Estimate plausible piecewise constant hazard rates from summary summary event proportions

Given estimates of the event probability at one or more fixed times, the corresponding piecewise hazard rates can be determined through closed-form formulae. This utility function can be useful when simulating trial datasets with plausible event rates.

Usage

prop_to_haz(probs, cutpoints = NULL, endtime)

Arguments

probs: vector. Cumulative event probabilities at each cutpoint and at endtime, in that order. Its length must be one greater than the number of cutpoints. With no cutpoints, supply a single probability at endtime.
cutpoints: finite, positive, strictly increasing vector of interior times at which the baseline hazard changes. Default is NULL, which corresponds to a simple (non-piecewise) exponential model.
endtime: scalar. Time at which final element in probs corresponds to. Typically this would be the study endpoint time.

Value

Vector of constant hazard rates for each time piece defined by cutpoints.

Details

Given \(J-1\) interior cutpoints, then there are J intervals defined as: \([s_0, s_1)\), \([s_1, s_2)\), \(\dots\), \([s_{J-1}, s_{J})\), with conditions that \(s_0 = 0\) and \(s_J = \infty\). Each interval corresponds to constant hazard \(\lambda_j\).

Examples

lambda <- prop_to_haz(0.15, endtime = 36) # 15% probability at 36-months
all.equal(pexp(36, lambda), 0.15)
#> [1] TRUE

# 15% probability at 12-months, and 30% at 24-months
prop_to_haz(c(0.15, 0.30), 12, 24)
#> [1] 0.01354324 0.01617967
PWEALL::pwe(12, prop_to_haz(c(0.15, 0.30), 12, 24), c(0, 12))$dist
#> [1] 0.15
PWEALL::pwe(24, prop_to_haz(c(0.15, 0.30), 12, 24), c(0, 12))$dist
#> [1] 0.3