Which expression would be better in formal academic writing?
I believe both ways would be fine, but would like to know any subtle difference in nuance.
Both of these are awkward and redundant.
Say: "The incidence is approximately 80%."
or: "The incidence approaches 80%".
“The proportion/percentage of incidence” doesnt make sense. Everything is an incident. What might make sense: “The percentage of incidents involving bicycles”.
“Percentage” would be something like 33.3%. “Proportion” would be “one in three”.
If the discipline is epidemiology, medicine, or anything related, then both are wrong. This was potentially a specialist question and I'm not sure how well it fits this SE, but here are my reflections. In peer reviewed work, a native English speaking peer reviewer would probably be willing to suggest some corrections, but it's definitely not their job to proofread the entire paper. We would often suggest that the writer hire a proofreader separately, which I recognize can be a financial barrier.
Generally, people trained in statistics would interpret proportion on a scale of 0 to 1. That is, 0.5 is 50%. Proportion and percentage reflect the same concept, but are calculated differently. You would be understood if you reported a proportion of 50%, but it is wrong. We'd say something like:
79.8% of the astronauts in our sample had spaceflight accidents.
We would normally report the exact figure rounded to an appropriate number of decimal places. If you have the exact percentage or the exact numerator and denominator reported in your table, you may be able to say approximately 80% in the text, but it might be regarded as unusual.
Incidence is a measure of the number of new cases. It doesn't make sense at all to report a percent, and readers might not know what you mean. While the topic of incidence is more complex, we'd normally say something like
The incidence rate of spacecraft accidents was 1.2 cases per 100,000 spaceflights.
Or
The incidence rate of spacecraft accidents was 1.2 cases per 100,000 person-years.
One person-year is one person at risk for one year. Briefly, you might have one different astronaut flying for each month of a year. That's a total of one person-year at risk.
There is a small difference, in that when describing percentage, you must give a value out of one hundred. As for proportion, you can say 8 out of 10 times.... or 4 out of 5.
