Compute quantiles corresponding to target probabilities for primary event censored delays

This function computes the quantiles (delay values) that correspond to specified probabilities in the primary event censored distribution. For a given probability p, it computes the delay value q such that P(X ≤ q) = p, where X follows the primary event censored distribution. The distribution accounts for both the delay distribution and the primary event timing distribution.

Usage

qprimarycensored(
  p,
  pdist,
  pwindow = 1,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  ...
)

qpcens(
  p,
  pdist,
  pwindow = 1,
  D = Inf,
  dprimary = stats::dunif,
  dprimary_args = list(),
  ...
)

Arguments

p: Vector of probabilities between 0 and 1 for which to compute corresponding 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
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 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 delay values (quantiles) corresponding to the input probabilities

Details

For each probability p, the function computes the delay value q such that P(X ≤ q) = p, where X follows the primary event censored distribution. This is done by inverting the primary event censored CDF.

The function creates a primarycensored object using new_pcens() and then computes the quantiles using pcens_quantile(). This approach allows for analytical solutions when available, falling back to numerical methods when necessary.

For example, if p = 0.5, the function returns the median delay - the value where 50% of censored events occur by this time and 50% occur after.

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

Examples

# Compute delays where 25%, 50%, and 75% of events occur by (quartiles)
# Using lognormal delays with uniform primary events
qprimarycensored(c(0.25, 0.5, 0.75), plnorm, meanlog = 0, sdlog = 1)
#> [1] 1.022948 1.540771 2.498358

# Same quartiles but with exponential growth in primary events
qprimarycensored(
  c(0.25, 0.5, 0.75), plnorm,
  dprimary = dexpgrowth,
  dprimary_args = list(r = 0.2), meanlog = 0, sdlog = 1
)
#> [1] 0.000000 1.557111 2.514701

# Same quartiles but with truncation at 10
qprimarycensored(
  c(0.25, 0.5, 0.75), plnorm,
  dprimary = dexpgrowth,
  dprimary_args = list(r = 0.2), meanlog = 0, sdlog = 1, D = 10
)
#> [1] 0.000000 1.541789 2.459511