proc logistic with link cloglog

[bikashten]

Hello,

I have a survey data with probable dementia (yes/no) and two independent factors.

I used this logistic model and try to estimate the relative risk using log-binomial model. I am wondering how can I convert the beta estimate into relative risk (RR). I used the estimate statement to calculate the relative risk, but I am not sure about it. Does it give the relative risk. Help!!!

proc surveylogistic data=work.final;
class Immigrant (ref='0') Race (ref='1');
model prob_dementia(event='1') = Immigrant Race/link=cloglog;
weight Weight;
estimate "immigrant vs non-immigrant" Immigrant 1 -1/exp;
run;

Here is the output calculated using estimate option.

SAS Output

A

Analysis of Maximum Likelihood Estimates
Parameter		Estimate	Standard Error	t Value	Pr > |t|
Intercept		-1.6232	0.0664	-24.46	<.0001
Immigrant	1	0.0629	0.0738	0.85	0.3943
Race	2	0.1642	0.0751	2.19	0.0289
Race	4	-0.2129	0.1208	-1.76	0.0780
NOTE: The degrees of freedom for the t tests is 5226.

Association of Predicted Probabilities and Observed Responses
Percent Concordant	26.0	Somers' D	0.031
Percent Discordant	23.0	Gamma	0.063
Percent Tied	51.0	Tau-a	0.009
Pairs	4106232	c	0.515

Estimate
Label	Estimate	Standard Error	DF	t Value	Pr > |t|	Exponentiated
immigrant vs non-immigrant	0.06287	0.07380	5226	0.85	0.3943	1.0649

[StatDave]

The CLOGLOG link does not result in a log binomial model. See this note for estimating a relative risk based on a logistic model. You can use an ordinary logistic model (fit in PROC LOGISTIC or SURVEYLOGISTIC), and then use the NLMeans macro as shown there.