Computational Resources for Exact Conditional Logistic Regression

Many problems require a prohibitive amount of time and memory for exact computations, depending on the speed and memory available on your computer. For such problems, consider whether exact methods are really necessary. Stokes, Davis, and Koch (2000) suggest looking at exact p-values when the sample size is small and the approximate p-values from the unconditional analysis are less than 0.10, and they provide rules of thumb for determining when various models are valid.

A formula does not exist that can predict the amount of time and memory necessary to generate the exact conditional distributions for a particular problem. The time and memory required depends on several factors, including the total sample size, the number of parameters of interest, the number of nuisance parameters, and the order in which the parameters are processed. To provide a feel for how these factors affect performance, 19 data sets containing Nobs observations consisting of up to 10 independent uniform binary covariates (X1,...,XN) and a binary response variable (Y), are generated, and the following statements create exact conditional distributions for X1 conditional on the other covariates by using the default METHOD=NETWORK. Figure 51.12 displays results obtained on a 400Mhz PC with 768MB RAM running Microsoft Windows NT.

   data one;
      do obs=1 to HalfNobs;
         do Y=0 to 1;
            X1=round(ranuni(0));
            ...
            XN=round(ranuni(0));
            output;
         end;
      end;
   options fullstimer;
   proc logistic exactonly exactoptions(method=network maxtime=1200);
      class X1...XN / param=ref;
      model Y=X1...XN;
      exact X1 / outdist=dist;
   run;

Figure 51.12 Mean Time and Memory Required

At any time while PROC LOGISTIC is deriving the distributions, you can terminate the computations by pressing the system
interrupt key sequence (see the SAS Companion for your system) and choosing to stop computations. If you run out of memory, see the SAS Companion for your system to see how to allocate more.

You can use the EXACTOPTIONS option MAXTIME= to limit the total amount of time PROC LOGISTIC uses to derive all of the exact distributions. If PROC LOGISTIC does not finish within that time, the procedure terminates.

Calculation of frequencies are performed in the log scale by default. This reduces the need to check for excessively large frequencies but can be slower than not scaling. You can turn off the log scaling by specifying the NOLOGSCALE option in the MODEL statement. If a frequency in the exact distribution is larger than the largest integer that can be held in double precision, a warning is printed to the SAS log. But since inaccuracies due to adding small numbers to these large frequencies might have little or no effect on the statistics, the exact computations continue.

You can monitor the progress of the procedure by submitting your program with the EXACTOPTIONS option STATUSTIME=. If the procedure is too slow, you can try another method by specifying the EXACTOPTIONS option METHOD=, you can try reordering the variables in the MODEL statement (note that CLASS variables are always processed before continuous covariates), or you can try reparameterizing your classification variables as in the following statement:

   class class-variables / param=ref ref=first order=freq;