I have taken the data from a field trial established to screen the sugarcane varieties for sugarcane grassy shoot diseases(GSD). RCBD with three replicates was used to establish the trial. Standard varieties are not available for GSD. Therefore, comparison and rating will not be possible.
The number of GSD infected clumps (phenotypically) and # of total clumps had been taken as the main data of the trial in the one-month intervals from 1 to 12 months (12 disease counts). Disease incidence was calculated. In addition, yield data were taken.
1. Could you please explain what kind of statistical analysis is suitable for analyzing the data taken here in order to find the varietal response for the GSD by the SAS program based on disease data?
2. What data (# disease clumps or disease incidence) is appropriate to use for analysis? Further, it would be a great support if anyone can give an idea of how to write CLASS and MODEL statements of SAS for analyzing this data.
Thank you
You can analyze either number of infected clumps or disease incidence (that I understand as number of infected clumps / number of total clumps). The first is count data that follow Poisson or Negative Binomial distribution whereas the second is a proportion that follow a binomial distribution. Therefore, classical methods like Analysis of Variance (ANOVA), a specific case of general linear model, are not appropriate even with prior data transformation like root square or arcsinus (O'Hara and Kotz, 2010; Wharton and Hui, 2011).
Ignoring the repeated measurement, considering data for each month separately, it is highly advisable to use Generalized Linear Model (GLM) with appropriate distributions and link functions that lead to Poisson regression for number of infected clumps and logistic regression for disease incidence. For Poisson regression, overdispersion should be checked and if it is present, use Negative Binomial regression instead of Poisson regression.
To take into consideration repetition in time, the likely correlation between time points (months) should be considered by using Generalized Estimating Equations (GEE) or Generalized Linear Mixed Models (GLMM) (Gbur et al, 2012; Stroup, 2013; Yirga et al, 2020).
In SAS, GLM is done using PROC GENMOD while GLMM is done using PROC GLIMMIX.
- Gbur EE, Stroup WW et al. (2012). Analysis of Generalized Linear Mixed Models
in the Agricultural and Natural Resources Sciences. ASA, SSSA, CSSA. See chapter 5.
- O’Hara RB and Kotze DJ. (2010). Do not log-transform count data. Methods in Ecology and Evolution, 1: 118-122.
- Stroup WW. (2013). Generalized Linear Mixed Models: Concepts, Methods, and Applications. CRC Press. See Chapter 14.
Warton DI and Hui FKC. (2011). The arcsine is asinine: the analysis of proportions in ecology. Ecology, 92: 3-10.
- Yirga AA, Melesse SF, Henry G. Mwambi HG, and Ayele DG. (2020). Negative binomial mixed models for analyzing longitudinal CD4 count data. Scientific Reports, 10: 16742.
The analysis will be easier if you can represent the measured quantities as one value for each experimental unit (plot). That is, I imagine that yield will be measured only once per plot, at the end of the experiment. If it is possible (and reasonable and desirable) to handle disease incidence this way, that will eliminate the need for a repeated measures analysis.
Beyond that, if you are not very familiar with analysis by general linear model (PROC GLM) or generalized linear model (PROC GENMOD), you will probably want to consult with someone in your department or a statistics department that can help you determine what the best model would be for the disease data.
Dear Salvatore,
There are basically 4 different ways of analyzing repeated measures data (Schober and Vetter, 2018):
- Using a summary statitics like a mean value over the 12 or, as you suggested, using only the last measure (12th month)
- Do separate analysis (ANOVA) for each month
- Do a global analysis considering all times using a repeated measurement ANOVA or a Multivariate ANOVA
- Use GEE or GLMM
The first 2 approaches ignore, unfotunately, the time factor while the last 2 ones take it into consideration. However, the last approach is the most appropriate one to consider for correlated data, with eventually missing data, unbalanced design, etc.
There are harmful consequences if correlation between data, from repeated measures, is ignored (Sainani, 2010).
- Sainani K. (2010). The importance of accounting for correlated observations. Physical Medicine and Rehabilitation, 2: 858-861.
- Schober P and Vetter TR. (2018). Repeated Measures Designs and Analysis of Longitudinal Data: If at First You Do Not Succeed—Try, Try Again. Anesthesia and Analgesia, 127: 569–575.
Stroup (2015) is an excellent paper for agricultural applications for non normal data like proportions and counts using GEE and GLMM.
Stroup WW. (2015). Rethinking the Analysis of Non-Normal Data in Plant and Soil Science. Agronomy Journal, 107: 811-827.
Dear Ahmed Douaik and Sal Mangiafico
Thank you for your comprehensive reply to the question. I just want further clarification about your reply
As you suggested to ignore the repeated data taken from the monthly interval, what would happen if I used the highest disease incidence or highest disease clumps number among the 12 counts to do ANOVA with GLM?
Usually, the highest disease incidence has shown in 6th or 7th, or 8th counts. So, finalize the results with the highest disease data of each variety would give one data for all varieties
Another thing is, if I used DI it would be misleading the results as follow.
Suppose a particular variety has 5 infected clumps among 10 total clumps in a plot.
DI= 5/10*100%
=50%
Another variety has 5 infected clumps among 25 total clumps in a plot
DI=5/25*100%
=20%
In point of my view, # infected clumps will give fair weight on each variety other than DI. What would you think about the point?
Y.A.P.K. Dayasena ,
A) Just to be clear, I'm not saying that condensing observations to one summary value per plot would be better. It's just that if you are not very familiar with analysis of experiments, viewing things this way may be easier. (And often just as useful.)
1) It may make sense to use the highest disease indicator, or it may make sense to use an average indicator over time. I don't know. Let's just say you have a rating scale of 1 to 9. If you had three weeks, and plot A had ratings of 6, 6, 6, and plot B had ratings of 9, 0, 0, is it better to summarize these as maximums (6, 9), or averages (6, 3) ? I don't know which makes more sense.
2) Likewise, I don't know if # or DI would be a better disease measure. It depends which makes more sense.
3) Often when I'm dealing with these kinds of experiments, I might use multiple DV's. That is, yield is one DV, but include average and maximum disease, and # and DI. Each of them may be meaningful. Of course, as you have more dependent variables you are analyzing, you increase the risk of finding spurious significant results, simply by chance.
B) As to the model to use for DI or # : Running a traditional Ordinary Least Squares (OLS) Anova (with PROC GLM), may or may not be appropriate. It's important to understand the assumptions of this kind of model, or to consult with someone who can help you. It is probably more appropriate to use a generalized linear model (with PROC GENMOD or PROC GLIMMIX) with these kinds of measurements. Once you decide what measurements you are going to use, you may be able to get some more specific advice, but it sometimes depends on the nature of the observed data.
Dayasena,
I absolutely not suggested to ignore repetition in time as was clarified also by Salvatore; on the contrary, I highly recommended to consider repeated measures using GLMM! Why you measured 12 times if you want to ignore the temporal variation? Repeated measures allow you to study the trend or the dynamic of the disease therefore permitting you to estimate when the disease is at its maximum in order for example to apply a pesticide.
Even if you want to ignore time and you want to look at the highest incidence, there is a problem: the highest value for the different varieties and blocks may be for different times!
Also, DI is not misleading since you are using proportions whereas using only number of infected may be lmisleading, especially if total number of clumps is different for varities and blocks.
