estHRbound: Estimate hazard ratios at an efficacy or non-efficacy...

In mjuraska/seqDesign: Simulation and Group-Sequential Monitoring of Randomized Treatment Efficacy Trials with Time-to-Event Endpoints

Estimate hazard ratios at an efficacy or non-efficacy stopping boundary defined using the Wald CI approach in an event-driven 2-arm trial design

Description

Assuming an exponential survival model, hazard ratios are estimated at an efficacy or non-efficacy stopping boundary, defined using the Wald CI approach, at each group-sequential analysis in an event-driven 2-arm trial design.

Usage

estHRbound(boundType = c("eff", "nonEff"), nullHR, alpha, nEvents, randFrac)

Arguments

boundType	a character string specifying if the one-sided null hypothesis is of the form H_0: θ ≥q θ_0 ("eff", default) or H_0: θ ≤q θ_0 ("nonEff"), where θ is the hazard ratio and θ_0 is specified by nullHR
nullHR	a nonnegative numeric value specifying the hazard ratio, θ_0, under the null hypothesis. If the null hypothesis differs across multiple analyses, nullHR may be a numeric vector of equal length as alpha.
alpha	a numeric vector of two-sided nominal significance levels (e.g., those defined by the O'Brien-Fleming group-sequential test)
nEvents	a numeric vector of numbers of events at which analyses are performed. The lengths of alpha and nEvents must be the same, and the components of the two vectors must correspond to each other.
randFrac	a fraction of subjects randomized to the group considered in the hazard ratio's numerator

Details

Using an exponential survival model and sample estimates \widehat{λ}_1 and \widehat{λ}_2 of the group-specific hazard rates, the asymptotic variance of the log hazard ratio estimator \log \widehat{θ} = \log (\widehat{λ}_1 / \widehat{λ}_2) is employed together with the approximation E\{δ | λ_1\} = (\widehat{λ}_1 / \widehat{λ}_2)\, E\{δ | λ_2\}. The resultant variance approximation is \mathrm{var} \{\log \widehat{θ}\} = (1/D) \{ 2 + p \, \widehat{θ} / (1 - p) + (1 - p) / (p \, \widehat{θ}) \}, where D is the arm-pooled number of events nEvents and p is the randomization fraction randFrac.

Value

A data frame (with rows corresponding to the components of alpha and nEvents) of point estimates of the hazard ratio at the stopping boundary and the pertaining monitoring-adjusted (1 - α^{\ast}) \times 100\% confidence intervals, where α^{\ast} is the overall two-sided type 1 error rate.

Examples

## O'Brien-Fleming test of H0: HR >= 0.7 (for efficacy) at 
## 35%, 70%, and 100% of the total information under 1:1 randomization
estHRbound("eff", nullHR=0.7, alpha=c(0.00030, 0.01466, 0.04548), 
           nEvents=c(53, 106, 151), randFrac=0.5)

## O'Brien-Fleming test of H0: HR <= 0.5 (for non-efficacy) at
## 35%, 70%, and 100% of the total information under 1:1 randomization
estHRbound("nonEff", nullHR=0.5, alpha=c(0.00030, 0.01466, 0.04548), 
           nEvents=c(53, 106, 151), randFrac=0.5)

mjuraska/seqDesign documentation built on Dec. 14, 2022, 4:26 p.m.