obs_pairs_mtml {phylosamp}

Expected number of observed pairs assuming multiple-transmission and multiple-linkage

Description

This function calculates the expected number of pairs observed in a sample of size M. The multiple-transmission and multiple-linkage method assumes the following:

1. Each case i is, on average, the infector of R cases in the population (N)

2. Each case i is allowed to be linked by the linkage criteria to multiple cases j in the sampled population (M).

3. Linkage events are independent of one another (i.e, linkage of case i to case j has no bearing on linkage of case i to any other sample).

Usage

obs_pairs_mtml(chi, eta, rho, M, R)

Arguments

chi

scalar or vector giving the specificity of the linkage criteria

eta

scalar or vector giving the sensitivity of the linkage criteria

rho

scalar or vector giving the proportion of the final outbreak size that is sampled

M

scalar or vector giving the number of cases sampled

R

scalar or vector giving the effective reproductive number of the pathogen

Value

scalar or vector giving the expected number of linked pairs observed in the sample

Author(s)

John Giles, Shirlee Wohl and Justin Lessler

See Also

Other obs_pairs: exp_links(), obs_pairs_mtsl(), obs_pairs_stsl()

Examples

# Perfect sensitivity and specificity
obs_pairs_mtml(eta=1, chi=1, rho=0.5, M=100, R=1)

obs_pairs_mtml(eta=0.99, chi=0.9, rho=1, M=50, R=1)

obs_pairs_mtml(eta=0.99, chi=0.9, rho=0.5, M=100, R=1)