pmax_normal

Calculate posterior probability that a particular arm is the best in a trial using Bayesian response-adaptive randomization with
a control group (the Thall \(\&amp;\) Wathen method). The conjugate prior distributions follow Normal (\(N({\sf mean},{\sf sd})\)) distributions for 
continuous outcomes with known variance in each arm and can be specified individually.

Some response-adaptive randomization methods commonly found in literature are included in this package. These methods include the randomized play-the-winner rule for binary endpoint (Wei and Durham (1978) <doi:10.2307/2286290>), the doubly adaptive biased coin design with minimal variance strategy for binary endpoint (Atkinson and Biswas (2013) <doi:10.1201/b16101>, Rosenberger and Lachin (2015) <doi:10.1002/9781118742112>) and maximal power strategy targeting Neyman allocation for binary endpoint (Tymofyeyev, Rosenberger, and Hu (2007) <doi:10.1198/016214506000000906>) and RSIHR allocation with each letter representing the first character of the names of the individuals who first proposed this rule (Youngsook and Hu (2010) <doi:10.1198/sbr.2009.0056>, Bello and Sabo (2016) <doi:10.1080/00949655.2015.1114116>), A-optimal Allocation for continuous endpoint (Sverdlov and Rosenberger (2013) <doi:10.1080/15598608.2013.783726>), Aa-optimal Allocation for continuous endpoint (Sverdlov and Rosenberger (2013) <doi:10.1080/15598608.2013.783726>), generalized RSIHR allocation for continuous endpoint (Atkinson and Biswas (2013) <doi:10.1201/b16101>), Bayesian response-adaptive randomization with a control group using the Thall \& Wathen method for binary and continuous endpoints (Thall and Wathen (2007) <doi:10.1016/j.ejca.2007.01.006>) and the forward-looking Gittins index rule for binary and continuous endpoints (Villar, Wason, and Bowden (2015) <doi:10.1111/biom.12337>, Williamson and Villar (2019) <doi:10.1111/biom.13119>).

Chuyao Xu

RARtrials

Response-Adaptive Randomization in Clinical Trials

Thomas Lumley

Alain Vandal

Sofia S. Villar

Kyle J. Wathen

pmax_normal function

<dl><dt>armn</dt>
<dd>number of arms in the trial with values up to 5. When <code>armn</code>=2,
only <code>mean1</code> to <code>mean2</code> and <code>sd1</code> to <code>sd2</code> need to be specified.
When <code>armn</code>=3, only <code>mean1</code> to <code>mean3</code> and <code>sd1</code> to <code>sd3</code> need to be specified.
When <code>armn</code>=4, only <code>mean1</code> to <code>mean4</code> and <code>sd1</code> to <code>sd4</code> need to be specified.
When <code>armn</code>=5, <code>mean1</code> to <code>mean5</code> and <code>sd1</code> to <code>sd5</code> need to be specified.</dd>
<dt>mean1, sd1</dt>
<dd>mean and sd in Normal(mean,sd) for the arm to calculate the allocation probability of.</dd>
<dt>mean2, sd2</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>
<dt>mean3, sd3</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>
<dt>mean4, sd4</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>
<dt>mean5, sd5</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>
<dt>side</dt>
<dd>direction of a one-sided test, with values 'upper' or 'lower'.</dd>
<dt>...</dt>
<dd>additional arguments to be passed to <code><a href="/link/integrate?package=RARtrials&version=0.0.2" data-mini-rdoc="RARtrials::integrate">integrate</a></code> (such as rel.tol) from this function.</dd></dl>

Arguments

Posterior Probability that a Particular Arm is the Best for Continuous Endpoint with Known Variances — pmax_normal

<dl>

<dt>armn</dt>
<dd>number of arms in the trial with values up to 5. When <code>armn</code>=2,
only <code>mean1</code> to <code>mean2</code> and <code>sd1</code> to <code>sd2</code> need to be specified.
When <code>armn</code>=3, only <code>mean1</code> to <code>mean3</code> and <code>sd1</code> to <code>sd3</code> need to be specified.
When <code>armn</code>=4, only <code>mean1</code> to <code>mean4</code> and <code>sd1</code> to <code>sd4</code> need to be specified.
When <code>armn</code>=5, <code>mean1</code> to <code>mean5</code> and <code>sd1</code> to <code>sd5</code> need to be specified.</dd>


<dt>mean1, sd1</dt>
<dd>mean and sd in Normal(mean,sd) for the arm to calculate the allocation probability of.</dd>


<dt>mean2, sd2</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>


<dt>mean3, sd3</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>


<dt>mean4, sd4</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>


<dt>mean5, sd5</dt>
<dd>mean and sd in Normal(mean,sd) for one of the remaining arms.</dd>


<dt>side</dt>
<dd>direction of a one-sided test, with values 'upper' or 'lower'.</dd>


<dt>...</dt>
<dd>additional arguments to be passed to <code><a href='https://rdrr.io/r/stats/integrate.html'>integrate</a></code> (such as rel.tol) from this function.</dd>

</dl>

pmax_normal: Posterior Probability that a Particular Arm is the Best for Continuous Endpoint with Known Variances

Description

Usage

Value

Arguments

Details

Examples