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I have a question regarding odds ratios for a project I'm working on. For my analysis to determine if there was a significant change in access to a service at a certain type of facility from one year to the next, I am using beta regression and odds ratios. This allows me to evaluate that a significant change in odds from year to the next represents a significant change in the rate of access to a particular service from one year to another. This is simple enough. However, this gets complicated when my baseline reference group for odds ratio has a -/+ slope and another group does not have the same slope of the reference group. In the example I’ve provided, the reference group is ’FAC A'. As you can see the baseline odds change from year to year (-.0446, -.0408, -.037) and so does the change in 'FAC B' facilities. However, because these FAC B change relative to FAC A it is possible that the actual proportion of FAC B facilities increase each year while still showing a significantly lower rate of access compared to the reference group, (e.g. the difference remains negative due to the reference group changes in rate not remaining constant). Do any of you have any suggestions as to how to account for this when interpreting my results? Is it possible to simply subtract the difference in odds ratio from the reference group with the other groups and then assess a change in rate from year to year? Would it be possible to create an artificial 'FAC H' group in which I leave all proportions at a constant throughout all years and use this as my baseline/reference group? Would this reflect more accurate changes in ORs across all other facilities? I recognize there is a conversation here regarding clinical versus statistical significance and I am also interested in hearing your feedback on this. Thanks for your time!

Odd/change in odd ratios for service among facilities each year

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