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,

Usage

num_cohort_outcomes(num_patient_outcomes, cohort_size)

Arguments

num_patient_outcomes: integer, number of distinct possible outcomes for each single patient
cohort_size: integer, number of patients in the cohort

Value

integer, number of distinct possible cohort outcomes

Examples

# As described in example, N or T in a cohort of three:
num_cohort_outcomes(num_patient_outcomes = 2, cohort_size = 3)
#> [1] 4
# Also described in example, E, T, B or N in a cohort of three:
num_cohort_outcomes(num_patient_outcomes = 4, cohort_size = 3)
#> [1] 20