dbivanorm

Density of the bivariate normal distribution

internal

Plan optimal sample size allocation and go/no-go decision rules
for phase II/III drug development programs with time-to-event, binary or
normally distributed endpoints when assuming fixed treatment effects or a
prior distribution for the treatment effect, using methods from Kirchner et al.
(2016) <doi:10.1002/sim.6624> and Preussler (2020). Optimal is in the sense of
maximal expected utility, where the utility is a function taking into account
the expected cost and benefit of the program. It is possible to extend to more
complex settings with bias correction (Preussler S et al. (2020)
<doi:10.1186/s12874-020-01093-w>), multiple phase III trials (Preussler et
al. (2019) <doi:10.1002/bimj.201700241>), multi-arm trials (Preussler et al.
(2019) <doi:10.1080/19466315.2019.1702092>), and multiple endpoints
(Kieser et al. (2018) <doi:10.1002/pst.1861>).

Lukas D. Sauer

drugdevelopR

Utility-Based Optimal Phase II/III Drug Development Planning

Stella Erdmann

Johannes Cepicka

Marietta Kirchner

Meinhard Kieser

dbivanorm function

<dl><dt>x</dt>
<dd>integral variable</dd>
<dt>y</dt>
<dd>integral variable</dd>
<dt>mu1</dt>
<dd>mean of second endpoint</dd>
<dt>mu2</dt>
<dd>mean of first endpoint</dd>
<dt>sigma1</dt>
<dd>standard deviation of first endpoint</dd>
<dt>sigma2</dt>
<dd>standard deviation of second endpoint</dd>
<dt>rho</dt>
<dd>correlation between the two endpoints</dd></dl>

Arguments

Density of the bivariate normal distribution — dbivanorm

<dl>

<dt>x</dt>
<dd>integral variable</dd>


<dt>y</dt>
<dd>integral variable</dd>


<dt>mu1</dt>
<dd>mean of second endpoint</dd>


<dt>mu2</dt>
<dd>mean of first endpoint</dd>


<dt>sigma1</dt>
<dd>standard deviation of first endpoint</dd>


<dt>sigma2</dt>
<dd>standard deviation of second endpoint</dd>


<dt>rho</dt>
<dd>correlation between the two endpoints</dd>

</dl>

dbivanorm: Density of the bivariate normal distribution

Description

Usage

Value

Arguments