# Grid Search Optimization for BOIN-ET Design Boundaries Performs grid search optimization to determine optimal threshold values for toxicity and efficacy boundaries used in BOIN-ET dose-escalation and de-escalation decisions. This function implements the foundational calibration step for Bayesian Optimal Interval designs, ensuring that the decision boundaries (lambda1, lambda2, eta1) are optimally chosen to minimize incorrect dose selection decisions across various clinical scenarios. The optimization process balances the competing objectives of avoiding under-dosing (missing therapeutic opportunities), over-dosing (exposing patients to excessive toxicity), and selecting ineffective doses (futility), making it critical for the overall performance of BOIN-ET designs. ```r gridoptim(pi = rep(1/6, 6), phi, phi1, phi2, delta, delta1, n = 100) ``` ## Arguments - `pi`: Numeric vector of length 6 specifying prior probabilities for the six dose-response hypotheses. Must sum to 1. Default is uniform priors (rep(1/6, 6)). Order corresponds to: (1) under-dosed both, (2) under-dosed toxicity only, (3) adequate both, (4) adequate toxicity only, (5) over-dosed toxicity/adequate efficacy, (6) over-dosed toxicity/under-dosed efficacy. - `phi`: Numeric value specifying the target toxicity probability. Must satisfy phi1 < phi < phi2. - `phi1`: Numeric value specifying the lower bound of acceptable toxicity probability range. Doses with toxicity <= phi1 are considered under-dosed for toxicity. Must be less than phi. - `phi2`: Numeric value specifying the upper bound of acceptable toxicity probability range. Doses with toxicity >= phi2 are considered over-dosed. Must be greater than phi. - `delta`: Numeric value specifying the target efficacy probability. This represents the desired minimum efficacy rate. Must be greater than delta1. - `delta1`: Numeric value specifying the lower bound of efficacy probability range. Doses with efficacy < delta1 are considered sub-therapeutic. Must be less than delta. - `n`: Numeric value specifying the reference sample size for boundary optimization. Default is 100. This affects the granularity of decision probabilities but optimal boundaries are relatively robust to this choice within typical phase I sample size ranges. ## Returns A data frame containing the optimal boundary values: - **lambda1**: Optimal lower toxicity boundary for dose escalation decisions. - **lambda2**: Optimal upper toxicity boundary for dose de-escalation decisions. - **eta1**: Optimal lower efficacy boundary for dose selection decisions. These boundaries should satisfy: phi1 <= lambda1 <= phi <= lambda2 <= phi2 and delta1 <= eta1 <= delta. ## Details The grid search optimization addresses the fundamental problem in dose-finding: determining decision boundaries that minimize the probability of incorrect dosing decisions. The method considers six possible true dose-response scenarios: Grid Search Methodology: Search Space Construction: * lambda1 range : (phi1,phi) in 0.01 increments * lambda2 range : (phi,phi2) in 0.01 increments * eta1 range : (delta1,delta) in 0.01 increments * Total combinations : Typically 50-200 combinations depending on ranges Evaluation Criteria: For each boundary combination, the function calculates the probability of incorrect selection by: 1. Computing decision probabilities under each hypothesis 2. Weighting by prior hypothesis probabilities 3. Summing across all incorrect decision scenarios 4. Selecting boundaries that minimize total probability of incorrect decision ## Note * Parameter constraints must be satisfied: phi1 \< phi \< phi2 and delta1 \< delta * Prior probabilities in pi must sum to 1.0 * Grid search resolution is 0.01, providing good balance of precision and speed * Results are relatively robust to moderate changes in reference sample size (n) ## Examples ```r phi <- 0.30 # 30% target toxicity phi1 <- 0.05 # 5% lower toxicity bound phi2 <- 0.45 # 45% upper toxicity bound delta <- 0.60 # 60% target efficacy delta1 <- 0.35 # 35% minimum efficacy threshold optimal_boundaries <- gridoptim( phi = phi, phi1 = phi1, phi2 = phi2, delta = delta, delta1 = delta1 ) print(optimal_boundaries) # Verify boundary relationships cat("\\nBoundary Verification:\\n") cat("phi1 <= lambda1 <= phi:", phi1, "<=", optimal_boundaries$lambda1, "<=", phi, "->", phi1 <= optimal_boundaries$lambda1 && optimal_boundaries$lambda1 <= phi, "\\n") cat("phi <= lambda2 <= phi2:", phi, "<=", optimal_boundaries$lambda2, "<=", phi2, "->", phi <= optimal_boundaries$lambda2 && optimal_boundaries$lambda2 <= phi2, "\\n") cat("delta1 <= eta1 <= delta:", delta1, "<=", optimal_boundaries$eta1, "<=", delta, "->", delta1 <= optimal_boundaries$eta1 && optimal_boundaries$eta1 <= delta, "\\n") ``` ## References * Takeda, K., Taguri, M., & Morita, S. (2018). BOIN-ET: Bayesian optimal interval design for dose finding based on both efficacy and toxicity outcomes. **Pharmaceutical Statistics**, 17(4), 383-395. ## See Also `boinet` and `tite.boinet` which use optimized boundaries, `obd.select` for dose selection using the optimized boundaries.

gridoptim function