Compute the primary event censored CDF for delays

This function computes the primary event censored cumulative distribution function (CDF) for a given set of quantiles. It adjusts the CDF 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

pprimarycensoreddist(
  q,
  pdist,
  pwindow = 1,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  pdist_name = NULL,
  dprimary_name = NULL,
  ...
)

ppcens(
  q,
  pdist,
  pwindow = 1,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  pdist_name = NULL,
  dprimary_name = NULL,
  ...
)

Arguments

q

Vector of quantiles

pdist

Distribution function (CDF)

pwindow

Primary event window

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

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 pdist

Value

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

Details

The primary event censored CDF is computed by integrating the product of the delay distribution function (CDF) and the primary event distribution function (PDF) over the primary event window. The integration is adjusted for truncation if a finite maximum delay (D) is specified.

The primary event censored CDF, \(F_{\text{cens}}(q)\), is given by: $$ F_{\text{cens}}(q) = \int_{0}^{pwindow} F(q - p) \cdot f_{\text{primary}}(p) \, dp $$ where \(F\) is the CDF of the delay distribution, \(f_{\text{primary}}\) is the PDF of the primary event times, and \(pwindow\) is the primary event window.

If the maximum delay \(D\) is finite, the CDF is normalized by dividing by \(F_{\text{cens}}(D)\): $$ F_{\text{cens,norm}}(q) = \frac{F_{\text{cens}}(q)}{F_{\text{cens}}(D)} $$ where \(F_{\text{cens,norm}}(q)\) is the normalized CDF.

This function creates a primary_censored_dist object using new_primary_censored_dist() and then computes the primary event censored CDF using primary_censored_cdf(). This abstraction allows for automatic use of analytical solutions when available, while seamlessly falling back to numerical integration when necessary.

Note: For analytical detection to work correctly, pdist and dprimary must be directly passed as distribution functions, not via assignment or pdist_name and dprimary_name must be used to override the default extraction of the function name.

See also

new_primary_censored_dist() and primary_censored_cdf()

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

Examples

# Example: Lognormal distribution with uniform primary events
pprimarycensoreddist(c(0.1, 0.5, 1), plnorm, meanlog = 0, sdlog = 1)
#> [1] 0.0002753888 0.0475094632 0.2384217081

# Example: Lognormal distribution with exponential growth primary events
pprimarycensoreddist(
  c(0.1, 0.5, 1), plnorm,
  dprimary = dexpgrowth,
  dprimary_args = list(r = 0.2), meanlog = 0, sdlog = 1
)
#> [1] 0.0002496934 0.0440815583 0.2290795695