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Compute Serial Interval Component Integrals for All Transmission Routes

Source: R/integrate_components_wrapper.R
integrate_components_wrapper.Rd

This wrapper function efficiently computes the likelihood contributions for all relevant transmission route components for a given index case-to-case (ICC) interval. It is a key component of the Vink method's Expectation-Maximization algorithm for estimating serial interval parameters from outbreak data.

Usage

integrate_components_wrapper(d, mu, sigma, dist = "normal")

Arguments

d

numeric; the index case-to-case (ICC) interval in days. Represents the time difference between the symptom onset of the index case (latest case) and the current case being evaluated. Must be non-negative

mu

numeric; the mean of the serial interval distribution in days. Must be positive for meaningful epidemiological interpretation

sigma

numeric; the standard deviation of the serial interval distribution in days. Must be positive

dist

character; the assumed underlying distribution family for the serial interval. Must be either "normal" or "gamma". Defaults to "normal". Gamma distribution is often preferred for serial intervals as it naturally restricts to positive values

Value

numeric vector; integrated likelihood values for each relevant transmission route component. The length depends on the distribution:

  • Normal distribution: 7 values (components 1-7)

  • Gamma distribution: 4 values (components 1, 2, 4, 6)

Details

The function handles different integration scenarios based on the distribution type and ICC interval value:

  • For normal distribution: Uses all 7 components representing the full mixture of transmission routes (co-primary, primary-secondary with positive and negative components, primary-tertiary, and primary-quaternary routes)

  • For gamma distribution: Uses components 1, 2, 4, and 6 only, as the gamma distribution naturally handles only positive serial intervals, eliminating the need for negative component pairs

  • For ICC interval = 0: Uses upper integration (lower = FALSE) representing the special case of simultaneous symptom onset

  • For ICC interval > 0: Uses lower integration (lower = TRUE) representing the standard transmission likelihood calculation

This function is primarily used internally by si_estim() as part of the E-step in the EM algorithm. Each component represents a different hypothesis about the transmission route:

  • Component 1: Co-primary transmission (simultaneous exposure)

  • Components 2-3: Primary-secondary transmission (direct transmission)

  • Components 4-5: Primary-tertiary transmission (second generation)

  • Components 6-7: Primary-quaternary transmission (third generation)

For gamma distributions, components 3, 5, and 7 are omitted because the gamma distribution naturally handles the asymmetry that these components would otherwise model in the normal distribution case.

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

integrate_component, si_estim, flower, fupper, f0

Examples

# Basic example with normal distribution
# Returns 7 component values for ICC interval of 10 days
integrate_components_wrapper(d = 10, mu = 15, sigma = 3, dist = "normal")
#> [1] 1.193978e-02 3.369814e-02 1.997254e-16 1.547844e-06 6.921256e-21
#> [6] 1.234742e-11 5.012834e-26

# Same parameters with gamma distribution
# Returns 4 component values (components 1, 2, 4, 6)
integrate_components_wrapper(d = 10, mu = 15, sigma = 3, dist = "gamma")
#> [1] 1.196761e-02 3.355068e-02 2.444605e-10 6.004790e-24

# Special case: ICC interval of 0 (simultaneous onset)
integrate_components_wrapper(d = 0, mu = 12, sigma = 2, dist = "normal")
#> [1] 2.791926e-01 1.042142e-08 1.371410e-09 1.145498e-16 1.483522e-17
#> [6] 1.434277e-24 1.847568e-25