obd.select: Optimal Biological Dose Selection

Description

Selects the optimal biological dose (OBD) from a set of candidate doses by balancing toxicity and efficacy considerations using various utility-based methods. The OBD is the dose that optimizes the risk-benefit trade-off, typically used in oncology trials where both safety and therapeutic effect must be considered simultaneously.

Usage

obd.select(
  probt, probe, method,
  phi, phi1, phi2,
  delta, delta1,
  tterm, eterm, stopT, stopE,
  w1, w2,
  plow.ast, pupp.ast,
  qlow.ast, qupp.ast,
  psi00, psi11)

Value

Integer value representing the index of the selected optimal biological dose. The returned value corresponds to the position in the input vectors probt

and probe. If no dose meets the stopping criteria, the function behavior depends on the implementation of the underlying utility functions.

Arguments

probt: Numeric vector of estimated toxicity probabilities for each dose level. Values should be between 0 and 1.
probe: Numeric vector of estimated efficacy probabilities for each dose level. Values should be between 0 and 1. Must have same length as probt.
method: Character string specifying the method for OBD selection. Must be one of: "utility.weighted", "utility.truncated.linear", "utility.scoring", or "max.effprob".
phi: Target toxicity probability (used in "max.effprob" method).
phi1: Lower bound of acceptable toxicity probability range. Used for defining toxicity intervals in some methods.
phi2: Upper bound of acceptable toxicity probability range. Used as toxicity threshold in "utility.weighted" method.
delta: Target efficacy probability.
delta1: Lower bound of acceptable efficacy probability range.
tterm: Numeric vector of probabilities of meeting toxicity stopping criteria for each dose. Same length as probt.
eterm: Numeric vector of probabilities of meeting efficacy stopping criteria for each dose. Same length as probe.
stopT: Toxicity stopping threshold. Doses are excluded if tterm < (1 - stopT).
stopE: Efficacy stopping threshold. Doses are excluded if eterm < (1 - stopE).
w1: Weight parameter for toxicity-efficacy trade-off in "utility.weighted" method. Higher values emphasize efficacy more heavily.
w2: Weight parameter for penalty imposed on toxic doses in "utility.weighted" method. Higher values penalize toxicity more heavily.
plow.ast: Lower threshold of toxicity for the linear truncated utility function (used in "utility.truncated.linear" method).
pupp.ast: Upper threshold of toxicity for the linear truncated utility function (used in "utility.truncated.linear" method).
qlow.ast: Lower threshold of efficacy for the linear truncated utility function (used in "utility.truncated.linear" method).
qupp.ast: Upper threshold of efficacy for the linear truncated utility function (used in "utility.truncated.linear" method).
psi00: Utility score for the outcome (toxicity=FALSE, efficacy=FALSE) in "utility.scoring" method.
psi11: Utility score for the outcome (toxicity=TRUE, efficacy=TRUE) in "utility.scoring" method.

Details

The function implements four different methods for OBD selection:

Method 1: "utility.weighted" Uses a weighted utility function that combines toxicity and efficacy probabilities with user-specified weights. Higher weight on w1 emphasizes efficacy, while higher weight on w2 penalizes toxicity more heavily.

Method 2: "utility.truncated.linear" Employs piecewise linear utility functions with truncation points for both toxicity and efficacy. This method allows for more flexible modeling of the utility surface with different slopes in different probability ranges.

Method 3: "utility.scoring" Uses a discrete scoring system based on four possible outcomes: (no toxicity, no efficacy), (no toxicity, efficacy), (toxicity, no efficacy), and (toxicity, efficacy).

Method 4: "max.effprob" Maximizes efficacy probability among doses with acceptable toxicity profiles. First identifies the maximum tolerated dose (MTD), then selects the dose with highest efficacy probability among acceptable doses.

The function only considers doses that meet both toxicity and efficacy stopping criteria (controlled by stopT and stopE parameters).

References

Thall, P. F., & Cook, J. D. (2004). Dose-finding based on efficacy-toxicity trade-offs. Biometrics, 60(3), 684-693.
Yin, G., Li, Y., & Ji, Y. (2006). Bayesian dose-finding in phase I/II clinical trials using toxicity and efficacy odds ratios. Biometrics, 62(3), 777-784.
Houede, N., Thall, P. F., Nguyen, H., Paoletti, X., & Kramar, A. (2010). Utility-based optimization of combination therapy using ordinal toxicity and efficacy in phase I/II trials. Biometrics, 66(2), 532-540.
Zhou, H., Murray, T. A., Pan, H., & Yuan, Y. (2018). Comparative review of novel model-assisted designs for phase I clinical trials. Statistics in Medicine, 37(20), 2892-2922.

Examples

Run this code

# Example 1: Using utility.weighted method
probt <- c(0.05, 0.15, 0.30, 0.50, 0.65)
probe <- c(0.10, 0.25, 0.45, 0.60, 0.55)
tterm <- c(0.95, 0.90, 0.85, 0.75, 0.60)
eterm <- c(0.90, 0.85, 0.80, 0.85, 0.70)

obd_weighted <- obd.select(
  probt = probt, probe = probe,
  method = "utility.weighted",
  phi2 = 0.35, w1 = 1.0, w2 = 0.5,
  tterm = tterm, eterm = eterm,
  stopT = 0.10, stopE = 0.10
)

# Example 2: Using max.effprob method
obd_maxeff <- obd.select(
  probt = probt, probe = probe,
  method = "max.effprob",
  phi = 0.30,
  tterm = tterm, eterm = eterm,
  stopT = 0.10, stopE = 0.10
)

# Example 3: Using utility.scoring method
obd_scoring <- obd.select(
  probt = probt, probe = probe,
  method = "utility.scoring",
  psi00 = 0, psi11 = 60,
  tterm = tterm, eterm = eterm,
  stopT = 0.10, stopE = 0.10
)

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