mitey (version 0.2.0)

integrate_component: Integrate Serial Interval Component Functions for Likelihood Calculation

Description

This function performs numerical integration of serial interval component functions used in the Vink method for estimating serial interval distributions. It integrates the probability density functions for different transmission routes over specified intervals as part of the Expectation-Maximization algorithm.

Usage

integrate_component(
  d,
  mu,
  sigma,
  comp,
  dist = c("normal", "gamma"),
  lower = TRUE
)

Value

numeric; the integrated likelihood value for the specified component and data point. Used in the EM algorithm for serial interval estimation

Arguments

d

numeric; the index case-to-case (ICC) interval in days for which to calculate the likelihood contribution

mu

numeric; the mean of the serial interval distribution in days

sigma

numeric; the standard deviation of the serial interval distribution in days

comp

integer; the transmission route component number (1 to 7). See Details for component definitions

dist

character; the assumed underlying distribution of the serial interval. Must be either "normal" or "gamma". Defaults to "normal"

lower

logical; if TRUE (default), performs integration using flower and fupper functions. If FALSE, uses f0 function

Details

The function supports two integration modes:

• lower = TRUE: Integrates using flower and fupper functions over intervals [d-1, d] and [d, d+1] respectively, representing the likelihood contribution when case occurs at day d

• lower = FALSE: Integrates using f0 function over interval [d, d+1], representing an alternative likelihood formulation

The components represent different transmission routes in outbreak analysis:

• Component 1: Co-Primary (CP) transmission

• Components 2+3: Primary-Secondary (PS) transmission

• Components 4+5: Primary-Tertiary (PT) transmission

• Components 6+7: Primary-Quaternary (PQ) transmission

This function is primarily used internally by si_estim() as part of the Vink method for estimating serial interval parameters from outbreak data.

References

Vink MA, Bootsma MCJ, Wallinga J (2014). Serial intervals of respiratory infectious diseases: A systematic review and analysis. American Journal of Epidemiology, 180(9), 865-875.

See Also

flower, fupper, f0, si_estim

Examples

# Basic example with lower integration (default)
# Component 2 represents primary-secondary transmission
integrate_component(d = 15, mu = 12, sigma = 3, comp = 2, dist = "normal", lower = TRUE)

# Upper integration example
integrate_component(d = 15, mu = 12, sigma = 3, comp = 2, dist = "normal", lower = FALSE)

# Using gamma distribution
integrate_component(d = 10, mu = 8, sigma = 2, comp = 1, dist = "gamma", lower = TRUE)

# Component 1 (co-primary transmission) with normal distribution
integrate_component(d = 5, mu = 10, sigma = 3, comp = 1, dist = "normal", lower = TRUE)

# Compare different components for the same data point
d_val <- 20
mu_val <- 15
sigma_val <- 4

# Calculate for components 1, 2, and 4 (different transmission routes)
sapply(c(1, 2, 4), function(comp) {
  integrate_component(d_val, mu_val, sigma_val, comp, "normal", lower = TRUE)
})