5.5 Estimation of odds ratios, relative risks and risk differences
Suppose we want to describe the population relationship between two binary variables, say whether experiencing dry mouth in the past 12 months (the variable \(\texttt{ORH_EXP_DRM_MCQ}\) and sex (the variable \(\texttt{SEX_ASK_TRM}\)). The following codes can be used to produce estimates of odds ratios, relative risks and risk differences.
R
There is no formal support from the \(\texttt{R} \texttt{survey}\) package to produce unadjusted odds ratios, relative risks, risk differences, nor the related confidence intervals. For the relative risk, there is only one example on page 103 of the manual of \(\texttt{R}\) \(\texttt{survey}\)(Lumley 2019). The following \(\texttt{R}\) codes can produce results similar to other survey packages.
LogisticReg4.OR<-svyglm(ORH_EXP_DRM_MCQ ~ SEX_ASK_TRM ,
family = quasibinomial(link = "logit"), design = CLSA.design)
exp(coef(LogisticReg4.OR)[2]) ## odds ratio
exp(confint(LogisticReg4.OR)[2, ]) ## confidence interval
LogisticReg4.RR<-svyglm(ORH_EXP_DRM_MCQ ~ SEX_ASK_TRM ,
family = quasibinomial(link = "log"), design = CLSA.design)
exp(coef(LogisticReg4.RR)[2]) ## relative risk
exp(confint(LogisticReg4.RR)[2, ]) ## confidence interval
LogisticReg4.RD<-svyglm(ORH_EXP_DRM_MCQ ~ SEX_ASK_TRM ,
family = quasibinomial(link = "identity"), design = CLSA.design)
coef(LogisticReg4.RD)[2] ## risk difference
confint(LogisticReg4.RD)[2, ] ## Confidence interval SAS
We can obtain the unadjusted odds ratios, relative risks and risk differences by specifying the options, \(\texttt{OR}\) and \(\texttt{RISK}\) in the \(\texttt{table}\) statement. We can specify the order of the categorical variables by the \(\texttt{Proc Format}\). Usually, \(\texttt{SAS}\) only provides confidence intervals instead of standard errors for the estimates.
PROC Format;
VALUE $CBin 'Yes' = '1:Yes' 'No' = '2:No' ;
VALUE $genB 'F' = '2:Female' 'M' = '1:Male';
RUN;
PROC SURVEYFREQ data = CLSAData ORDER = FORMATTED ;
TABLE SEX_ASK_TRM * ORH_EXP_DRM_MCQ / OR RISK ;
STRATA GEOSTRAT_TRM;
WEIGHT WGHTS_INFLATION_TRM;
FORMAT ORH_EXP_DRM_MCQ $CBin. SEX_ASK_TRM $genB.;
RUN; SPSS
Analyze \(\rightarrow\) Complex Samples \(\rightarrow\) Crosstabs… \(\rightarrow\) Select the file “\(\texttt{CLSADesign.csaplan}\)” in the Plan panel \(\rightarrow\) click “Continue” \(\rightarrow\) select the corresponding variables to the “Rows”, “Factor” and target variable to the “Column” panels \(\rightarrow\) click “Statistics…” \(\rightarrow\) select “Confidence interval” and “Standard error” \(\rightarrow\) click “Odds Ratios”, “Risk difference” and “Relative risk” \(\rightarrow\) click “Continue” \(\rightarrow\) click “Continue” \(\rightarrow\) click “OK”.
Stata
There is no formal support from \(\texttt{Stata}\) \(\texttt{survey}\) package to produce unadjusted odds ratios, relative risks and risk differences and the confidence limits. However, the following codes can produce results similar to other survey packages.
Result comparison
| R | SAS | SPSS | Stata | |
|---|---|---|---|---|
| Odds ratio (M vs F) | 0.7539 | 0.7539 | 0.7539 | 0.7539 |
| 95% lower confidence limit | 0.4309 | 0.4306 | 0.4306 | 0.4309 |
| 95% upper confidence limit | 1.3188 | 1.3199 | 1.3199 | 1.3188 |
| Relative risk (M vs F) | 0.8023 | 0.8023 | 0.8023 | 0.8023 |
| 95% lower confidence limit | 0.5188 | 0.5184 | 0.5184 | 0.5188 |
| 95% upper confidence limit | 1.2408 | 1.2417 | 1.2417 | 1.2408 |
| Risk difference (M vs F) | -0.0485 | -0.0485 | -0.0485 | -0.0485 |
| 95% lower confidence limit | -0.1447 | -0.1448 | -0.1448 | -0.1447 |
| 95% upper confidence limit | 0.0477 | 0.0478 | 0.0478 | 0.0477 |
Note:
The estimates of odds ratios, relative risks and risk differences obtained by these procedures describe the relationship of the target variables and exposure groups in the population. The binomial regressions used here do not describe a model for the variables in the population. Thus, the results in this chapter may be different from the logistic regression results in the later session. The reason is due to the use of “analytic weights”, which are often rescaled within each stratum under stratified sampling.