Propensity Score Matching

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Propensity Score Matching

Russell Callaghan
Hello All,

I am conducting a study of treatment outcomes among adolescent cocaine abusers and methamphetamine abusers.  The cocaine abusers and the methamphetamine abusers have a number of large differences on observed covariates, and these differences can lead to biased estimates of the treatment effects.  I want to conduct a propensity score matching procedure, as outlined in D'Agostino, 1998 (Statistics in Medicine, 17, 2265-2281).  Using a logistic regression procedure, I have obtained a propensity score for each individual in both groups and, then, I performed a logit transformation of the propensity scores.  Now that I have the logit of propensity scores, I want to do the following steps in syntax:

1.  Randomly order individuals in the methamphetamine and cocaine groups
2.  Select the first methamphetamine subject
3.  All cocaine subjects within a preset amount (or calliper) of the methamphetamine subject's estimated logit of the propensity score are then selected.
4.  Mahalanobis distances, based on a given number of covariates, are calculated between these selected cocaine subjects and the target methamphetamine subject.
5. The closest cocaine subject and the selected methamphetamine target subject are then removed from the pool, and the process is repeated.
6. All remaining cocaine subjects are returned to the cocaine group, and these individuals are available for the next matching with the following target methamphetamine subject.
7. The procedure continues until all the methamphetamine abusers are matched.

This procedure is called the "Nearest available Mahalanobis metric matching within calipers defined by the propensity score" on page 2269 of D'Agostino, 1998.

Could someone please give me some tips on how to do this?  I've been struggling over the last few days with the syntax.
Thank you,
Russ

Dr. Russ Callaghan, PhD
Scientist
Centre for Addiction and Mental Health/
Department of Public Health Sciences
University of Toronto
33 Russell St.
Toronto, ON M5S 2S1
Phone: 416.535.8501 ext. 6599
Fax: 416.595.6899
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Re: Propensity Score Matching

Dan Zetu
What you want to do sounds pretty complicated. While I can't help you doing
all this complicated stuff, I may have a simpler solution for you.

First of all, why do you need Mahalanobis distance when you have the
propensity score already? I thought propensity score is used in lieu of the
Mahalanobis distance for matching purposes and it performs much better.

Here is what I would do.

1. Sort the metamphetamine abusers in descending order of propensity score.
2. Divide them into deciles or quintiles, each group containing the same
proportion
3. Match the crack abusers to these groups according to propensity score
4. Sig-test on your variables of interest to see whether there are still
differences between the two abuser groups within each stratum.

Trust me, this is easier and correct also.

Dan


>From: Russell Callaghan <[hidden email]>
>Reply-To: Russell Callaghan <[hidden email]>
>To: [hidden email]
>Subject: Propensity Score Matching
>Date: Mon, 24 Jul 2006 18:52:02 -0400
>
>Hello All,
>
>I am conducting a study of treatment outcomes among adolescent cocaine
>abusers and methamphetamine abusers.  The cocaine abusers and the
>methamphetamine abusers have a number of large differences on observed
>covariates, and these differences can lead to biased estimates of the
>treatment effects.  I want to conduct a propensity score matching
>procedure, as outlined in D'Agostino, 1998 (Statistics in Medicine, 17,
>2265-2281).  Using a logistic regression procedure, I have obtained a
>propensity score for each individual in both groups and, then, I performed
>a logit transformation of the propensity scores.  Now that I have the logit
>of propensity scores, I want to do the following steps in syntax:
>
>1.  Randomly order individuals in the methamphetamine and cocaine groups
>2.  Select the first methamphetamine subject
>3.  All cocaine subjects within a preset amount (or calliper) of the
>methamphetamine subject's estimated logit of the propensity score are then
>selected.
>4.  Mahalanobis distances, based on a given number of covariates, are
>calculated between these selected cocaine subjects and the target
>methamphetamine subject.
>5. The closest cocaine subject and the selected methamphetamine target
>subject are then removed from the pool, and the process is repeated.
>6. All remaining cocaine subjects are returned to the cocaine group, and
>these individuals are available for the next matching with the following
>target methamphetamine subject.
>7. The procedure continues until all the methamphetamine abusers are
>matched.
>
>This procedure is called the "Nearest available Mahalanobis metric matching
>within calipers defined by the propensity score" on page 2269 of
>D'Agostino, 1998.
>
>Could someone please give me some tips on how to do this?  I've been
>struggling over the last few days with the syntax.
>Thank you,
>Russ
>
>Dr. Russ Callaghan, PhD
>Scientist
>Centre for Addiction and Mental Health/
>Department of Public Health Sciences
>University of Toronto
>33 Russell St.
>Toronto, ON M5S 2S1
>Phone: 416.535.8501 ext. 6599
>Fax: 416.595.6899