1

I am looking for some insight in offering some context to my odds ratios. I did a simple model estimating the relationship between the planting space afforded trees and the presence/absence of sidewalk damage. Working with the model we get the following:

Odds of preventing damage:
50cm spacing between tree and sidewalk; OR = 2 (damage avoided)
100cm spacing between tree and sidewalk; OR = 4.6 (damage avoided)
150cm spacing between tree and sidewalk; OR = 9.7 (damage avoided)
etc....

In talking with some local engineers from my metro area, the following would be an example of expenses a hypothetical city of 500,000 could expect.

1,000,000 USD spent annually on sidewalk repairs related to trees. 500 USD to replace a typical slab. Therefore, 2000 slabs replaced annually

Is it possible to estimate potential savings if people just gave trees more space? My audience is non-scientific and showing them odds ratios really doesn't do much for them.

psboonstra
  • 1,745
  • 7
  • 12
Andrew Koeser
  • 13
  • 2

1 Answers1

0

ORs are not going to give you a complete answer. Rather, I think you are interested in estimating the probability of damage avoided given the spacing between a tree and the sidewalk. You can do this with a logistic regression model, for example. Denote this probability by $p(x)$, where $x$ is the spacing in cm. The expected cost to replace a single slab is $500[1-p(x)]$. The expected savings by moving a tree an additional $y$ cm away from the sidewalk would be the difference in expected costs, or $500[1-p(x)] - 500[1-p(x+y)] = 500[p(x+y)-p(x)]$.

Suppose $x=100$, $y=10$, $p(x)=0.90$, and $p(x+y)=0.95$, then you would expect to save $500[0.95-0.90]=25$ dollars in slab replacement costs for each tree that you plant 110cm away from the sidewalk instead of 100cm away.

psboonstra
  • 1,745
  • 7
  • 12