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 the cumulative probability up to q equals p in 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, the function finds the delay value where that proportion of events have occurred by that time in the primary event censored distribution. This is done by inverting the cumulative distribution function.

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