Interpreting Ratio of Two Probs: Can Higher Prop Survive?

[ericst]

If two 5-year survival probabilities are p1=.55 and p2=.41

the ratio is .55/.41 = 1.34 but since probabilities are in [0, 1] should I take the log first?
Which is the more appropriate way to interpret the ratio?

the ratio of logs is Log(.55)/log(.41) = .671
Which is less than one although the probability .55 > .41 so taking the reciprocal I get approximately 1.49

How to interpret this...

Can I say "people in the group with higher probability have about 1.5 times the chance to survive 5 years as a person in the other group." Or do I have to qualify it and add, "on the log scale"?

Or is the former way better (without logs)?

 

[jvicens]

it is important to consider the appropriate way to interpret the data and communicate it accurately. In this case, using the log scale may provide a more accurate representation of the data. This is because the log transformation helps to normalize the data and make it more easily comparable.

Therefore, in this scenario, it would be more appropriate to use the ratio of logs, which is approximately 0.671. This means that the group with a higher probability (p1=.55) has about 1.5 times the chance of survival as the group with a lower probability (p2=.41) on a log scale. It is important to mention the log scale when interpreting the results to avoid any confusion.

Using the log scale also allows for a clearer understanding of the differences in probabilities between the two groups. For example, if the probabilities were very close together (e.g. p1=.55 and p2=.54), the ratio of logs would be closer to 1, indicating that the difference in survival probabilities is not as significant.

In summary, using the log scale to interpret the ratio of survival probabilities is more appropriate as it provides a more accurate representation of the data and allows for a clearer understanding of the differences between the two groups.