phreg {eha}

Parametric Proportional Hazards Regression

Description

Proportional hazards model with parametric baseline hazard(s). Allows for stratification with different scale and shape in each stratum, and left truncated and right censored data.

Usage

phreg(
  formula = formula(data),
  data = parent.frame(),
  na.action = getOption("na.action"),
  dist = "weibull",
  cuts = NULL,
  init,
  shape = 0,
  param = c("canonical", "rate"),
  control = list(eps = 1e-08, maxiter = 20, trace = FALSE),
  singular.ok = TRUE,
  model = FALSE,
  x = FALSE,
  y = TRUE
)

Arguments

formula

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.

data

a data.frame in which to interpret the variables named in the formula.

na.action

a missing-data filter function, applied to the model.frame, after any subset argument has been used. Default is options()$na.action.

dist

Which distribution? Default is "weibull", with the alternatives "ev" (Extreme value), "gompertz", "pch" (piecewise constant hazards function), "loglogistic" and "lognormal". A special case like the exponential can be obtained by choosing "weibull" in combination with shape = 1, or "pch" without cuts.

cuts

Only used with dist = "pch". Specifies the points in time where the hazard function jumps. If omitted, an exponential model is fitted.

init

vector of initial values of the iteration. Default initial value is zero for all variables.

shape

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. Only relevant for the Weibull and Extreme Value distributions.

param

Applies only to the Gompertz distribution: "canonical" is defined in the description of the Gompertz distribution; "rate" transforms scale to 1/log(scale), giving the same parametrization as in Stata and SAS. The latter thus allows for a negative rate, or a "cure" (Gompertz) model. The default is "canonical"; if this results in extremely large scale and/or shape estimates, consider trying "rate".

control

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).

singular.ok

Not used.

model

Not used.

x

Return the design matrix in the model object?

y

Return the response in the model object?

Details

The parameterization is the same as in coxreg and coxph, but different from the one used by survreg (which is not a proportional hazards modelling function). The model is

S(t; a, b, \beta, z) = S_0((t/b)^a)^{\exp((z-mean(z))\beta)}

where S0 is some standardized survivor function.

Value

A list of class c("phreg", "coxreg") with components

coefficients

Fitted parameter estimates.

cuts

Cut points for the "pch" distribution. NULL otherwise.

hazards

The estimated constant levels in the case of the "pch" distribution. NULL otherwise.

var

Covariance matrix of the estimates.

loglik

Vector of length two; first component is the value at the initial parameter values, the second componet is the maximized value.

score

The score test statistic (at the initial value).

linear.predictors

The estimated linear predictors.

means

Means of the columns of the design matrix, except those columns corresponding to a factor level. Otherwise all zero.

w.means

Weighted (against exposure time) means of covariates; weighted relative frequencies of levels of factors.

n

Number of spells in indata (possibly after removal of cases with NA's).

n.events

Number of events in data.

terms

Used by extractor functions.

assign

Used by extractor functions.

wald.test

The Wald test statistic (at the initial value).

y

The Surv vector.

isF

Logical vector indicating the covariates that are factors.

covars

The covariates.

ttr

Total Time at Risk.

levels

List of levels of factors.

formula

The calling formula.

call

The call.

method

The method.

convergence

Did the optimization converge?

fail

Did the optimization fail? (Is NULL if not).

pfixed

TRUE if shape was fixed in the estimation.

Warning

The lognormal and loglogistic distributions are included on an experimental basis for the moment. Use with care, results may be unreliable!

The gompertz distribution has an exponentially increasing hazard function under the canonical parametrization. This may cause instability in the convergence of the fitting algorithm in the case of near-exponential data. It may be resolved by using param = "rate".

Note

The lognormal and loglogistic baseline distributions are extended to a three-parameter family by adding a "proportionality" parameter (multiplying the baseline hazard function). The log of the estimated parameter turns up as '(Intercept)' in the printed output. The reason for this extension is that the standard lognormal and loglogistic distributions are not closed under proportional hazards.

Author(s)

Göran Broström

See Also

coxreg, check.dist, link{aftreg}.

Examples

data(mort)
fit <- phreg(Surv(enter, exit, event) ~ ses, data = mort)
fit
plot(fit)
fit.cr <- coxreg(Surv(enter, exit, event) ~ ses, data = mort)
check.dist(fit.cr, fit)