get_tpi {escalation}

Get an object to fit the TPI dose-finding model.

Description

The toxicity probability interval (TPI)is a dose-escalation design by Ji et al.

Usage

get_tpi(
  num_doses,
  target,
  k1,
  k2,
  exclusion_certainty,
  alpha = 0.005,
  beta = 0.005,
  ...
)

Arguments

num_doses

Number of doses under investigation.

target

We seek a dose with this probability of toxicity.

k1

The K1 parameter in TPI determines the upper bound of the equivalence interval. See Details.

k2

The K2 parameter in TPI determines the lower bound of the equivalence interval. See Details.

exclusion_certainty

Numeric, threshold posterior certainty required to exclude a dose for being excessively toxic. The authors discuss values in the range 0.7 - 0.95. Set to a value > 1 to suppress the dose exclusion mechanism. The authors use the Greek letter xi for this parameter.

alpha

First shape parameter of the beta prior distribution on the probability of toxicity.

beta

Second shape parameter of the beta prior distribution on the probability of toxicity.

...

Extra args are passed onwards.

Value

an object of type selector_factory that can fit the TPI model to outcomes.

Details

The design seeks a dose with probability of toxicity p_{i} close to a target probability p_{T} by iteratively calculating the interval

p_{T} - K_{2} \sigma_{i} < p_{i} < p_{T} + K_{1} \sigma_{i}

In this model, K_{1} and K_{2} are specified constants and \sigma_{i} is the standard deviation of p_{i} arising from a Bayesian beta-binomial conjugate model

p_{i} | data \sim Beta(\alpha + x_{i}, \beta + n_{i} - x_{i}),

where x_{i} is the number of toxicities observed and n_{i} is the number of patients treated at dose i, and \alpha and \beta are hyperparameters for the beta prior on p_{i}. A dose is excluded as inadmissible if

P(p_{i} > p_{T} | data) > \xi

The trial commences at a starting dose, possibly dose 1. If dose i has just been evaluated in patient(s), dose selection decisions proceed by calculating the posterior probability that the true toxicity rate at dose i belongs to the three partition regions p_{i} < p_{T} - K_{2} \sigma_{i}, p_{T} - K_{2} \sigma_{i} < p_{i} < p_{T} + K_{1} \sigma_{i}, and p_{i} > p_{T} + K_{2} \sigma_{i}, corresponding to decisions escalate, stay, and de-escalate dose, respectively. Further to this are rules that prevent escalation to an inadmissible dose. In their paper, the authors demonstrate acceptable operating performance using \alpha = \beta = 0.005, K_{1} = 1, K_{2} = 1.5 and \xi = 0.95. See the publications for full details.

References

Ji, Y., Li, Y., & Bekele, B. N. (2007). Dose-finding in phase I clinical trials based on toxicity probability intervals. Clinical Trials, 4(3), 235–244. https://doi.org/10.1177/1740774507079442

Ji, Y., & Yang, S. (2017). On the Interval-Based Dose-Finding Designs, 1–26. Retrieved from https://arxiv.org/abs/1706.03277

Examples

target <- 0.25
model1 <- get_tpi(num_doses = 5, target = target, k1 = 1, k2 = 1.5,
  exclusion_certainty = 0.95)

outcomes <- '1NNN 2NTN'
model1 %>% fit(outcomes) %>% recommended_dose()