estimate_theta_hat {bumblebee}

estimate_theta_hat Estimates conditional probability of linkage (transmission flows)

Description

This function estimates theta_hat, the relative probability of transmission within and between population groups accounting for variable sampling rates among population groups. This relative probability is also refferred to as transmission flows.

Usage

estimate_theta_hat(df_counts_and_p_hat, ...)

## Default S3 method:
estimate_theta_hat(df_counts_and_p_hat, ...)

Arguments

df_counts_and_p_hat

A data.frame returned by the function: estimate_p_hat()

...

Further arguments.

Details

For a population group pairing (u,v), the estimated transmission flows within and between population groups u and v, are represented by the vector theta_hat,

\hat{\theta} = ( \hat{\theta}_{uu}, \hat{\theta}_{uv}, \hat{\theta}_{vu}, \hat{\theta}_{vv} ) ,

and are computed as

\hat{\theta_{ij}} = Pr(pair from groups (i,j) | pair is linked), where i = u,v and j = u,v ,

\hat{\theta_{ij}} = \frac{N_{ij}p_{ij}}{ \sum_m \sum_{n \ge m}N_{mn}p_{mn}}, where i = u,v and j = u,v ,

See bumblebee website for more details https://magosil86.github.io/bumblebee/.

Value

Returns a data.frame containing:

• H1_group, Name of population group 1

• H2_group, Name of population group 2

• number_hosts_sampled_group_1, Number of individuals sampled from population group 1

• number_hosts_sampled_group_2, Number of individuals sampled from population group 2

• number_hosts_population_group_1, Estimated number of individuals in population group 1

• number_hosts_population_group_2, Estimated number of individuals in population group 2

• max_possible_pairs_in_sample, Number of distinct possible transmission pairs between individuals sampled from population groups 1 and 2

• max_possible_pairs_in_population, Number of distinct possible transmission pairs between individuals in population groups 1 and 2

• num_linked_pairs_observed, Number of observed directed transmission pairs between samples from population groups 1 and 2

• p_hat, Probability that pathogen sequences from two individuals randomly sampled from their respective population groups are linked

• est_linkedpairs_in_population, Estimated transmission pairs between population groups 1 and 2

• theta_hat, Estimated transmission flows or relative probability of transmission within and between population groups 1 and 2 adjusted for sampling heterogeneity. More precisely, the conditional probability that a pair of pathogen sequences is from a specific population group pairing given that the pair is linked.

Methods (by class)

• default: Estimates conditional probability of linkage (transmission flows)

References

1. Magosi LE, et al., Deep-sequence phylogenetics to quantify patterns of HIV transmission in the context of a universal testing and treatment trial – BCPP/ Ya Tsie trial. To submit for publication, 2021.

2. Carnegie, N.B., et al., Linkage of viral sequences among HIV-infected village residents in Botswana: estimation of linkage rates in the presence of missing data. PLoS Computational Biology, 2014. 10(1): p. e1003430.

See Also

See estimate_p_hat to prepare input data to estimate theta_hat

Examples

library(bumblebee)
library(dplyr)

# Estimate transmission flows within and between population groups accounting for variable
# sampling among population groups

# We shall use the data of HIV transmissions within and between intervention and control
# communities in the BCPP/Ya Tsie HIV prevention trial. To learn more about the data 
# ?counts_hiv_transmission_pairs and ?sampling_frequency


# Load and view data
#
# The input data comprises counts of observed directed HIV transmission pairs within 
# and between intervention and control communities in the BCPP/Ya Tsie trial,
# sampling information and the probability of linkage between individuals sampled
# from intervention and control communities (i.e. \code{p_hat})
#
# See ?estimate_p_hat() for details on estimating p_hat
results_estimate_p_hat <- estimated_hiv_transmission_flows[, c(1:10)]

results_estimate_p_hat

# Estimate theta_hat
results_estimate_theta_hat <- estimate_theta_hat(df_counts_and_p_hat = results_estimate_p_hat)

# View results
results_estimate_theta_hat