thtap2thta: Obtain theta from pooled theta (model without treatment).

In agpower: Recurrent Event Analysis Planning for Robust Andersen-Gill Model

Obtain theta from pooled theta (model without treatment).

Description

Function transforms estimate of blinded pooled theta (from misspecified model without adjusting for treatment) to estimate of theta for model adjusting for treatment.

Usage

thtap2thta(bta1, thtap, ar = 0.5, thtawarning = FALSE)

Arguments

bta1	log-transform of assumed rate ratio.
thtap	Estimate of the variance of the frailty parameter under misspecification (no adjustment for treatment).
ar	Allocation ratio (Number in control / Total).
thtawarning	If TRUE indicates how many estimates of theta were negative before setting to 0. Default FALSE.

Details

This function assumes a recurrent event distribution with exponential baseline function and frailty parameter distribution with mean 1 and variance \theta, and derives from expectations of the variance under misspecification.

Specifically, the following relationship between the frailty variance for the misspecified model (\theta_p) and correctly specified model (\theta) is used

\theta_p = Var(Z \cdot \exp{\beta}) = c^2 - 2pc - 2(1-p)\exp{\beta}c + (p + (1-p)\exp{2\beta})(\theta + 1)

, where c = E(Z\exp{X\beta}) and p = ar.

Value

An estimate of the variance of the frailty parameter when the model includes treatment.

Examples

thtap2thta(2, log(c(0.8, 0.7, 0.6)))

agpower documentation built on June 8, 2025, 2 p.m.