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) and minimum delay (L). The function allows for custom primary event distributions and delay distributions.

Usage

pprimarycensored(
  q,
  pdist,
  pwindow = 1,
  L = 0,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  ...
)

ppcens(
  q,
  pdist,
  pwindow = 1,
  L = 0,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  ...
)

Arguments

q

Vector of quantiles

pdist

Distribution function (CDF). The package can identify base R distributions for potential analytical solutions. For non-base R functions, users can apply add_name_attribute() to yield properly tagged functions if they wish to leverage the analytical solutions.

pwindow

Primary event window

L

Minimum delay (lower truncation point). If greater than 0, the distribution is left-truncated at L. This is useful for modelling generation intervals where day 0 is excluded, particularly when used in renewal models. Defaults to 0 (no left truncation).

D

Maximum delay (upper truncation point). If finite, the distribution is truncated at D. If set to Inf, no upper 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 pcd_primary_distributions() for examples. The package can identify base R distributions for potential analytical solutions. For non-base R functions, users can apply add_name_attribute() to yield properly tagged functions if they wish to leverage analytical solutions.

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

...

Additional arguments to be passed to pdist

Value

Vector of primary event censored CDFs, normalized over [L, D] if truncation is applied

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 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 truncation is applied (finite D or L > 0), the CDF is normalized: $$ F_{\text{cens,norm}}(q) = \frac{F_{\text{cens}}(q) - F_{\text{cens}}(L)}{ F_{\text{cens}}(D) - F_{\text{cens}}(L)} $$ where \(F_{\text{cens,norm}}(q)\) is the normalized CDF. For values \(q \leq L\), the function returns 0; for values \(q \geq D\), it returns 1.

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

See methods(pcens_cdf) for which combinations have analytical solutions implemented.

See also

new_pcens() and pcens_cdf()

Primary event censored distribution functions dprimarycensored(), qprimarycensored(), rprimarycensored()

Examples

# Example: Lognormal distribution with uniform primary events
pprimarycensored(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
pprimarycensored(
  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

# Example: Left-truncated distribution (e.g., for generation intervals)
pprimarycensored(
  c(1, 2, 3), plnorm,
  L = 1, D = 10,
  meanlog = 0, sdlog = 1
)
#> [1] 0.0000000 0.5461907 0.7719056