Cox-Regression with time-dependent covariate

[la volta statistics]

Hi all

I am doing a Cox-Regression with data from patients. The time frame starts
when a patient is delivered to the hospital. A patient stays there normally
for several days and either survives or dies. Surviving patients are
followed then for several yeas in the post-hospital time.

One of my covariates (dichotomous) describes whether the patient had a shock
when he was delivered to the hospital. This variable is violating the
assumption of proportional hazard.
I therefore defined a time-dependent covariate as a function of the time
surviving.

TIME PROGRAM.
COMPUTE T_COV_shock = T_ * shock_presentation .
COXREG
  time  /STATUS=Status(1)
  /METHOD=ENTER shock_presentation T_COV_shock
  /CRITERIA=PIN(.05) POUT(.10) ITERATE(20) .


I get the following results:

                                B               sig             Exp(B)
shock_presentation      2.540           < 0.001 12.69
T_COV_shock                     -0.48           < 0.001 0.619

How would I describe those results? I see that the risk for dying is much
higher for patients with a shock at the hospital presentation
(shock_presentation). But how would I explain the time dependent covariate
for the shock (T_COV_shock)?

Thanks, Christian


*******************************
la volta statistics
Christian Schmidhauser, Dr.phil.II
Weinbergstrasse 108
Ch-8006 Zürich
Tel: [phone]
Fax: [phone]
mailto:[hidden email]

[Marta García-Granero]

Hi Christian

lvs> One of my covariates (dichotomous) describes whether the patient had a shock
lvs> when he was delivered to the hospital. This variable is violating the
lvs> assumption of proportional hazard.
lvs> I therefore defined a time-dependent covariate as a function of the time
lvs> surviving.

lvs> TIME PROGRAM.
lvs> COMPUTE T_COV_shock = T_ * shock_presentation .
lvs> COXREG
lvs>   time  /STATUS=Status(1)
lvs>   /METHOD=ENTER shock_presentation T_COV_shock
lvs>   /CRITERIA=PIN(.05) POUT(.10) ITERATE(20) .


lvs> I get the following results:

lvs>                            B           sig      Exp(B)
lvs> shock_presentation      2.540      < 0.001     12.69
lvs> T_COV_shock             -0.48      < 0.001      0.619

lvs> How would I describe those results?

lvs>  I see that the risk for dying is much
lvs> higher for patients with a shock at the hospital presentation
lvs> (shock_presentation). But how would I explain the time dependent covariate
lvs> for the shock (T_COV_shock)?

The T_COV_ is in fact an interaction term. This means that the effect
of shock presentation on survival depends on time, and, therefore,
there is no simple answer to the question "What effect has shock on
patients' survival?" The high HR (exp(b)) you observe is valid when
time EQ 0 (shortly after shock, the death risk is very high). The
negative slope for T_COV_ indicates that the risk decreases as time
goes on, that is, the negative effect of shock on survival is diluted
with time.

Plot estimated shock HR against time (I use Excel for that, but SPSS
could be used too, I believe) as a form of explaining what's going on.
Ask me again (here, at the list) if you need help for plotting the
interaction (simply COMPUTE estHR=EXP(2.54-0.48*time, and plot estHR
against time).

HTH

--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)

[Hector Maletta]

Before reading Marta's response I had thought os using the occurrence of shock as a stratification variable. This generates a different baseline survival curve for patients with and without shock. This may solve the problem in a simpler manner, if I am not much mistaken.

Hector

----- Mensaje original -----
De: Marta García-Granero <[hidden email]>
Fecha: Jueves, Septiembre 7, 2006 7:24 pm
Asunto: Re: Cox-Regression with time-dependent covariate

> Hi Christian
>
> lvs> One of my covariates (dichotomous) describes whether the
> patient had a shock
> lvs> when he was delivered to the hospital. This variable is
> violating the
> lvs> assumption of proportional hazard.
> lvs> I therefore defined a time-dependent covariate as a function
> of the time
> lvs> surviving.
>
> lvs> TIME PROGRAM.
> lvs> COMPUTE T_COV_shock = T_ * shock_presentation .
> lvs> COXREG
> lvs>   time  /STATUS=Status(1)
> lvs>   /METHOD=ENTER shock_presentation T_COV_shock
> lvs>   /CRITERIA=PIN(.05) POUT(.10) ITERATE(20) .
>
>
> lvs> I get the following results:
>
> lvs>                            B           sig      Exp(B)
> lvs> shock_presentation      2.540      < 0.001     12.69
> lvs> T_COV_shock             -0.48      < 0.001      0.619
>
> lvs> How would I describe those results?
>
> lvs>  I see that the risk for dying is much
> lvs> higher for patients with a shock at the hospital presentation
> lvs> (shock_presentation). But how would I explain the time
> dependent covariate
> lvs> for the shock (T_COV_shock)?
>
> The T_COV_ is in fact an interaction term. This means that the effect
> of shock presentation on survival depends on time, and, therefore,
> there is no simple answer to the question "What effect has shock on
> patients' survival?" The high HR (exp(b)) you observe is valid when
> time EQ 0 (shortly after shock, the death risk is very high). The
> negative slope for T_COV_ indicates that the risk decreases as time
> goes on, that is, the negative effect of shock on survival is diluted
> with time.
>
> Plot estimated shock HR against time (I use Excel for that, but SPSS
> could be used too, I believe) as a form of explaining what's going on.
> Ask me again (here, at the list) if you need help for plotting the
> interaction (simply COMPUTE estHR=EXP(2.54-0.48*time, and plot estHR
> against time).
>
> HTH
>
> --
> Regards,
> Dr. Marta García-Granero,PhD           [hidden email]
> Statistician
>
> ---
> "It is unwise to use a statistical procedure whose use one does
> not understand. SPSS syntax guide cannot supply this knowledge,
> and it
> is certainly no substitute for the basic understanding of statistics
> and statistical thinking that is essential for the wise choice of
> methods and the correct interpretation of their results".
>
> (Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)
>

[Marta García-Granero]

Hi Hector

HM> Before reading Marta's response I had thought os using the
HM> occurrence of shock as a stratification variable. This generates a
HM> different baseline survival curve for patients with and without
HM> shock. This may solve the problem in a simpler manner, if I am not
HM> much mistaken.

Your idea doesn't answer Christian's question: how to interpret a
significant T_COV_. The fact that the effect of shock on survival
depends on time can't be ignored by stratifying by shock. It's the
baseline survival curve for shock=yes that is causing the problem. An
interaction can't be ignored, it has to be explained, since it adds an
important information from a clinical point of view.

Warmest regards,
Marta

[Hector Maletta]

I thought, Marta, that it is not exactly an interaction with time but two different situations, two different kinds of events. One is arriving at the hospital with the disease plus the shock, the other is arriving with the disease and no shock, and each has completely different survival curves.  The baseline for patients with shocks shows death occurring earlier, of course, because they are in more danger of dying shortly after arrival, so fewer cases survive that early phase compared to no-shock cases, but the difference will show in the baseline curves, one of them dropping sharply after arrival and the other more gently and slowly.

Perhaps I should have been more radical: not two strata in the same Cox regression, but two Cox regressions altogether.

But you are my favourite mathematical statistician, so I believe you if you say this line of reasoning is wrong.
Hector.

----- Mensaje original -----
De: Marta García-Granero <[hidden email]>
Fecha: Viernes, Septiembre 8, 2006 10:23 am
Asunto: Re: Cox-Regression with time-dependent covariate

> Hi Hector
>
> HM> Before reading Marta's response I had thought os using the
> HM> occurrence of shock as a stratification variable. This
> generates a
> HM> different baseline survival curve for patients with and without
> HM> shock. This may solve the problem in a simpler manner, if I am not
> HM> much mistaken.
>
> Your idea doesn't answer Christian's question: how to interpret a
> significant T_COV_. The fact that the effect of shock on survival
> depends on time can't be ignored by stratifying by shock. It's the
> baseline survival curve for shock=yes that is causing the problem. An
> interaction can't be ignored, it has to be explained, since it
> adds an
> important information from a clinical point of view.
>
> Warmest regards,
> Marta
>

[Marta García-Granero]

Hi Hector

I have been quite busy, sorry for the delay in answering ( a
statistics course on survival analysis at the university for
researchers, BTW). I'm sending you a PDF file with a research paper
where they discuss the lack of hazard ratio proportionality in terms
of an interaction with time (patients and methods section).

HM> I thought, Marta, that it is not exactly an interaction with
HM> time

It IS an interaction term with time, believe me (since I can have some
trouble trying to translate all this to English, perhaps I can write
to you privately in our common language and then you translate it to
the whole list - you are much better than I writing in English).

HM> but two different situations, two different kinds of events.
HM> One is arriving at the hospital with the disease plus the shock,
HM> the other is arriving with the disease and no shock, and each has
HM> completely different survival curves.

Yes they are different, that's why shock is significant. The fact that
the T_COV_ is also significant say that the Hazard Ratio (simplifying
it a bit, the ratio of the slopes of both survival curves) changes
with time, it is not constant (as Cox regression assumes).

HM> The baseline for patients
HM> with shocks shows death occurring earlier, of course, because they
HM> are in more danger of dying shortly after arrival, so fewer cases
HM> survive that early phase compared to no-shock cases, but the
HM> difference will show in the baseline curves, one of them dropping
HM> sharply after arrival and the other more gently and slowly.

The interaction with time comes from the fact that the baseline curve
for shock=yes will drop sharply only at first, and afterwards the drop
will become gentler, as you put it. It is the fact that the ratio of
the slopes is not constant over time that provokes the failure of the
proportional hazards assumption.

HM> Perhaps I should have been more radical: not two strata in
HM> the same Cox regression, but two Cox regressions altogether.

Definitely not if the purpose of the model is explaining the effect of
shock on survival, you can't compare what you split in separate
models. What you must do is stratify by time (separate your model in
short, medium and long term effect of the variable on survival, see
the paper I'll be sending to you in another message).

HM> But you are my favourite mathematical statistician, so I
HM> believe you if you say this line of reasoning is wrong.

I'm flattered! But I like being contested now and then.



--
Regards,
Dr. Marta García-Granero,PhD           mailto:[hidden email]
Statistician

---
"It is unwise to use a statistical procedure whose use one does
not understand. SPSS syntax guide cannot supply this knowledge, and it
is certainly no substitute for the basic understanding of statistics
and statistical thinking that is essential for the wise choice of
methods and the correct interpretation of their results".

(Adapted from WinPepi manual - I'm sure Joe Abrahmson will not mind)