I have some responses behaving as yes/no (e.g. whether a treatment was succesful or not) and a number of preoperative and surgical parameters that may be predictors of it. Now I can make logistic regressions, but how to jump from statistical significance of the predictors to interpretation? Further, which is the best algorithmic way to comput logistic regressions?
The estimated value of the predictor is the log of the odds ratio (OR). Assuming your method returns a standard error, the 95% confidence interval is exp(p-1.96*se) to exp(p+1.96*se). OR < 1 means the predcitor decreases the probability of successful treatment, while OR > 1 increases it. For a continuous value, the OR will be per unit (year of age, point of BMI). For a category variable, the OR will compare each category versus a reference -- if you don't specifiy one, programs will usually pick the first one alphabetically.
If you have interactions in there, then the parameters can be harder to interpret. In that case, it helps to center continuous variables (age, BMI, etc) so you're looking at increases or decreases relative to the mean.
I like the 'lrm' function in the rms package from R.
Thanks, does it make sense to determine the value of the predictors leading to a logistic probability of 50% as a separation metric?
If yes, how should I proceed when multiple predictors are considered together?
For classical regression analyses stepwise backwards multilinear regression is regarded as suboptimum and principal components analyses is considered more rigorous. How should I proceed with logistic regression is multiple variables are potential predictors, but I want to discriminate which ones are most likely the adequate set of predictors (stepwise backwards multilinear logistic regression)?
Is there any advantage of logistic regression compared to e.g. separation of the two normal distributions of populations scoring 0 and populations scoring 1; or cumulative linear regression?
Thank you in advance, and sorry for including so many questions at once. I hope you (or someone else out here in ResearchGate) can help me.
Answering your questions in succession:
What value to use as a threshold depends on what you consider to be a high probability. More than half? I know for complications 10% can be considered a high probability.
The rms package I mentioned includes a nomogram function which can generate a scoring table. You find out how many points are generated by the parameter values at hand and then you compare the total points vs a table of points and probabilities.
Re stepwise backward vs principal components, remember that while all statistical models are wrong, some are useful [George Box]. I find an advantage of a backward stepwise approach is that I can show someone both a full and a trimmed model. Principal components are harder to explain to non-statisticians.
Logistic regression allows you to show the association between a predictor and the rate of an outcome. A t-test or ANOVA just lets you say whether predictors are different between yes and no, and by how much on average.
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