Hello All,

I have a technical mixed model question to pose to the group. 

First the setup… to simplify the scenario; let’s say my outcome is individual patient cost for two time periods (year 1 and 2).  Costs for each patient are greater than 0 and it is possible for patients to have data at year 1 only, year 2 only, or both year 1 and 2.  For those patients with data only at 1 time point, their data is NOT missing.  Rather, it is because their cost is 0 for that year and I am not interested in including 0s in the mean estimates.  For now, let’s also say I am satisfied assuming a normal distribution for the analysis.  I wish to estimate the mean cost for both years as well as estimate and test for a difference between the two years.  However, I am truly only interested in estimates equivalent to the arithmetic means (not including 0 costs and not accounting for subjects without observations at both time points given this data really is not missing).  Mixed models (specifically I am using SAS proc mixed with a subject specific random intercept or using compound symmetry to structure the residual covariance matrix) are great for handling missing observations.  In this scenario the estimates are impacted by individuals having only one observation and, thus, are not equal to the arithmetic mean… I do not want this (I know… odd given this is a benefit of mixed model analysis).

So my question is, given this scenario is it possible to get mean estimates the same as the arithmetic means with standard errors accounting for the repeated measures?

Thank you for reading this post and any insights will be much appreciated!

Best,
Derek

------------------------------
Derek Blankenship
------------------------------

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

Hello All,

I have a technical mixed model question to pose to the group. 

First the setup… to simplify the scenario; let’s say my outcome is individual patient cost for two time periods (year 1 and 2).  Costs for each patient are greater than 0 and it is possible for patients to have data at year 1 only, year 2 only, or both year 1 and 2.  For those patients with data only at 1 time point, their data is NOT missing.  Rather, it is because their cost is 0 for that year and I am not interested in including 0s in the mean estimates.  For now, let’s also say I am satisfied assuming a normal distribution for the analysis.  I wish to estimate the mean cost for both years as well as estimate and test for a difference between the two years.  However, I am truly only interested in estimates equivalent to the arithmetic means (not including 0 costs and not accounting for subjects without observations at both time points given this data really is not missing).  Mixed models (specifically I am using SAS proc mixed with a subject specific random intercept or using compound symmetry to structure the residual covariance matrix) are great for handling missing observations.  In this scenario the estimates are impacted by individuals having only one observation and, thus, are not equal to the arithmetic mean… I do not want this (I know… odd given this is a benefit of mixed model analysis).

So my question is, given this scenario is it possible to get mean estimates the same as the arithmetic means with standard errors accounting for the repeated measures?

Thank you for reading this post and any insights will be much appreciated!

Best,
Derek

------------------------------
Derek Blankenship
------------------------------

Response to 1st question: Yes, patients with no data (no cost) for a given year are not included in the data set.

Response to 2nd question: Yes, LS-means for year 1 and 2 as well as difference between the two years (I will need to obtain this via contrast/estimate statements given the true study design is more complex).

Thank you for thinking about this!

------------------------------
Derek Blankenship

Original Message:
Sent: 08-17-2016 17:08
From: Paul Thompson
Subject: Unmixing mixed models?

Specifically what do you have in the cases that you have no observation for Person 2022 on a given year? Do you have any value for them? You should simply omit them from the dataset for that year.

 

As to the "estimate not equal to the arithmetic mean", the estimates of what in particular? Do you mean the least-square means for Y1 and Y2?

 

 

Hello All, I have a technical mixed model question to pose to the group. First the setup to simplify the scenario; lets say my outcome is... -posted to the "Statistical Consulting Section" community

Please Do Not Forward, use the options to the right to forward or reply. Statistical Consulting Section   Post New Message   Unmixing mixed models? Reply to Group Reply to Sender Aug 17, 2016 4:55 PM Derek Blankenship Hello All, I have a technical mixed model question to pose to the group.  First the setup… to simplify the scenario; let's say my outcome is individual patient cost for two time periods (year 1 and 2).  Costs for each patient are greater than 0 and it is possible for patients to have data at year 1 only, year 2 only, or both year 1 and 2.  For those patients with data only at 1 time point, their data is NOT missing.  Rather, it is because their cost is 0 for that year and I am not interested in including 0s in the mean estimates.  For now, let's also say I am satisfied assuming a normal distribution for the analysis.  I wish to estimate the mean cost for both years as well as estimate and test for a difference between the two years.  However, I am truly only interested in estimates equivalent to the arithmetic means (not including 0 costs and not accounting for subjects without observations at both time points given this data really is not missing).  Mixed models (specifically I am using SAS proc mixed with a subject specific random intercept or using compound symmetry to structure the residual covariance matrix) are great for handling missing observations.  In this scenario the estimates are impacted by individuals having only one observation and, thus, are not equal to the arithmetic mean… I do not want this (I know… odd given this is a benefit of mixed model analysis). So my question is, given this scenario is it possible to get mean estimates the same as the arithmetic means with standard errors accounting for the repeated measures? Thank you for reading this post and any insights will be much appreciated! Best, Derek ------------------------------ Derek Blankenship ------------------------------   Reply to Group   Reply to Sender   View Thread   Recommend   Forward   Flag as Inappropriate   Post New Message     You are subscribed to "Statistical Consulting Section" as paul.thompson@sanfordhealth.org. To change your subscriptions, go to My Subscriptions. To unsubscribe from this community discussion, go to Unsubscribe.

This may help  answer your questions. Econometricians, use "Tobit" models when the data includes both continuous (cost) and zero data. The Tobit model was developed by James Tobin, who won the Nobel for his many contributions. here's a link for a  multivariate tobit and a repeated measures tobit. 

 http://www.sciencedirect.com/science/article/pii/S0169716105800410   

STATA has a module http://www.stata.com/stata-news/news28-4/censored-outcomes-and-tobit/

------------------------------
Chris Barker, Ph.D.
Consultant and
Adjunct Associate Professor of Biostatistics


---
"In composition you have all the time you want to decide what to say in 15 seconds, in improvisation you have 15 seconds."
-Steve Lacy

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

Hello All,

I have a technical mixed model question to pose to the group. 

First the setup… to simplify the scenario; let’s say my outcome is individual patient cost for two time periods (year 1 and 2).  Costs for each patient are greater than 0 and it is possible for patients to have data at year 1 only, year 2 only, or both year 1 and 2.  For those patients with data only at 1 time point, their data is NOT missing.  Rather, it is because their cost is 0 for that year and I am not interested in including 0s in the mean estimates.  For now, let’s also say I am satisfied assuming a normal distribution for the analysis.  I wish to estimate the mean cost for both years as well as estimate and test for a difference between the two years.  However, I am truly only interested in estimates equivalent to the arithmetic means (not including 0 costs and not accounting for subjects without observations at both time points given this data really is not missing).  Mixed models (specifically I am using SAS proc mixed with a subject specific random intercept or using compound symmetry to structure the residual covariance matrix) are great for handling missing observations.  In this scenario the estimates are impacted by individuals having only one observation and, thus, are not equal to the arithmetic mean… I do not want this (I know… odd given this is a benefit of mixed model analysis).

So my question is, given this scenario is it possible to get mean estimates the same as the arithmetic means with standard errors accounting for the repeated measures?

Thank you for reading this post and any insights will be much appreciated!

Best,
Derek

------------------------------
Derek Blankenship
------------------------------

Thank you, Paul.  After talking with SAS support and digging into their documentation there does not appear to be a way to "unmix" the mixed model.  This is because the variance and covariance parameters are used to estimate B.  In other (messy matrix notation) words... B = (X`V^-1X)^- X`V^-1 Y

------------------------------
Derek Blankenship

Original Message:
Sent: 08-17-2016 21:25
From: Paul Thompson
Subject: Unmixing mixed models?

Least-square means are computed as L'B, where B is the coefficient matrix. So how is B computed when there are missing rows in the X matrix?

 

(X'X)- X'Y – if the X matrix is simply based on what is there, I see only present values.

 

So list the X matrix – you can do that in Mixed I believe.

 

Or add a 0 value for some of the missing cases. Do you get the same ls means? If so, then the X matrix is formed by adding missing rows.

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

Hello All,

I have a technical mixed model question to pose to the group. 

First the setup… to simplify the scenario; let’s say my outcome is individual patient cost for two time periods (year 1 and 2).  Costs for each patient are greater than 0 and it is possible for patients to have data at year 1 only, year 2 only, or both year 1 and 2.  For those patients with data only at 1 time point, their data is NOT missing.  Rather, it is because their cost is 0 for that year and I am not interested in including 0s in the mean estimates.  For now, let’s also say I am satisfied assuming a normal distribution for the analysis.  I wish to estimate the mean cost for both years as well as estimate and test for a difference between the two years.  However, I am truly only interested in estimates equivalent to the arithmetic means (not including 0 costs and not accounting for subjects without observations at both time points given this data really is not missing).  Mixed models (specifically I am using SAS proc mixed with a subject specific random intercept or using compound symmetry to structure the residual covariance matrix) are great for handling missing observations.  In this scenario the estimates are impacted by individuals having only one observation and, thus, are not equal to the arithmetic mean… I do not want this (I know… odd given this is a benefit of mixed model analysis).

So my question is, given this scenario is it possible to get mean estimates the same as the arithmetic means with standard errors accounting for the repeated measures?

Thank you for reading this post and any insights will be much appreciated!

Best,
Derek

------------------------------
Derek Blankenship
------------------------------

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