Example 71.1 Dosage Levels

In this example, Dose is a variable representing the level of a stimulus, N represents the number of subjects tested at each level of the stimulus, and Response is the number of subjects responding to that level of the stimulus. Both probit and logit response models are fit to the data. The LOG10 option in the PROC PROBIT statement requests that the log base 10 of Dose is used as the independent variable. Specifically, for a given level of Dose, the probability of a positive response is modeled as

The probabilities are estimated first by using the normal distribution function (the default) and then by using the logistic distribution function. Note that, in this model specification, the natural rate is assumed to be zero.

The LACKFIT option specifies lack-of-fit tests and the INVERSECL option specifies inverse confidence limits.

In the DATA step that reads the data, a number of observations are generated that have a missing value for the response. Although the PROBIT procedure does not use the observations with the missing values to fit the model, it does give predicted values for all nonmissing sets of independent variables. These data points fill in the plot of fitted and observed values in the logistic model displayed in Output 71.1.7. The plot, requested with the PLOT=PREDPPLOT option, displays the estimated logistic cumulative distribution function and the observed response rates.

The following statements produce Output 71.1.1:

      data a;
         infile cards eof=eof;
         input Dose N Response @@;
         Observed= Response/N;
         output;
         return;
      eof: do Dose=0.5 to 7.5 by 0.25;
              output;
           end;
         datalines;
      1 10 1  2 12 2  3 10 4  4 10 5
      5 12 8  6 10 8  7 10 10
      ;

   proc probit log10;
      model Response/N=Dose / lackfit inversecl itprint;
      output out=B p=Prob std=std xbeta=xbeta;
   run;