fmax

The function <code>fmax()</code> will return the value of f(z), which is the value of the density function of the
maximum of two normally distributed random variables.

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

fmax function

<dl><dt>z</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 for the maximum of two normally distributed random variables — fmax

<dl>

<dt>z</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>

fmax: Density for the maximum of two normally distributed random variables

Description

Usage

Value

Arguments

Details