tite.boinet: TITE-BOIN-ET: Time-to-Event Bayesian Optimal Interval Design

Description

Conducts simulation studies of the TITE-BOIN-ET (Time-to-Event Bayesian Optimal Interval design to accelerate dose-finding based on both Efficacy and Toxicity outcomes) design. This advanced extension of BOIN-ET addresses the practical challenges of late-onset outcomes and rapid patient accrual in modern oncology trials by incorporating time-to-event information and allowing continuous enrollment without waiting for complete outcome assessment.

The TITE-BOIN-ET design is particularly valuable for immunotherapy, targeted therapy, and other novel agents where Late-onset toxicity is common and causes major logistic difficulty for existing adaptive phase I trial designs, which require the observance of toxicity early enough to apply dose-escalation rules for new patients.

Usage

tite.boinet(
  n.dose, start.dose, size.cohort, n.cohort,
  toxprob, effprob,
  phi = 0.3, phi1 = phi*0.1, phi2 = phi*1.4,
  delta = 0.6, 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)

Value

A list object of class "tite.boinet" containing:

toxprob: True toxicity probabilities used in simulation.
effprob: True efficacy probabilities used in simulation.
phi: Target toxicity probability.
delta: Target efficacy probability.
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).
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.

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: Numeric vector of length n.dose specifying the true toxicity probabilities for each dose level. Used for simulation scenarios. Should reflect cumulative toxicity over tau.T period.
effprob: Numeric vector of length n.dose specifying the true efficacy probabilities for each dose level. Used for simulation scenarios. Should reflect cumulative efficacy over tau.E period.
phi: Numeric value between 0 and 1 specifying the target toxicity probability. Represents the maximum acceptable toxicity rate. Default is 0.3 (30%).
phi1: Numeric value specifying the highest toxicity probability that is deemed sub-therapeutic such that dose-escalation should be pursued. Doses with toxicity <= phi1 are considered under-dosed. Default is phi*0.1.
phi2: Numeric value specifying the lowest toxicity probability that is deemed overly toxic such that dose de-escalation is needed. Doses with toxicity >= phi2 are considered over-dosed. Default is phi*1.4.
delta: Numeric value between 0 and 1 specifying the target efficacy probability. Represents the desired minimum efficacy rate. Default is 0.6 (60%).
delta1: Numeric value specifying the minimum probability deemed efficacious such that the dose levels with efficacy < delta1 are considered sub-therapeutic. Default is 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. Should reflect the expected time course of relevant toxicities.
tau.E: Numeric value specifying the efficacy assessment window in days.
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 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(toxicity > 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(efficacy < 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), "fp.logistic" (fractional polynomial), or "multi.iso" (model averaging of multiple unimodal isotopic regression). 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.

Details

Key Advantages:

1. Continuous Accrual: Unlike standard BOIN-ET which waits for complete outcome assessment, TITE-BOIN-ET allows continuous patient enrollment by utilizing both complete and pending (censored) outcome data. This can significantly reduce trial duration.

2. Late-Onset Outcome Handling: The design explicitly models time-to-event outcomes, making it suitable for:

Immune-related adverse events that may occur months after treatment
Delayed efficacy responses common in immunotherapy
Targeted agents with cumulative toxicity effects

3. Flexible Assessment Windows: Different assessment periods for toxicity (tau.T) and efficacy (tau.E) accommodate the reality that safety and efficacy endpoints often have different time courses.

4. Correlated Outcomes: The design can model correlation between toxicity and efficacy through copula functions, reflecting the biological relationship between these endpoints.

Statistical Methodology:

Time-to-Event Integration: The design uses a weighted likelihood approach where:

Complete observations receive full weight
Pending observations receive fractional weight based on follow-up time
Weight = (observation time) / (assessment window)

Decision Algorithm: At each interim analysis, the design:

Updates outcome estimates using complete and pending data
Applies the same decision boundaries as BOIN-ET (lambda1, lambda2, eta1)
Makes dose escalation/de-escalation decisions
Continues enrollment while maintaining safety monitoring

When to Choose TITE-BOIN-ET:

Expected late-onset toxicity
Delayed efficacy assessment
Rapid accrual
Trial duration is a critical constraint

Consider Standard BOIN-ET When:

Outcomes occur within 2-4 weeks
Slow accrual allows waiting for complete data
Preference for simpler designs

References

Takeda, K., Morita, S., & Taguri, M. (2020). TITE-BOIN-ET: Time-to-event Bayesian optimal interval design to accelerate dose-finding based on both efficacy and toxicity outcomes. Pharmaceutical Statistics, 19(3), 335-349.
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.

Examples

Run this code

# Example 1: Immunotherapy trial with delayed immune-related toxicity
# Scenario: CAR-T therapy with cytokine release syndrome and delayed efficacy

n.dose      <- 4  # Four dose levels
start.dose  <- 1
size.cohort <- 6  # Larger cohorts for immunotherapy
n.cohort    <- 8  # Total: 48 patients

# CAR-T dose levels with delayed toxicity pattern
toxprob <- c(0.10, 0.25, 0.40, 0.55)  # Including delayed immune toxicity
effprob <- c(0.20, 0.50, 0.70, 0.75)  # Strong efficacy at higher doses

# Immunotherapy-appropriate targets
phi   <- 0.35  # Higher toxicity tolerance
delta <- 0.60  # Target response rate

# Extended assessment windows for immune effects
tau.T   <- 84   # 12 weeks for immune-related AEs
tau.E   <- 112  # 16 weeks for response assessment
accrual <- 7    # Weekly enrollment

# Delayed toxicity/efficacy parameters
alpha.T1 <- 0.6  # Most toxicity in later period
alpha.E1 <- 0.7  # Most responses delayed
te.corr  <- 0.3  # Moderate positive correlation

results_cart <- tite.boinet(
  n.dose = n.dose, start.dose = start.dose,
  size.cohort = size.cohort, n.cohort = n.cohort,
  toxprob = toxprob, effprob = effprob,
  phi = phi, delta = delta,
  alpha.T1 = alpha.T1, alpha.E1 = alpha.E1,
  tau.T = tau.T, tau.E = tau.E,
  te.corr = te.corr, accrual = accrual,
  estpt.method = "obs.prob",  # Conservative for small sample
  obd.method = "utility.weighted",
  w1 = 0.4, w2 = 1.2,  # Balanced approach with toxicity penalty
  n.sim = 40
)

cat("Expected trial duration:", results_cart$duration, "days\\n")
cat("OBD selection probabilities:\\n")
print(results_cart$prop.select)

# Example 2: Targeted therapy with rapid accrual
# Scenario: Tyrosine kinase inhibitor with fast enrollment

n.dose      <- 5
size.cohort <- 3
n.cohort    <- 15  # 45 patients total

# Targeted therapy dose-response
toxprob <- c(0.05, 0.12, 0.22, 0.35, 0.52)
effprob <- c(0.15, 0.35, 0.55, 0.65, 0.60)  # Plateau effect

phi   <- 0.30
delta <- 0.50

# Shorter windows for targeted therapy
tau.T   <- 28   # 4 weeks for acute toxicity
tau.E   <- 56   # 8 weeks for response
accrual <- 3    # Very rapid accrual (every 3 days)

# More uniform timing
alpha.T1 <- 0.5
alpha.E1 <- 0.5
te.corr  <- 0.1  # Weak correlation

results_tki <- tite.boinet(
  n.dose = n.dose, start.dose = start.dose,
  size.cohort = size.cohort, n.cohort = n.cohort,
  toxprob = toxprob, effprob = effprob,
  phi = phi, delta = delta,
  alpha.T1 = alpha.T1, alpha.E1 = alpha.E1,
  tau.T = tau.T, tau.E = tau.E,
  te.corr = te.corr, accrual = accrual,
  gen.event.time = "weibull",
  gen.enroll.time = "exponential",  # Variable enrollment
  estpt.method = "fp.logistic",  # Smooth modeling
  obd.method = "max.effprob",
  n.sim = 40
)

# Compare duration to standard BOIN-ET (hypothetical)
standard_duration <- tau.E + (n.cohort * size.cohort * accrual)
cat("TITE duration:", results_tki$duration, "days\\n")
cat("Standard BOIN-ET would take ~", standard_duration, "days\\n")
cat("Time savings:", standard_duration - results_tki$duration, "days\\n")

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