I am reviewing an article. They ran the statistics with multivariate logistic regression. One parameter (say parameter a) came out with an odds ratio of 0.98 (95% confidence interval of 0.97-0.99) and a p value of "0.003". Another logistic regression the authors ran regarding another parameter (parameter c, a result of parameter b divided by parameter a) came out with an OR of 69 (95%CI of 8.39- 567.5) and a p value of "
Without seeing the data or knowing the type of software used in the analysis, I would provide some general information and start with important questions regarding the author’s reporting of analysis. Typical logistic regression requires a few initial tests. Have the researchers provided any overall parameters, such as the Omnibus Tests of Model Coefficients, providing goodness of fit indicators like Chi Square? Was Homer and Lemeshow Test conducted and reported for reliability? The usefulness of the model can also be determined by the Cox & Snell R Square and the Nagelkerke R Square Value that shows the amount of variation in the dependent variable explained by the model (sometimes these are referred to a pseudo R square statistics). Positive, negative predictive values as well as the sensitivity of the model also help to interpret the final calculations. And there is more! The Wald test provides the individual value for each statistic in which P
I would also ask the number cases that did not fit the model. Appears in Casewise List. Acceptable range of the ZResid is between -2.5 and +2.5. Any ZResid over 2.5 should be reviewed for data entry or other error. If accurately entered, then this data should be removed from the final analysis and testing rerun on the final sample size.
It does not make sense to me either.
The CI of parameter a indicates that it is practically irrelevant. The obtained significance is a rather academic thing. With an OR so close to 1, the value or status of a is irrelevant for all practical purposes.
The CI of parameter c may be wide, but it indicates that ORs of less than 8 are already quite incompatible with the data. Thus, - whatever the OR may be - it is large enough to be practically relevant.
My conclusion is therefore: forget a, use c!
Jochen Wilhelm You said it more clearly but do you agree that I have presented information that most must be clarified in the overall presentation of information and how the value of 1 presents a special interpretation of the ODDS RATIO and impact on the CI range?
Dear Beth, I am sorry but I stuggle understanding your post and your question. I agree (if that is what you meant) that all hypotheses an analysis relies on must make sense. However, I don't agree that formal tests of the hypotheses are sensible, as "significance" does not imply "relevance" (and non-significance does not imply non-relevance as well). It's a matter of subject knowledge and understanding of the data and the analysis used.
An odds ratio of 1 means that the odds in both groups/conditions are just identical, and values close to 1 means that they are very similar. Apart from that, I don't see what should be "special" on any particular value of the odds ratio. If we use data to "estimate" an odds ratio, we would actually have to use a Bayesian approach, because this neccesarily requires that we state a probability distribution over the possible values of the odds ratio. This is usually not done, because it is nessecarily subjective (as it integrated what *we know* about the subject) and it goes beyond using only the data at hand. The "estimate" that is provided by the software (from the standard analyses) is just that hypothetical value for the OR, for which the likelihood of the observed data under the specified model is maximal. This may not neccesarily be any good estimate for a "real" value that we should "believe" in. The p-value is the probability that the likelihood ratio from this maximum likelihood to the maximum likelihood obtained when the model is restricted at a hypothesized value (usually that OR=1) is larger than the one observed from the current data. The (1-a)-CI is the interval of possible OR values at which the p-values is 1 or OR
Jochen Wilhelm Thanks. I should have started with the last sentence of my original. Have a happy new year.
The odds ratio is the change associated with a one-unit increase in the predictor variable. If this predictor is measured in small units, the OR will be close to one and can still be significant.
Here is a logistic regression which shows that a one-gramme increase in the weight of a baby increases the odds of delivery by emergency section by a factor of 1.000867!. The trouble is that the weight is in grammes! It would be more logical to take baby weight in units of 100 grammes, or even kilos.
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