chi-square or Fisher exact test
I have a statistical question about chi-square and/or Fisher exact test.
I have a cohort data studying the cause of infection in BRD with variables such as age, gender, breed etc; where each cattle could have single or co-infection from a total of 11 common bacteria or viruses. Thus, the category may not be fully discrete with a single cattle having positive outcome for more than 1 infection.
I wanted to study the association of each of the 11 infections (yes or no) with age and other above listed factors using a chi-square or fisher exact tests?
What is the best way to analyze this? Should I run 11 tests one by one for each infection against one factor each? I will run post hoc tests with two variables if I have more than two variables (such as age).
Please advise.
Rather than just "association", look at "interaction".
CHAID (chi-square-automatic-interaction-detection) also known as "decision trees", similar to CART (classification and regression trees) analysis is a method that I would recommend.
If you set infection (or not) as the dichotomous dependent target variable being predicted by the multivariate independent predictors (Age, Gender, any other attributes, etc.) CHAID modeling will produce a "c-statistic" , similar to BLR (binary logistic regression) that can be used to calculate and plot the area under the receiver operating characteristic (AUROC) curve, same as BLR, as a way to evaluate how good the model is (at the admitted risk of over fitting).
But when exploring data for significant content, you want a method that will rapidly identify and suggest the best candidates for inclusion in the well defined final trimmed model that consists only of independently predictive variables.
With the CHAID method, the model alpha threshold can be preemptively set at any level. Setting alpha at greater than 0.05 as the threshold for hierarchical branching results in more branches, lower than 0.05 results in fewer branches. The higher up the branch occurs in the resulting tree cascade, the more powerful the factor is. Similar to Odds Ratio (OR) in BLR, the higher the OR, the more variation that the IV factor is explaining in the DV, and the more important the variable is. The BLR method is also recommended if your sample size is large enough to support the assumptions of the BLR model. CHAID (like all the chi-square tests) will work with smaller data sets (30 - 40 observations) whereas BLR usually will not.
Scale or ordinals (Age days, weeks, months, years; weight, height, etc. ; non-linear weighted scales: none 0, low 1, medium 3, high 9) also work in CHAID "as is". Findings can always be reproduced at each tree "branch" by using either the "Likelihood Ratio" or "Pearson" chi-square method, and of course, Fisher Exact.
CHAID is way underutilized (my opinion). The "branching" in the tree shows the hierarchical interactions that are embedded in the data, at the given level of statistical significance (alpha) that has been specified for the model.
- https://www.statisticssolutions.com/non-parametric-analysis-chaid/
Article CHAID Decision Tree: Methodological Frame and Application
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