Modeling Death a Continuous Variable: Needing Help to Think Outside (The Wooden) Box

[Max Gunther]

Dear SPSSers,

We are looking at the effect of a drug that was randomized between two
groups. We expect patients who were randomized to drug A to do significantly
better than drug B. We would ideally like to operationalize this by using a
continuous variable that we can call "severity of illness." Since many of
the patients die while they are being studied, and they die at higher rates
in the drug B group, it ends up making *the data look like drug B patients
do better because there are no "severity of illness" ratings since they they
are deceased.*

*I would ideally like to use death as a quantitative end point of the
continuous variable "severity of illness" but am not sure how to do this.*

Our group has been trying for years to correctly account for this, and we
have come up with various ways; however, none of them is very satisfactory
and I would welcome any opinions to help us with this problem. Also, just
FYI: this work has also made progress in decreasing the use of drug B.

--
Max Gunther, PhD

Department of Radiological Sciences
Center for Health Services Research
Vanderbilt University Medical Center
Nashville, TN www.ICUdelirium.org

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[Burleson,Joseph A.]

Use survival analysis, Cox Regression, for example.

Joe Burleson

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Max Gunther
Sent: Thursday, August 28, 2008 4:54 PM
To: [hidden email]
Subject: Modeling Death a Continuous Variable: Needing Help to Think
Outside (The Wooden) Box

Dear SPSSers,

We are looking at the effect of a drug that was randomized between two
groups. We expect patients who were randomized to drug A to do
significantly
better than drug B. We would ideally like to operationalize this by
using a
continuous variable that we can call "severity of illness." Since many
of
the patients die while they are being studied, and they die at higher
rates
in the drug B group, it ends up making *the data look like drug B
patients
do better because there are no "severity of illness" ratings since they
they
are deceased.*

*I would ideally like to use death as a quantitative end point of the
continuous variable "severity of illness" but am not sure how to do
this.*

Our group has been trying for years to correctly account for this, and
we
have come up with various ways; however, none of them is very
satisfactory
and I would welcome any opinions to help us with this problem. Also,
just
FYI: this work has also made progress in decreasing the use of drug B.

--
Max Gunther, PhD

Department of Radiological Sciences
Center for Health Services Research
Vanderbilt University Medical Center
Nashville, TN www.ICUdelirium.org

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[Maguin, Eugene]

Max,

I agree with Joe Burleson's recommendation of survival analysis. I'd like to
suggest that one possibility MAY be a so-called two part model. It would
require multiple measuresments over time of severity. Two part models have
been used to model initiation and growth of alcohol or drug use, for
example. You have the opposite situation. Know that I've read about these
models; but I've never constructed one. So I may be completely misinformed
it laughable. Perhaps others with more experience will comment.

Gene Maguin

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[Neda Faregh]

Max, you might want also to consider risk curves. You could plot risk curves
for each treatment (drug A and B). Each estimate on the curve would then be
the proportion reporting a pre-set number of "consequences/adverse effects"
from the treatment. Then you can find the optimal limit using receiver
operating characteristic (ROC) analysis. I am assuming you would be
interested in dose-response, which the ROC analysis would provide for the
complete range of doses for each treatment. Hope this helps.

Neda

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Gene Maguin
Sent: Friday, August 29, 2008 11:15 AM
To: [hidden email]
Subject: Re: Modeling Death a Continuous Variable: Needing Help to Think
Outside (The Wooden) Box

Max,

I agree with Joe Burleson's recommendation of survival analysis. I'd like to
suggest that one possibility MAY be a so-called two part model. It would
require multiple measuresments over time of severity. Two part models have
been used to model initiation and growth of alcohol or drug use, for
example. You have the opposite situation. Know that I've read about these
models; but I've never constructed one. So I may be completely misinformed
it laughable. Perhaps others with more experience will comment.

Gene Maguin

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To be completly outside the box I just had a vague idea.
You basically have a truncated variable. Eg is somebody is dead you
cannot observer the severity of his illness anymore.
In econometrics the use the so called "Tobit model" for such
variables. It might be worth a look whether you can utilize it for
your needs.
Best,
Stefan



On Sun, Aug 31, 2008 at 6:09 PM, Neda Faregh <[hidden email]> wrote:

> Max, you might want also to consider risk curves. You could plot risk curves
> for each treatment (drug A and B). Each estimate on the curve would then be
> the proportion reporting a pre-set number of "consequences/adverse effects"
> from the treatment. Then you can find the optimal limit using receiver
> operating characteristic (ROC) analysis. I am assuming you would be
> interested in dose-response, which the ROC analysis would provide for the
> complete range of doses for each treatment. Hope this helps.
>
> Neda
>
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
> Gene Maguin
> Sent: Friday, August 29, 2008 11:15 AM
> To: [hidden email]
> Subject: Re: Modeling Death a Continuous Variable: Needing Help to Think
> Outside (The Wooden) Box
>
> Max,
>
> I agree with Joe Burleson's recommendation of survival analysis. I'd like to
> suggest that one possibility MAY be a so-called two part model. It would
> require multiple measuresments over time of severity. Two part models have
> been used to model initiation and growth of alcohol or drug use, for
> example. You have the opposite situation. Know that I've read about these
> models; but I've never constructed one. So I may be completely misinformed
> it laughable. Perhaps others with more experience will comment.
>
> Gene Maguin
>
> =====================
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> =====================
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[Max Gunther]

Thanks to everyone on your very useful comments. We are going to look into
each of these. Several people suggested using survival analysis, which
unless there is some trick that we are missing, would not work easily to
quantify death as the extreme end of a continuous variable. As I understand
it, the continuous aspect of survivor analysis is the length of time until
death or censorship and I'm not sure how to work that into a basic
regression model with health on the y axis and time on the x axis. In other
words, unless I am mistaken, it will let you add a continuous variable for
time, but not for severity of illness per se where death would still be
categorical.

The direction that seems most promising would be some way to quantify,
yet *accurately
*weight, severity of illness scores with death being the far end of the
spectrum. We have thought of a few ways to do this, but it is not obvious.
For example, one suggestion that I liked was to substitute the patent's
worst severity of illness score before they died as their severity of
illness score after their death. This seems logical; however, the problem is
that I think it will end up overestimating the effect of the drug
randomization. For example, because we looking at relationships between one
of two drug groups and patent's severity of illness, there is the potential
for someone to have died right at the beginning of the drug randomization,
yet they are going to have a heavy weight for all of the remaining days of
the study and for the apparent effect of that drug on severity of illness,
even though they may have only been given the drug for 1 day; in reality, we
would have data for 4  when we can only really state a relationship for the
first one when they were alive (we only measured the drug for 5 days).

Even if we do use some method like this, we will need to reference some
papers with presidents for this type of analysis - any suggestions for
papers that might be useful will be greatly appreciated.

Once again thanks to everyone for their very helpful contributions!

Best of wishes,

--
Max Gunther, PhD

Department of Radiological Sciences
Center for Health Services Research
Vanderbilt University Medical Center
Nashville, TN www.ICUdelirium.org


On Thu, Aug 28, 2008 at 3:53 PM, Max Gunther <[hidden email]> wrote:

> Dear SPSSers,
>
> We are looking at the effect of a drug that was randomized between two
> groups. We expect patients who were randomized to drug A to do significantly
> better than drug B. We would ideally like to operationalize this by using a
> continuous variable that we can call "severity of illness." Since many of
> the patients die while they are being studied, and they die at higher rates
> in the drug B group, it ends up making *the data look like drug B patients
> do better because there are no "severity of illness" ratings since they they
> are deceased.*
>
> *I would ideally like to use death as a quantitative end point of the
> continuous variable "severity of illness" but am not sure how to do this.*
>
> Our group has been trying for years to correctly account for this, and we
> have come up with various ways; however, none of them is very satisfactory
> and I would welcome any opinions to help us with this problem. Also, just
> FYI: this work has also made progress in decreasing the use of drug B.
>
> --
> Max Gunther, PhD
>
> Department of Radiological Sciences
> Center for Health Services Research
> Vanderbilt University Medical Center
> Nashville, TN www.ICUdelirium.org
>

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[Richard Ristow]

To weigh in late, with the advantage of reading other responses --

At 04:53 PM 8/28/2008, Max Gunther wrote:

>We are looking at the effect of a drug that was
>randomized between two groups. We would ideally
>like to operationalize this by using a
>continuous variable that we can call "severity
>of illness." Since many of the patients die
>while they are being studied, and they die at
>higher rates in the drug B group, it ends up
>making *the data look like drug B patients do
>better because there are no "severity of
>illness" ratings since they are deceased.*
>
>*I would ideally like to use death as a
>quantitative end point of the continuous
>variable "severity of illness" but am not sure how to do this.*

Let me restate this, as I understand it:

You have an operational measure "severity of
illness." You are satisfied that it is (or
measures) the underlying quantity of interest,
and that it is of scale level. It is the dependent variable in your analysis.

You wish to make deceased patients available for
analysis, by assigning them a "severity" score.
It looks like (this is less clear),

1. You are comfortable with giving all deceased
patients the same severity score

2. Your severity scale is closed-ended; that is,
there it has an inherent maximum value. You wish
to assign deceased patients some score higher than this maximum value.

3. You want the result to still be a valid scale-level value.

I suggest,
a. Simply assign deceased patients the maximum
severity score. You can then argue that, since
the 'correct' value is probably higher than this,
and group B has higher mortality, your analysis
is conservative in that it has a bias against finding group B inferior.

b. You can cut loose from your severity score and
use mortality as your outcome measure. You should
carry out and publish this analysis, in any case.

c. Finally, just how sure are you, that your
severity measure is scale-level in the first
place? A lot of people would consider ordinal
analysis in your situation; and for that, all you
need do is assign deceased patients some
convenient severity value above the top of the scale.

On SPSSX-L, I think of Marta García-Granero and
Anita van der Kooij as the experts on ordinal
analysis, far beyond my level; there are others,
as well. I don't know if anybody wants to weigh in on the idea.

-Best of good fortune,
  Richard

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