Calculate expected number of transmission links in a sample

This function calculates the expected number of observed pairs in the sample that are linked by the linkage criteria. The function requires the sensitivity and specificity of the linkage criteria, and sample size \(M\). Assumptions about transmission and linkage (single or multiple) can be specified.

translink_expected_links_obs(
  sensitivity,
  specificity,
  rho,
  M,
  R = NULL,
  assumption = "mtml"
)

Arguments

sensitivity

scalar or vector giving the sensitivity of the linkage criteria

specificity

scalar or vector giving the specificity 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 (default=NULL)

assumption

a character vector indicating which assumptions about transmission and linkage criteria. Default = 'mtml'. Accepted arguments are:

1. 'stsl' for the single-transmission single-linkage assumption.

2. 'mtsl' for the multiple-transmission single-linkage assumption.

3. 'mtml' for the multiple-transmission multiple-linkage assumption.

Value

scalar or vector giving the expected number of observed links in the sample

See also

Other transmission linkage functions: translink_expected_links_obs_mtml(), translink_expected_links_obs_mtsl(), translink_expected_links_obs_stsl(), translink_expected_links_true_mtml(), translink_expected_links_true_mtsl(), translink_expected_links_true_stsl(), translink_expected_links_true(), translink_fdr(), translink_prob_transmit_mtml(), translink_prob_transmit_mtsl(), translink_prob_transmit_stsl(), translink_prob_transmit(), translink_samplesize(), translink_tdr()

Author

John Giles, Shirlee Wohl, and Justin Lessler

Examples

# The simplest case: single-transmission, single-linkage, and perfect sensitivity
translink_expected_links_obs(sensitivity=1, specificity=0.9, rho=0.5, M=100, assumption='stsl')
#> Calculating expected number of links assuming single-transmission and single-linkage
#> [1] 49.99926

# Multiple-transmission and imperfect sensitivity
translink_expected_links_obs(sensitivity=0.99, specificity=0.9, rho=1, M=50, R=1, assumption='mtsl')
#> Calculating expected number of links assuming multiple-transmission and single-linkage
#> [1] 57.3837

# Small outbreak, larger sampling proportion
translink_expected_links_obs(sensitivity=0.99, specificity=0.95, rho=1, M=50, 
R=1, assumption='mtml')
#> Calculating expected number of links assuming multiple-transmission and multiple-linkage
#> [1] 108.25

# Large outbreak, small sampling proportion
translink_expected_links_obs(sensitivity=0.99, specificity=0.95, 
rho=0.05, M=1000, R=1, assumption='mtml')
#> Calculating expected number of links assuming multiple-transmission and multiple-linkage
#> [1] 25022