time-to-event-methods

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:

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:

# 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 Implementation:

# 4-month delay, max weight 2
data |> wlr(weight = mb(delay = 4, w_max = 2))

# Unlimited weight growth
data |> wlr(weight = mb(delay = 6, w_max = Inf))

Early Zero Weights (Xu et al., 2017)

Design: Exactly zero weight for early period, then standard logrank.

When to Use:

• Want to completely ignore early period
• Regulatory acceptance of early exclusion

simtrial Implementation:

# Zero weight for first 6 months
data |> wlr(weight = early_zero(early_period = 6))