Test of agreement for presence/absence by month

[#1]

Hi,

I collected data on the monthly occurrence of a parasite and the monthly occurrence of a histological lesion in the tissues where the parasite infects.  The parasite is strongly seasonal - peak prevalence and intensities occur in March and April.  The lesions are more spread out throughout the year but appear to be more common in those months.  So for each (lesion or parasite), I can construct a contingency table (2x12) to demonstrate the months where the prevalence of lesions and parasites are highest.  What I would like to do is test how closely the parasites and lesions agree.  Is there a test of agreement to compare monthly lesion and parasite prevalence?  

I can disregard month and construct a contingency table of parasite and lesion.  The results show a Kappa of 0.0248 with a P = 0.5804.  Also, Bowker's test for symmetry (greater than 2x2 contingency table) indicates symmetry of disagreement chisq =22.6, P <0.001.  I would take these results that there is no strong measure of agreement between the lesion and parasite overall.  However, this doesn't account for month.

[#2]

I don't believe that using the nominal modeling type would cause a singularity in the CMH tests, especially since you have only two levels for X and for Y.

Yes, the null hypothesis is no association between X and Y.

Yes, the unstratified contingency analysis is highly significant (LRT chi square > 65, p-value < 0.0001). (Note that chi square cannot be used to assess the strength of the association, only its significance.)

Yes, the relevant CMH test (General Association of Categories) is highly significant (chi square > 40, p-value < 0.0001). The stratification helps assure that the association is consistently present across the strata, if that question must be answered. The CMH test also somewhat relaxes the sample size requirement for the chi square statistic, which is not an issue in this case. (No more than 20% of cells with expected count less than 5.)

[#3]

Thanks for your help!