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 | | 105 Noncases | | Total | | 1100 | | Risk |.1.05 | | | | Point estimate | [95% Conf. Interval] | Risk difference |.05 | Risk ratio | 2 | cs suc tr if s==1 | tr | | Exposed Unexposed | Total Cases | | 595 Noncases | | Total | | 1100 | | Risk |.95.5 | | | | Point estimate | [95% Conf. Interval] | Risk difference |.45 | Risk ratio | 1.9 |

Binomial regression with log link. binreg suc tr s ts,rr nolog Residual df = 2196 No. of obs = 2200 Pearson X2 = Deviance = Dispersion = Dispersion = Bernoulli distribution, log link | EIM suc | Risk Ratio Std. Err. z P>|z| [95% Conf. Interval] tr | s | ts | 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

2X2 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 = 2196 No. of obs = 2200 Pearson X2 = 2200 Deviance = Dispersion = Dispersion = Bernoulli distribution, identity link Risk difference coefficients | EIM suc | Coef. Std. Err. z P>|z| [95% Conf. Interval] tr | s | ts | _cons | This regression analysis gives us the ‘difference between 2 estimated risk differences’