Relative risks and survival probabilities from a survival fit

For each row of newdata, the linear predictor d = x'b + a at that row's levels is assembled exactly as in the fit. type = "risk" returns exp(d) WITHOUT the intercept – the relative risk against the baseline, the RRS of the book's tables (p.291): above 1 is more risk of failure. type = "survival" returns S(t) = exp(-(lambda t)^rho * exp(d)) (Eqn 16.4), the probability of still being alive at time – the book's p.292 numbers – with the lambda of the fit, given or estimated, so the intercept rho * log(lambda) is included (earlier versions left an ESTIMATED lambda out of S(t)). A reference level contributes zero; a level absent from the fit's data is an error, not a silent zero. An indirect() term contributes (n - 1)^(-d) sum_j a_S,j over the pen mates of the row IN newdata: the pen column must be there (otherwise the prediction is refused), and the mates are the distinct animals of that pen among the rows of newdata, counted with the static rule (mates = "all") whatever the fit used.

Usage

# S3 method for class 'breeding_fit_surv'
predict(
  object,
  newdata,
  time = NULL,
  type = c("risk", "survival"),
  entry = NULL,
  ...
)

Arguments

object

result of model_survival()

newdata

data.frame with the fixed and random columns of the formula and the pen column of every indirect() term. The random column may hold any animal of the pedigree (a sire without a record included) – that is how the book computes the percentage of live daughters.

time

survival mode only: the time (one number, or one per row of newdata) at which to evaluate S(t); numeric, so a factor or text is refused rather than read as its codes (the same holds for entry)

type

"risk" (default) for the relative risk exp(d), "survival" for S(time)

entry

survival mode only: the time (one number, or one per row) the animal is known alive at; the result is then S(time | entry) = S(time) / S(entry), the survival over the piece (entry, time] of an elementary record. For an animal whose covariates change along its life, the survival to the end is the PRODUCT of this over its pieces (each with its own covariates), which is how the time-dependent model of model_survival(entry =, subject =) reads

...

unused, kept for the generic

Value

a numeric vector, one value per row of newdata