nll_two_inf_subpops_obs function

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

Function returning negative log-likelihood (nll) for patterns of mortality in infected and uninfected treatments when an infected population harbours two identified, or 'observed', subpopulations of hosts experiencing different patterns of virulence, e.g. with/without visible signs of infection.

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

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
• 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, respectively; each defaults to the Weibull distribution
• infsubpop: name of data frame column identifying the two subpopulations of infected hosts; '1' or '2'

Details

The nll is based on six parameters, the location and scale parameters for background mortality, plus separate location and scale parameters for each of the two infected subpopulations.

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

# create column 'infsubpop' in data01, fill with '0'
    data01$infsubpop <- 0

# infsubpop = '1' for individuals in infected treatments (g == 1)
  # with visible signs of sporulation (Sporulation = 1)
# infsubpop = '2' for individuals in infected treatments (g == 1)
  # with no visible signs of sporulation (Sporulation = 0)
    data01$infsubpop[data01$g == 1 & data01$Sporulation == 1] <- 1
    data01$infsubpop[data01$g == 1 & data01$Sporulation == 0] <- 2

    head(data01)

# 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){
        nll_two_inf_subpops_obs(
          a1 = a1, b1 = b1, a2 = a2, b2 = b2, a3 = a3, b3 = b3,
          data = data01,
          time = t,
          censor = censored,
          infected_treatment = g,
          d1 = "Frechet",
          d2 = "Weibull",
          d3 = "Weibull",
          infsubpop = infsubpop
        )}

# step #2: send 'prep_function' to 'mle2' for maximum likelihood estimation
    m01 <- mle2(
      m01_prep_function,
      start = list(a1 = 3, b1 = 1, a2 = 2, b2 = 0.5, a3 = 2, b3 = 0.5)
      )

    summary(m01)

See Also

nll_exposed_infected

nll_two_inf_subpops_unobs