Sorry, I misread your original description of your experiment and did not realize that each of the animals in your study received 2 to 4 treatments.  However, your original description also states that you took only one surgical procedure for each animal so that there is a "perfect correlation between the procedure type and the animal".  I'm now confused about the meaning of "treatment" and the meaning of "surgical procedure type".  Are they the same or different?  Instead of selecting only one surgical procedure for each animal, would you find it valuable to model the pattern/order of surgical procedures each animal underwent? In any case, the variance/covariance estimate displayed in the output from the RANDOM statement is the variability in the outcome associated with Animal_ID (?=procedure type) after accounting for the fixed effect of Treatment.   A dichotomous or binary outcome can have variability because you've specified a statistical distribution (the binomial distribution) for this outcome in your MODEL statement.  Even though each animal has only one outcome, the distribution of outcomes across all animals is specified as having a binomial distribution, which does have a mean and a variance. If you wish, you can also estimate the value of the random effect for each animal by adding the option, SOLUTION, to the RANDOM statement:     RANDOM intercept / subject=Animal_ID solution; You did not provide the code for your PROC LOGISTIC program.  Perhaps the discrepancy between the reported significance probability of T2 vs. T3 and the odds ratio for T2 whose 95% confidence interval excludes 1.00 (and therefore should yield a statistically significant probability) results from using the default "effect" coding for treatment in the PROC LOGISTIC CLASS statement. ... View more

No, you didn't do anything wrong, as far as I can tell. The 95% confidence intervals are wide because you have small sample sizes in your two control and one treatment groups.  The third and the fourth estimates in your list of output estimates show that the odds ratios for the duration of treatment one or more minutes long are much less common for treatment 3 than that for either treatment 1 or treatment 2.  The only way to narrow these confidence intervals is to increase the sample sizes in your study. The covariance estimate for the random effect of animal is actually the (same) variance estimate for each animal because your data contain only one observation for each animal.  Although the standard error for this estimate is not the best estimate of its variability, because this standard error exceeds the value of the estimate, accounting for the random effect of each animal probably does not affect much the (fixed) treatment effects on the outcome.  If you wish, you can compare the output for the current model with that for a model that omits the random effect of animal (fixed-effect only model).  In summary, the relatively small variance estimate for each animal indicates a relatively negligible effect on the treatment comparisons. ... View more

If your data, according to the specifications of the PROC FASTCLUS algorithm, contains fewer than K clusters, then PROC FASTCLUS will display only that fewer-than-K number of clusters.  As an example, generate data whose variable values contain only ten different values so that only ten different patterns of these variable values occur in 1,000 observations.  If you specify MAXCLUSTERS=15, PROC FASTCLUS will find and display only ten clusters of observations, not 15. You can write a SAS macro to specify different values of MAXCLUSTERS. If you do not specify the SEED option data set, PROC FASTCLUS selects as its initial cluster seeds observations from the input SAS data set.  If the latter show patterns that are correlated, then the clusters PROC FASTCLUS generates may not be very good in describing the range of variable values in the input SAS data set.  Instead of using this SEED option data set, some researchers recommend instead generating a uniformly distributed random number for each observation on the input SAS data set and then sorting these observations by this random number before using this input SAS data set in PROC FASTCLUS.  This way, any arbitrary patterns found in the order of the observations from the original input SAS data set are broken up so that the observations from this input SAS data set  provide initial cluster seeds that better "represent" the pattern of variable values in the observations of the input SAS data set. The RADIUS option is less a convergence criterion than a criterion to select initial cluster seeds (observations)  so that these latter seeds are "far enough apart" from previously selected initial cluster seeds.  This option is somewhat of an alternative to specifying a value for the MAXCLUSTERS option. I don't know of a "best" convergence criterion for PROC FASTCLUS.  What I would suggest that you do is to read the documentation chapter for SAS/STAT, "Introduction to Clustering Procedures", that describes how different SAS clustering procedures work and what are their strengths and weaknesses.  This may help you decide whether PROC FASTCLUS is the most appropriate procedure for your applications.  The PROC FASTCLUS documentation also hints on how to improve the separation among the clusters it finds. ... View more

To answer your question, no. SAS software that accounts for the study design of complex sample surveys like the design-based PROC SURVEYLOGISTIC is not based on maximum likelihoood estimation.  Thus, Firth's method is inapplicable in this procedure.  However, some have attempted to mimic this design-based analysis of complex sample surveys using model-based methods like generalized linear mixed models in PROC GLIMMIX. Since SAS code to replicate Firth's method is available at    http://cemsiis.meduniwein.ac.at/kb/wf/software/statistische-software/fllogistf/, you may be able to adapt this code to a PROC GLIMMIX model for analyzing complex sample surveys. ... View more

Try rescaling your original data so that the variables you are trying to estimate have the same order of magnitude to see if the infinite likelihood problem resolves.  If this problem does resolve, then re-rescale your resulting variance and covariance estimates using the standard formulas (see, for example, the entry for "Variance" on Wikipedia):    Var(aX) = a*a*Var(X), and    Cov(aX,bY) = a*b*Cov(X,Y). For example, if Y is about 1,000 times the magnitude of X, rescale Y by dividing it by 1,000.  Estimate the variance-covariance matrix for X and the rescaled Y using SAS's PROC MIXED or PROC GLIMMIX.  Then the variance of the original Y would equal 1,000*1,000*Var(Rescaled-Y) = 1,000,000*Var(Rescaled-Y).  The covariance between X and the original Y would equal 1*1,000*Cov(X, Rescaled-Y). = 1,000*Cov(X, Rescaled-Y). Although tedious to perform for 13 traits (169 terms in the variance-covariance matrix), this may help you to solve your problem. ... View more

Read the PROC MIXED documentation section on convergence problems.  This section discusses both the problem of an infinite likelihood and the problem when two of the covariance parameters are several orders of magnitude apart, which seems to be true in your example.  This section also discusses possible solutions to each of these problems. ... View more

Your first pair of odds ratios use Treatment #3 as the reference group for the other two treatments.  In a cumulative logit model as SAS parameterizes it, these odds ratios show the odds of being in the lower category of the dependent variable outcome, Response, for Treatments # 1 and #2 relative to the odds of Treatment #3 being in that lower category.  Since these odds ratios are much less than 1.00, the odds of being in the lower Response category for both Treatments #1 and #2 are much less than the odds of being in the lower Response category for Treatment #3. Or, as an alternative interpretation that focuses on Treatment #3, those receiving Treatment #3 are much more likely to be in these lower Response categories than those receiving Treatments #1 and #2:  About 100 times [=1/0.01] more likely to be in a lower Response category than Treatment #1 and about 25 times [=1/0.04] more likely to be in a lower Response category than Treatment #2.  You can specify the option, DESCENDING, on the PROC GLIMMMIX statement to determine these "reciprocal" odds ratios for being more likely for Treatments #1 and #2 to be in these upper Response categories than Treatment #3. ... View more

Defining a new variable to distinguish observations within an animal is only meant as an arbitrary index for that observation.  The purpose of the new variable is to identify different observations to SAS.  Specifically, the second RANDOM statement in the SAS code that I listed before,     random ordered_value_repeated_measure / subject=id type=cs residual; uses the name of that new variable, "ordered_value_repeated_measure", to identify the repeated-measure observations within each animal subject identified by the variable, ID.  Because each repeated-measure observation is not ordered, the name I used for this new variable is not appropriate, and sorting by that variable within each animal in the prior PROC SORT step is no longer relevant. Nonetheless, providing a name for this repeated-measure allows SAS to calculate the "effects" of the repeated measures in this model.  The use of a variance-covariance structure like compound symmetry (for example, TYPE=CS in this code) or unrestricted (TYPE=UN) does not depend on whether the repeated measure is ordinal or nominal; use of an autoregressive-order-1 structure (TYPE=AR(1)) or a spatial covariance structure (TYPE=SP(etc.)) would be inappropriate when the repeated measure is nominal, as it appears to be here. In summary, defining a new variable to distinguish repeated-measure observations within an animal is still worthwhile. ... View more

You might try something like the following as a start:     proc sort data=dataset;         by id ordered_value_repeated_measure ;     run;     proc glimmix data=dataset order=internal order=internal;         class X1 X2 Y;         model y(order=internal descending ref=last)=X1 / dist=multinomial link=cumlogit ddfm=kenwardroger oddsratio;         lsmeans X1 / cl diff adjust=tukey adjdfe=row;         random X2 / solution cl gcorr;         random ordered_value_repeated_measure / subject=id type=cs residual;     run;     quit; The PROC SORT sorts the input data by ID and the ordered value of the repeated measure. This PROC GLIMMIX model assumes an ordinal, integer-valued dependent variable, Y, which is distributed multinomially with a cumulative logit link and a fixed-effect independent variable, X1.  The value of Y=0 is defined as the reference category for the dependent variable.  The denominator degrees of freedom is adjusted by the Kenward-Roger method when both categorical fixed effects and random effects occur in the model.  Odds ratios are calculated as measures of effect in this cumulative logit model.  The independent variables, X1 and X2, and the dependent variable, Y, are categorical classification variables.   The LSMEANS statement calculates the "adjusted" means of the dependent variable, Y, their differences, and their 95% confidence intervals for the levels of the categorical independent variable, X1; the significance probabilities for these mean differences are adjusted for multiple comparisons using the Tukey pairwise method. The first RANDOM statement specifies X2 as a random variable across all study subjects.  The second RANDOM statement specifies the value of the ordered value of the repeated measure within each study subject, indexed by the variable, ID, as a repeated measure with the RANDOM statement option, RESIDUAL; the type of the residual variance-covariance structure is assumed to be that of compound symmetry. ... View more