Modelling risk ratios and risk differences this is
- Slides: 8
Modelling risk ratios and risk differences …this is *new* methodology…
2 X 2 table • p = pr(disease) • … now model log(p) instead of log(p/(1 -p))
Stratified analysis
Recall our post-op success example with pre-op treatment and surgery type • . cs suc tr if s==0 • • • • • | tr | | Exposed Unexposed | Total -----------------+---------Cases | 100 5 | 105 Noncases | 900 95 | 995 -----------------+---------Total | 1000 100 | 1100 | | Risk |. 1. 05 |. 0954545 | | | Point estimate | [95% Conf. Interval] |------------+-----------Risk difference |. 05 |. 0034122. 0965878 Risk ratio | 2 |. 8342841 4. 79453 +------------------------ • • • • | tr | | Exposed Unexposed | Total -----------------+---------Cases | 95 500 | 595 Noncases | 5 500 | 505 -----------------+---------Total | 1000 | 1100 | | Risk |. 95. 5 |. 5409091 | | | Point estimate | [95% Conf. Interval] |------------+-----------Risk difference |. 45 |. 3972264. 5027736 Risk ratio | 1. 9 | 1. 759944 2. 051202 +------------------------ . cs suc tr if s==1
Binomial regression with log link • . binreg suc tr s ts, rr nolog • • • Residual df Pearson X 2 Dispersion • • • Bernoulli distribution, log link ---------------------------------------| EIM suc | Risk Ratio Std. Err. z P>|z| [95% Conf. Interval] -------+--------------------------------tr | 2. 892149 1. 55 0. 120. 8343162 4. 794345 s | 10 4. 370155 5. 27 0. 000 4. 24631 23. 54986 ts |. 95. 425393 -0. 11 0. 909. 3949761 2. 284948 --------------------------------------- = = = 2196 2199. 985 1. 001815 No. of obs = 2200 Deviance = 2115. 866 Dispersion =. 9635093 • This regression analysis gives us the • ‘ratio of the 2 estimated risk ratios’ • • = 1. 9/2. 0 = 0. 95 • Compare the p-value (0. 909) with the ‘test of homogeneity’ in the classical analysis
2 X 2 table • …now model p instead of log(p)
Stratified analysis
Binomial regression with an identity link • . binreg suc tr s ts, rd nolog • • • Residual df Pearson X 2 Dispersion • • • Bernoulli distribution, identity link Risk difference coefficients ---------------------------------------| EIM suc | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------+--------------------------------tr |. 05. 0237697 2. 10 0. 035. 0034122. 0965878 s |. 45. 0269258 16. 71 0. 000. 3972264. 5027736 ts |. 4. 0359166 11. 14 0. 000. 3296048. 4703952 _cons |. 05. 0217945 2. 29 0. 022. 0072836. 0927164 --------------------------------------- = = = 2196 2200 1. 001821 No. of obs = 2200 Deviance = 2115. 866 Dispersion =. 9635093 • This regression analysis gives us the ‘difference between 2 estimated risk differences’
