# Obtain Optimal Design Parameters for DTE-BOP2 Design 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. ```r 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 - `median.1`: Numeric. The overall median survival time for the standard-of-care (SOC) arm under the null hypothesis. - `median.2`: Numeric. The overall median survival time for the experimental arm under the alternative hypothesis. - `gprior.E_1`: Optional. A numeric vector of length two specifying the shape and scale parameters of the inverse-gamma prior for the pre-separation mean survival time (i.e., 1/hazard rate). If NULL, the default is `c(4,3/log(2)*median.1)` - `gprior.E_2`: Optional. A numeric vector of length two specifying the shape and scale parameters of the inverse-gamma prior for the post-separation mean survival time (i.e., 1/hazard rate). If NULL, the default is `c(4,6/log(2)*median.1)` - `L`: Numeric. The lower bound of the delayed treatment effect (DTE) separation timepoint. - `U`: Numeric. The upper bound of the delayed treatment effect (DTE) separation timepoint. - `S_likely`: Numeric. The most likely value of the DTE separation timepoint. Defaults to the midpoint of `L` and `U`. - `lambda.seq`: A vector. The sequence of $\lambda$ in $1-\lambda(n/N)^{\gamma}$ - `gamma.seq`: A vector. The sequence of $\gamma$ in $1-\lambda(n/N)^{\gamma}$ - `trunc.para`: Vector value with two elements. The first element is the shape parameter for the truncated gamma prior and the second one is the scale parameter. - `Uniform`: Logical value. * `Default` FALSE. The truncated gamma distribution for the separation time will be utilized. * `If TRUE` the average type I error and power are calculated based on 20 evenly divided points in the interval $[L,U]$. - `err1`: Type I error rate. - `nsim`: Integer. Number of simulations to generate. Default is 10000. - `n.interim`: A vector of sample sizes per arm at each interim analysis. * Each element except the last represents an interim sample size per arm. * The final element is the total sample size N per arm. - `rate`: Numeric value. Patient accrual rate (e.g., patients per month). - `FUP`: Numeric value. Duration of follow-up. Default is 6 month/year in the context. - `track`: Logical value. If true, it will report the current lambda value in the running simulations. - `control`: Logical value. If TRUE, the type I error will be additionally controlled at control point. Default is FALSE. - `control.point`: Vector. It specifies the points where the type I error is controlled. ## Returns 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 ```r # 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 ) ```

get.optimal_2arm_piecewise function