Wednesday, June 28, 2006

Logistic Regression & Odds Ratios

We seldom or ever get to use inferential statistics when we do M&E. I think that there might actually be room for including some of these statistics in our evaluations. Here is an example of how logistic regression was used to inform a VCT centre's marketing campaign:

We used logistic regression to determine which sets of factors associate significantly with a person's propensity to go for an HIV test. The survey covered various knowledge questions (e.g. can HIV be transfered via a toothbrush?), biographical information (how old are you, are you married?) and a variety of risk factors (did you use a condom last time you had intercourse, have you had more than one sexual partner over the past year). The intention was to find out who to market VCT services to. For example, if we found that men who had multiple partners and are younger than 25 and have at least matric are more likely to test than those who are older than 25 or do not have matric, then there is a whole marketing campaign right there!

The logistic regression yields an odds ratio and an adjusted mean.

An odds ratio indicates the likelihood that a specific indicator or scale is associated with a behaviour occurring or not occurring. If the odds ratio is larger than 1, then it indicates that it is likely that the indicator is associated with the occurrence of the outcome variable. If the odds ratio is smaller than 1, then it indicates that is likely that the indicator will be associated with the non-occurrence of the outcome variable.

For example, if we are checking whether having tested previously would co-occur with the intention to test in future, we may get the following results.
Unadjusted Means for
Intention to test
No Yes Odds Ratio
Person tested previously 0.28 0.58 3.51
Because the odds ratio is positive, we can conclude that people that tested previously are about 3 times more likely to intend to test in future. The unadjusted means confirm this: If a person is likely to test (he / she falls in the Yes category) he or she “scores” 0.58 out of 1 (Where 1 indicates that the person did test previously) while a person that is not likely to test (he / she falls in the No category) only “scores” 0.28 out of 1.

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