# Trial implementation

Here we demonstrate how to use this package to implement and run an actual trial. Only two functions are needed: one for each stage.

## Stage 1: Establish the safety profile for all initial doses.

The first stage requires only the calculation of the likelihood of safety for each dose, based on observed binary toxicity (yes/no DLT). The function takes as input the cohort size (equal number of patients assigned at each dose, default is 3), number of DLTs observed, the acceptable and unacceptable toxicity rates, and the likelihood threshold value (default is 2). This function is used after enrolling each dose.

For example, suppose we have the following data for a dose. Do we escalate to the next dose level, or declare this dose unsafe and move on to stage 2?

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# Acceptable (p_yes) and unacceptable (p_no) DLT rates used for establishing safety
p_no <- 0.40
p_yes <- 0.15

# Likelihood-ratio (LR) threshold
K <- 2

# Cohort size used in stage 1
coh.size <- 3

# number of observed DLTs
x <- 1
LRtox(coh.size, x, p_no, p_yes, K)
## [1] "Safe/Escalate"
## $LR ## [1] 0.75 Based on this data, because LR=0.75 > 1/2 (1/K) we would escalate to the next dose. However, if we observed 2 DLTs instead of 1, we would not because LR < 1/2 LRtox(coh.size, x = 2, p_no, p_yes, K) ## [1] "Unsafe/Stop" ##$LR
## [1] 0.2

The program can be implemented for each dose to test its safety.

## Stage 2: Adaptive randomization based on efficacy outcomes.

Once we have determined which doses are safe, we can move on to stage 2 and begin collecting information about effectiveness. If only only one dose was determined as safe in stage 1, then stage 2 will be omitted. The function at stage 2 returns the updated randomization probabilities and the dose allocation for the next enrolled patient, based on the observed efficacies up to that point in the trial.

As input, this function requires a vector of observed efficacies (for each patient) and a vector of the corresponding dose levels.

y.eff <- c(9, 1, 0, 34, 10, 27, 38, 42, 60, 75, 48, 62)
d.safe <- c(1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4)
rand.prob(y.eff, d.safe)
## $Rand.Prob ## [1] 0.02037092 0.16578310 0.35098480 0.46286117 ## ##$Next.Dose
## [1] 4

In this example, the randomization probabilities for doses 1-4 are given by \$Rand.Prob, and the next patient will be enrolled on dose level 4.