Is my Standard Error formula for Age-Standardized Rates (ASR) correct?

General
1

I’m working on calculating Age-Standardized Mortality Rates (ASR) for cervical cancer (C53) in R using direct standardization. I’ve managed to get the rates, but I’m struggling to be 100% sure about my Standard Error (SE) calculation.

I am assuming a Poisson distribution for the counts. Here is my current summarise block:

summarise(
# Age-Standardized Rate
ASR= sum((deaths/ pop_at_risk) * std_pop, na.rm = TRUE),

# Standard Error of the ASR - This is where I have doubts
se_asr= sqrt(sum((std_pop^2) * (deaths/ (pop_at_risk^2)), na.rm = TRUE))
)

Variables:

  • deaths: Observed counts per age group .
  • pop_at_risk: Local population for each group .
  • std_pop: Standard reference population weights .

My specific questions:

  1. Is this the correct way to propagate the error for a weighted sum of Poisson variables?
  2. I’ve been told I might need to divide the final se_asr and ASR by sum( std_pop) . Is that correct?
  3. Should I be worried about groups with zero counts (deaths= 0) that might be missing from my data frame before the sum ?
2

Hi @juandmaz
I expect you will get quicker replies if you post this question on Stack Overflow with “rstats” and “statistics” tags.

3

Can you please describe the reasoning that led you to the formula you used?