# Can estimated values with wide confidence intervals be used calculate association or correlation coefficients?

I want to test for an association between socioeconomic deprivation and death rates. My data are raw death counts and deprivation ranks for a set of small geographic areas. Some areas have very low death counts. This will lead to high standard errors (SE) in those areas when I apply indirect age- and sex- standardisation (to generate standardised mortality ratios; SMR).

My question: If I have a sufficiently large number of areas is it valid to calculate a bivariate correlation coefficient despite the high SE in some areas? Essentially, am I able to assume the distribution of errors in the calculated SMRs tends to zero?

I've seen this done for directly standardised proportions at similar geographic scales (e.g. supp table 1 in https://www.sciencedirect.com/science/article/pii/S1353829216300156) but nor for SMRs. And I hope to understand the underlying reasons/for against using this method.

EDIT: Deprivation is represented here as an ordinal variable: ranks from 1 to N, where N ~6000.

• Welcome to the site! Of course, you are "able" to do this, and you'll get a result that isn't total nonsense. But you'll be ignoring the fact that some of those SMRs are better nailed down than others, as you seem to already understand. You would need to model the death counts as coming from some kinda Poisson process to be totally precise. Otherwise, you could use a formula for heteroscedastic correlation, using the Poisson mean-variance relationship to estimate variances for each SMR, or something like that. Jul 25 at 22:15
• Maybe you could edit your question to tell us what deprivation means, in this context? Jul 26 at 12:52
• Edited to add detail. @kjetilbhalvorsen Jul 26 at 16:57
• Welcome to the site! I don't know what are your level of knowledge in this setting but have you considered using a Bayesian statistic model? The small nunbers will ibfluence less the overall result. Also, if this is your primary outcome, why don't you also add a regression analysis (probably a poisson regression, based on the data you provided) to the raw correlation in order to have a prediction model? Jul 26 at 17:05
• I've never looked at Bayesian stats and the purpose of the analysis here isn't strictly to find the precise degree of association between the two variables. I'm actually comparing four ways of ranking deprivation and assessing if there's any substantial difference between them. I'd intended to calculate bivariate association coefficients and compare CI's between the four methods. I had planned on adding a regression and comparing coefficients, so looks like I'll head down the Poisson route. Thanks all! Jul 26 at 17:20