Table 1 Characteristics of the Design model, the Data-Generating models and the Analysis models
Design Model: | Weibull baseline hazard (constant event rate), proportional hazards (PH), treatment effect HR = 0.67, maximum time t = 50 | ||
h(t) = λγtγ − 1 exp. (βXTRT) where λ = 0.10, γ = 1.0, β = − 0.4 and XTRT = 0,1 for control and treatment groups | |||
Data Generating Models (DGMs): | Weibull baseline hazard (decreasing, constant and increasing event rates), non-proportional hazards | ||
Event rate scenario | Baseline hazard values | Non-proportional hazard change times | |
Lag until effect, HR = 1 if t ≤ tlag, HR = 0.67 if t > tlag; h(t) = λγtγ − 1 exp. (βXTRT × I(t > tlag)) | |||
Decreasing | λd = 0.15, γd = 0.9 | tlag = 0, 1, 3 or 10; tlag = 0 are PH DGMs | |
Constant | λc = 0.10, γc = 1.0 | ||
Increasing | λi = 0.07, γi = 1.1 | ||
Early effect ceasing, HR = 0.67 if t ≤ tearly, HR = 1 if t > tearly; h(t) = λγtγ − 1 exp. (βXTRT × I(t ≤ tearly)) | |||
Decreasing | λd = 0.15, γd = 0.9 | tearly = 3,10,20,50; tearly = 50 are PH DGMs | |
Constant | λc = 0.10, γc = 1.0 | ||
Increasing | λi = 0.07, γi = 1.1 | ||
Analysis Models: | Cox PH (Cox) | hi(t) = h0(t) exp. (βXTRT) | Average HR from all events in t |
Landmark (LM) | hi(t) = h0(t) exp. (βXTRT × I(t > tLM)) | Average HR from events after tLMa | |
Piecewise exponential (PE1) | hi(t) = λj exp. (βXTRT) | Average HR from all events in t | |
Piecewise exponential (PE2) | hi(t) = λj exp. (βXTRT × I(t > tPE)) | Average HR from events after tPEb | |
Royston Parmar PH (RP (PH)) | ln (Hi(t)) = s (ln(t)|γs,k0) + βXTRT | Average HR from all events in t | |
∆RMST from all events in t | |||
RP time-dependent (RP (TD)) | ln (Hi(t)) = s (ln(t)|γs,k0) + s (ln(t))XTRT + βXTRT | ∆RMST from all events in t | |
Accelerated Failure Time (AFT) | ln (ti) = βXTRT + εi | Average TR from all events in t | |