CARAEE_Alloc: Allocation Function of CARA Designs Based on Efficiency and...

In caradpt: Covariate-Adjusted Response-Adaptive Designs for Clinical Trials

Allocation Function of CARA Designs Based on Efficiency and Ethics for Binary and Continuous Response.

Description

Calculating the probability of assigning the upcoming patient to treatment A based on the patient's covariates and the previous patients' covariates and responses for CARAEE procedure.

Usage

CARAEE_Alloc(ptsb.cov, ptsb.t, ptsb.Y, ptnow.cov, gamma, response)

Arguments

ptsb.cov	a n x k covariate matrix of previous patients.
ptsb.t	a treatment vector of previous patients with length n.
ptsb.Y	a response vector of previous patients with length n.
ptnow.cov	a covariate vector of the incoming patient with length k.
gamma	a non-negative number. A tuning parameter that reflects the importance of the efficiency component compared to the ethics component.
response	the type of the response. Options are "Binary" or "Cont".

Details

Covariate-Adjusted Response-Adaptive with Ethics and Efficiency (CARAEE) Design: The CARAEE procedure balances both ethical considerations and statistical efficiency when assigning subjects to treatments.

As a start-up rule, m_0 subjects are assigned to each treatment using a balanced randomization scheme.

Assume that m \geq 2m_0 subjects have been assigned, and their responses \{\boldsymbol{X}_i, i = 1, \ldots, m\} and covariates \{\boldsymbol{Z}_i, i = 1, \ldots, m\} are observed. Let \hat{\boldsymbol{\theta}}(m) = \left( \hat{\theta}_1(m), \hat{\theta}_2(m) \right), where \hat{\theta}_k(m) is the maximum likelihood estimate of the treatment-specific parameter \theta_k based on the data for treatment group k.

For the incoming subject (m+1) with covariates \boldsymbol{Z}_{m+1}, we define the efficiency and ethics measures for each treatment as: \boldsymbol{d}(\boldsymbol{Z}, \boldsymbol{\theta}) = \left(d_1(\boldsymbol{Z}, \theta), d_2(\boldsymbol{Z}, \theta)\right), \quad \boldsymbol{e}(\boldsymbol{Z}, \boldsymbol{\theta}) = \left(e_1(\boldsymbol{Z}, \theta), e_2(\boldsymbol{Z}, \theta)\right).

The allocation probability of assigning subject (m+1) to treatment 1 is given by:

\phi_{m+1}(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m)) = \frac{e_1(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m)) \cdot d_1^\gamma(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m))} {e_1(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m)) \cdot d_1^\gamma(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m)) + e_2(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m)) \cdot d_2^\gamma(\boldsymbol{Z}_{m+1}, \hat{\boldsymbol{\theta}}(m))}.

This allocation rule is scale-invariant in both efficiency and ethics components due to its ratio-based form. The tuning parameter \gamma \geq 0 controls the trade-off between the two: when \gamma = 0, the assignment is based purely on ethical considerations; larger values of \gamma increase the emphasis on statistical efficiency. More details can be found in Hu, Zhu & Zhang(2015).

Value

prob	Probability of assigning the upcoming patient to treatment A for binary and continuous response.

References

Hu, J., Zhu, H., & Hu, F. (2015). A unified family of covariate-adjusted response-adaptive designs based on efficiency and ethics. Journal of the American Statistical Association, 110(509), 357–367.

Examples

set.seed(123)

n_prev = 40
covariates = cbind(Z1 = rnorm(n_prev), Z2 = rnorm(n_prev))
treatment = sample(c(0, 1), n_prev, replace = TRUE)
response = rbinom(n_prev, size = 1, prob = 0.6)

# Simulate new incoming patient
new_patient_cov = c(Z1 = rnorm(1), Z2 = rnorm(1))

# Run allocation function
result = CARAEE_Alloc(
 ptsb.cov = covariates,
 ptsb.t = treatment,
 ptsb.Y = response,
 ptnow.cov = new_patient_cov,
 response = "Binary",
 gamma=1
)
print(result$prob)

caradpt documentation built on Aug. 28, 2025, 9:09 a.m.