Nivolumab KM data used for reconstructing PFS KM curve

Description

Kaplan-Meier (KM) survival data for the experimental arm (nivolumab) extracted from a published figure using PlotDigitizer. This dataset is used to reconstruct the progression-free survival (PFS) KM curve in the CheckMate 017 study.

Usage

data(Experimental)

Format

A data frame with two variables:

time

Numeric. Time points (in months).

survival

Numeric. Estimated survival probabilities at corresponding time points.

Examples

data(Experimental)
head(Experimental)

Docetaxel KM data used for reconstructing PFS KM curve

Description

Kaplan-Meier (KM) survival data for the standard-of-care (SOC) arm (docetaxel), extracted using PlotDigitizer from a published KM curve. This dataset is used to reconstruct the progression-free survival (PFS) curve for trial simulation and validation.

Usage

data(SOC)

Format

A data frame with two variables:

time

Numeric. Time points (e.g., in months) at which survival probabilities are estimated.

survival

Numeric. Estimated survival probability corresponding to each time point.

Examples

data(SOC)
head(SOC)

Compute the Total Time-on-Test (TTOT) Statistic

Description

Calculates the Total Time-on-Test (TTOT) statistic for a given vector of event times and censoring indicators. The TTOT function is commonly used in survival analysis for visualizing and assessing the cumulative hazard or comparing survival patterns between groups.

Usage

TTOT_fun(data, tA = 0, tB = 10000, t)

Arguments

Value

This function calculates the total time-on-test (TTOT) for a given dataset within the time interval (tA,tB).

Examples

# Generate sample survival data
set.seed(123)
sim_time <- generate_pe(n = 20, t = 1, lambda1 = 1, lambda2 = 0.5)
sim_status <- sample(c(0, 1), 20, replace = TRUE)
Data <- data.frame(Time = sim_time, Status = sim_status)
# Compute TTOT when time = 1
TTOT_fun(Data, t = 1)

Calculate Sample Sizes for a Two-Stage Trial Design.

Description

Computes the required sample sizes for the interim and final analyses in a two-stage trial design, based on pre-specified operating characteristics such as desired power, type I error rate assumptions.

Usage

Two_stage_sample_size(
  median.1,
  median.2,
  gprior.E_1 = NULL,
  gprior.E_2 = NULL,
  L,
  U,
  S_likely = (L + U)/2,
  trunc.para = c(1, 1),
  err1,
  err2,
  FUP,
  rate,
  weight = 0.5,
  method = "optimal",
  earlystop_prob = NULL,
  seed = NULL
)

Arguments

Value

A numeric vector of length 2. The first element is the required sample size for interim analysis, and the second element is the total sample size for final analysis in a two-stage design.

Examples

# Define design parameters
median.1 <- 4       # Median survival for standard-of-care
median.2 <- 6       # Median survival for experimental arm
L <- 2              # Lower bound of separation time
U <- 2.5            # Upper bound of separation time
S_likely <- 2.28    # Most likely separation time
rate <- 6           # Accrual rate (patients/month)
FUP <- 6            # Follow-up duration (months)
err1 <- 0.1         # Type I error
err2 <- 0.15        # Type II error


  Two_stage_sample_size(
    median.1 = median.1,
    median.2 = median.2,
    L = L,
    U = U,
    S_likely = S_likely,
    err1 = err1,
    err2 = err2,
    FUP = FUP,
    rate = rate,
    weight = 0.5,
    method = "optimal"
  )

Compute Weighted Least Squares Error (Internal)

Description

This function calculates the weighted least squares (WLS) error between simulated truncated Gamma samples and expert-provided statistics. It is used internally by trunc_gamma_para() and is not intended for direct user access.

Usage

compute_wls_error(sim_data, expert_values, weights)

Arguments

Value

Numeric. The weighted least squares error.

Computes the hazard ratio between post- and pre-separation periods, provides the 95% Bayesian credible interval, and makes a Go/No-Go decision based on the trial data. This function is intended for interim and final analyses in two-arm survival trials with delayed treatment effects.

Description

Computes the hazard ratio between post- and pre-separation hazard rates, along with the 95% Bayesian credible interval. Based on the user-supplied survival data, the function also provides a Go/No-Go decision for interim or final analysis in two-arm survival trials with delayed treatment effects

Usage

conduct(
  data_E,
  data_C,
  median.1,
  median.2,
  gprior.E_1 = NULL,
  gprior.E_2 = NULL,
  L,
  U,
  trunc.para = c(1, 1),
  lambda,
  gamma,
  nmax,
  S_likely = (L + U)/2,
  value = FALSE
)

Arguments

Value

A list with the following components:

Examples

conduct(data_E, data_C, median.1 = 2.8, median.2 = 3.5, L = 2, U = 2.5,
        trunc.para = c(1, 1), lambda = 0.95, gamma = 1, nmax = 63, S_likely = 2.3)
        

Return expected event number at interim analysis and final analysis.

Description

Based on the overall median times (median.1, median.2), the most likely separation timepoint, accrual rate and follow-up duration, this function will return the expected number of events in total at each interim analysis and final analysis based on the simulations.

Usage

event_fun(
  median.1,
  median.2,
  S_likely = (L + U)/2,
  n.interim,
  rate,
  FUP,
  n.sim = 1000,
  seed = NULL
)

Arguments

Value

A data frame with two columns: the first column indicates the stage label, and the second column contains the expected number of events for each stage.

Examples

result <- event_fun(
median.1 = 2.8,
median.2 = 3.5,
S_likely = 2.1,
n.interim = c(28,40),
rate = 6,
FUP = 6
)

Generate event times from a piecewise exponential distribution.

Description

Generates random event times under a piecewise exponential distribution, where different constant hazard rates apply before and after a specified separation timepoint. This is commonly used for simulating survival data with delayed treatment effects.

Usage

generate_pe(n, t, lambda1, lambda2)

Arguments

Value

A numeric vector of length n, representing simulated survival times drawn from a piecewise exponential distribution with hazard rate lambda1 before time t, and lambda2 after time t. Times are expressed in the same time unit as specified in the hazard rate (typically months)

Examples

set.seed(42)
generate_pe(1000, 1, 1, 0.5)

Obtain Optimal Design Parameters for DTE-BOP2 Design

Description

Computes the optimal tuning parameters \lambda and \gamma for use in posterior decision rules of two-arm, multi-stage survival trials under a piecewise exponential model with delayed treatment effect. These parameters are selected to control the type I error and maximize power, given user-specified interim sample sizes, prior distribution for the delayed separation timepoint, and hypothesized median survival times.

Usage

get.optimal_2arm_piecewise(
  median.1,
  median.2,
  gprior.E_1 = NULL,
  gprior.E_2 = NULL,
  L,
  U,
  S_likely = (L + U)/2,
  lambda.seq = seq(0.5, 0.975, by = 0.025),
  gamma.seq = seq(0, 1, by = 0.1),
  trunc.para,
  Uniform = FALSE,
  err1,
  nsim,
  n.interim,
  rate,
  FUP,
  track = TRUE,
  control = FALSE,
  control.point = NULL
)

Arguments

Value

A list with the following components:

optimal

A numeric vector of length four. Contains the optimal values of \lambda and \gamma, along with the average type I error and average power achieved under these tuning parameters.

oc.mat

A numeric matrix containing all evaluated combinations of \lambda and \gamma that satisfy the type I error constraint. Each row includes values for \lambda, \gamma, average type I error, and average power.

Examples

# Define design and simulation parameters
median.1 <- 6
median.2 <- 10
L <- 2.6
U <- 3.4
S_likely <- 2.7
trunc.para <- c(1, 1)
rate <- 3
FUP <- 9
err1 <- 0.15
n.interim <- c(30, 50)  # Each arm has 30 patients at interim and 50 at final

get.optimal_2arm_piecewise(
  median.1 = median.1,
  median.2 = median.2,
  L = L,
  U = U,
  Uniform = FALSE,
  S_likely = S_likely,
  trunc.para = trunc.para,
  err1 = err1,
  n.interim = n.interim,
  rate = rate,
  FUP = FUP,
  track = TRUE,
  nsim = 10000
)

Compute Operating Characteristics for Two-Arm Piecewise Exponential Designs

Description

Computes the operating characteristics (e.g., type I error, power, and other performance metrics) of a two-arm survival trial design under the DTE-BOP2 framework with delayed treatment effect, based on a piecewise exponential model. This function is typically used after selecting design parameters (e.g., lambda, gamma) to assess the statistical properties of the proposed design.

Usage

getoc_2arm_piecewise(
  median.true,
  gprior.E_1 = NULL,
  gprior.E_2 = NULL,
  lambda,
  gamma,
  n.interim,
  L,
  U,
  S_likely = (L + U)/2,
  Uniform = FALSE,
  trunc.para,
  rate,
  FUP = 6,
  nsim = 1000,
  track = FALSE,
  seed = NULL
)

Arguments

Value

A list with the following components:

earlystop

Numeric. The proportion of simulated trials that stopped early due to futility or predefined stopping rules.

reject

Numeric. The proportion of trials in which the null hypothesis ($H_0$) was rejected.

average.patients

Numeric. The average number of patients enrolled across all simulated trials.

trial.duration

Numeric. The average total duration of the trial (in months), including follow-up.

Examples

# Define trial parameters
median.1 <- 6
median.2 <- 9
trunc.para <- c(1, 1)
rate <- 3
FUP <- 9
n.interim <- c(30, 50)  # Each arm: 30 pts at interim, 50 pts at final
# Run operating characteristics computation
getoc_2arm_piecewise(median.true = c(median.1, median.2),
Uniform = FALSE,lambda = 0.9,gamma = 1,n.interim = n.interim,
  L = 3,U = 3,S_likely = 3,FUP = FUP,trunc.para = trunc.para,
  rate = rate,nsim = 1)

Generate Random Variables from a Truncated Gamma Distribution.

Description

Simulates random variables from a truncated gamma distribution, where the gamma distribution is bounded between user-specified lower and upper limits. This function is typically used to define priors (e.g., for the separation time in delayed treatment effect models).

Usage

rtrunc_gamma(n, L, U, shape, scale)

Arguments

Value

A numeric vector of length n, containing random variables drawn from a gamma distribution truncated to the interval [L, U].

Examples

rtrunc_gamma(10, 1, 1, 1, 1)

Estimate Shape and Scale Parameters for Truncated Gamma Distribution

Description

This function estimates the shape and scale parameters of a truncated Gamma distribution based on expert-provided summary statistics, including the mean, median, standard deviation, and selected quantiles. Parameter estimation is performed using a grid search combined with weighted least squares optimization. Parallel computing is employed to accelerate the estimation process.

Usage

trunc_gamma_para(
  L,
  U,
  expert_data,
  weights = c(10, 10, 2, 1, 1),
  num_cores = 4,
  seed = NULL
)

Arguments

Value

A list with the following components:

shape

Numeric. Estimated shape parameter of the Gamma distribution.

scale

Numeric. Estimated scale parameter of the Gamma distribution.

Examples

# Define expert-provided summary data
expert_data_correct <- list(
  list(mean = 2.2, median = 2.27, sd = NULL, q25 = NULL, q975 = NULL),  # Expert A
  list(mean = 2.1, median = 2.3,  sd = NULL, q25 = NULL, q975 = NULL),  # Expert B
  list(mean = NULL, median = 2.31, sd = NULL, q25 = NULL, q975 = NULL)  # Expert C
)

  # Estimate parameters using truncated gamma prior
  trunc_gamma_para(L = 2,U = 2.5,expert_data = expert_data_correct,num_cores = 4)