How do you present results of a proprtional hazards model when the outcome is a good thing? We have run several Cox proportional hazards models. One of the outcomes is a beneficial thing (discharge from hospital), while the others are all negative outcomes (these are not competing outcomes but separate datasets and tests). My colleagues and I worry that readers will misinterpret our results since the outcome of being discharged is a good result and we want it to happen as early as possible, so a hazard ratio > 1 is good. But for all the others, HR < 1 is good. In all cases we do actually get the consistent results that our exposure variable correlates with the "good" outcome.
My colleagues want me to just "invert" the model and get the opposite sign, as one often can do, by just changing our definitions around. However, I don't see how this is possible for proportional hazards: the outcome must be an event, not the lack of an event. I can't make an outcome of non-discharge, for example, to see that lack of the exposure is correlated with non-discharge. How can I present this data in a way that makes it clear?
My best thoughts are to either spell this out very clearly in the caption and main body and/or to swap the plot of effect sizes about HR=1 (so that visually 'up' is always good, but 'up' is decreasing HR for some and increasing HR for others).
Already colleagues have been confused by the plots, so this is a well-founded fear!

I think it would be simplest just to spell things out clearly in the axis labels, figure captions and text. Don't underestimate the intelligence of your audience. Just be very clear. I certainly agree with your comment that exposure-variable coding is best kept consistent within a report.
One thing that might help would be to invert the display of your "good" outcome so that it's visually distinct from that of the "bad" outcomes. With discharge as the event, a standard plot of decreasing "survival" over time, $S(t)$, is the probability that a patient is still in the hospital beyond a certain time. If you display instead the cumulative probability that a patient has been discharged, $1-S(t)$, you get an upward rising plot that should make the distinction between "good" and "bad" outcomes a bit clearer.
