Generate random samples from a primary event censored distribution

This function generates random samples from a primary event censored distribution. It adjusts the distribution by accounting for the primary event 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

rprimarycensored(
  n,
  rdist,
  pwindow = 1,
  swindow = 1,
  L = 0,
  D = Inf,
  rprimary = stats::runif,
  rprimary_args = list(),
  oversampling_factor = 1.2,
  ...
)

rpcens(
  n,
  rdist,
  pwindow = 1,
  swindow = 1,
  L = 0,
  D = Inf,
  rprimary = stats::runif,
  rprimary_args = list(),
  oversampling_factor = 1.2,
  ...
)

Arguments

n

Number of random samples to generate.

rdist

Function to generate random samples from the delay distribution for example stats::rlnorm() for lognormal distribution.

pwindow

Primary event window

swindow

Integer specifying the window size for rounding the delay (default is 1). If swindow = 0 then no rounding is applied.

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.

rprimary

Function to generate random samples from the primary distribution (default is stats::runif()).

rprimary_args

List of additional arguments to be passed to rprimary.

oversampling_factor

Factor by which to oversample the number of samples to account for truncation (default is 1.2).

...

Additional arguments to be passed to the distribution function.

Value

Vector of random samples from the primary event censored distribution censored by the secondary event window.

Details

The mathematical formulation for generating random samples from a primary event censored distribution is as follows:

1. Generate primary event times (p) from the specified primary event distribution (f_p) with parameters phi, defined between 0 and the primary event window (pwindow): $$p \sim f_p(\phi), \quad p \in [0, pwindow]$$

2. Generate delays (d) from the specified delay distribution (f_d) with parameters theta: $$d \sim f_d(\theta)$$

3. Calculate the total delays (t) by adding the primary event times and the delays: $$t = p + d$$

4. Apply upper truncation to remove delays >= D: $$t_{upper} = \{t \mid t < D\}$$

5. Round the delays to the nearest secondary event window (swindow): $$t_{rounded} = \lfloor \frac{t_{upper}}{swindow} \rfloor \times swindow$$

6. Apply lower truncation on the rounded values to ensure observed delays are >= L: $$t_{valid} = \{t_{rounded} \mid t_{rounded} \geq L\}$$

The function oversamples to account for potential truncation and generates additional samples if needed to reach the desired number of valid samples.

See also

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

Examples

# Example: Lognormal distribution with uniform primary events
rprimarycensored(10, rlnorm, meanlog = 0, sdlog = 1)
#>  [1] 1 1 1 2 1 1 0 2 1 2

# Example: Lognormal distribution with exponential growth primary events
rprimarycensored(
  10, rlnorm,
  rprimary = rexpgrowth, rprimary_args = list(r = 0.2),
  meanlog = 0, sdlog = 1
)
#>  [1] 1 0 1 1 0 0 1 2 2 1

# Example: Left-truncated distribution (e.g., for generation intervals)
rprimarycensored(10, rlnorm, L = 1, D = 10, meanlog = 0, sdlog = 1)
#>  [1] 1 1 1 1 1 1 2 1 2 2