Re: st: Main effect for time-varying covariate

[Nicole Boyle <nicboyle@gmail.com>]

Steve, your thoughts mirror much of my inner dialogue recently! Thanks
for your input. It's got me thinking quite a bit (as you can see by
the lengthiness of this post).

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

I treated Z the same way that I would treat a typical fixed variable
in a Cox model, since each individual's covariate value input into the
model, and not the coefficient value output from the model, depends on
time.

After I split per each failure time and assigned Z's values per each
failure time per each subject, I fit the model for the outcome of
infection with Z as a fixed covariate:
.    quietly stcox var1 var2 Z, schoenfeld(sch*) scaledsch(sca*)
The Therneau and Grambsch tests for non-zero slopes of the Schoenfeld
residuals were conducted:
.    stphtest, detail
The scaled Schoenfeld residuals and their lowess smooths were also
plotted over time for visual assessment of PH:
.    stphtest, plot(Z) msym(oh)

The results of these analyses supported the notion of Z's independence
from time.


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

I haven't been entirely clear in my previous posts. My study concerns
describing incidence per hospital, and there are two hospitals. My
previous mention of plotting CIFs concerned plotting overall
cause-specific CIFs per each hospital (for both causes: infection
[outcome of interest] and death [competing]) before any covariates are
involved.

But to answer your question, thus far, I have not considered plotting
anything (CIFs or hazard functions) for Cox cause-specific covariate
effects, let alone Z. With regards to the inherent underlying question
of "What effects, if any, should I present?" I see these as my
options:

Option 1: Plot functions for EVERY covariate for BOTH cause-specific
versions (infection and death) for BOTH hospitals. That's a lot of
clutter.

Option 2: Plot functions for only those covariates found to be
significant. I'm not comfortable with data-driven decisions, and this
feels data-driven.

Option 3: Plot functions for only those covariates considered (a
priori) to be the most important in this analysis. Z might be
considered the "most important" covariate, as it was one of the
primary scientific questions. However, I'm not sure if this is the
best approach, since this study is largely exploratory, and only
plotting Z might take the limelight away from other [possibly more]
important covariates. Z's importance doesn't mean that other
covariates are necessarily UNimportant.

Option 4: Plot no covariate effect functions. This avoids the
downfalls of options 1-3, but also doesn't add any information.

Any suggestions?


> 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.

This "switchers" and "stayers" method is a very interesting idea!
Thanks for explaining this; I'd never heard of it before.

Wouldn't you have to make sure that those "stayers" remain "stayers"
throughout observation, or would it be sufficient enough to make sure
that the following two CIF functions look about the same?

   CIF for Z(t)=0, for all t (including switchers and never-switchers)
   CIF for Z(t)=0, for all t (ONLY including never-switchers)

Or is this^ what you meant by, "You can check this by estimating
separate F0s for the subgroup and its complement"?

Do you know of a reference where I could learn more?


Now, one more question of my own:
I've fit Cox models to estimate cause-specific covariate effects where
cause=infection [outcome of interest] and censored=death [our
"competing risk"]. However, I haven't yet considered fitting models
where cause=DEATH and censored=infection.

With cause-specific Cox models, is this necessary to fit separate
models for the outcome of interest (cause=infection) AND the competing
cause (cause=death)? Or is it considered good practice to only fit
models for the outcome of interest (cause=infection)?


Nicole

On Mon, Sep 9, 2013 at 3:53 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>
> 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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