Standardizing Rates

1. Standardizing Rates Nam Bains October 15th, 2007 Statistics and Analysis in Public Health APHEO

2. Acknowledgements Sue Bondy Brenda Coleman Mary-Anne Pietrusiak

3. Overview • What and why • Choice of standard population • Age vs. age/sex vs. sex-specific • Small numbers • How many age groups? • Variance formulae

4. What is standardization? A procedure that adjusts for differences in population structure and provides a single summary measure for the comparison of populations. Typically used to adjust for age and sex Direct: Rates in study population (PHU) are applied to a standard population distribution (Canada). Indirect: Uses rates from a standard population (Ontario) to derive expected number of events in a study population (PHU).

5. Why standardize? • Examining crude rates alone can be misleading if underlying populations are different (age-specific rates are better) But • Cumbersome to compare age-specific rates especially when doing large number of comparisons

6. Crude vs. age-standardized morality rate (Brant PHU, all causes)

7. Crude vs. age-standardized morality rate (Toronto PHU, respiratory disease)

8. Age-standardization: Sample calculation Sum

9. 4,000,000 / 28,300,000 = 0.1413 Age-standardization: Sample calculation II

10. 0-4 5-9 10-14 USA 2000 15-19 20-24 USA 1940 25-29 30-34 Canada 1991 35-39 40-44 European 45-49 50-54 WHO World 55-59 60-64 65-69 World ('Segi') 70-74 75-79 80-84 85+ Choice of standard population 12,000 10,000 8,000 6,000 4,000 2,000 -

11. Different standard populations USA 1940 Canada 1991 World “Segi” USA 2000 European WHO World

12. Ontario cancer mortality rates calculated using different standard populations

13. Choice of standard population: considerations • When several different populations are being compared, a ‘pooled’ standard minimizes the variance of the adjusted rates • In examining trends, an appropriate standard is one that reflects the average structure of the population over the time period • The standard should be similar to the population of interest • It should not change frequently (all historic data would need to be recomputed) • It should be used consistently to ensure comparability of rates Choi, 1999. Am J Epi

14. Suggested standard population

15. Age versus Age/Sex • Adjusts for underlying differences in age and sex distribution simultaneously • Disadvantage • with so many stratum, numbers are spread thin • Rates are NOT COMPARABLE to those that are age-standardized

16. Age/sex standardization: Sample calculation

17. Age-standardized rates ≠ Age/sex standardized rates ≠ Sex-specific age standardized rates (Rates for females standardized to the Female Standard population or Rate for males standardized to the Male Standard population)

18. How many age categories? Lots (detailed age groups) • better control of the effect of any differences in age distributions but, • lots of strata means there might not be enough events (larger variance) Fewer (broad groups) • will produce less precise adjustment • broad groups (i.e., 65+) will not be sensitive to changes in age-specific rates within that group Other considerations • availability of data (i.e., CCHS)

19. Age categories

20. All cause age-standardized mortality rate, per 100,000 population, Elgin St. Thomas PHU, 2001

21. All cause age-specific mortality rates, Ontario 2001

22. Small numbers • age-standardized rates based on a small number of events will be unstable and exhibit large amount of random variation • NCHS cutoff: 25 events • 10-24: Calculate SMR (indirect) or crude rate • <10: conduct case reviews

23. Variance estimates “There are a few in public health who believe that confidence intervals should not be used around estimates derived from 'population' statistics such as the death rate in a given population, because they believe there is no statistical uncertainty in such estimates. This belief is contrary to the statistical theory underlying confidence intervals, and the biological and random processes governing the occurrence of events such as deaths and illnesses.” Washington State Dept. of Health Guidelines for using confidence intervals for public health assessment Vital or administrative data are not subject to sampling error, but can be affected by errors in the registration process or incomplete registration. Also, for the purposes of analytic work, the events that occur can be thought of as one of a series of possible results that could have arisen under the same circumstances (i.e., subject to random variation). Curtin LR, Klein RJ. 1995. NCHS.

24. Variance estimates • Based on binomial distribution • Spiegelman, Lilienfeld • NCHS, Statistics Canada (for vital events) • Not great when <100 events • Based on Poisson distribution • Based on Gamma distribution • Better for small numbers • Based on Chi-square • SeerStat • With adjustment for non-independent events • Carriere & Roos, Stukel

25. 2 Pi ∑Pi ri (1-ri) pi ∑ * Pi = Standard Population in age strata i ri = age-specific rate for study population pi = Study population in age strata i Based on Binomial distribution

26. 2 Pi ∑Pi ri di 2 ∑ * Pi = Standard Population in age strata i ri = age-specific rate for study population di = number of deaths in Study population in age strata i Based on Poisson approximation

27. 2 Pi ∑Pi di pi ∑ * 2 Pi = Standard Population in age strata i pi = Study population in age strata i di = number of deaths in Study population in age strata i Based on Poisson approximation

28. Other issues • How to treat cells with 0 values • When NOT to standardize • When age-specific rates are not constant over time (i.e., not moving in parallel), the comparison of age-standardized rates over that time period is not valid • The choice of standard population could affect the results in these cases

29. Next steps… • Finish report and sample calculations • Add recommendations / best practices • Incorporate recommendations into Core Indicators for Public Health

30. Standardizing Rates Nam Bains Project Lead, Health System Intelligence Project (HSIP) nbains@hsip.on.ca