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Modelling risk ratios and risk differences

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

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Modelling risk ratios and risk differences

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  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’

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