Re: st: Main effect for time-varying covariate

[Phil Clayton <philclayton@internode.on.net>]

Make sure you are aware of the inferential problems using time-varying covariates in the Fine-Gray regression model. This is discussed in the "[ST] stcrreg" manual at the end of the "Multiple records per subject" section.

It wouldn't be hard to program a wrapper for generating and plotting the Schoenfeld-like residuals. That's essentially what -estat phtest, plot()- does (take a look at -viewsource stphtest.ado-)

Phil

On 31/08/2013, at 4:23 AM, Nicole Boyle <nicboyle@gmail.com> wrote:

> Thanks for the helpful response! It seems I have falsely
> gained the impression that "stsplit" is functionally
> equivalent to, but just more labor-intensive than, using
> the "tvc" option. Per your advice, I'm going to try out
> stsplit; it certainly seems to be the more intuitive route.
> 
> Thanks very much!
> Nicole
> 
> 
> Steve:
> I appreciate the caution you exercised when addressing my
> question. I see that your intention was to avoid giving out
> poor/misleading advice, so I thank you for voluntarily taking
> your personal time to do so. I apologize for my unintended
> lack of clarity when attempting to answer your inquiries.
> 
> Concerning your responses, thank you for being so thorough!
> Although I'm admittedly far from fluent in stats (e.g. I'm lost
> on #5, even with your explanation and corrections), you've
> been very helpful in elucidating this whole "tvc" situation.
> 
> Thanks so much!
> Nicole
> 
> 
> _Sidenote:_
> Just for the record, unlike stcox, stcrreg doesn't allow for the
> plotting of Schoenfeld residuals, just "Schoenfeld-like residuals,"
> which (IMHO) are cumbersome to generate and feel like an
> unintended workaround.
> http://www.stata.com/statalist/archive/2010-10/msg00756.html
> Nor will stcrreg allow for testing the non-zero slope (rho) of those
> residuals, as Adam has also previously discussed:
> http://www.stata.com/statalist/archive/2013-08/msg00181.html
> It's a bummer. This is an issue in Stata 12. I'm hoping
> Stata 13 has these PH testing options to available for stcrreg,
> but it doesn't appear so (according to those new features listed
> on stata.com/stata13).
> 
> 
> On Thu, Aug 29, 2013 at 12:03 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>> "The HR exp((b1 + b2*exp(-0.35*_t)) compares hazards for (x0+1) and x0"
>> should be:
>> The HR exp((b1 + b2*exp(-0.35*_t)) compares hazards for (x(t)+1) and x(t).
>> 
>> 
>> The second sentence should be: "I consider it professionally irresponsible
>> to answer a question if I'm unsure that a poster has accurately characterized
>> the substantive problem."
>> S.
>> 
>> 
>> Nicole, Statalist is not a help line in which responders are obligated to
>> answer questions, as asked. I consider it professionally irresponsible
>> to answer a question if I'm that a poster has accurately characterized
>> the substantive problem. Your initial question showed some uncertainty,
>> so I asked you to "describe what it [your covariate] is and how its
>> values are determined." You didn't do this, so I asked again.
>> 
>> 
>> As you've observed, the tvc() option is confusing. In particular, it is
>> not used only for testing the PH assumption. So let's review the
>> possibilities,
>> 
>> 1. Your covariate "z", say, assumed 0-1, is time-varying. If z appears
>> only in the main variable list for -stcrreg- (or -stcox-), you are
>> making the PH assumption, and the estimated hazard ratio exp(b)
>> describes the relative hazard of occurrence for someone with Z, compared
>> to someone without z.
>> 
>> 2. You say you are not interested in assessing the PH assumption, but
>> how can you know that it's true?. You check it as follows:
>> 
>> a) Include the covariate in the tvc() list, which by default enters the
>> covariate into an interaction with _t. However the default assumes that
>> the HR increases or decreases with time and will miss non-linear
>> interactions (e.g. the HR rises, then falls).
>> 
>> b) The preferred approach is to first plot the Schoenfeld residuals
>> against time. (Grambsch, Patricia M, and Terry M Therneau. 1994.
>> Proportional hazards tests and diagnostics based on weighted residuals.
>> Biometrika 81, no. 3: 515-526.). These plots will suggest the form of
>> the expression to use in the texp() option.
>> 
>> 3. In 2a, the covariate appears in both the main and tvc() lists. But it
>> is possible to fit a PH model with a time-varying covariate that is
>> entered *only* in the tvc() list. This can occur if the effect of
>> covariate is proportional to a known function of time. The example on p.
>> 137 of the Survival manual shows a decay function:
>> 
>> . stcox age, tvc(drug1 drug2) texp(exp(-0.35*_t))
>> 
>> Here the effects of the drug "wear off".
>> 
>> 4. To elaborate on this example, suppose that a continuous "exposure" x0
>> is measured at time 0, but is subject to the same decay function. as
>> above. Thus x(t) = x0*exp(-0.35*t)
>> 
>> You can tell Stata about this in two ways:
>> 
>> a. Create the split data set with the value for x from the equation above.
>> Then put x into the main predictor list:
>> 
>> . stcox x
>> 
>> (I show -stcox-, since I don't know what your -stcrreg- command looks
>> like.)
>> 
>> b. Enter x0 into the tvc() list:
>> 
>> . stcox , tvc(x0) texp(exp(-0.35*_t))
>> 
>> In both cases, x(t) = x0*exp(-0.35*t) and the hazard ratio compares the
>> hazards for (x(t)+1) and x(t). The HR is still constant at all values of
>> t.
>> 
>> 5. It is also possible to allow for a differential effect of x at
>> baseline, still keeping the PH assumption.
>> 
>> . stcox x0, tvc(x0) exp(-0.35*_t)
>> 
>> Here the equation for the log hazard function is:
>> 
>> log(h(t|x0) = log(h(t) + x0*(b1 + b2*exp(-0.35*_t))
>> 
>> The HR exp((b1 + b2*exp(-0.35*_t)) compares hazards for (x0+1) and x0
>> 
>> 6. Finally, one can prepare the data as in 2a, but then check the PH
>> assumption with the tvc() statement and residual plots.
>> 
>> . stcox x, tvc(x)
>> 
>> Steve
>> 
>> 
>> 
>> 
>> On Aug 28, 2013, at 5:36 PM, Nicole Boyle wrote:
>> 
>> Forgive me, but I don't understand how discussing these nuances is relevant
>> when addressing the original inquiry: determining the theoretical utility and
>> interpretation of a time-varying covariate whose time-invariant component has
>> been excluded from the model. These concerns seem more in line with a
>> discussion about lead/length time bias.
>> 
>> Nevertheless, to assuage your concerns, these patients are continually
>> monitored for the presence of this particular risk factor, regardless
>> of exhibited symptoms.
>> 
>> ________________________________________
>> From: owner-statalist@hsphsun2.harvard.edu
>> [owner-statalist@hsphsun2.harvard.edu] on behalf of Steve Samuels
>> [sjsamuels@gmail.com]
>> Sent: Wednesday, August 28, 2013 1:34 PM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: Main effect for time-varying covariate
>> 
>> Nichole:
>> 
>> Please explain what the risk factor is and how its activation depends
>> on the medical records. Perhaps you mean that the presence of the risk
>> factor is known only after some test, and that test is recorded in the
>> records. If so, the fact that the test is made at time "t" doesn't
>> preclude the presence of the factor before "t". Also, if the test was
>> made in response to certain symptoms, then other issues arise.
>> 
>> Steve
>> 
>> 
>> On Aug 27, 2013, at 5:00 PM, Boyle, Nicole M wrote:
>> 
>> Hi Steve,
>> 
>> Thanks for your response! I've elaborated on the issue in more
>> (perhaps excessive) detail:
>> 
>> 
>> ***Variable details***
>> I'd like to model a binary variable as time-varying. This binary
>> variable will model the onset of a particular
>> risk factor. All patients under study enter into the study with this
>> risk factor "turned off." The timing of
>> when this risk factor "turns on" depends entirely on each patient's
>> medical records (and for some patients,
>> this risk factor may never "turn on"). This risk factor can only go
>> from "off" to "on"; the reverse ("on" to "off")
>> is not possible.
>> 
>> 
>> ***Reason for modeling this var as time-varying***
>> I would like to model this particular risk factor as a time-varying
>> covariate in order to assess its association
>> with the outcome while avoiding possible immortal time bias. In other
>> words, I'd like assess the hazard ratio
>> (at any instantaneous time during observation) for the outcome event
>> comparing those with the risk factor
>> "turned on" vs. those with the risk factor "turned off", accounting
>> for the possibility that a patient's risk factor
>> may be "turned on" at any time before or after his/her outcome event.
>> 
>> 
>> ***Stata's covariate vs. coefficient distinction***
>> Right now, the closest I can find to an answer is a mention in the
>> Stata Statistical Analysis Manual:
>> 
>>      http://www.stata.com/manuals13/ststcox.pdf#ststcoxRemarksandexamples
>> 
>> In said manual, Cox models are run with and without the time-invariant
>> component (on page 12 and pages
>> 13-14, respectively). The Stata manual differentiates between models
>> fit with time-varying COVARIATES
>> (without the time-invariant component) from models fit with
>> time-varying COEFFICIENTS (with the time-invariant
>> component), saying
>> 
>>    "Above we used tvc() and texp() to demonstrate fitting models
>> with time-varying covariates, but
>>     these options can also be used to fit models with time-varying
>> coefficients."
>> 
>> I think this aforementioned covariate/coefficient distinction may be
>> the source of my confusion. From the
>> manual's suggestion, it seems like adding this time-invariant
>> component (aka: "main effect") will only test
>> the proportional hazards assumption of the coefficient.
>> 
>> 
>> Thanks,
>> Nicole
>> ________________________________________
>> From: owner-statalist@hsphsun2.harvard.edu
>> [owner-statalist@hsphsun2.harvard.edu] on behalf of Steve Samuels
>> [sjsamuels@gmail.com]
>> Sent: Wednesday, August 21, 2013 2:13 PM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: Main effect for time-varying covariate
>> 
>> I'd need to know details about the internal covariate before I can
>> answer your question. So please describe what it is and how its values
>> are determined.
>> 
>> Steve
>> 
>> On Aug 20, 2013, at 7:14 PM, Boyle, Nicole M wrote:
>> 
>> Hi all,
>> 
>> I'm modeling a multivariable competing risks regression model
>> (stcrreg), and I want to include an internal
>> time-varying covariate.
>> 
>> (1) Should I include a main effect for this time-varying covariate in
>> the model? (I'm not trying to test
>> the proportionality assumption here)
>> 
>> (2) How does one report the overall value and significance of this
>> time-varying variable?
>> 
>> Thanks,
>> Nicole
>> 
>> (my apologies if this is a duplicate... 1st email bounced)
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