Generate dosing decisions (E, S, D or DU) of the i3+3 design for user-specified number of participants.
get_decision_i3plus3(pT = NULL,
EI = NULL,
npts = 12)get_decision_i3plus3() returns:
(1) a dataframe containing the decisions (E, S, D or DU) for each combination of y and n ($tab),
(2) a list ($setup) containing user input parameters, such as target, EI, npts, etc.
a numeric value that specifies the target DLT rate (\(p_T\)).
a vector that specifies the equivalence interval (EI).
the number of participants within which dosing decisions are generated.
Denote the current dose \(d\). Let \(n_d\) and \(y_d\) represent the number of participants treated at dose \(d\) and the number of participants experienced DLT, respectively. Let \(p_d\) be the toxicity probability at dose \(d\). Also, denote \(\frac{y_d}{n_d}\) the observed toxicity rate at the current dose.
The i3+3 design uses the following decision rules.
If \(\frac{y_d}{n_d}\) is lower than the escalation boundary (i.e. below the EI), the decision is to escalate to the next higher dose; if \(\frac{y_d}{n_d}\) is between the escalation and de-escalation boundaries (i.e. inside the EI), the decision is to stay at the current dose; if \(\frac{y_d}{n_d}\) is higher than the de-escalation boundary (i.e. above the EI), there are two options: option one, if \(\frac{y_d-1}{n_d}\) is lower than the escalation boundary (i.e., below the EI), the decision is to stay at the current dose; option two, else if \(\frac{y_d-1}{n_d}\) is equal to or higher than the escalation boundary, the decision is to de-escalate to the next lower dose.
Also, the i3+3 design includes a dose exclusion rule. Let \(p_T\) represents the target DLT rate. If \(Pr(p_d > p_T | y_d , n_d ) > 0.95\), dose \(d\) and those higher than \(d\) are removed from the trial since they are deemed excessively toxic.
Liu M., Wang, SJ. and Ji, Y. (2020). The i3+3 Design for Phase I Clinical Trials, Journal of biopharmaceutical statistics, 30(2):294–304.
get_decision_i3plus3(pT = 0.25,
EI = c(0.2,0.3),
npts = 12)
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