Analyzing CFU data with GLIMMIX

[Kholif]

Dear All:

I have a weak background about statistical analysis and need some help me to do analyzes of my data about bacterial count from cecum of cows. I would like to to run the analyses as "Bacterial count values were log transformed, and then a Poisson regression model was fitted using the PROC GENMOD of SAS, with log of bacterial counts as the response variables, and diet (Control, T00, T05 or T10) as the factor explanatory variable, assuming that the random residual variance follows a Poisson distribution. A logistic regression model for binary data (PROC GENMOD of SAS) was used to analyse mortality data".

My data is:

Additives	REP	G-negative (log10cfu/g)	Coliform (log10cfu/g)	Ecoli (log10cfu/g)
T00	1	7.85	7.80	6.20
T00	2	7.56	6.95	6.56
T00	3	7.95	7.32	6.55
T00	4	8.02	7.56	6.15
T00	5	7.77	7.87	6.68
T00	6	7.65	7.74	6.32
T05	1	8.68	3.80	4.60
T05	2	8.95	4.15	4.84
T05	3	8.64	4.03	4.56
T05	4	8.72	3.78	4.72
T05	5	8.85	3.68	4.35
T05	6	8.60	3.82	4.60
T10	1	8.36	4.90	4.80
T10	2	8.32	5.20	4.95
T10	3	8.06	5.03	4.65
T10	4	7.98	4.86	5.25
T10	5	8.35	4.93	5.03
T10	6	8.41	5.22	4.75

In a published article, I have seen the result of using GENMOD of SAS as the following table:

Table: Caecal bacterial counts (log CFU/g; mean and confidence limits) of animals fed the experimental diets

	Experimental diets
	Control	T1	T2	T3	P-value
E. coli	5.6a (4.12-7.04)	5.4a (3.93-6.81)	3.9ab (2.66-5.10)	3.1b (2.03-4.23)	0.023
Bacteroides spp.	5.0 (3.56-6.34)	4.9 (3.54-6.28)	4.5 (3.22-5.86)	4.2 (2.95-5.49)	0.854
Lactobacillus spp.	3.2a (2.11-4.33)	3.3a (2.18-4.43)	2.2ab (1.29-3.13)	1.6b (0.78-2.32)	0.034

Another friend recommend the use of a Poisson distribution for the GLIMMIX model without telling me how to run it.

My questions are:

(1) Which one (GENMOD or GLIMMIX) is the best for my data?

(2) Please provide me with the code to use in SAS.

Best regards,

Ahmed

[sld]

If your experimental design is not mixed (for example, if all observations are independent, and you do not have blocks or repeated measures), then you can use either GENMOD or GLIMMIX.

If you post your attempt at code, someone in the Community would probably be happy to help.

I recommend learning more about generalized linear models before you go farther with your analysis. There are two misleading statements in your quote, which makes me think that the source of this quote is not your best resource for methodology:

I would like to to run the analyses as "Bacterial count values were log transformed, and then a Poisson regression model was fitted using the PROC GENMOD of SAS, with log of bacterial counts as the response variables, and diet (Control, T00, T05 or T10) as the factor explanatory variable, assuming that the random residual variance follows a Poisson distribution. A logistic regression model for binary data (PROC GENMOD of SAS) was used to analyse mortality data"

1. You do not use log-transformed counts with a Poisson distribution. Instead you use counts on their original scale; the model uses a log link function internally.

2. There is no "residual variance" in a generalized linear model with a Poisson distribution because the variance is a function of the mean and cannot be estimated separately. For the Poisson, the mean and the variance are equal.

Your counts are very large and you may not actually need to use a Poisson distribution; assuming normality might work just fine. The Poisson distribution is useful when mean count is small; as the mean count increases the Poisson distribution approaches the normal distribution (http://wiki.stat.ucla.edu/socr/index.php/AP_Statistics_Curriculum_2007_Limits_Norm2Poisson). 

I hope this helps.