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Dataplot Vol 2 Vol 1

POSITIVE PREDICTIVE VALUE

Name:
    POSITIVE PREDICTIVE VALUE (LET)
Type:
    Let Subcommand
Purpose:
    Compute the positive predictive value between two binary variables.
Description:
    Given two variables with n parired observations where each variable has exactly two possible outcomes, we can generate the following 2x2 table:

        Variable 2  
      Variable 1 Success Failure Row Total

      Success N11 N12 N11 + N12
      Failure N21 N22 N21 + N22

      Column Total N11 + N21 N12 + N22 N

    The parameters N11, N12, N21, and N22 denote the counts for each category.

    Success and failure can denote any binary response. Dataplot expects "success" to be coded as "1" and "failure" to be coded as "0". Some typical examples would be:

    1. Variable 1 denotes whether or not a patient has a disease (1 denotes disease is present, 0 denotes disease not present). Variable 2 denotes the result of a test to detect the disease (1 denotes a positive result and 0 denotes a negative result).

    2. Variable 1 denotes whether an object is present or not (1 denotes present, 0 denotes absent). Variable 2 denotes a detection device (1 denotes object detected and 0 denotes object not detected).

    In these examples, the "ground truth" is typically given as variable 1 while some estimator of the ground truth is given as variable 2.

    The positive predictive value is then N11/(N11+N21). This is the conditional probability of variable 1 being true given that variable 2 is true. In the context of the first example above, this is the probability that the disease is present when there is a positive test result.

    Fleiss and his co-authors recommend positive predictive value and negative predictive value as an alternative to false positive and false negative due to the fact that the definitions of false positive and false negative have been inconsistent in the literature.

Syntax:
    LET <par> = POSITIVE PREDICTIVE VALUE <y1> <y2>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y1> is the first response variable;
                <y2> is the second response variable;
                <par> is a parameter where the computed positive predictive value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = POSITIVE PREDICTIVE VALUE Y1 Y2
    LET A = POSITIVE PREDICTIVE VALUE Y1 Y2 SUBSET TAG > 2
Note:
    The two variables must have the same number of elements.
Note:
    There are two ways you can define the response variables:

    1. Raw data - in this case, the variables contain 0's and 1's.

      If the data is not coded as 0's and 1's, Dataplot will check for the number of distinct values. If there are two distinct values, the minimum value is converted to 0's and the maximum value is converted to 1's. If there is a single distinct value, it is converted to 0's if it is less than 0.5 and to 1's if it is greater than or equal to 0.5. If there are more than two distinct values, an error is returned.

    2. Summary data - if there are two observations, the data is assummed to be the 2x2 summary table. That is,

        Y1(1) = N11
        Y1(2) = N21
        Y2(1) = N12
        Y2(2) = N22
Note:
    The following additional commands are supported

      TABULATE FALSE POSITIVE Y1 Y2 X
      CROSS TABULATE FALSE POSITIVE Y1 Y2 X1 X2

      POSITIVE PREDICTIVE VALUE PLOT Y1 Y2 X
      CROSS TABULATE POSITIVE PREDICTIVE VALUE PLOT Y1 Y2 X1 X2

      BOOTSTRAP POSITIVE PREDICTIVE VALUE PLOT Y1 Y2
      JACKNIFE POSITIVE PREDICTIVE VALUE PLOT Y1 Y2
Default:
    None
Synonyms:
    None
Related Commands: Reference:
    Fleiss, Levin, and Paik (2003), "Statistical Methods for Rates and Proportions", Third Edition, Wiley, chapter 1.
Applications:
    Categorical Data Analysis
Implementation Date:
    2007/4
Program:
     
    let n = 1
    .
    let p = 0.2
    let y1 = binomial rand numb for i = 1 1 100
    let p = 0.1
    let y2 = binomial rand numb for i = 1 1 100
    .
    let p = 0.4
    let y1 = binomial rand numb for i = 101 1 200
    let p = 0.08
    let y2 = binomial rand numb for i = 101 1 200
    .
    let p = 0.15
    let y1 = binomial rand numb for i = 201 1 300
    let p = 0.18
    let y2 = binomial rand numb for i = 201 1 300
    .
    let p = 0.6
    let y1 = binomial rand numb for i = 301 1 400
    let p = 0.45
    let y2 = binomial rand numb for i = 301 1 400
    .
    let p = 0.3
    let y1 = binomial rand numb for i = 401 1 500
    let p = 0.1
    let y2 = binomial rand numb for i = 401 1 500
    .
    let x = sequence 1 100 1 5
    .
    let a = positive predictive value y1 y2 subset x = 1
    tabulate positive predictive value y1 y2 x
    .
    label case asis
    xlimits 1 5
    major xtic mark number 5
    minor xtic mark number 0
    xtic mark offset 0.5 0.5
    ytic mark offset 0.05 0.05
    y1label Positive Predictive Value
    x1label Group ID
    character x blank
    line blank solid
    .
    positive predictive value plot y1 y2 x
        
    plot generated by sample program

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Date created: 06/06/2007
Last updated: 10/07/2016

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