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Regression with a censored response

Source: R/further-regression.R
tda_zreg.Rd

tda_zreg/tda_zreg1 are TDA's zreg/zreg1: least squares with a censoring indicator, a Buckley-James estimator where right-censored cases are iteratively reweighted rather than dropped or treated as exact.

Usage

tda_zreg(formula, data, censor, options = list(), dir = tempfile("tda"), ...)

tda_zreg1(
  formula,
  data,
  censor,
  dates = NULL,
  options = list(),
  dir = tempfile("tda"),
  ...
)

Arguments

formula

a two-sided formula.

data

a data frame.

censor

the censoring indicator, as a name or a vector: TRUE or 1 marks a case whose response is censored, as in survival::Surv. See Details for how this maps to TDA's yw=.

options

a named list of further TDA options, passed through.

dir

working directory.

...

passed to tda_run.

dates

for tda_zreg1, the names of the event-date columns in data – zreg1's xv=; each becomes the time-varying indicator date <= t at every step.

Value

An object of class tda_fit.

Details

censor follows R's convention (survival::Surv()'s): TRUE or 1 marks a case whose response is censored. TDA's own yw= runs the other way – a case counts as exact when its indicator is zero – so this is translated for you, the same correction tda_lsreg1 documents for its cen=. Sent through unflipped, zreg recovers essentially nothing of a known relationship (a near-zero slope); flipped, it recovers it closely, checked against the uncensored least-squares fit.

The iteration often hits mxit (default 20) without TDA's tolerance test passing, even once the estimates have stopped moving – tda_run then warns “TDA did not converge”. Raising options = list(mxit = ...) rarely changes the estimate by more than its last few iterations already did; check by comparing coefficients at two values of mxit rather than assuming the warning means the fit is unusable.

tda_zreg1 is TDA's zreg1, the residual-life variant: instead of one fit, it refits the Buckley-James regression of the remaining lifetime (\(Y - t\)) at every time step \(t = 0, 1, 2, \ldots\) while more than 10 cases remain at risk, and the result is the whole trajectory of coefficients over time. Time-varying covariates enter as event dates (dates, TDA's xv=): at each step, a date column becomes the indicator "has this event happened by \(t\)" (date <= t), so its coefficient traces how experiencing the event shifts expected remaining lifetime. It takes the same plain one-row-per-case frame as tda_zreg, plus the date columns – the dichotomisation over time is the time variation.

See also

Other regression: TDA_FAMILIES, TDA_QRMODELS, tda_freg(), tda_gdf(), tda_l1reg(), tda_lsreg(), tda_mlrc_design(), tda_mreg(), tda_nlreg(), tda_npreg()

Examples

set.seed(1)
d <- data.frame(x = round(rnorm(50), 2))
d$y <- round(2 - 0.8 * d$x + rnorm(50, sd = 0.4), 3)
d$cen <- as.integer(d$y > 2.2)
d$yc <- pmin(d$y, 2.2)
# zreg iterates to reweight the censored cases; a "did not converge"
# warning here is typical of the method, not a sign the fit is wrong.
# True coefficients are 2 and -0.8, so this should land close to them.
zr <- tda_zreg(yc ~ x, d, censor = "cen")
#> Warning: TDA did not converge after 21 iterations
coef(zr)
#> Intercept         x 
#>  2.029259 -0.800771 
head(fitted(zr))
#> [1] 2.5337452 1.8851207 2.7019071 0.7480259 1.7650050 2.6858916
predict(zr, newdata = data.frame(x = c(0, 1)))
#> [1] 2.029259 1.228488