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  • 1.  Dropping strata after grading the samples

    Posted 08-21-2011 18:07
    I would appreciate advice on this situation.  I give my opinion and believe I am okay on this but would appreciate feedback.  Have kept it general but believe the essential details are captured. 

    Projection of an overpayment from an audit.

     

    A system of accounts that can be thought of as partitioned into four areas A - D is to be audited for payment error.    A stratified sample plan is used having four strata:  A,B, C and D.

     

    Simple random samples are drawn from each of the four strata.

     

    In analysis of the samples, the reviewers  notice that strata A and C results are much more interesting.  Higher error rate and more serious problems.  Management asks the statistician if the extrapolation or projection can be done just on the high error rate accounts: A and C.

     

    (*) Generally, it is not good to change the plan in the middle of the work.

     

     The statistician responds that "Yes, that can be done since they(A and C)  are independent random samples and so the problem can be treated as a two strata situation and the usual formulas for estimation of a total such as in Ott's text applied in the same way as would have been for the four strata case."  The other two sample results from B and D can be collected or corrected ( the over / underpayments in the samples) as "actuals" i.e. no extrapolation.

     

    Aside from the observation (*), I don't see anything wrong with this. I don't particularly feel comfortable with this but have no "proof" that something is wrong.  By "this" I mean planning one thing and then changing it somewhat.    I would appreciate any observations or comments. 

    I am never completely sure the right way to post something on this ASA site so if I am doing it the wrong way please let me know.  Thanks again,

    Greg Dobbins


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    J. Dobbins
    Delmarva Foundation
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  • 2.  RE:Dropping strata after grading the samples

    Posted 08-21-2011 18:17

    If after you look at the data you specifically pick A and C to look at because they have high rates you have destroyed the random smaple property for inference.  No you cannot treat the problem as a two sample problem in comparing strata A with C.
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    Michael Chernick
    Director of Biostatistical Services
    Lankenau Institute for Medical Research
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  • 3.  RE:Dropping strata after grading the samples

    Posted 08-21-2011 20:01
    1. What Chernick said, if you are comparing A and C.

    2. I'm a bit lost.  You are doing a projection. If you are projecting to the total (all strata), then obviously you can't ignore the B and D strata.  If they have fewer errors, you need to reflect that lower error rate in the overall projection.

    3.  If you are assigned to get a projection for strata A, a projection for strata B, a projection for strata C, and a projection for strata D, and your client indicates that B and D are no longer of interest and they just want (i.e. will pay you for) projections on A and C, then you can get a projection for A, and a projection for C, since presumably those are the same projections you would produce for these strata if you were producing all four.

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    Michael Kruger
    Information Resources Inc
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  • 4.  RE:Dropping strata after grading the samples

    Posted 08-21-2011 20:10

    If you are computing projections I suppose you can generate the projections in the manner you choose.  The issue is statistical inference.  You can't do inference as though the two groups are random samples.  They were picked out specifically because they were unusual or extreme.  This would be like taking a random sample of size 5 say pick the maximum and do inference as though that variable was a simple random sample of size one when it in fact has the distirbution of the maximum of a random sample of size 5.
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    Michael Chernick
    Director of Biostatistical Services
    Lankenau Institute for Medical Research
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    Original Message


  • 5.  RE:Dropping strata after grading the samples

    Posted 08-21-2011 21:55

    This is the idea.  Client is no longer interested in B and D.   Just A and C.  These are medical claims for Ambulance transport.  A and C present transport from hospital to another hospital coded HH. A is for ground and C is for Air.  B and D represent air and ground but for transport from somewhere else other than a hospital to a hospital NH).  A and C are populations of claims for transport from hospital to another hospital coded HH and they have repective random samples that were graded for medical necessity.  THe findings of the samples here would be projected to the populations A and C  only.  It is just that after looking at the samples from B and D the client is no longer interested due to low error rate (the claims were for the most part justified).

    Greg


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    J. Dobbins
    Delmarva Foundation
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    Original Message


  • 6.  RE:Dropping strata after grading the samples

    Posted 08-21-2011 21:58

    That doesn't change anything A and C were picked based on the observed data.
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    Michael Chernick
    Director of Biostatistical Services
    Lankenau Institute for Medical Research
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    Original Message