Survival analysis - interaction of continuous predictors

[Larry Hawk]

I am interested in whether an impulsivity scale (called upps_urgency)
predicts earlier lapse, particularly for people who have more quit-related
increases in craving and withdrawal.  All of these measures are continuous.
Moreover, treatment predicts lapse, so we'd want to covary for that first.
So, I believe we'd have a model like that below -- except that we don't know
the best way to introduce interaction terms.  In many models, I'd simply
compute the interaction term as a crossproduct of mean-centered predictors.
Would we take the same approach here?  Is there a better way?


COXREG firstlapse
 /STATUS=failure(1)
 /METHOD=ENTER txgroupn
 /METHOD=ENTER upps_urgency craveincrease withdrawincrease
 /METHOD= ENTER *****interaction terms here*****
 /PRINT=CI(95)
 /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

Once we figure out how to test the interaction, let's assume for the moment
that it is significant.  How would one follow-up such an interaction (our
prediction would be that upps_urgency predicts more rapid lapse better as
withdrawal increases)?  Thoughts on graphs that would illustrate such an
effect?

If there is no quick way to provide feedback on this, perhaps you could
recommend a reading or 3 on how best to approach our research questions.

--

Larry W. Hawk, Jr., Ph.D.
Associate Professor of Psychology
231 Park Hall, Box 604110
The University of Buffalo, SUNY
Buffalo, NY 14260-4110
Phone: [phone]
Fax: [phone]
E-mail: [hidden email] or [hidden email]

=====================
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[Burleson,Joseph A.]

Larry:

What you propose is certainly possible.

While many researchers take the easy way out and dichotomize (or tri-,
etc.) their continuous variable of interest, this loses power. Keeping
the continuum allows for the most powerful test of the hypotheses. That
said, it may be important to see it there is a linear relationship
first, keeping in mind that a curvilinear relationship can also be in
the works!

More complications: Before testing the interaction between two
continuous variables, you might consider that a simpler model might
suffice in that the Tx might interact with any of the three continuums
alone, a dichotomous X continuous interaction. Finally, there is always
the possibility of a Tx X Cont1 X Cont2 interaction, probably
unnecessarily esoteric. But the Tx variable probably deserves some
primacy in your model, I would think.

Having said that, you could explore this "full" (too full!) model,
putting each predictor in sequentially, paying attention to the
chi-square at each step more than the final wald tests.

Note that since the Tx presumably comes "after" the withdrawal
variables, in the sense that they are "person" variables, Tx maybe
should come last. Note that there may be no logical order to the 3
person variables, hence in the same step: impossible to disentangle
within that (3 df) step, but a necessity.

 COXREG firstlapse
 /STATUS=failure(1)
/METHOD=ENTER upps_urgency craveincrease withdrawincrease
/METHOD=ENTER txgroupn
/METHOD=ENTER upps_urgency*craveincrease upps_urgency*withdrawincrease
craveincrease*withdrawincrease
/METHOD=ENTER txgroupn*upps_urgency txgroupn*craveincrease
txgroupn*withdrawincrease
 /METHOD=ENTER txgroupn*upps_urgency*craveincrease
txgroupn*upps_urgency*withdrawincrease
txgroupn*craveincrease*withdrawincrease
/PRINT=CI(95)
 /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

Finally, be sensitive to your sample size: Assuming that Tx is two
levels (1 df), then each of the predictors, main or interaction above,
is 1 df. This can get too elaborate and is certainly bordering on
"fishing" unless there are hypotheses.

Interpretation: One can dichotomize the continuums after the fact and
explore the patterns: But there are ways to interpret that are better.
Jacard has illustrations of ANOVA and logistic regression in the Sage
series, and the analog would apply for survival. It involves the
utilization of the odds ratio of the interaction, always in light of its
antecedent main effects. I would defer to others on the art of doing
this. West & Aikens text on complex interactions is extremely helpful on
this.

Joe Burleson

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Larry Hawk
Sent: Tuesday, August 19, 2008 12:17 PM
To: [hidden email]
Subject: Survival analysis - interaction of continuous predictors

I am interested in whether an impulsivity scale (called upps_urgency)
predicts earlier lapse, particularly for people who have more
quit-related
increases in craving and withdrawal.  All of these measures are
continuous.
Moreover, treatment predicts lapse, so we'd want to covary for that
first.
So, I believe we'd have a model like that below -- except that we don't
know
the best way to introduce interaction terms.  In many models, I'd simply
compute the interaction term as a crossproduct of mean-centered
predictors.
Would we take the same approach here?  Is there a better way?


COXREG firstlapse
 /STATUS=failure(1)
 /METHOD=ENTER txgroupn
 /METHOD=ENTER upps_urgency craveincrease withdrawincrease
 /METHOD= ENTER *****interaction terms here*****
 /PRINT=CI(95)
 /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

Once we figure out how to test the interaction, let's assume for the
moment
that it is significant.  How would one follow-up such an interaction
(our
prediction would be that upps_urgency predicts more rapid lapse better
as
withdrawal increases)?  Thoughts on graphs that would illustrate such an
effect?

If there is no quick way to provide feedback on this, perhaps you could
recommend a reading or 3 on how best to approach our research questions.

--

Larry W. Hawk, Jr., Ph.D.
Associate Professor of Psychology
231 Park Hall, Box 604110
The University of Buffalo, SUNY
Buffalo, NY 14260-4110
Phone: [phone]
Fax: [phone]
E-mail: [hidden email] or [hidden email]

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
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[Hector Maletta]

I agree in general with Joseph Burleson's comments. However, an additional
word: continuous variables may have a lot of "noise", especially in
relatively small samples, and outliers (or simply cases relatively off the
curve, whatever form the curve has) may greatly influence the results;
dichotomizing or trichotomizing or creating an ordinal variable tends to
eliminate this danger. Before using the continuous variables and their
interactions, check that they are "well behaved", i.e. that they follow a
curve of some type along time, with not much variance or sudden jumps up and
down along the way. If so, you may benefit from some smoothing approach,
e.g. using an instrumental variables approach (predicting the covariate by
regression on other variables, and then using the predicted value of the
covariate, instead of its actual value, in your equation).
Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Burleson,Joseph A.
Sent: 19 August 2008 15:32
To: [hidden email]
Subject: Re: Survival analysis - interaction of continuous predictors

Larry:

What you propose is certainly possible.

While many researchers take the easy way out and dichotomize (or tri-,
etc.) their continuous variable of interest, this loses power. Keeping
the continuum allows for the most powerful test of the hypotheses. That
said, it may be important to see it there is a linear relationship
first, keeping in mind that a curvilinear relationship can also be in
the works!

More complications: Before testing the interaction between two
continuous variables, you might consider that a simpler model might
suffice in that the Tx might interact with any of the three continuums
alone, a dichotomous X continuous interaction. Finally, there is always
the possibility of a Tx X Cont1 X Cont2 interaction, probably
unnecessarily esoteric. But the Tx variable probably deserves some
primacy in your model, I would think.

Having said that, you could explore this "full" (too full!) model,
putting each predictor in sequentially, paying attention to the
chi-square at each step more than the final wald tests.

Note that since the Tx presumably comes "after" the withdrawal
variables, in the sense that they are "person" variables, Tx maybe
should come last. Note that there may be no logical order to the 3
person variables, hence in the same step: impossible to disentangle
within that (3 df) step, but a necessity.

 COXREG firstlapse
 /STATUS=failure(1)
/METHOD=ENTER upps_urgency craveincrease withdrawincrease
/METHOD=ENTER txgroupn
/METHOD=ENTER upps_urgency*craveincrease upps_urgency*withdrawincrease
craveincrease*withdrawincrease
/METHOD=ENTER txgroupn*upps_urgency txgroupn*craveincrease
txgroupn*withdrawincrease
 /METHOD=ENTER txgroupn*upps_urgency*craveincrease
txgroupn*upps_urgency*withdrawincrease
txgroupn*craveincrease*withdrawincrease
/PRINT=CI(95)
 /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

Finally, be sensitive to your sample size: Assuming that Tx is two
levels (1 df), then each of the predictors, main or interaction above,
is 1 df. This can get too elaborate and is certainly bordering on
"fishing" unless there are hypotheses.

Interpretation: One can dichotomize the continuums after the fact and
explore the patterns: But there are ways to interpret that are better.
Jacard has illustrations of ANOVA and logistic regression in the Sage
series, and the analog would apply for survival. It involves the
utilization of the odds ratio of the interaction, always in light of its
antecedent main effects. I would defer to others on the art of doing
this. West & Aikens text on complex interactions is extremely helpful on
this.

Joe Burleson

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Larry Hawk
Sent: Tuesday, August 19, 2008 12:17 PM
To: [hidden email]
Subject: Survival analysis - interaction of continuous predictors

I am interested in whether an impulsivity scale (called upps_urgency)
predicts earlier lapse, particularly for people who have more
quit-related
increases in craving and withdrawal.  All of these measures are
continuous.
Moreover, treatment predicts lapse, so we'd want to covary for that
first.
So, I believe we'd have a model like that below -- except that we don't
know
the best way to introduce interaction terms.  In many models, I'd simply
compute the interaction term as a crossproduct of mean-centered
predictors.
Would we take the same approach here?  Is there a better way?


COXREG firstlapse
 /STATUS=failure(1)
 /METHOD=ENTER txgroupn
 /METHOD=ENTER upps_urgency craveincrease withdrawincrease
 /METHOD= ENTER *****interaction terms here*****
 /PRINT=CI(95)
 /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).

Once we figure out how to test the interaction, let's assume for the
moment
that it is significant.  How would one follow-up such an interaction
(our
prediction would be that upps_urgency predicts more rapid lapse better
as
withdrawal increases)?  Thoughts on graphs that would illustrate such an
effect?

If there is no quick way to provide feedback on this, perhaps you could
recommend a reading or 3 on how best to approach our research questions.

--

Larry W. Hawk, Jr., Ph.D.
Associate Professor of Psychology
231 Park Hall, Box 604110
The University of Buffalo, SUNY
Buffalo, NY 14260-4110
Phone: [phone]
Fax: [phone]
E-mail: [hidden email] or [hidden email]

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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For a list of commands to manage subscriptions, send the command
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[Larry Hawk]

Thanks to Pablo Mora, Joseph Burleson, and Hector Maletta for the very
thoughtful and helpful replies.
-Larry
--

Larry W. Hawk, Jr., Ph.D.
Associate Professor of Psychology
231 Park Hall, Box 604110
The University of Buffalo, SUNY
Buffalo, NY 14260-4110
Phone: [phone]
Fax: [phone]
E-mail: [hidden email] or [hidden email]


On Tue, Aug 19, 2008 at 2:48 PM, Hector Maletta <[hidden email]>wrote:

> I agree in general with Joseph Burleson's comments. However, an additional
> word: continuous variables may have a lot of "noise", especially in
> relatively small samples, and outliers (or simply cases relatively off the
> curve, whatever form the curve has) may greatly influence the results;
> dichotomizing or trichotomizing or creating an ordinal variable tends to
> eliminate this danger. Before using the continuous variables and their
> interactions, check that they are "well behaved", i.e. that they follow a
> curve of some type along time, with not much variance or sudden jumps up
> and
> down along the way. If so, you may benefit from some smoothing approach,
> e.g. using an instrumental variables approach (predicting the covariate by
> regression on other variables, and then using the predicted value of the
> covariate, instead of its actual value, in your equation).
> Hector
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Burleson,Joseph A.
> Sent: 19 August 2008 15:32
> To: [hidden email]
> Subject: Re: Survival analysis - interaction of continuous predictors
>
> Larry:
>
> What you propose is certainly possible.
>
> While many researchers take the easy way out and dichotomize (or tri-,
> etc.) their continuous variable of interest, this loses power. Keeping
> the continuum allows for the most powerful test of the hypotheses. That
> said, it may be important to see it there is a linear relationship
> first, keeping in mind that a curvilinear relationship can also be in
> the works!
>
> More complications: Before testing the interaction between two
> continuous variables, you might consider that a simpler model might
> suffice in that the Tx might interact with any of the three continuums
> alone, a dichotomous X continuous interaction. Finally, there is always
> the possibility of a Tx X Cont1 X Cont2 interaction, probably
> unnecessarily esoteric. But the Tx variable probably deserves some
> primacy in your model, I would think.
>
> Having said that, you could explore this "full" (too full!) model,
> putting each predictor in sequentially, paying attention to the
> chi-square at each step more than the final wald tests.
>
> Note that since the Tx presumably comes "after" the withdrawal
> variables, in the sense that they are "person" variables, Tx maybe
> should come last. Note that there may be no logical order to the 3
> person variables, hence in the same step: impossible to disentangle
> within that (3 df) step, but a necessity.
>
>  COXREG firstlapse
>  /STATUS=failure(1)
> /METHOD=ENTER upps_urgency craveincrease withdrawincrease
> /METHOD=ENTER txgroupn
> /METHOD=ENTER upps_urgency*craveincrease upps_urgency*withdrawincrease
> craveincrease*withdrawincrease
> /METHOD=ENTER txgroupn*upps_urgency txgroupn*craveincrease
> txgroupn*withdrawincrease
>  /METHOD=ENTER txgroupn*upps_urgency*craveincrease
> txgroupn*upps_urgency*withdrawincrease
> txgroupn*craveincrease*withdrawincrease
> /PRINT=CI(95)
>  /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).
>
> Finally, be sensitive to your sample size: Assuming that Tx is two
> levels (1 df), then each of the predictors, main or interaction above,
> is 1 df. This can get too elaborate and is certainly bordering on
> "fishing" unless there are hypotheses.
>
> Interpretation: One can dichotomize the continuums after the fact and
> explore the patterns: But there are ways to interpret that are better.
> Jacard has illustrations of ANOVA and logistic regression in the Sage
> series, and the analog would apply for survival. It involves the
> utilization of the odds ratio of the interaction, always in light of its
> antecedent main effects. I would defer to others on the art of doing
> this. West & Aikens text on complex interactions is extremely helpful on
> this.
>
> Joe Burleson
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Larry Hawk
> Sent: Tuesday, August 19, 2008 12:17 PM
> To: [hidden email]
> Subject: Survival analysis - interaction of continuous predictors
>
> I am interested in whether an impulsivity scale (called upps_urgency)
> predicts earlier lapse, particularly for people who have more
> quit-related
> increases in craving and withdrawal.  All of these measures are
> continuous.
> Moreover, treatment predicts lapse, so we'd want to covary for that
> first.
> So, I believe we'd have a model like that below -- except that we don't
> know
> the best way to introduce interaction terms.  In many models, I'd simply
> compute the interaction term as a crossproduct of mean-centered
> predictors.
> Would we take the same approach here?  Is there a better way?
>
>
> COXREG firstlapse
>  /STATUS=failure(1)
>  /METHOD=ENTER txgroupn
>  /METHOD=ENTER upps_urgency craveincrease withdrawincrease
>  /METHOD= ENTER *****interaction terms here*****
>  /PRINT=CI(95)
>  /CRITERIA=PIN(.05) POUT(.10) ITERATE(20).
>
> Once we figure out how to test the interaction, let's assume for the
> moment
> that it is significant.  How would one follow-up such an interaction
> (our
> prediction would be that upps_urgency predicts more rapid lapse better
> as
> withdrawal increases)?  Thoughts on graphs that would illustrate such an
> effect?
>
> If there is no quick way to provide feedback on this, perhaps you could
> recommend a reading or 3 on how best to approach our research questions.
>
> --
>
> Larry W. Hawk, Jr., Ph.D.
> Associate Professor of Psychology
> 231 Park Hall, Box 604110
> The University of Buffalo, SUNY
> Buffalo, NY 14260-4110
> Phone: [phone]
> Fax: [phone]
> E-mail: [hidden email] or [hidden email]
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the command
> INFO REFCARD
>
>
>

=====================
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