nll_two_inf_subpops_unobs function

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

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

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.

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)

See Also

nll_exposed_infected

nll_two_inf_subpops_obs