmtx:
',.do j=1 %to 5;
use &&w&j:
read all into &&vv&j var {&&w&j);
%end:
%do k=1 %to 12;
a&k•aij(l%eval(&k" 14-1 3):%eval(&k"14), IJ;
spmr&k=didot(l&k, 1IJ!(ddotdot"(a"k'"whatj));
ava&k=fuzz((((a&k##2)'"whatj)-((a&k'"whatj)##2))/ddotdot);
coef&k=(ava&k##.S)/((a&k'"whatj)"(&alpha##.S));
lci&k=(1 -coef&k)*spmr&k;
uci&k=(1 +Coef& k) •spmr&k;
%end;
tlci&rc=lci1 %do X=2 %to 12;
/llci&x
0
/oend;;
tspmr&rc:spmr1 %do y=2 %to 12;
//spmr&y
%end;;
tuci&rc=uci1 %do Z=2 %to 12;
//uci&z
%end;;
store tlci&rc tspmr&rc tuci&rc;
finish;
run mainmtx;
quit;
%mend mtrix:
%mtrix(ddotj,ddotdot,didot,whatj.aij)
%main(.025, 1)
%main(.025,2)
%main(.025,3)
proc iml worksize=200;
%do a=1 %to 3;
load tlci&a tspmr&a tuci&a;
%end;
lbi={'AII Causes(! )','All Malig. Neoplasms(3)','8reast Cancer(17)',
'Cervix(! 9)', 'Malig. Melanoma(25)', 'Cerebrovascular Disease(38)',
'All Heart(39)', 'Ischemic Heart Disease(41 )',
'Accidents and Violence'56)','Suicides(60)',
'Endometrial Ca.(63)','0varium Cancer(64)/;
start prtcal;
print "/odo b=1 %to 3;
tlci&b tspmr&b tuci&b
%end;;
lrr=tlci1 ttuci2;
rr=tspmrt ftspmr2:
urr=tucit ftlci2:
print lrr rr urr lbl;
finish;
run prtcal;
quit;
References
Kupper, L.L., et al., On The Utility Of Proportional Mortality Analysis, J. Chron. Dis. 1978, Vol. 31.
pp. 15·22. Pergamon Press.
NESUG '91 Proceedings