optimal_tte {drugdevelopR}

Optimal phase II/III drug development planning with time-to-event endpoint

Description

The function optimal_tte 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 time-to-event endpoints (Kirchner et al., 2016). The assumed true treatment effects can be assumed to be fixed or modelled by a prior distribution. When assuming fixed true treatment effects, planning can also be done with the user-friendly R Shiny app basic. The app prior visualizes the prior distributions used in this package. Fast computing is enabled by parallel programming.

Usage

optimal_tte(
  w,
  hr1,
  hr2,
  id1,
  id2,
  d2min,
  d2max,
  stepd2,
  hrgomin,
  hrgomax,
  stephrgo,
  alpha,
  beta,
  xi2,
  xi3,
  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, see this Shiny application for the choice of weights

hr1

first assumed true treatment effect on HR scale for prior distribution

hr2

second assumed true treatment effect on HR scale for prior distribution

id1

amount of information for hr1 in terms of number of events

id2

amount of information for hr2 in terms of number of events

d2min

minimal number of events for phase II

d2max

maximal number of events for phase II

stepd2

step size for the optimization over d2

hrgomin

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

hrgomax

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

stephrgo

step size for the optimization over HRgo

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 by Schoenfeld's formula (Schoenfeld 1981)

xi2

assumed event rate for phase II, used for calculating the sample size of phase II via n2 = d2/xi2

xi3

event rate for phase III, used for calculating the sample size of phase III in analogy to xi2

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 HR scale, default: 1

stepm1

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

stepl1

lower boundary for effect size category "large" in HR scale = upper boundary for effect size category "medium" in HR 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

fixed

choose if true treatment effects are fixed or random, if TRUE hr1 is used as a fixed effect and hr2 is ignored

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_HR, which is the assumed hazards ratio used for planning the phase III study when the phase II is skipped. It is calculated as the exponential function of the median of the prior function.

num_cl

number of clusters used for parallel computing, default: 1

Format

data.frame containing the optimization results (see Value)

Value

The output of the function is a data.frame object containing the optimization results:

u

maximal expected utility under the optimization constraints, i.e. the expected utility of the optimal sample size and threshold value

HRgo

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

d2

optimal total number of events for phase II

d3

total expected number of events for phase III; rounded to next natural number

d

total expected number of events in the program; d = d2 + d3

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

Kirchner, M., Kieser, M., Goette, H., & Schueler, A. (2016). Utility-based optimization of phase II/III programs. Statistics in Medicine, 35(2), 305-316.

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.

Schoenfeld, D. (1981). The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika, 68(1), 316-319.

See Also

optimal_binary, optimal_normal, optimal_bias, optimal_multitrial and optimal_multiarm

Examples

# Activate progress bar (optional)
## Not run: 
progressr::handlers(global = TRUE)

## End(Not run)
# Optimize

optimal_tte(w = 0.3,                    # define parameters for prior
  hr1 = 0.69, hr2 = 0.88, id1 = 210, id2 = 420,   # (https://web.imbi.uni-heidelberg.de/prior/)
  d2min = 20, d2max = 100, stepd2 = 5,            # define optimization set for d2
  hrgomin = 0.7, hrgomax = 0.9, stephrgo = 0.05,  # define optimization set for HRgo
  alpha = 0.025, beta = 0.1, xi2 = 0.7, xi3 = 0.7, # drug development planning parameters
  c2 = 0.75, c3 = 1, c02 = 100, c03 = 150,        # fixed/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,                # expected benefit for each effect size category
  gamma = 0,                                      # population structures in phase II/III
  fixed = FALSE,                                  # true treatment effects are fixed/random
  skipII = FALSE,                                 # skipping phase II 
  num_cl = 1)                                     # number of cores for parallelized computing