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Set up: I have a epidemiological study with a dose-response curve with a series of relative risk estimates (risk ratio of mortality risk exposed compared to mortality risk unexposed) along a curve. The curve only has a few points, but I am using it to model a continuum of points in a health impact assessment using a piecewise linear regression between each pair of points. For each slope, I have two sets of confidence intervals (point a and point b) and I need to combine them to make a unified 95% CI lower and upper bound slope. To do this, I am trying to run a monte carlo analysis with 1000+ iterations to model the distribution of slopes and then select the mean, lower, and upper bound slopes to apply to my analysis.

Issue: in the epi study, I only have the central, upper and lower bound RR estimate for a given exposure level but I need to calculate the SD to run the monte carlo analysis. I do not know how many observations were included in the study for a given point on the RR curve.

Question: is it possible to calculate the SD of RR for a point on the curve using only the mean and 95% CI? All the answers to this question have recommended using the approach found here, with requires an input for N. https://handbook-5-1.cochrane.org/chapter_7/7_7_3_2_obtaining_standard_deviations_from_standard_errors_and.htm#:~:text=The%20standard%20deviation%20for%20each,should%20be%20replaced%20by%205.15.

Just to make a concrete example, let's just say there are two points on the relative risk curve and I want to monte carlo model a distribution of slopes between these two points based on the mean and CIs. If that's the data I have, how can I estimate the SD?

At exposure = 10, 0.90 with a symmetrical 95% CI of (0.87, 0.94).

At exposure = 20; 0.95 with a symmetrical 95% CI of (0.90, 1.00).

Thank you in advance!

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  • $\begingroup$ When you say "SD", I assume you mean standard deviation, but standard deviation of what? Do you mean the standard error of the estimate of the RR? Also, symmetric confidence intervals are quite unusual for RRs; do you know how these were obtained? $\endgroup$
    – Noah
    Commented Nov 29, 2022 at 17:55
  • $\begingroup$ @Noah Thanks, yes standard deviation. Sorry, I should have specified. The epidemiological study is a meta-analysis of pooled relative risks so I think the SD is the distribution of RR from studies that reported RR at each exposure point. I suppose therefore the n may equal the number of studies rather than population? Then again, in a meta-analysis each study is weighted by random effects so perhaps the overall mean/CI reflects the full population? Have you ever seen anything like this? Here's a link to the study FWIW. ijbnpa.biomedcentral.com/articles/10.1186/… $\endgroup$
    – Matthew Raifman
    Commented Nov 29, 2022 at 18:14
  • $\begingroup$ That makes a lot more sense. Given the context, this is out of my area of expertise, sorry. $\endgroup$
    – Noah
    Commented Nov 29, 2022 at 18:19
  • $\begingroup$ @Noah thanks for the questions all the same! $\endgroup$
    – Matthew Raifman
    Commented Nov 29, 2022 at 18:20

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