Modelling risk ratios and risk differences

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 s0
• 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 s1

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
  Pgtz 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

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
  Pgtz 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