Proportional hazards model with baseline hazard(s) from the Weibull family of distributions. Allows for stratification with different scale and shape in each stratum, and left truncated and right censored data.
weibreg(formula = formula(data), data = parent.frame(),
na.action = getOption("na.action"), init, shape = 0,
control = list(eps = 1e-04, maxiter = 10, trace = FALSE),
singular.ok = TRUE, model = FALSE, x = FALSE, y = TRUE, center = TRUE)a formula object, with the response on the left of a ~ operator, and the terms on the right. The response must be a survival object as returned by the Surv function.
a data.frame in which to interpret the variables named in the formula.
a missing-data filter function, applied to the
model.frame, after any subset argument has been used.
Default is options()$na.action.
vector of initial values of the iteration. Default initial value is zero for all variables.
If positive, the shape parameter is fixed at that value (in each stratum). If zero or negative, the shape parameter is estimated. If more than one stratum is present in data, each stratum gets its own estimate.
a list with components eps (convergence
criterion), maxiter (maximum number of iterations), and
silent (logical, controlling amount of output). You can
change any component without mention the other(s).
Not used.
Not used.
Return the design matrix in the model object?
Return the response in the model object?
Deprecated, and not used. Will be removed in the future.
A list of class c("weibreg", "coxreg") with components
Fitted parameter estimates.
Covariance matrix of the estimates.
Vector of length two; first component is the value at the initial parameter values, the second componet is the maximized value.
The score test statistic (at the initial value).
The estimated linear predictors.
Means of the columns of the design matrix.
Weighted (against exposure time) means of covariates; weighted relative frequencies of levels of factors.
Number of spells in indata (possibly after removal of cases with NA's).
Number of events in data.
Used by extractor functions.
Used by extractor functions.
The Surv vector.
Logical vector indicating the covariates that are factors.
The covariates.
Total Time at Risk.
List of levels of factors.
The calling formula.
The call.
The method.
Did the optimization converge?
Did the optimization fail? (Is NULL if not).
TRUE if shape was fixed in the estimation.
The print method print.weibreg doesn't work if
threeway or higher order interactions are present.
Note further that covariates are internally centered, if center =
TRUE, by this function,
and this is not corrected for in the output. This affects the estimate
of \(\log(scale)\), but nothing else. If you don't like this, set
center = FALSE.
The parameterization is the same as in coxreg
and coxph, but different
from the one used by survreg.
The model is
$$h(t; a, b, \beta, z) = (a/b) (t/b)^{a-1} exp(z\beta)$$
This is in correspondence with Weibull. To compare
regression coefficients
with those from survreg you need to divide by estimated shape
(\(\hat{a}\)) and change sign. The p-values and test statistics are
however the same, with one exception; the score test is done at
maximized scale and shape in weibreg.
This model is a Weibull distribution with shape parameter \(a\) and scale parameter \(b \exp(-z\beta / a)\)
# NOT RUN {
dat <- data.frame(time = c(4, 3, 1, 1, 2, 2, 3),
status = c(1, 1, 1, 0, 1, 1, 0),
x = c(0, 2, 1, 1, 1, 0, 0),
sex = c(0, 0, 0, 0, 1, 1, 1))
weibreg( Surv(time, status) ~ x + strata(sex), data = dat) #stratified model
# }
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