phreg {eha} | R Documentation

## 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, center = 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.

`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?
`center` | Logical, only affects plotting. Results are reported as is, without centering. See Details.

### 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

S0((t/b)^a)^exp((z - mean(z)) beta)

where S0 is some standardized survivor function.

If `center = TRUE` (default), graphs show the "baseline" distribution at the means of (continuous) covariates, and for the reference category in case of factors (avoiding representing "flying pigs"). If `center = FALSE` the baseline distribution is at the value zero of all covariates. It is usually a good idea to use `center = FALSE` in combination with "precentering" of covariates, that is, subtracting a reference value, ideally close to the center of the covariate distribution. In that way, the "reference" will be the same for all subsets of the data.

### 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, if `center = TRUE`. 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).
`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)

[Package eha version 2.6.0 Index]