Re: st: margins after stcox with time-dependent covariate

[Steve Samuels <sjsamuels@gmail.com>]

Mario Petretta asked about -margins- after -stcox-.

Maarten (http://www.stata.com/statalist/archive/2013-03/msg00000.html)
stated that -margins- after -stcox- can deal with quantities related to
the estimated hazard ratios. This is because -margins- operates on e(b).
He recommends -stpm2-, but, -margins- after -stpm2- cannot operate on
all functions of the baseline hazard.

For example,

. margins i.x, predict(meansurv)
works, but
. margins i.x, predict(hazard)
does not.

I agree with Maarten that -stpm2- is preferable to -stcox- for computing
descriptive statistics for a survival distribution. Notably, -stpm2- has
a  -predict, hazard - command with at() options. I recommend that Mario
use these to describe the two-way interaction in his model. He will need
to center remaining variables and also use the "zero" option.

For time-dependent covariates. I think that the plotted hazard function
is the only useful descriptive summary. (Hazard ratios are comparative
summaries). The survival function starting from time 0 is not
descriptive when covariate values change. What would the curve S(t|
X(t)= c ) describe? It would describe survival only for a population for
whom the value of X was C throughout.

Data with time-dependent covariates is multiple record data. -stcox- has
a cluster(id) option that ensures correct standard errors for such data,
 but-stpm2- does not. An earlier version, -stpm- by Patrick Royce (from
SSC), does have the cluster option, so Mario should use that for
estimating standard errors. Like -stpm2-, -stpm- has a tvc() option for
estimating time-varying-coefficients of some variables. This is useful
for checking for non-proportionality. The algorithm in -stpm2- is more
flexible than that in -stpm-, so I would do the check with -stpm2-.

One other point: Mario -stsplit- at failures. This works for
-stcox- because only values at failures are relevant. But it will not
work for -stpm- or -stpm2-, which require the exact times of change for
time-dependent covariates. The last example in the Manual entry for
-stset- shows how to prepare this kind of data. There is also a Stata
Tip by Ben Jann: Stata tip 8: Splitting time-span records with
categorical time-varying covariates. The Stata Journal (2004), 4, Number
2, pp. 221–222. This can be downloaded for free.

Steve
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