nll_proportional_virulence function

Negative log-likelihood function: nll proportional virulence

Function assuming hazard functions describing virulence are proportional among infected treatments.

nll_proportional_virulence(
  a1 = a1,
  b1 = b1,
  a2 = a2,
  b2 = b2,
  theta = theta,
  data = data,
  time = time,
  censor = censor,
  infected_treatment = infected_treatment,
  reference_virulence = reference_virulence,
  d1 = "Weibull",
  d2 = "Weibull"
)

Arguments

• a1, b1: location and scale parameters describing background mortality
• a2, b2: location and scale parameters describing mortality due to infection
• theta: a constant describing the proportional relationship of virulence; theta > 0
• 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 identifying 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
• reference_virulence: name of data frame column identifying the infected treatment to use as a reference when estimating virulence; value of 1 the reference treatment and 2 for treatment to be compared
• d1, d2: names of probability distributions describing background mortality and mortality due to infection, respectively; both default to the Weibull distribution

Details

The proportional hazards assumption requires, h1(t) / h2(t) = c, where h1(t) and h2(t) are two hazard functions at time t, and c is a constant. In this function the hazard functions for the increased mortality due to infection are assumed to be proportional for different infection treatments within the same experiment.

In the default form, one infected treatment is denoted '1' and used as the reference treatment for virulence against which the virulence in a second infected population, '2', is scaled. The default function can be extended to compare multiple treatments against the reference (see vignette: Worked examples II)

Examples

data01 <- data_lorenz

# create column 'reference_virulence' with values of 1 and 2 when
  # Infectious.dose = 5000 and 160000, respectively, otherwise 0

data01$reference_virulence <- ifelse(data01$g == 0, 0,
 ifelse(data01$g == 1, ifelse(data01$Infectious.dose == 5000, 1,
   ifelse(data01$Infectious.dose == 160000, 2, 0)), 0)
 )

m01_prep_function <- function(
  a1 = a1, b1 = b1, a2 = a2, b2 = b2, theta = theta){
    nll_proportional_virulence(
      a1 = a1, b1 = b1, a2 = a2, b2 = b2, theta = theta,
      data = data01,
      time = t,
      censor = censored,
      infected_treatment = g,
      reference_virulence = reference_virulence,
      d1 = 'Gumbel', d2 = 'Weibull')
      }

m01 <- mle2(m01_prep_function,
  start = list(a1 = 23, b1 = 5, a2 = 4, b2 = 0.2, theta = 1)
  )

summary(m01)

# virulence in the high dose treatment is estimated as
 # ~ 6x greater than in the low dose treatment