nll_two_inf_subpops_unobs {anovir}

Negative log-likelihood function: two unobserved subpopulations of infected hosts

Description

Function returning negative log-likelihood (nll) for patterns of mortality in infected and uninfected treatments when an infected population is assumed to harbour two distinct subpopulations of hosts experiencing different virulence. The nll is based on seven parameters, the location and scale parameters for background mortality, separate location and scale parameters for each of the two infected subpopulations, and a parameter estimating the proportions of the two subpopulations

Usage

nll_two_inf_subpops_unobs(
  a1 = a1,
  b1 = b1,
  a2 = a2,
  b2 = b2,
  a3 = a3,
  b3 = b3,
  p1 = p1,
  data = data,
  time = time,
  censor = censor,
  infected_treatment = infected_treatment,
  d1 = "Weibull",
  d2 = "Weibull",
  d3 = "Weibull"
)

Arguments

a1, b1

location and scale parameters describing background mortality

a2, b2

location and scale parameters describing mortality due to infection in one subpopulation

a3, b3

location and scale parameters describing mortality due to infection in the other subpopulation

p1

parameter estimating the proportion of infected hosts in the first of the two subpopulations; 0 <= p1 <= 1

data

name of data frame containing survival data

time

name of data frame column identifying time of event; time > 0

censor

name of data frame column idenifying if event was death (0) or right-censoring (1)

infected_treatment

name of data frame column identifying if data are from an infected (1) or uninfected (0) treatment

d1, d2, d3

names of probability distributions chosen to describe background mortality and mortality due to infection in each subpopulation, respectively; defaults to the Weibull distribution

Details

p1 is the estimated proportion of hosts associated with the location and scale parameters a2, b2; 0 <= p1 <= 1.

It is assumed the patterns of mortality within each subpopulation act independently of one another.

See Also

nll_exposed_infected nll_two_inf_subpops_obs

Examples

# example using data from Parker et al
    data01 <- data_parker

# step #1: parameterise nll function to be passed to 'mle2'
    m01_prep_function <- function(
      a1 = a1, b1 = b1, a2 = a2, b2 = b2, a3 = a3, b3 = b3, p1 = p1){
        nll_two_inf_subpops_unobs(
          a1 = a1, b1 = b1, a2 = a2, b2 = b2, a3 = a3, b3 = b3, p1 = p1,
          data = data01,
          time = t,
          censor = censored,
          infected_treatment = g,
          d1 = "Frechet",
          d2 = "Weibull",
          d3 = "Weibull"
          )}

# step #2: send 'prep_function' to 'mle2' for maximum likelihood estimation
    m01 <- mle2(
      m01_prep_function,
      start = list(a1 = 2, b1 = 1,
                   a2 = 2, b2 = 0.3,
                   a3 = 2, b3 = 0.7,
                   p1 = 0.5)
      )

    summary(m01)