Communicating complex information: the interpretation of statistical interaction in multiple logistic regression analysis.

Abstract

With the availability of statistical software packages, more and more complex statistical models can be easily applied to research data. It is crucial that care be taken when communicating complex information from these statistical models. Just like in a general linear model analysis, where the coefficient for an interaction term does not have a “slope” interpretation, when an interaction effect is included in a multiple logistic regression model, the odds ratios (ORs) based on coefficient estimates are not all meaningful, and the correct ORs to report need to be recalculated. In a recent article, Forsyth et al.1 studied the effect of HIV voluntary counseling and testing on reproduction planning among adults in 2 developing countries. A statistical interaction between pregnancy intention at baseline and HIV serostatus was included in the logistic regression models and was found to be statistically significant among women. The authors reported an OR of 0.1 for the interaction effect and stated that the women more likely to be pregnant were not using contraceptives (OR = 0.1) and were HIV infected (OR = 3.0), whereas partner pregnancy rates were not different by HIV serostatus among men. The article concluded that “HIV diagnosis may influence reproduction planning for women but not for men.” Based on Tables 3 and 5, the logistic regression model is of the following form: 1 where βs are logistic regression coefficients and Iplanned is an indicator variable that equals 1 when the woman is planning a pregnancy; it equals 0 when she is not. Same for Iinfected, an indicator variable for HIV infected nor not. On the basis of the results (Table 3), the estimates of the coefficients for the multiple logistic regression model for women were: 2 3 4 Because of the interaction effect, the meaningful ORs for comparisons need to be derived as follows. For women who were not planning a pregnancy, the odds ratio for those with HIV infection versus without infection is 5 For women who were planning a pregnancy, the odds ratio for those with HIV infection versus without is 6 For women who were not HIV infected, the odds ratio for women who were planning a pregnancy versus those who were not is 7 For women who were infected, the odds ratio for women who were planning a pregnancy versus those who were not is 8 For a comparison of women who were infected and were planning a pregnancy versus those who were not infected and were not planning a pregnancy, the odds ratio is 9 Whether women who were more likely to be pregnant were not using contraceptives seems to depend on their HIV infection status; whether they were more likely to be HIV infected depends on their pregnancy planning status. Similarly, based on Table 5, the corresponding estimates of coefficients for men were 10 11 12 and the corresponding ORs for partner pregnancy can be calculated as Even though the statistical significance of these comparisons will depend on the correlations among the coefficient estimates, which were not available from the article, both men and women seem to show very similar patterns. Among those who were not planning a pregnancy, HIV infection status tended to increase the odds of a pregnancy, whereas among those who had planned a pregnancy, the HIV infection status tended to decrease the odds of a pregnancy. Care needs to be taken when interpreting and reporting results from complex statistical models. To correctly interpret the results from a multiple logistic regression analysis and arrive at meaningful conclusions, it is crucial that appropriate steps be taken to properly incorporate statistical interaction effect.