1. Modelling risk ratios and risk differences …this is *new* methodology…

2. 2 X 2 table p = pr(disease) … now model log(p) instead of log(p/(1-p))

3. Stratified analysis

4. 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 +-----------------------------------------------. cs suc tr if s==1 | tr | | Exposed Unexposed | Total -----------------+------------------------+---------- Cases | 95 500 | 595 Noncases | 5 500 | 505 -----------------+------------------------+---------- Total | 100 1000 | 1100 | | Risk |.95.5 |.5409091 | | | Point estimate | [95% Conf. Interval] |------------------------+---------------------- Risk difference |.45 |.3972264.5027736 Risk ratio | 1.9 | 1.759944 2.051202 +-----------------------------------------------

5. Binomial regression with log link. binreg suc tr s ts,rr nolog Residual df = 2196 No. of obs = 2200 Pearson X2 = 2199.985 Deviance = 2115.866 Dispersion = 1.001815 Dispersion =.9635093 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 ------------------------------------------------------------------------------ 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

6. 2X2 table …now model p instead of log(p)

7. Stratified analysis

8. Binomial regression with an identity link. binreg suc tr s ts,rd nolog Residual df = 2196 No. of obs = 2200 Pearson X2 = 2200 Deviance = 2115.866 Dispersion = 1.001821 Dispersion =.9635093 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 ------------------------------------------------------------------------------ This regression analysis gives us the ‘difference between 2 estimated risk differences’