Exact Logistic Regression output help

[bripetersen]

Hi all! I am a first-time exact logistic regression user in graduate school now and it seems that there is limited information online about how to interpret results. I was hoping that someone may be able to tell me if I am on the right track here? Thank you in advance, I really appreciate it! If there's any other information that I need to include, please let me know and I am happy to. 

"The goal of the exact conditional test in Table 10 is to determine what the likelihood of the observed response is with respect to all possible responses. In this case, the p-value (0.1807) leads to a failure to reject the null hypothesis that there is no relationship between length (years) of military service and incidence of enamel defects. Additionally, the exact parameter estimates show that the slope is estimated to be -0.0701. Because the 95% confidence interval for the odds ratio of the slope contains 1, the odds of the presence of enamel defects do not increase significantly with an increase in military service length. As such, the association between years of military service and presence of enamel defects was not significant in this sample."

Table 10

[bripetersen]

Oh gosh, I had a brain fart moment, please ignore what I said about the confidence intervals. That interval does NOT contain 1. facepalm!

[Reeza]

Yes it does, the odds ratio contains the value 1 in the CI, (0.825, 1.029)

Your odds ratio is 0.933. Assuming enamel decays is your event (Depends on how you wrote your code, check your log) then it means for each year of service, your 0.933 less likely to develop enamel decay compared to whatever you other group is, but the confidence interval includes 1 so it means that effect is not statistically significant. I'm guessing you have a low number of observations here?

Your slope is not -0.701 that is the parameter estimate for years and you take the exponent to get the odds ratio. 

However, if you're looking for the effects over time, I'm not sure that logistic regression is the right statistical method. 

[bripetersen]

Thank you so much! I was looking at the wrong CI, you are correct. Getting back into the swing of classes alongside writing my thesis has been a bit fuzzy! I do have a low number of observations, which is why I opted for an exact log reg rather than a standard logistic regression. Below is the relevant blurb from my materials/methods section that will hopefully provide more context as to why I used this test. Please do feel free to chime in if I am not on the right track! I am very grateful, thank you. To summarize, I am looking at deceased individuals from the USS Oklahoma (Pearl Harbor casualties) and comparing the yes/no presence of incidence of enamel defects vs. the years of active military service they had completed upon death. I study forensic anthropology. 

"To compare the presence of each type of non-specific indicators of stress against military service length, the use of logistic regression tests was initially desired. The exact logistic regression test was used due to a small sample size (Bujang et al., 2018). Exact logistic regression is a statistical method that is used to model binary outcome variables where the log-odds are then modeled as a linear combination of independent variables; it is used when the sample size is not large or complete enough for a regular logistic regression (“Exact Logistic Regression”, n.d.). This testing is used to examine the association between a categorical or continuous independent variable with a dichotomous dependent variable, which is a two-level categorical variable. The variables in these tests were military service length as a quantitative (continuous) variable and then the presence of skeletal pathology is a categorical (binary) variable."

[StatDave]

sounds fine to me.

[Ksharp]

Calling @StatDave 

[StatDave · Accepted solution]

The first sentence in your conclusions is a bit odd - I wouldn't say that it tests against "all possible responses" - but the rest of it sounds fine.