time-to-event-methodslisted

# Time-to-Event Methods ## When to Use This Skill - Selecting appropriate analysis methods for survival endpoints - Handling non-proportional hazards scenarios - Implementing weighted logrank tests - Designing MaxCombo tests - Using RMST or milestone endpoints ## Analysis Methods Overview ### Standard Logrank Test **When Optimal:** - Proportional hazards assumption holds - Treatment effect constant over time **Formula:** ``` Z = Σ(O_trt - E_trt) / √(Var) ``` **simtrial Implementation:** ```r data |> wlr(weight = fh(rho = 0, gamma = 0)) ``` ### Fleming-Harrington Weighted Logrank **Weight Function:** ``` w(t) = S(t)^ρ × (1 - S(t))^γ ``` **Parameter Effects:** | ρ | γ | Emphasis | Best For | |---|---|----------|----------| | 0 | 0 | Uniform (standard LR) | Proportional hazards | | 0 | 0.5 | Moderate late | Moderate delayed effect | | 0 | 1 | Strong late | Strong delayed effect | | 1 | 0 | Early | Early divergence | | 0.5 | 0.5 | Balanced | Crossing hazards | **simtrial Implementation:** ```r # Late emphasis data |> wlr(weight = fh(rho = 0, gamma = 0.5)) # Early emphasis data |> wlr(weight = fh(rho = 1, gamma = 0)) ``` ### Magirr-Burman (MB) Weights **Design:** Zero weight before delay, then increasing weight. **Parameters:** - `delay`: Time before weights increase - `w_max`: Maximum weight cap **Formula:** ``` w(t) = min(w_max, S(min(t, τ*))^(-1)) ``` **When to Use:** - Known delay in treatment effect - Clear scientific rationale for delay period **simtrial I