Appendix - the Interpretation of the Partial Proportional Odds Model (PPOM)

Appendix - The interpretation of the partial proportional odds model (PPOM)

A partial proportional odds model can be used to preserve the ordinal nature of an outcome measure where all of the possible dichotomies of the outcome are considered together. In this paper, the outcome has three levels (not limited, limited a little, limited a lot) and hence can be dichotomised in two ways - Figure A1 below.

Figure A1 Illustration of the dichotomies made in a partial proportional odds model:

No A little A lot of limitation limitation limitation

The model is examined to determine whether the proportional odds assumption is true, i.e. is the odds ratio the same at each dichotomy in the outcome variable, using a likelihood ratio test. If this assumption is true, the same odds ratio represents both dichotomies. If this is the case for all independent variables in the regression model, this is termed a proportional odds model (POM). If the assumption is false then a different odds ratio is associated with each dichotomy in the outcome. If this occurs for one or more of the independent variables, the model is a partial POM.

Results presented in Table 3 are used to illustrate the interpretation of the resulting odds ratios (OR).

The proportional odds assumption associated with socio-economic classification was true and hence only one OR is presented. Those in manual occupations were significantly more likely to be limited (either a little or a lot) than those in non-manual occupations (OR 1.42; 95% CI 1.28, 1.56). Equivalently, those in manual occupations were more likely to be limited a lot compared to being not limited at all or limited a little (1.42;

1.28, 1.56). The proportional odds assumption associated with gender was false and hence two odds ratios are presented. Females were significantly more likely to be limited (either a little or a lot) than males (1.13;

1.03, 1.24). However, gender was not significantly associated with being limited a lot compared to being not limited at all or limited a little (0.97; 0.86, 1.10). That is to say, gender can distinguish between any and no limitation, but it cannot distinguish different levels of limitation.