Figure 2

Prostate Cancer Trial: Treatment R D ( t ). Left: Estimate of treatment R D(t) and N N T(t) in the prostate cancer diethylstilbestrol trial by different methods. Continuous line: CGPM with the Cox proportional hazard model. The estimated R D(t) is increasing through follow-up time. Broken line: CGPM with a Cox model with a time dependent treatment effect (interaction treatment by time modeled with a B-spline with 1 knot at the median of the failure time distribution). There is no treatment effect until month 20, then R D(t) increases until month 40. Dotted line: estimate obtained using the transformation model with identity link. The R D(t) estimate is negative at the beginning of follow-up (harmful treatment) then becomes positive after about 20 months (beneficial treatment) reflecting the differential impact on cardiovascular and cancer deaths. On the top: three period Cox model used by Kay. The log hazard ratio is positive in the first period (0.09) [0−13], then becomes negative in the second (-0.40), (13−32], and in the third (-0.31), (32−∞), periods. The three period model was preferred to the overall Cox model according to likelihood ratio, accounting for non-proportional hazards. Right: estimated population averaged survival probability for the two intervention groups of the prostate cancer trial. The estimate from the time-dependent Cox model is reported from left to the right. The estimate from the transformation model with identity link is reported from right to the left. It is possible to observe a crossing of the survival curves.