thtap2thta {agpower} | R Documentation |
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)))