Visualizing Categorical Data: powerlog

The powerlog macro ( get powerlog.sas)

Power for logistic regression, quantitative predictor

Usage

  %powerlog(p1=.08, p2=%str(.16, .24));

Parameters

DATA=

Specifies the name of an input data set containing the variables P1, P2, ALPHA, POWER, and RSQ in all combinations for which power is desired. If an input DATA= data set is specified, the program ignores values for the P1=, P2=, ALPHA=, POWER=, and RSQ= parameters.

P1=

is the estimated probability of the event at the mean value of the quantitative predictor.

P2=

is the estimated probability of the event at an X-value equal to the X-mean plus one standard deviation. You may specify a list of values separated by commas, a range of the form x TO y BY z, or a combination of these. However, you must surround the P2= value with %STR() if any commas appear in it. For example,

        p2=.10 to .30 by .05
        p2=%str(.10, .13, .20)

ALPHA=

is the desired Type I error probability for a *one-sided* test of H0: beta(x) = 0

POWER=

is the desired power of the test.

RSQ=

is the squared multiple correlation of the predictor with all other predictors. Use RSQ=0 for a 1-predictor model.

PLOT=

is a specification for plotting the results. The default is PLOT=N * POWER=RSQ. No plots are produced if PLOT= is blank.

PLOTBY=

is another variable in the OUT= data set. A separate plot is produced for each level of the PLOTBY variable. The default is THETA, the odds-ratio determined by the values of P1 and P2.

OUT=

Specifies the name of the output data set.

Examples

• Modelling the relation of the probability of heart disease on X = cholesterol. If previous studies suggest that heart disease occurs with P1=0.08 at the mean level of cholesterol, what is the sample size required to detect a 50% increase (P2 = 1.5*.08 = .12), or an 87.5% increase (P2 = 1.875*.08 = .15) in the probability of heart disease, when cholesterol increases by one standard deviation?

  If age is another predictor, how does sample size vary with the RSQ between cholesterol and age? Assume the RSQ varies between 0.2 and 0.4.

  %include vcd(powerlog);        *-- or include in an autocall library;
  %powerlog(p1=.08, p2=%str(.12, .15), rsq=%str(.2, .4) );
  

  This produces the printed output below:

     One-tailed test, alpha=.05, p1=.08 p2=.12, .15
  
     --------------------------------------------
     |                  |Pr(event) at X_mean+std|
     |                  |-----------------------|
     |                  |   0.12    |   0.15    |
     |                  |-----------+-----------|
     |                  | R**2 (X,  | R**2 (X,  |
     |                  | other Xs) | other Xs) |
     |                  |-----------+-----------|
     |                  | 0.2 | 0.4 | 0.2 | 0.4 |
     |------------------+-----+-----+-----+-----|
     |Power             |     |     |     |     |
     |------------------|     |     |     |     |
     |0.7               |  429|  572|  183|  245|
     |------------------+-----+-----+-----+-----|
     |0.75              |  488|  650|  207|  276|
     |------------------+-----+-----+-----+-----|
     |0.8               |  558|  744|  235|  314|
     |------------------+-----+-----+-----+-----|
     |0.85              |  646|  861|  270|  361|
     |------------------+-----+-----+-----+-----|
     |0.9               |  765| 1020|  318|  424|
     --------------------------------------------
  

  Two graphs are produced, one for P2=.12, and the other for P2=.15.
• The probability of a positive response is estimated as P1=0.5 at the mean of X. What sample sizes are required if the probability at the mean of X plus 1 std ranges from 0.6 - .75?

  %powerlog(p1=.5, p2=%str(.6, .65, .7, .75), rsq=0, plot = N * power = p2);
  

  This produces the printed output below:

     One-tailed test, alpha=.05, p1=.5 p2=.6, .65, .7, .75
  
     --------------------------------------------
     |                  |Pr(event) at X_mean+std|
     |                  |-----------------------|
     |                  | 0.6 |0.65 | 0.7 |0.75 |
     |------------------+-----+-----+-----+-----|
     |Power             |     |     |     |     |
     |------------------|     |     |     |     |
     |0.7               |  126|   63|   46|   50|
     |------------------+-----+-----+-----+-----|
     |0.75              |  143|   72|   52|   56|
     |------------------+-----+-----+-----+-----|
     |0.8               |  164|   82|   59|   62|
     |------------------+-----+-----+-----+-----|
     |0.85              |  190|   94|   67|   70|
     |------------------+-----+-----+-----+-----|
     |0.9               |  225|  111|   79|   81|
     --------------------------------------------
  

  The graphical output shows how sample size depends on the value of P2 for various levels of power.

See also