topic Re: Calculating confidence interval for multiple groups of risk ratios in Statistical Procedures

Calculating confidence interval for multiple groups of risk ratios

carmong — Mon, 26 Sep 2022 23:55:40 GMT

I have a question regarding calculating confidence intervals (95%) in SAS for multiple exposure groups (with one being the reference group). The numbers below represent the number of people who were exposed versus the number of people who became ill along with the cum incidence, sickness rate and risk ratio.

I calculated the following risk ratios by hand with the 18 - 29 group being the reference group and I have the following questions:

- Is it possible to calculate confidence intervals for multiple exposure groups in SAS and if so, what proc and syntax would be used?

- Would I input the table below in SAS order to calculate the confidence intervals in SAS, or would the risk ratios and confidence intervals have to be calculated in SAS (using the raw data)?

	Sick	Exposed	cum incidence	rate	risk ratio	Confidence Interval
18 – 29	3	10323	0.000291	0.03
30-49	23	13450	0.00171	0.2	5.9
50-64	37	5307	0.006972	0.7	24.0
65-79	77	2014	0.038232	3.8	131.6
80+	73	653	0.111792	11.2	384.7

Re: Calculating confidence interval for multiple groups of risk ratios

StatDave — Tue, 27 Sep 2022 01:22:19 GMT

This can be done using a Poisson model and the LSMEANS statement as shown below. See also this note. The Exponentiated columns in the first LSMEANS table reproduce your rates and in the table of differences gives the ratios and confidence intervals. Note the use of the log of the exposed counts as an offset in the Poisson model.

data b;
input age $ Nsick Nexp;
off=log(Nexp);
datalines;
   18-29	3	10323	0.000291	0.03	 	 
   30-49	23	13450	0.00171	0.2	5.9	 
   50-64 	37	5307	0.006972	0.7	24.0	 
   65-79	77	2014	0.038232	3.8	131.6	 
   80+	73	653	0.111792	11.2	384.7	 
;
proc genmod;
class age(ref="18-29");
model Nsick=age / dist=poisson offset=off;
lsmeans age / diff=control("18-29") exp cl plots=none;
run;

Re: Calculating confidence interval for multiple groups of risk ratios

carmong — Wed, 05 Oct 2022 23:31:08 GMT

Here is what I got when I tried the code: Is there supposed to be a "mean" in the age Least Squares Means table?

Analysis Of Maximum Likelihood Parameter Estimates
Parameter		DF	Estimate	Standard Error	Wald 95% Confidence Limits		Wald Chi-Square	Pr > ChiSq
Intercept		1	0.0000	0.0098	-0.0193	0.0193	0.00	1.0000
age	30-49	1	0.0000	0.0131	-0.0256	0.0256	0.00	1.0000
age	50-64	1	0.0000	0.0169	-0.0331	0.0331	0.00	1.0000
age	65-79	1	0.0000	0.0244	-0.0477	0.0477	0.00	1.0000
age	80+	1	0.0000	0.0404	-0.0791	0.0791	0.00	1.0000
age	18-29	0	0.0000	0.0000	0.0000	0.0000	.	.
Scale		0	1.0000	0.0000	1.0000	1.0000

age Least Squares Means
age	Estimate	Standard Error	z Value	Pr > \|z\|	Alpha	Lower	Upper	Exponentiated	Exponentiated Lower	Exponentiated Upper
30-49	0	0.008623	0.00	1.0000	0.05	-0.01690	0.01690	1.0000	0.9832	1.0170
50-64	0	0.01373	0.00	1.0000	0.05	-0.02690	0.02690	1.0000	0.9735	1.0273
65-79	0	0.02228	0.00	1.0000	0.05	-0.04367	0.04367	1.0000	0.9573	1.0446
80+	0	0.03913	0.00	1.0000	0.05	-0.07670	0.07670	1.0000	0.9262	1.0797
18-29	0	0.009842	0.00	1.0000	0.05	-0.01929	0.01929	1.0000	0.9809	1.0195

Differences of age Least Squares Means
age	_age	Estimate	Standard Error	z Value	Pr > \|z\|	Alpha	Lower	Upper	Exponentiated	Exponentiated Lower	Exponentiated Upper
30-49	18-29	0	0.01309	0.00	1.0000	0.05	-0.02565	0.02565	1.0000	0.9747	1.0260
50-64	18-29	0	0.01689	0.00	1.0000	0.05	-0.03311	0.03311	1.0000	0.9674	1.0337
65-79	18-29	0	0.02436	0.00	1.0000	0.05	-0.04774	0.04774	1.0000	0.9534	1.0489
80+	18-29	0	0.04035	0.00	1.0000	0.05	-0.07909	0.07909	1.0000	0.9240	1.0823

Re: Calculating confidence interval for multiple groups of risk ratios

StatDave — Thu, 06 Oct 2022 03:47:51 GMT

You must not have run the code exactly as shown in my previous post since all of your parameter estimates are zero. And no, there shouldn't be a Mean column since the ILINK option is not specified. The EXP option is taking care of that.

Re: Calculating confidence interval for multiple groups of risk ratios

carmong — Thu, 06 Oct 2022 06:10:06 GMT

Here is what I typed into SAS, where did I go wrong?

data a;
input age $ Hosp Nhosp;
off=log (Nhosp);
datalines;

18-29 3 10323 0.000291 0.03
30-49 23 13450 0.00171 0.2 5.9
50-64 37 5307 0.006972 0.7 24.0
65-79 77 2014 0.038232 3.8 131.6
80+ 73 653 0.111792 11.2 384.7
;

proc genmod;
class age(ref="18-29");
model Nhosp=age / dist=poisson offset=off;
lsmeans age / diff=control("18-29") exp cl plots=none;
run;

Here is the log:

1 data a;
2 input age $ Hosp Nhosp;
3 off=log (Nhosp);
4 datalines;

NOTE: SAS went to a new line when INPUT statement reached past the end of a line.
NOTE: The data set WORK.A has 5 observations and 4 variables.
NOTE: DATA statement used (Total process time):
real time 0.47 seconds
cpu time 0.04 seconds

11 ;

NOTE: Writing HTML Body file: sashtml.htm
12 proc genmod;
13 class age(ref="18-29");
14 model Nhosp=age / dist=poisson offset=off;
15 lsmeans age / diff=control("18-29") exp cl plots=none;
16 run;

NOTE: Fitting saturated model. Scale will not be estimated.
NOTE: Algorithm converged.
NOTE: The scale parameter was held fixed.
NOTE: The structure of the LSMeans table has changed from an earlier release of SAS.
NOTE: The structure of the Diffs table has changed from an earlier release of SAS.
NOTE: PROCEDURE GENMOD used (Total process time):
real time 2.31 seconds
cpu time 0.29 seconds

Re: Calculating confidence interval for multiple groups of risk ratios

StatDave — Thu, 06 Oct 2022 14:00:35 GMT

Should be model hosp=age not model nhosp=age.

Re: Calculating confidence interval for multiple groups of risk ratios

carmong — Thu, 06 Oct 2022 15:37:42 GMT

I tried running it again and got a different result. Perhaps its the spacing with the data section that made a difference? I noticed that there was spacing in your code, for the datalines, but when I typed mine in, I didn't space.

Analysis Of Maximum Likelihood Parameter Estimates
Parameter		DF	Estimate	Standard Error	Wald 95% Confidence Limits		Wald Chi-Square	Pr > ChiSq
Intercept		1	-8.1435	0.5774	-9.2751	-7.0119	198.95	<.0001
age	30-49	1	1.7723	0.6138	0.5692	2.9754	8.34	0.0039
age	50-64	1	3.1777	0.6003	2.0011	4.3542	28.02	<.0001
age	65-79	1	4.8794	0.5885	3.7260	6.0329	68.75	<.0001
age	80+	1	5.9524	0.5891	4.7978	7.1070	102.10	<.0001
age	18-29	0	0.0000	0.0000	0.0000	0.0000	.	.
Scale		0	1.0000	0.0000	1.0000	1.0000

Re: Calculating confidence interval for multiple groups of risk ratios

StatDave — Thu, 06 Oct 2022 15:53:39 GMT

Those are the parameter estimates I get from my code. The spacing isn't important. The LSMEANS tables should also be what I got and should be what you are looking for.

Re: Calculating confidence interval for multiple groups of risk ratios

StatDave — Thu, 06 Oct 2022 15:53:49 GMT

Those are the parameter estimates I get from my code. The spacing isn't important. The LSMEANS tables should also be what I got and should be what you are looking for.

Re: Calculating confidence interval for multiple groups of risk ratios

carmong — Thu, 06 Oct 2022 16:41:08 GMT

Here are the other two tables:

age Least Squares Means
age	Estimate	Standard Error	z Value	Pr > \|z\|	Alpha	Lower	Upper	Exponentiated	Exponentiated Lower	Exponentiated Upper
30-49	-6.3712	0.2085	-30.56	<.0001	0.05	-6.7799	-5.9626	0.001710	0.001136	0.002573
50-64	-4.9659	0.1644	-30.21	<.0001	0.05	-5.2881	-4.6436	0.006972	0.005051	0.009623
65-79	-3.2641	0.1140	-28.64	<.0001	0.05	-3.4874	-3.0407	0.03823	0.03058	0.04780
80+	-2.1911	0.1170	-18.72	<.0001	0.05	-2.4205	-1.9617	0.1118	0.08888	0.1406
18-29	-8.1435	0.5774	-14.10	<.0001	0.05	-9.2751	-7.0119	0.000291	0.000094	0.000901

Differences of age Least Squares Means
age	_age	Estimate	Standard Error	z Value	Pr > \|z\|	Alpha	Lower	Upper	Exponentiated	Exponentiated Lower	Exponentiated Upper
30-49	18-29	1.7723	0.6138	2.89	0.0039	0.05	0.5692	2.9754	5.8842	1.7668	19.5975
50-64	18-29	3.1777	0.6003	5.29	<.0001	0.05	2.0011	4.3542	23.9904	7.3971	77.8061
65-79	18-29	4.8794	0.5885	8.29	<.0001	0.05	3.7260	6.0329	131.56	41.5138	416.91
80+	18-29	5.9524	0.5891	10.10	<.0001	0.05	4.7978	7.1070	384.68	121.24	1220.48

Re: Calculating confidence interval for multiple groups of risk ratios

StatDave — Thu, 06 Oct 2022 16:50:03 GMT

That's correct. Again, the Exponentiated columns in the first table give the risk estimates for each age group, and in the second table, the risk ratios comparing each group to the reference age group.