# [R] coxph linear.predictors

David Winsemius dwinsemius at comcast.net
Wed Oct 27 19:14:54 CEST 2010

```On Oct 27, 2010, at 12:12 PM, Bond, Stephen wrote:

> I would like to be able to construct hazard rates (or unconditional
> death prob)

Hazards are not probabilities (since probabilities are constrained to
the range [0,1] and hazards are unbounded upward.)

> for many subjects from a given survfit.
>
> This will involve adjusting the ( n.event/n.risk)
> with (coxph object )\$linear.predictors
> I must be having another silly day as I cannot reproduce the linear
> predictor:
>
> fit <- coxph(Surv(futime, fustat) ~ age, data = ovarian)
> fit\$linear.predictors[1]
> [1] 2.612756

That's the linear predictor (the beta*X) and that particular number
only applies to the first case.

>
> coef(fit)*model.matrix(fit)[1,1]
>     age
> 11.69021
>

I don't know what that might be and you are not telling us what you
think it is.

> The above is based on the help listing for coxph.object
> coefficients: the coefficients of the linear predictor, which multiply
>          the columns of the model matrix.  If the model is
>          over-determined there will be missing values in the vector
>          corresponding to the redundant columns in the model matrix.
>
> Also, please comment whether n.event/n.risk

The Nelson-Aalen estimator of the cumulative hazard as a function of
intervals prior to t is sum( n-event(t)/ n.risk(t))

> gives the baseline hazard exp(alpha) ?

No. The "baseline hazard", as you are calling this, would be an
estimate for persons with all covariates = 0, so in this case is for
women of age=0. (Not a particularly interpretable result in many
situations. The baseline hazard following treated ovarian cancer for
neonates is not medically sensible.)

What is the purpose of this request? Is someone telling you you need
to provide estimates for instantaneous hazards?

--

David Winsemius, MD
West Hartford, CT

```