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Derive piecewise-constant hazard rates from cumulative event probabilities

Source: R/prop_to_haz.R
prop_to_haz.Rd

Converts cumulative event probabilities at specified follow-up times into the corresponding piecewise-constant hazard rates. This is useful for expressing data-generation assumptions in terms of clinically interpretable event probabilities.

Usage

prop_to_haz(probs, cutpoints = NULL, endtime)

Arguments

probs

A required numeric vector of finite cumulative event probabilities in [0, 1) 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. Values must be non-decreasing and are not recycled.

cutpoints

NULL (the default), or a numeric vector of finite, positive, strictly increasing interior times at which the event hazard changes. NULL corresponds to a simple (non-piecewise) exponential model.

endtime

A required single finite, positive numeric value giving the follow-up time corresponding to the final element of probs. It must be later than every cutpoint and use the same time unit.

Value

A numeric vector of non-negative hazard rates, with one value for each interval defined by cutpoints and endtime.

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 \(\lambda_j\). This is the PWEALL representation of the continuous generating hazard. Changing the value at an isolated cutpoint does not alter the cumulative probabilities calculated here. When observed event times are assigned to analysis intervals, goldilocks uses (s_{j-1}, s_j], matching the survival counting-process convention, so an event at \(s_j\) belongs to the interval ending there.

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