### Ordinal Logistic Regression
inflam< -c(rep("Nil",4), rep("Mild",31), rep("Moderate",29), rep("Severe",9),
          rep("Nil",8), rep("Mild",23), rep("Moderate",18), rep("Severe",23))
inflam<-factor(inflam,levels=c("Nil","Mild","Moderate","Severe"),ordered=T)
trt<-c(rep("nonGM",73),rep("GM",72))
pigs<-data.frame(trt,inflam)
table(pigs$trt,pigs$inflam)

library(ordinal)
olreg<-clm(inflam~trt, data=pigs, link="logit")
summary(olreg)

##-- Output: --##

> table(pigs$trt,pigs$inflam)
       
        Nil Mild Moderate Severe
  GM      8   23       18     23
  nonGM   4   31       29      9

> summary(olreg)
formula: inflam ~ trt
data:    pigs

 link  threshold nobs logLik  AIC    niter max.grad cond.H 
 logit flexible  145  -183.73 375.46 5(0)  5.29e-08 1.5e+01

Coefficients:
         Estimate Std. Error z value Pr(>|z|)
trtnonGM  -0.3893     0.3060  -1.272    0.203

So, another analysis (probably the "best" analysis for this data) shows no significant difference between treatment groups.

Yes, logit is as you described (I think it’s the default, but I didn’t want to chance that the default was “probit”).

I don’t have any big disagreements regarding accounting for a gender:treatment interaction. I only mentioned that above since, as I’m not familiar with pig gastric inflammation (I’m a neuroscientist by training…), I don’t know if there’s some compelling prior information for including or excluding it.

IMO, it is necessary to include gender in the model or analyze them separately. Gender and its interaction with treatment is a potential source of variability and should be accounted for in the model. There is no reason to expect that genders would react similarly to the treatments. Some people will suggest that, because gender is non-significant, we can ignore it when modeling. I do not subscribe to that line of thought, however. Non-significance does not imply no effect, AKA, never accept the null hypothesis. It was a factor in the design and should be accounted for in the model.

Glad to see so many people familiar with R out there. although it is not a package I know well, it is a powerful tool.

library(ordinal)
d <- data.frame(
    Severity = as.factor(c(rep(c(0,1,2,3),4))),
    Treatment = c(rep(c(rep("NoGMO",4),rep("GMO",4)),2)),
    Gender = c(rep("M", 8), rep("F", 8)),
    Count = c(1,16,17,2,4,12,12,8,3,15,12,7,4,11,6,15)
)
summary(clm(Severity ~ Gender*Treatment, weights=Count, data=d, link="logit"))

The results are about the same as those from SAS. I'm unsure that a Gender:Treatment interaction makes biological sense, so one can simply use a "+" instead of the "*", but the results don't really change. Likewise, you can simply ignore gender and the results are still similarly non-significant (unsurprisingly).

I’ve had some requests regarding another analysis of this data, so I’ll put it here. Data of this type is often handled using logistic regression, and the ordinal aspect using a cumulative logit transformation. Below is such an analysis (in SAS. Sorry, I am not up to speed in R). I have also incorporated gender into the treatment structure as a 2 x 2 factorial. Is this the correct analysis? Maybe, if you accept the assumptions

data pig;
	input severity trt$ gender $ count;
	cards;
	0	NoGMO	M	1
	1	NoGMO	M	16
	2	NoGMO	M	17
	3	NoGMO	M	2
	0	GMO	M	4
	1	GMO	M	12
	2	GMO	M	12
	3	GMO	M	8
	0	NoGMO	F	3
	1	NoGMO	F	15
	2	NoGMO	F	12
	3	NoGMO	F	7
	0	GMO	F	4
	1	GMO	F	11
	2	GMO	F	6
	3	GMO	F	15
;

proc logistic;
	class trt gender;
 	weight count;
	model severity =gender trt gender*trt;
	oddsratio trt ;
run;

– Partial Results –

               Type 3 Analysis of Effects

                                       Wald
             Effect          DF     Chi-Square    Pr > ChiSq

             gender           1        0.9547        0.3285
             trt              1        1.7931        0.1805
             trt*gender       1        0.4476        0.5035

       Odds Ratio Estimates and Wald Confidence Intervals

Label                                Estimate         95% CL
trt GMO vs NoGMO at gender=F         0.543       0.234     1.259
trt GMO vs NoGMO at gender=M         0.815       0.350     1.896

– End Partial Results –