Fwd: Statistical Consulting Section: modeling a binomial outcome measured multiple days

[Art Kendall]

I thought that we had a discussion about repeated dichotomous data on this list.  However, I must be using the wrong search specifications in the archives because I did not find it. 

Does anyone recall what that discussion was about so that I can send the url for those posts?

Is anybody familiar enough with the new procedure for GEE to say it might be a place to look?

Art Kendall
Social Research Consultants


-------- Original Message --------

Subject:	Statistical Consulting Section: modeling a binomial outcome measured multiple days
Date:	Fri, 06 May 2011 15:16:41 -0400
From:	Nancy Buderer [hidden email]
Reply-To:	[hidden email]
To:	Arthur Kendall [hidden email]

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modeling a binomial outcome measured multiple days

From:	Nancy Buderer
To:	Statistical Consulting Section
Posted:	5/6/2011 3:17:00 PM
Subject:	modeling a binomial outcome measured multiple days
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I am an independent consultant and have a complicated dataset.  I appreciate your ideas on how to approach this problem. 

The purpose of the study is to describe the factors associated with blood transfusion and to determine their relative importance in a cohort of patients with a certain condition. The investigators are interested in developing a model that predicted the physicians' decision to transfuse.  The results of the study could be used to modify hospital transfusion practices.

This is a retrospective study, post hoc / secondary analysis using a dataset that was collected for a different multicenter study.

The outcome the investigators want to model is whether or not a patient was transfused on any given day during their hospital stay.  Transfusion (yes/no) is measured daily until the patient is discharged. 

Variables collected include one-time measurements (e.g.,  demographics, baseline lab values, other conditions)  as well as daily measurements (e.g., lab values).  Most lab values were measured on days 1 - 7, but not all (some are measured days 1-4 and day 7). 

The dataset includes about 1000 patients.  These patients collectively had 502 transfusions out of 6496 patient days.

The analysis are complicated by several considerations:

• Multiple measures per patient.  If patient-day is the unit of observation, then days from the same patient are correlated.

• Patients can have days of transfusion as well as days without transfusion.

• Data are censored; patients contribute different numbers of days to the model.

• Time series - The decision to transfuse on a given day may be dependent on whether or not the patient was transfused on the previous day (s).

• Data are censored for various reasons - discharge, death, other complicating factor. Patients contribute different numbers of days.

• Some factors are measured only once, while others are measured daily.

• Data are not missing at random.  Data are usually missing for clinically-related reasons.  Results are missing on a given day because the physician did not think that it was necessary to order the test or to record that particular variable on a particular day.  The model would need to include the fact that a test was ordered or not ordered.  If the test was ordered, then  the model would need to include the result of the test (which is usually a continuous variable, e.g., serum creatinine could take any value > 0 mg/dL or be not done).  If the test was not ordered, then this effect may also be important to model.

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Nancy Buderer, MS
Biostatistician & Research Consultant
[hidden email]
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[Bruce Weaver]

The data Nancy describes have a multilevel structure, with daily data at level 1 and "one-time" (or patient level) data at level 2.  I'm still on v18, but I believe the new multilevel GENLIN procedure in v19 can perform multilevel regression with a binomial error distribution and a variety of link functions (e.g., logit link if you want mulilevel logistic and odds ratios, or an identity link function if you want risk differences, etc).  Someone who has v19 may be able to comment further.

HTH.

Art Kendall wrote

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">

 

   
   
 
 
    I thought that we had a discussion about repeated
      dichotomous data on this list.  However, I must be using the wrong
      search specifications in the archives because I did not find it. 
     
     
      Does anyone recall what that discussion was about so that I can
      send the url for those posts?
     
      Is anybody familiar enough with the new procedure for GEE to say
      it might be a place to look?
     
      Art Kendall
      Social Research Consultants
     
   
    -------- Original Message --------
   
     
       
          Subject:
          Statistical Consulting Section: modeling a binomial
            outcome measured multiple days
       
       
          Date:
          Fri, 06 May 2011 15:16:41 -0400
       
       
          From:
          Nancy Buderer <[hidden email]>
       
       
          Reply-To:
         
          [hidden email] 
       
       
          To:
          Arthur Kendall <[hidden email]>
       
     
   
   
   
   
    Please Do Not Forward, use the options
      to the right to forward or reply.
       
   
     
       
         
           
             
               
                 
                   
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                               modeling

                                  a binomial outcome measured multiple
                                  days
                             
                               
                             
                                   
                             
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           
                                               From:
                                             
                                                Nancy

                                                  Buderer  
                                           
                                           
                                               To:
                                             
                                                Statistical

                                                  Consulting Section
                                             
                                           
                                           
                                               Posted:
                                             
                                                5/6/2011

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                                               Subject:
                                             
                                                modeling a
                                                  binomial outcome
                                                  measured multiple days
                                             
                                           
                                           
                                               Message:
                                               
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           
                                             
                                               
                                               
                                               
                                             
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                                                  This
                                                 
                                                 
                                             
                                           
                                         
                                       
                                     
                                   
                                   
                                       
                                         
                                          I
                                              am an independent
                                              consultant and have
                                              a complicated dataset. 
                                              I appreciate your ideas on
                                              how to approach this
                                              problem. 
                                          The
                                              purpose of the study is to
                                              describe the factors
                                              associated with blood
                                              transfusion and to
                                              determine their relative
                                              importance in a cohort of
                                              patients with a certain
                                              condition. The
                                              investigators are
                                              interested in developing a
                                              model that predicted the
                                              physicians' decision to
                                              transfuse.  The results of
                                              the study could be used to
                                              modify hospital
                                              transfusion practices.
                                          This
                                              is a retrospective study,
                                              post hoc / secondary
                                              analysis using a dataset
                                              that was collected for a
                                              different multicenter
                                              study.
                                          The
                                              outcome the investigators
                                              want to model is whether
                                              or not a patient was
                                              transfused on any given
                                              day during their hospital
                                              stay.  Transfusion
                                              (yes/no) is measured daily
                                              until the patient is
                                              discharged. 
                                          Variables
                                              collected include one-time
                                              measurements (e.g.,
                                               demographics, baseline
                                              lab values, other
                                              conditions)  as well as
                                              daily measurements (e.g.,
                                              lab values).  Most lab
                                              values were measured on
                                              days 1 - 7, but not all
                                              (some are measured days
                                              1-4 and day 7). 
                                          The

                                              dataset includes about
                                              1000 patients.  These
                                              patients collectively had
                                              502 transfusions out of
                                              6496 patient days.
                                          The
                                              analysis are complicated
                                              by several considerations:
                                         
                                            Multiple measures per
                                              patient.  If patient-day
                                              is the unit of
                                              observation, then days
                                              from the same patient are
                                              correlated.
                                         
                                         
                                            Patients can have days
                                              of transfusion as well as
                                              days without transfusion.
                                         
                                         
                                            Data are censored;
                                              patients contribute
                                              different numbers of days
                                              to the model.
                                         
                                         
                                            Time series - The
                                              decision to transfuse on a
                                              given day may be dependent
                                              on whether or not the
                                              patient was transfused on
                                              the previous day (s).
                                         
                                         
                                            Data are censored for
                                              various reasons -
                                              discharge, death, other
                                              complicating factor.
                                              Patients contribute
                                              different numbers of days.
                                         
                                         
                                            Some factors are
                                              measured only once, while
                                              others are measured daily.
                                         
                                         
                                            Data are not missing at
                                              random.  Data are usually
                                              missing for
                                              clinically-related
                                              reasons.  Results are
                                              missing on a given day
                                              because the physician did
                                              not think that it was
                                              necessary to order the
                                              test or to record that
                                              particular variable on a
                                              particular day.  The model
                                              would need to include the
                                              fact that a test was
                                              ordered or not ordered. 
                                              If the test was ordered,
                                              then  the model would need
                                              to include the result of
                                              the test (which is usually
                                              a continuous variable,
                                              e.g., serum creatinine
                                              could take any value >
                                              0 mg/dL or be not done). 
                                              If the test was not
                                              ordered, then this effect
                                              may also be important to
                                              model.
                                         
                                         
-------------------------------------------
                                          Nancy Buderer, MS
                                          Biostatistician & Research
                                          Consultant
                                          [hidden email] 
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[Rich Ulrich]

I'll offer a massive simplification of the statistical problem.

I notice that there are 1000 patients, and 502 transfusion events.
Since some patients had more than one, there are fewer than 500
patients with a transfusion....  Presumably the others were selected
by criteria which do need to be noted.

The model should be divided into two questions -  "Transfusion: Yes/no";
and "When".  Or perhaps the main interest will be satisfied by the
first question alone.  Or, the answers to the first question should
be the starting point for looking at the second question.

The question of "When"  might be simplified, also, by deciding to
model the occurrence of "First transfusion".  Whether it is worth
looking at additional transfusions could depend on the amount of
data available.



----------------------------------------

> Date: Sat, 7 May 2011 06:36:07 -0700
> From: [hidden email]
> Subject: Re: Fwd: Statistical Consulting Section: modeling a binomial outcome measured multiple days
> To: [hidden email]
>
> The data Nancy describes have a multilevel structure, with daily data at
> level 1 and "one-time" (or patient level) data at level 2. I'm still on
> v18, but I believe the new multilevel GENLIN procedure in v19 can perform
> multilevel regression with a binomial error distribution and a variety of
> link functions (e.g., logit link if you want mulilevel logistic and odds
> ratios, or an identity link function if you want risk differences, etc).
> Someone who has v19 may be able to comment further.
>
> HTH.
>

--
Rich Ulrich


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[Ryan]

Art,

 

A GEE/Generalized Linear Model can be fit employing the GENLIN procedure in SPSS. GENLIN is capable of fitting various generalized linear models that account for correlation among repeated measures.

 

I provide a simple example below which assumes data are derived from a logistic regression equation with correlation among repeated observations. Note that data for 1000 subjects are generated, all of whom are measured 50 times. Also note that a time-varying covariate, x1, was incorporated into the model.

 

**I wrote the code below very fast. Apologies if there are any typos.

 

HTH,

 

Ryan

 

*Generate Data.
set seed 98765432.

 

new file.
inp pro.

 

comp ID = -99.
comp x1 = -99.
comp b0 = -99.
comp b1 = -99.
comp rand_eff = -99.
comp time = -99.

 

leave ID to time.

 

 loop ID = 1 to 1000.
    comp b0 = -0.5.
    comp b1 = 1.0.
    comp rand_eff = sqrt(.3)*rv.normal(0,1).

 

    loop time = 1 to 50.
       comp x1 = rv.normal(2,1).
       comp eta  = b0 + b1*x1 + rand_eff.
       comp p = exp(eta) / (1 + exp(eta)).
       comp y = rv.bernoulli(p).

 

    end case.
  end loop.
 end loop.

end file.
end inp pro.

exe.

 

Delete variables b0 b1 rand_eff eta p.

 

GENLIN y (REFERENCE=FIRST) WITH x1
  /MODEL x1 INTERCEPT=YES
 DISTRIBUTION=BINOMIAL LINK=LOGIT
  /REPEATED SUBJECT=ID WITHINSUBJECT=time SORT=YES CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
    COVB=ROBUST MAXITERATIONS=100 PCONVERGE=1e-006(ABSOLUTE) UPDATECORR=1
  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.

 

On Sat, May 7, 2011 at 7:42 AM, Art Kendall <[hidden email]> wrote:

I thought that we had a discussion about repeated dichotomous data on this list.  However, I must be using the wrong search specifications in the archives because I did not find it. 

Does anyone recall what that discussion was about so that I can send the url for those posts?

Is anybody familiar enough with the new procedure for GEE to say it might be a place to look?

Art Kendall
Social Research Consultants


-------- Original Message --------

Subject:	Statistical Consulting Section: modeling a binomial outcome measured multiple days
Date:	Fri, 06 May 2011 15:16:41 -0400
From:	Nancy Buderer [hidden email]
Reply-To:	[hidden email]
To:	Arthur Kendall [hidden email]

Please Do Not Forward, use the options to the right to forward or reply.

ASA | Discussions | Statistical Consulting Section

FEEDBACK | QUESTIONS

modeling a binomial outcome measured multiple days

From:	Nancy Buderer
To:	Statistical Consulting Section
Posted:	5/6/2011 3:17:00 PM
Subject:	modeling a binomial outcome measured multiple days
Message:

View Profile

Add Contact

Blog This

I am an independent consultant and have a complicated dataset.  I appreciate your ideas on how to approach this problem. 

The purpose of the study is to describe the factors associated with blood transfusion and to determine their relative importance in a cohort of patients with a certain condition. The investigators are interested in developing a model that predicted the physicians' decision to transfuse.  The results of the study could be used to modify hospital transfusion practices.

This is a retrospective study, post hoc / secondary analysis using a dataset that was collected for a different multicenter study.

The outcome the investigators want to model is whether or not a patient was transfused on any given day during their hospital stay.  Transfusion (yes/no) is measured daily until the patient is discharged. 

Variables collected include one-time measurements (e.g.,  demographics, baseline lab values, other conditions)  as well as daily measurements (e.g., lab values).  Most lab values were measured on days 1 - 7, but not all (some are measured days 1-4 and day 7). 

The dataset includes about 1000 patients.  These patients collectively had 502 transfusions out of 6496 patient days.

The analysis are complicated by several considerations:

• Multiple measures per patient.  If patient-day is the unit of observation, then days from the same patient are correlated.

• Patients can have days of transfusion as well as days without transfusion.

• Data are censored; patients contribute different numbers of days to the model.

• Time series - The decision to transfuse on a given day may be dependent on whether or not the patient was transfused on the previous day (s).

• Data are censored for various reasons - discharge, death, other complicating factor. Patients contribute different numbers of days.

• Some factors are measured only once, while others are measured daily.

• Data are not missing at random.  Data are usually missing for clinically-related reasons.  Results are missing on a given day because the physician did not think that it was necessary to order the test or to record that particular variable on a particular day.  The model would need to include the fact that a test was ordered or not ordered.  If the test was ordered, then  the model would need to include the result of the test (which is usually a continuous variable, e.g., serum creatinine could take any value > 0 mg/dL or be not done).  If the test was not ordered, then this effect may also be important to model.

-------------------------------------------
Nancy Buderer, MS
Biostatistician & Research Consultant
[hidden email]
-------------------------------------------

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[Ryan]

One more point--I specified an EXCHANGEABLE covariance structure based on the data simulation. When working with real-world data, however, one often observes more complex covariance structures. One such structure that immediately comes to mind when dealing with temporal data is the first-order autoregressive structure. Generally speaking, the first-order autoregressive structure assumes decaying correlations as observations become more distant in time. Another covariance structure to consider would be the unstructured type, though this may be overkill depending on the data.

 

Ryan

On Sun, May 8, 2011 at 10:53 PM, R B <[hidden email]> wrote:

Art,

 

A GEE/Generalized Linear Model can be fit employing the GENLIN procedure in SPSS. GENLIN is capable of fitting various generalized linear models that account for correlation among repeated measures.

 

I provide a simple example below which assumes data are derived from a logistic regression equation with correlation among repeated observations. Note that data for 1000 subjects are generated, all of whom are measured 50 times. Also note that a time-varying covariate, x1, was incorporated into the model.

 

**I wrote the code below very fast. Apologies if there are any typos.

 

HTH,

 

Ryan

 

*Generate Data.
set seed 98765432.

 

new file.
inp pro.

 

comp ID = -99.
comp x1 = -99.
comp b0 = -99.
comp b1 = -99.
comp rand_eff = -99.
comp time = -99.

 

leave ID to time.

 

 loop ID = 1 to 1000.
    comp b0 = -0.5.
    comp b1 = 1.0.
    comp rand_eff = sqrt(.3)*rv.normal(0,1).

 

    loop time = 1 to 50.
       comp x1 = rv.normal(2,1).
       comp eta  = b0 + b1*x1 + rand_eff.
       comp p = exp(eta) / (1 + exp(eta)).
       comp y = rv.bernoulli(p).

 

    end case.
  end loop.
 end loop.

end file.
end inp pro.

exe.

 

Delete variables b0 b1 rand_eff eta p.

 

GENLIN y (REFERENCE=FIRST) WITH x1
  /MODEL x1 INTERCEPT=YES
 DISTRIBUTION=BINOMIAL LINK=LOGIT
  /REPEATED SUBJECT=ID WITHINSUBJECT=time SORT=YES CORRTYPE=EXCHANGEABLE ADJUSTCORR=YES
    COVB=ROBUST MAXITERATIONS=100 PCONVERGE=1e-006(ABSOLUTE) UPDATECORR=1
  /PRINT CPS DESCRIPTIVES MODELINFO FIT SUMMARY SOLUTION.

 

On Sat, May 7, 2011 at 7:42 AM, Art Kendall <[hidden email]> wrote:

I thought that we had a discussion about repeated dichotomous data on this list.  However, I must be using the wrong search specifications in the archives because I did not find it. 

Does anyone recall what that discussion was about so that I can send the url for those posts?

Is anybody familiar enough with the new procedure for GEE to say it might be a place to look?

Art Kendall
Social Research Consultants


-------- Original Message --------

Subject:	Statistical Consulting Section: modeling a binomial outcome measured multiple days
Date:	Fri, 06 May 2011 15:16:41 -0400
From:	Nancy Buderer [hidden email]
Reply-To:	[hidden email]
To:	Arthur Kendall [hidden email]

Please Do Not Forward, use the options to the right to forward or reply.

ASA | Discussions | Statistical Consulting Section

FEEDBACK | QUESTIONS

modeling a binomial outcome measured multiple days

From:	Nancy Buderer
To:	Statistical Consulting Section
Posted:	5/6/2011 3:17:00 PM
Subject:	modeling a binomial outcome measured multiple days
Message:

View Profile

Add Contact

Blog This

I am an independent consultant and have a complicated dataset.  I appreciate your ideas on how to approach this problem. 

The purpose of the study is to describe the factors associated with blood transfusion and to determine their relative importance in a cohort of patients with a certain condition. The investigators are interested in developing a model that predicted the physicians' decision to transfuse.  The results of the study could be used to modify hospital transfusion practices.

This is a retrospective study, post hoc / secondary analysis using a dataset that was collected for a different multicenter study.

The outcome the investigators want to model is whether or not a patient was transfused on any given day during their hospital stay.  Transfusion (yes/no) is measured daily until the patient is discharged. 

Variables collected include one-time measurements (e.g.,  demographics, baseline lab values, other conditions)  as well as daily measurements (e.g., lab values).  Most lab values were measured on days 1 - 7, but not all (some are measured days 1-4 and day 7). 

The dataset includes about 1000 patients.  These patients collectively had 502 transfusions out of 6496 patient days.

The analysis are complicated by several considerations:

• Multiple measures per patient.  If patient-day is the unit of observation, then days from the same patient are correlated.

• Patients can have days of transfusion as well as days without transfusion.

• Data are censored; patients contribute different numbers of days to the model.

• Time series - The decision to transfuse on a given day may be dependent on whether or not the patient was transfused on the previous day (s).

• Data are censored for various reasons - discharge, death, other complicating factor. Patients contribute different numbers of days.

• Some factors are measured only once, while others are measured daily.

• Data are not missing at random.  Data are usually missing for clinically-related reasons.  Results are missing on a given day because the physician did not think that it was necessary to order the test or to record that particular variable on a particular day.  The model would need to include the fact that a test was ordered or not ordered.  If the test was ordered, then  the model would need to include the result of the test (which is usually a continuous variable, e.g., serum creatinine could take any value > 0 mg/dL or be not done).  If the test was not ordered, then this effect may also be important to model.

-------------------------------------------
Nancy Buderer, MS
Biostatistician & Research Consultant
[hidden email]
-------------------------------------------

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