Get an object to fit the TPI dose-finding model.
The toxicity probability interval (TPI)is a dose-escalation design by Ji et al.
get_tpi( num_doses, target, k1, k2, exclusion_certainty, alpha = 0.005, beta = 0.005, ... )
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. |
an object of type selector_factory that can fit the
TPI model to outcomes.
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} σ_{i} < p_{i} < p_{T} + K_{1} σ_{i}
In this model, K_{1} and K_{2} are specified constants and σ_{i} is the standard deviation of p_{i} arising from a Bayesian beta-binomial conjugate model
p_{i} | data \sim Beta(α + x_{i}, β + 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 α and β are hyperparameters for the beta prior on p_{i}. A dose is excluded as inadmissible if
P(p_{i} > p_{T} | data) > ξ
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} σ_{i}, p_{T} - K_{2} σ_{i} < p_{i} < p_{T} + K_{1} σ_{i}, and p_{i} > p_{T} + K_{2} σ_{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 α = β = 0.005, K_{1} = 1, K_{2} = 1.5 and ξ = 0.95. See the publications for full details.
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
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()
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