# Optimal phase II/III drug development planning with binary endpoint

Source:`R/optimal_binary.R`

`optimal_binary.Rd`

The `optimal_binary`

function of the drugdevelopR package enables
planning of phase II/III drug development programs with optimal sample size
allocation and go/no-go decision rules for binary endpoints. In this case,
the treatment effect is measured by the risk ratio (RR). The assumed true
treatment effects can be assumed to be fixed or modelled by a prior
distribution. The R Shiny application
prior visualizes the prior
distributions used in this package. Fast computing is enabled by parallel
programming.

## Usage

```
optimal_binary(
w,
p0,
p11,
p12,
in1,
in2,
n2min,
n2max,
stepn2,
rrgomin,
rrgomax,
steprrgo,
alpha,
beta,
c2,
c3,
c02,
c03,
K = Inf,
N = Inf,
S = -Inf,
steps1 = 1,
stepm1 = 0.95,
stepl1 = 0.85,
b1,
b2,
b3,
gamma = 0,
fixed = FALSE,
skipII = FALSE,
num_cl = 1
)
```

## Arguments

- w
weight for mixture prior distribution

- p0
assumed true rate of control group, see here for details

- p11
assumed true rate of treatment group, see here for details

- p12
assumed true rate of treatment group, see here for details

- in1
amount of information for

`p11`

in terms of sample size, see here for details- in2
amount of information for

`p12`

in terms of sample size, see here for details- n2min
minimal total sample size for phase II; must be an even number

- n2max
maximal total sample size for phase II, must be an even number

- stepn2
step size for the optimization over n2; must be an even number

- rrgomin
minimal threshold value for the go/no-go decision rule

- rrgomax
maximal threshold value for the go/no-go decision rule

- steprrgo
step size for the optimization over RRgo

- alpha
one-sided significance level

- beta
type II error rate; i.e.

`1 - beta`

is the power for calculation of the number of events for phase III- c2
variable per-patient cost for phase II in 10^5 $

- c3
variable per-patient cost for phase III in 10^5 $

- c02
fixed cost for phase II in 10^5 $

- c03
fixed cost for phase III in 10^5 $

- K
constraint on the costs of the program, default: Inf, e.g. no constraint

- N
constraint on the total expected sample size of the program, default: Inf, e.g. no constraint

- S
constraint on the expected probability of a successful program, default: -Inf, e.g. no constraint

- steps1
lower boundary for effect size category "small" in RR scale, default: 1

- stepm1
lower boundary for effect size category "medium" in RR scale = upper boundary for effect size category "small" in RR scale, default: 0.95

- stepl1
lower boundary for effect size category "large" in RR scale = upper boundary for effect size category "medium" in RR scale, default: 0.85

- b1
expected gain for effect size category "small"

- b2
expected gain for effect size category "medium"

- b3
expected gain for effect size category "large"

- gamma
to model different populations in phase II and III choose

`gamma != 0`

, default: 0, see here for details- fixed
choose if true treatment effects are fixed or random, if TRUE p11 is used as fixed effect for p1

- skipII
skipII choose if skipping phase II is an option, default: FALSE; if TRUE, the program calculates the expected utility for the case when phase II is skipped and compares it to the situation when phase II is not skipped. The results are then returned as a two-row data frame,

`res[1, ]`

being the results when including phase II and`res[2, ]`

when skipping phase II.`res[2, ]`

has an additional parameter,`res[2, ]$median_prior_RR`

, which is the assumed effect size used for planning the phase III study when the phase II is skipped.- num_cl
number of clusters used for parallel computing, default: 1

## Value

The output of the function is a `data.frame`

object containing the optimization results:

- RRgo
optimal threshold value for the decision rule to go to phase III

- n2
total sample size for phase II; rounded to the next even natural number

- n3
total sample size for phase III; rounded to the next even natural number

- n
total sample size in the program; n = n2 + n3

- K
maximal costs of the program (i.e. the cost constraint, if it is set or the sum K2+K3 if no cost constraint is set)

- pgo
probability to go to phase III

- sProg
probability of a successful program

- sProg1
probability of a successful program with "small" treatment effect in phase III

- sProg2
probability of a successful program with "medium" treatment effect in phase III

- sProg3
probability of a successful program with "large" treatment effect in phase III

- K2
expected costs for phase II

- K3
expected costs for phase III

and further input parameters. Taking `cat(comment())`

of the
data frame lists the used optimization sequences, start and
finish date of the optimization procedure.

## References

IQWiG (2016). Allgemeine Methoden. Version 5.0, 10.07.2016, Technical Report. Available at https://www.iqwig.de/ueber-uns/methoden/methodenpapier/, assessed last 15.05.19.

## Examples

```
# Activate progress bar (optional)
if (FALSE) {
progressr::handlers(global = TRUE)
}
# Optimize
# \donttest{
optimal_binary(w = 0.3, # define parameters for prior
p0 = 0.6, p11 = 0.3, p12 = 0.5,
in1 = 30, in2 = 60, # (https://web.imbi.uni-heidelberg.de/prior/)
n2min = 20, n2max = 100, stepn2 = 4, # define optimization set for n2
rrgomin = 0.7, rrgomax = 0.9, steprrgo = 0.05, # define optimization set for RRgo
alpha = 0.025, beta = 0.1, # drug development planning parameters
c2 = 0.75, c3 = 1, c02 = 100, c03 = 150, # fixed and variable costs for phase II/III,
K = Inf, N = Inf, S = -Inf, # set constraints
steps1 = 1, # define lower boundary for "small"
stepm1 = 0.95, # "medium"
stepl1 = 0.85, # and "large" treatment effect size categories
b1 = 1000, b2 = 2000, b3 = 3000, # define expected benefits
gamma = 0, # population structures in phase II/III
fixed = FALSE, # true treatment effects are fixed/random
skipII = FALSE, # choose if skipping phase II is an option
num_cl = 2) # number of cores for parallelized computing
#> Optimization result:
#> Utility: 574.64
#> Sample size:
#> phase II: 100, phase III: 222, total: 322
#> Probability to go to phase III: 0.66
#> Total cost:
#> phase II: 175, phase III: 321, cost constraint: Inf
#> Fixed cost:
#> phase II: 100, phase III: 150
#> Variable cost per patient:
#> phase II: 0.75, phase III: 1
#> Effect size categories (expected gains):
#> small: 1 (1000), medium: 0.95 (2000), large: 0.85 (3000)
#> Success probability: 0.44
#> Success probability by effect size:
#> small: 0.06, medium: 0.13, large: 0.25
#> Significance level: 0.025
#> Targeted power: 0.9
#> Decision rule threshold: 0.85 [RRgo]
#> Parameters of the prior distribution:
#> p0: 0.6, p11: 0.3, p12: 0.5, in1: 30, in2: 60, w: 0.3
#> Treatment effect offset between phase II and III: 0 [gamma]
# }
```