# gBOIN-ET: Generalized Bayesian Optimal Interval Design for Ordinal Graded Outcomes Conducts simulation studies of the gBOIN-ET (generalized Bayesian Optimal Interval design for optimal dose-finding accounting for ordinal graded Efficacy and Toxicity) design. This extension of BOIN-ET utilizes ordinal (graded) outcome information rather than binary endpoints, providing more nuanced dose-finding decisions by incorporating the full spectrum of toxicity severity and efficacy response levels. Unlike traditional binary approaches that classify outcomes as simply "toxic/non-toxic" or "effective/ineffective," gBOIN-ET recognizes that clinical outcomes exist on a continuum. This design is particularly valuable when the degree of toxicity or efficacy response significantly impacts clinical decision-making and patient outcomes. ```r gboinet( n.dose, start.dose, size.cohort, n.cohort, toxprob, effprob, sev.weight, res.weight, phi, phi1 = phi*0.1, phi2 = phi*1.4, delta, delta1 = delta*0.6, alpha.T1 = 0.5, alpha.E1 = 0.5, tau.T, tau.E, te.corr = 0.2, gen.event.time = "weibull", accrual, gen.enroll.time = "uniform", stopping.npts = size.cohort*n.cohort, stopping.prob.T = 0.95, stopping.prob.E = 0.99, estpt.method = "obs.prob", obd.method = "max.effprob", w1 = 0.33, w2 = 1.09, plow.ast = phi1, pupp.ast = phi2, qlow.ast = delta1/2, qupp.ast = delta, psi00 = 40, psi11 = 60, n.sim = 1000, seed.sim = 100) ``` ## Arguments - `n.dose`: Integer specifying the number of dose levels to investigate. - `start.dose`: Integer specifying the starting dose level (1 = lowest dose). Generally recommended to start at the lowest dose for safety. - `size.cohort`: Integer specifying the number of patients per cohort. Commonly 3 or 6 patients, with 3 being standard for early-phase trials. - `n.cohort`: Integer specifying the maximum number of cohorts. Total sample size = size.cohort*n.cohort. - `toxprob`: Matrix (nrow = toxicity categories, ncol = n.dose) specifying true toxicity probabilities. Each column must sum to 1.0. Rows represent ordered toxicity levels from none to most severe. - `effprob`: Matrix (nrow = efficacy categories, ncol = n.dose) specifying true efficacy probabilities. Each column must sum to 1.0. Rows represent ordered response levels from none to best response. - `sev.weight`: Numeric vector of toxicity severity weights. Length must equal nrow(toxprob). Should be non-decreasing and reflect clinical impact. First element typically 0 (no toxicity). - `res.weight`: Numeric vector of efficacy response weights. Length must equal nrow(effprob). Should be non-decreasing and reflect clinical benefit. First element typically 0 (no response). - `phi`: Numeric target for normalized equivalent toxicity score (nETS). Should be calibrated for weighted scores, not binary probabilities. - `phi1`: Numeric lower boundary for nETS. Doses with nETS <= phi1 considered under-dosed for toxicity. Default phi*0.1. - `phi2`: Numeric upper boundary for nETS. Doses with nETS >= phi2 trigger de-escalation. Default phi*1.4. - `delta`: Numeric target for normalized equivalent efficacy score (nEES). Should reflect desired level of clinical benefit. - `delta1`: Numeric minimum threshold for nEES. Doses below this considered sub-therapeutic. Default delta*0.6. - `alpha.T1`: Numeric value specifying the probability that a toxicity outcome occurs in the late half of the toxicity assessment window. Used for event time generation. Default is 0.5. - `alpha.E1`: Numeric value specifying the probability that an efficacy outcome occurs in the late half of the efficacy assessment window. Used for event time generation. Default is 0.5. - `tau.T`: Numeric value specifying the toxicity assessment window in days. All toxicity evaluations must be completed within this period. - `tau.E`: Numeric value specifying the efficacy assessment window in days. All efficacy evaluations must be completed within this period. - `te.corr`: Numeric value between -1 and 1 specifying the correlation between toxicity and efficacy, specified as Gaussian copula parameter. Default is 0.2 (weak positive correlation). - `gen.event.time`: Character string specifying the distribution for generating event times. Options are "weibull" (default) or "uniform". A bivariate Gaussian copula model is used to jointly generate the time to first ordinal toxicity and efficacy outcome, where the marginal distributions are set to Weibull distribution when `gen.event.time="weibull"`, and uniform distribution when `gen.event.time="uniform"`. - `accrual`: Numeric value specifying the accrual rate (days), which is the average number of days between patient enrollments. Lower values indicate faster accrual. - `gen.enroll.time`: Character string specifying the distribution for enrollment times. Options are "uniform" (default) or "exponential". Uniform distribution is used when `gen.enroll.time="uniform"`, and exponential distribution is used when `gen.enroll.time="exponential"`. - `stopping.npts`: Integer specifying the maximum number of patients per dose for early study termination. If the number of patients at the current dose reaches this criteria, the study stops the enrollment and is terminated. Default is size.cohort*n.cohort. - `stopping.prob.T`: Numeric value between 0 and 1 specifying the early study termination threshold for toxicity. If P(nETS > phi) > stopping.prob.T, the dose levels are eliminated from the investigation. Default is 0.95. - `stopping.prob.E`: Numeric value between 0 and 1 specifying the early study termination threshold for efficacy. If P(nEES < delta1) > stopping.prob.E, the dose levels are eliminated from the investigation. Default is 0.99. - `estpt.method`: Character string specifying the method for estimating efficacy probabilities. Options: "obs.prob" (observed efficacy probabilitiesrates), or "fp.logistic" (fractional polynomial). Default is "obs.prob". - `obd.method`: Character string specifying the method for OBD selection. Options: "utility.weighted", "utility.truncated.linear", "utility.scoring", or "max.effprob" (default). - `w1`: Numeric value specifying the weight for toxicity-efficacy trade-off in "utility.weighted" method. Default is 0.33. - `w2`: Numeric value specifying the penalty weight for toxic doses in "utility.weighted" method. Default is 1.09. - `plow.ast`: Numeric value specifying the lower toxicity threshold for "utility.truncated.linear" method. Default is phi1. - `pupp.ast`: Numeric value specifying the upper toxicity threshold for "utility.truncated.linear" method. Default is phi2. - `qlow.ast`: Numeric value specifying the lower efficacy threshold for "utility.truncated.linear" method. Default is delta1/2. - `qupp.ast`: Numeric value specifying the upper efficacy threshold for "utility.truncated.linear" method. Default is delta. - `psi00`: Numeric value specifying the utility score for (toxicity=no, efficacy=no) in "utility.scoring" method. Default is 40. - `psi11`: Numeric value specifying the utility score for (toxicity=yes, efficacy=yes) in "utility.scoring" method. Default is 60. - `n.sim`: Integer specifying the number of simulated trials. Default is 1000. Higher values provide more stable operating characteristics. - `seed.sim`: Integer specifying the random seed for reproducible results. Default is 100. ## Returns A list object of class "gboinet" containing the following components: - **toxprob**: True toxicity probability matrix used in simulation. - **effprob**: True efficacy probability matrix used in simulation. - **nETS**: True normalized equivalent toxicity scores by dose level. - **nEES**: True normalized equivalent efficacy scores by dose level. - **phi**: Target normalized equivalent toxicity scores. - **delta**: Target normalized equivalent efficacy scores. - **lambda1**: Lower toxicity decision boundary. - **lambda2**: Upper toxicity decision boundary. - **eta1**: Lower efficacy decision boundary. - **tau.T**: Toxicity assessment window (days). - **tau.E**: Efficacy assessment window (days). - **accrual**: Accrual rate (days). - **ncat.T**: Number of ordinal toxicity outcome categories. - **ncat.E**: Number of ordinal efficacy outcome categories. - **estpt.method**: Method used for efficacy probability estimation. - **obd.method**: Method used for optimal biological dose selection. - **n.patient**: Average number of patients treated at each dose level across simulations. - **prop.select**: Percentage of simulations selecting each dose level as OBD. - **prop.stop**: Percentage of simulations terminating early without OBD selection. - **duration**: Expected trial duration in days. ## Details Conceptual Foundation: Binary vs Ordinal Paradigm: Traditional designs lose valuable information by dichotomizing outcomes: * Binary approach : Grade 3 or Grade 4 toxicity treated identically as "toxic" * Ordinal approach : Preserves clinically meaningful distinctions between severity levels * Information gain : More efficient use of patient data for dose-finding decisions Equivalent Toxicity/Efficacy Score Framework: The design converts ordinal categories into continuous scores: * ETS (Equivalent Toxicity Score) : Relative severity of different toxicity grades * EES (Equivalent Efficacy Score) : Relative effectiveness of different efficacy outcomes * Normalized scores (nETS, nEES) : Standardized to a scale ranging from 0 to 1 (quasi-Bernoulli probability) Decision Algorithm: Uses the same boundary-based logic as BOIN-ET but applied to normalized scores: * Escalate : When nETS \<= lambda1 AND nEES \<= eta1 * Stay : When lambda1 \< nETS \< lambda2 AND nEES \> eta1 * De-escalate : When nETS \>= lambda2 * Efficacy-guided : When lambda1 \< nETS \< lambda2 AND nEES \<= eta1 Key Advantages: 1. Enhanced Discrimination: * Better differentiation between dose levels with similar binary rates * Captures clinically meaningful severity gradations 2. Clinical Relevance: * Aligns with clinical practice where severity matters * Better reflection of risk-benefit trade-offs 3. Regulatory Appeal: * Utilizes standard grading systems (CTCAE, RECIST) * Transparent scoring methodology * Maintains model-assisted design simplicity Weight Selection: Example of Toxicity Weights (sev.weight): Should reflect clinical impact and patient burden: * Grade 0 and 1 : 0.0 * Grade 2 : 0.5 * Grade 3 : 1.0 * Grade 4 : 1.5 Example of Efficacy Weights (res.weight): Should reflect clinical benefit and durability: * PD : 0.0 * SD : 0.25 * PR : 1.0 * CR : 3.0 When to Use gBOIN-ET vs TITE-gBOIN-ET: Choose gBOIN-ET when: * Outcomes occur within reasonable assessment windows * Patient accrual allows waiting for complete outcome assessment * Preference for simpler, well-established approaches Choose TITE-gBOIN-ET when: * Late-onset outcomes are expected * Rapid accrual necessitates continuous enrollment * Trial duration constraints are critical ## Note * Matrix inputs require careful validation - rows must sum to 1.0 * Weight selection should involve clinical stakeholders and reflect patient preferences * Normalized equivalent scores may not directly correspond to familiar probability scales ## Examples ```r # Example 1: Targeted therapy with hepatotoxicity grading # Scenario: Kinase inhibitor with dose-dependent liver toxicity n.dose <- 5 start.dose <- 1 size.cohort <- 4 # Slightly larger for ordinal information n.cohort <- 12 # Hepatotoxicity categories: Normal, Grade 1, Grade 2, Grade 3+ # Progressive increase in severe hepatotoxicity with dose toxprob <- rbind( c(0.85, 0.70, 0.50, 0.35, 0.20), # Normal LFTs c(0.12, 0.20, 0.25, 0.25, 0.20), # Grade 1 elevation c(0.02, 0.08, 0.20, 0.30, 0.40), # Grade 2 elevation c(0.01, 0.02, 0.05, 0.10, 0.20) # Grade 3+ hepatotoxicity ) # Response categories: PD, SD, PR, CR # Plateau in efficacy at higher doses effprob <- rbind( c(0.70, 0.50, 0.30, 0.25, 0.30), # Progressive disease c(0.25, 0.35, 0.40, 0.35, 0.35), # Stable disease c(0.04, 0.12, 0.25, 0.30, 0.25), # Partial response c(0.01, 0.03, 0.05, 0.10, 0.10) # Complete response ) # Hepatotoxicity severity weights (clinical practice-based) sev.weight <- c(0.0, 0.3, 1.0, 3.0) # Strong penalty for Grade 3+ res.weight <- c(0.0, 0.2, 1.5, 3.5) # Preference for objective responses # Moderate toxicity tolerance for targeted therapy phi <- 0.60 # Accept moderate weighted hepatotoxicity delta <- 0.80 # Target meaningful weighted efficacy # Standard assessment windows for targeted therapy tau.T <- 42 # 6 weeks for LFT monitoring tau.E <- 56 # 8 weeks for response assessment accrual <- 7 # Weekly enrollment results_tki <- gboinet( n.dose = n.dose, start.dose = start.dose, size.cohort = size.cohort, n.cohort = n.cohort, toxprob = toxprob, effprob = effprob, sev.weight = sev.weight, res.weight = res.weight, phi = phi, delta = delta, tau.T = tau.T, tau.E = tau.E, accrual = accrual, estpt.method = "obs.prob", obd.method = "utility.weighted", w1 = 0.4, w2 = 1.2, n.sim = 100 ) # Display normalized equivalent scores (true values) cat("True Normalized Equivalent Scores:\\n") cat("nETS (Toxicity):", round(results_tki$nETS, 2), "\\n") cat("nEES (Efficacy):", round(results_tki$nEES, 2), "\\n") # Example 2: Chemotherapy with neuropathy grading # Scenario: Taxane with cumulative peripheral neuropathy n.dose <- 4 size.cohort <- 6 # Larger cohorts for safety n.cohort <- 8 # Neuropathy categories: None, Mild, Moderate, Severe # Cumulative dose-dependent neuropathy toxprob <- rbind( c(0.75, 0.55, 0.35, 0.20), # No neuropathy c(0.20, 0.30, 0.35, 0.30), # Mild neuropathy c(0.04, 0.12, 0.25, 0.35), # Moderate neuropathy c(0.01, 0.03, 0.05, 0.15) # Severe neuropathy ) # Response categories: No response, Minor, Major, Complete effprob <- rbind( c(0.60, 0.40, 0.25, 0.20), # No response c(0.30, 0.35, 0.35, 0.30), # Minor response c(0.08, 0.20, 0.30, 0.35), # Major response c(0.02, 0.05, 0.10, 0.15) # Complete response ) # Neuropathy-specific weights (functional impact) sev.weight <- c(0.0, 0.4, 1.2, 2.8) # Severe neuropathy major QoL impact res.weight <- c(0.0, 0.3, 1.8, 3.2) # Complete response highly valued phi <- 0.50 # Moderate neuropathy tolerance delta <- 0.80 # Target substantial response tau.T <- 84 # 12 weeks for neuropathy development tau.E <- 56 # 8 weeks for response assessment accrual <- 14 # Bi-weekly enrollment results_chemo <- gboinet( n.dose = n.dose, start.dose = start.dose, size.cohort = size.cohort, n.cohort = n.cohort, toxprob = toxprob, effprob = effprob, sev.weight = sev.weight, res.weight = res.weight, phi = phi, delta = delta, tau.T = tau.T, tau.E = tau.E, accrual = accrual, estpt.method = "obs.prob", obd.method = "utility.truncated.linear", n.sim = 100 ) # Compare with binary approximation binary_tox <- 1 - toxprob[1,] # Any neuropathy binary_eff <- effprob[3,] + effprob[4,] # Major + Complete response cat("Ordinal vs Binary Information:\\n") cat("Binary toxicity rates:", round(binary_tox, 2), "\\n") cat("Ordinal nETS scores:", round(results_chemo$nETS, 2), "\\n") cat("Binary efficacy rates:", round(binary_eff, 2), "\\n") cat("Ordinal nEES scores:", round(results_chemo$nEES, 2), "\\n") ``` ## References * Takeda, K., Morita, S., & Taguri, M. (2022). gBOIN-ET: The generalized Bayesian optimal interval design for optimal dose-finding accounting for ordinal graded efficacy and toxicity in early clinical trials. **Biometrical Journal**, 64(7), 1178-1191. * Yamaguchi, Y., Takeda, K., Yoshida, S., & Maruo, K. (2024). Optimal biological dose selection in dose-finding trials with model-assisted designs based on efficacy and toxicity: a simulation study. **Journal of Biopharmaceutical Statistics**, 34(3), 379-393. ## See Also `tite.gboinet` for time-to-event version with ordinal outcomes, `boinet` for binary outcome version, `obd.select` for dose selection methods, `utility.weighted`, `utility.truncated.linear`, `utility.scoring` for utility functions.

gboinet function