R/num_cohort_outcomes.R

In escalation: Modular Approach to Dose Finding Clinical Trials

#' Number of different possible outcomes for a cohort of patients
#'
#' Number of different possible outcomes for a cohort of patients, each of
#' which will experience one of a number of discrete outcomes. For instance, in
#' a typical phase I dose-finding trial, each patient will experience:
#' no-toxicity (N); or toxicity (T). The number of possible outcomes per patient
#' is two. For a cohort of three patients, the number of cohort outcomes is
#' four: NNN, NNT, NTT, TTT. Consider a more complex example: in a seamless
#' phase I/II trial with efficacy and toxicity outcomes, an individual patient
#' will experience one of four distinct outcomes: efficacy only (E); toxicity
#' only (T); both efficacy and toxicity (B) or neither. How many different
#' outcomes are there for a cohort of three patients? The answer is 20 but it is
#' non-trivial to see why. This convenience function calculates that number
#' using the formula for the number of combinations with replacement,
#'
#' @param num_patient_outcomes integer, number of distinct possible outcomes for
#' each single patient
#' @param cohort_size integer, number of patients in the cohort
#'
#' @return integer, number of distinct possible cohort outcomes
#' @export
#'
#' @examples
#' # As described in example, N or T in a cohort of three:
#' num_cohort_outcomes(num_patient_outcomes = 2, cohort_size = 3)
#' # Also described in example, E, T, B or N in a cohort of three:
#' num_cohort_outcomes(num_patient_outcomes = 4, cohort_size = 3)
num_cohort_outcomes <- function(num_patient_outcomes, cohort_size) {
  num <- factorial(num_patient_outcomes + cohort_size - 1)
  denom <- factorial(cohort_size) * factorial(num_patient_outcomes - 1)
  as.integer(num / denom)
}