Compute the primary event censored PMF for delays

This function computes the primary event censored probability mass function (PMF) for a given set of quantiles. It adjusts the PMF of the primary event distribution by accounting for the delay distribution and potential truncation at a maximum delay (D). The function allows for custom primary event distributions and delay distributions.

Usage

dprimarycensoreddist(
  x,
  pdist,
  pwindow = 1,
  swindow = 1,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  log = FALSE,
  pdist_name = NULL,
  dprimary_name = NULL,
  ...
)

dpcens(
  x,
  pdist,
  pwindow = 1,
  swindow = 1,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  log = FALSE,
  pdist_name = NULL,
  dprimary_name = NULL,
  ...
)

Arguments

x

Vector of quantiles

pdist

Distribution function (CDF)

pwindow

Primary event window

swindow

Secondary event window (default: 1)

D

Maximum delay (truncation point). If finite, the distribution is truncated at D. If set to Inf, no truncation is applied. Defaults to Inf.

dprimary

Function to generate the probability density function (PDF) of primary event times. This function should take a value x and a pwindow parameter, and return a probability density. It should be normalized to integrate to 1 over [0, pwindow]. Defaults to a uniform distribution over [0, pwindow]. Users can provide custom functions or use helper functions like dexpgrowth for an exponential growth distribution. See primary_dists.R for examples.

dprimary_args

List of additional arguments to be passed to dprimary. For example, when using dexpgrowth, you would pass list(min = 0, max = pwindow, r = 0.2) to set the minimum, maximum, and rate parameters

log

Logical; if TRUE, probabilities p are given as log(p)

pdist_name

A string specifying the name of the delay distribution function. If NULL, the function name is extracted using .extract_function_name(). Used to determine if a analytical solution exists for the primary censored distribution. Must be set if pdist is passed a pre-assigned variable rather than a function name.

dprimary_name

A string specifying the name of the primary event distribution function. If NULL, the function name is extracted using .extract_function_name(). Used to determine if a analytical solution exists for the primary censored distribution. Must be set if dprimary is passed a pre-assigned variable rather than a function name.

...

Additional arguments to be passed to the distribution function

Value

Vector of primary event censored PMFs, normalized by D if finite (truncation adjustment)

Details

The primary event censored PMF is computed by taking the difference of the primary event censored cumulative distribution function (CDF) at two points, \(d + \text{swindow}\) and \(d\). The primary event censored PMF, \(f_{\text{cens}}(d)\), is given by: $$ f_{\text{cens}}(d) = F_{\text{cens}}(d + \text{swindow}) - F_{\text{cens}}(d) $$ where \(F_{\text{cens}}\) is the primary event censored CDF.

The function first computes the CDFs for all unique points (including both \(d\) and \(d + \text{swindow}\)) using pprimarycensoreddist(). It then creates a lookup table for these CDFs to efficiently calculate the PMF for each input value. For non-positive delays, the function returns 0.

If a finite maximum delay \(D\) is specified, the PMF is normalized to ensure it sums to 1 over the range [0, D]. This normalization can be expressed as: $$ f_{\text{cens,norm}}(d) = \frac{f_{\text{cens}}(d)}{\sum_{i=0}^{D-1} f_{\text{cens}}(i)} $$ where \(f_{\text{cens,norm}}(d)\) is the normalized PMF and \(f_{\text{cens}}(d)\) is the unnormalized PMF. For the explanation and mathematical details of the CDF, refer to the documentation of pprimarycensoreddist().

See also

Primary event censored distribution functions pprimarycensoreddist(), rprimarycensoreddist()

Examples

# Example: Weibull distribution with uniform primary events
dprimarycensoreddist(c(0.1, 0.5, 1), pweibull, shape = 1.5, scale = 2.0)
#> [1] 0.1577952 0.2735269 0.3463199

# Example: Weibull distribution with exponential growth primary events
dprimarycensoreddist(
  c(0.1, 0.5, 1), pweibull,
  dprimary = dexpgrowth,
  dprimary_args = list(r = 0.2), shape = 1.5, scale = 2.0
)
#> [1] 0.1522796 0.2691280 0.3459055