Re: st: Main effect for time-varying covariate

[Steve Samuels <sjsamuels@gmail.com>]

Nichole, I like your plan in general, but I do have two questions:

To recapitulate: you have a binary Z(t) with values 0 or 1; people start
at Z = 0; some switch during followup and remain with Z = 1 thereafter.

My first question is one I asked earlier: On what grounds do you
exclude the possibility of non-proportional hazards for Z?

Second, how do you plan to to show the impact of that covariate on
cumulative incidence?

Below are a few recommendations. As the question applies to -stcox-, as
well as to -stcrreg-, I omit the sub-distribution terminology. I've left
out consideration of other covariates, but these obviously can be
accounted for.

1. Plot smoothed hazard functions for Z(t) = 0, all t, and Z(t) = 1, all
t. The shapes of the curves are of interest in themselves.

2. Plot and outfile CIFs that assume constant Z, as above:

F0(t) = CIF when Z(t) = 0 for all t

F1(t) = CIF when Z(t) = 1 for all t

As F1 and F0 are discontinuous, you may find it useful to interpolate to
values between event times

In your data, some people never switch, and F0 could be a good
description for this subgroup. You can check this by estimating separate
F0s for the subgroup and its complement.

Denote the maxima of F0 & F1 as Fmax0 and Fmax1, respectively.

3. Select several time points t* and estimate future CIFs for those who
switch at each t* ("switchers") and for those who don't switch
("stayers"), but who are at risk at t*. Here, I denote these CIFs
FF1(t|t*) and FF0(t|t*).

For t ≥ t*, FF1 and FF2 are estimated as follows:

switchers: FF1(t|t*) = (F1(t)-F1(t*))/(Fmax1-F1(t*))

stayers: FF0(t|t*) = (F0(t)-F0(t*))/(Fmax0-F0(t*))

FF0 and FF1 are zero at t*. As they start out with the same value,
plotting both on one graph allows one to visually assess the impact of
switching.

I end by noting that the future CIF approach works only because you have
the simplest type of time-varying covariate. Perhaps you can think of
CIF comparisons for other types.

Steve



> On Sep 5, 2013, at 2:48 PM, Nicole Boyle wrote:
> 
> Wonderful, Phil, thanks for the explanation! I'm going to go ahead and
> plot both outcomes.
> Thanks so much to Phil, Steve, and Adam... this has been a
> tremennnndously helpful and thought-provoking conversation. I have
> learned so much. I very much appreciate all the time each of you have
> taken to help me with this.
> 
> To sum up, here are the following analysis choices I've made per our
> discussion. Feel free to chime in if anything rubs you the wrong way:
> 
> -Modeling of hazard ratios will no longer be through the Fine-Gray
> model. Instead, covariate effects on the cause-specific hazard will be
> estimated through the Cox model, where the competing risk is censored.
> The only cause-specific event to be modeled will be the primary
> outcome of interest.
> 
> -The CIFs will be plotted in both forms:
>    * Cause-specific CIFs for both the primary outcome and competing
> outcome (-stcompet-)
>    * Subdistribution CIF for just the primary outcome (-stcrreg-).
> Simply for comparison's sake.
> 
> -I'm going to use -stsplit- instead of the -tvc- option to capture the
> time-varying nature of the time-varying risk factor, and then throw
> this risk factor into the model as a simple ["time-invariant"]
> covariate. I've decided to split at failure times, and expand the
> coding of the TVC risk factor to be "on" or "off" for each created
> time slot. Doing so will exploit the Cox model's maximum partial
> likelihood estimator property (briefly explained on page 13:
> http://www.stata.com/manuals13/ststsplit.pdf ).
> 
> Nicole
> 
> On Wed, Sep 4, 2013 at 4:17 PM, Phil Clayton
> <philclayton@internode.on.net> wrote:
>> From memory he used an example of breast cancer.
>> 
>> If you graph the CIF of cancer recurrence by age, older patients have a lower incidence of recurrence.
>> 
>> That looks good for older people until you graph the CIF of death - older patients have a higher incidence of death. Since death competes with recurrence, this makes the older patients look better on the recurrence CIF, but it's because they're dying before they get a chance to have recurrence. Doesn't look so good for older people any more.
>> 
>> You need to look at both outcomes in order to disentangle the competing events and understand what's actually going on. By selectively presenting one outcome you're not telling the whole story.
>> 
>> Phil
>> 
>> On 05/09/2013, at 6:37 AM, Nicole Boyle <nicboyle@gmail.com> wrote:
>> 
>>>> I went to a talk by Jason Fine last year and he gave the following general advice:
>>>> - use a Cox model for each of the competing outcomes (in your case infection & death)
>>>> - use a Fine-Gray model for each of the competing outcomes
>>>> - present all of those results
>>> 
>>> Thanks for the advice! What's the utility of presenting model results
>>> for the outcome of death if death is not an outcome of interest in my
>>> study? Feel free to direct me to a paper if you'd like.
>> 
>> 
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