Standardizing Rates Nam Bains October 15 th 2007

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

Acknowledgements Sue Bondy Brenda Coleman Mary-Anne Pietrusiak

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

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).

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

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

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

Age-standardization: Sample calculation Sum

Age-standardization: Sample calculation II Study Population (PHU) # deaths population Standard Population (Canada 1991) Weight = Wi= Pi (Pi) /∑ (Pi) Age Groups di pi 0 -10 5 20, 000 4, 000 10 -19 10 15, 000 20 -29 10 30 -39 Expected Crude Rate deaths r = di/ pi Di = ri * W 0. 1413 0. 000250 0. 000035 4, 000 0. 1413 0. 000667 0. 000094 15, 000 4, 600, 000 0. 1625 0. 000667 0. 000108 10 20, 000 4, 900, 000 0. 1731 0. 000500 0. 000087 40 -49 20 16, 000 3, 800, 000 0. 1343 0. 001250 0. 000168 50 -59 20 11, 000 2, 600, 000 0. 0919 0. 001818 0. 000167 60 -69 20 9, 000 2, 300, 000 0. 0813 0. 002222 0. 000181 70+ 40 9, 000 2, 100, 000 0. 0742 0. 004444 0. 000330 Sum 135 115, 000 28, 300, 000 1. 00 0. 001174 0. 001170 117. 39 116. 98 Rate per 100, 000 4, 000 / 28, 300, 000 = 0. 1413 i i

Choice of standard population 12, 000 10, 000 8, 000 6, 000 4, 000 2, 000 04 10 5 -9 15 -14 20 -19 25 -24 30 -29 35 -34 40 39 45 44 50 -49 55 54 60 59 -6 65 4 70 69 75 74 -7 80 9 -8 4 85 + USA 2000 USA 1940 Canada 1991 European WHO World ('Segi')

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

Ontario cancer mortality rates calculated using different standard populations

Choice of standard population: considerations 1. When several different populations are being compared, a ‘pooled’ standard minimizes the variance of the adjusted rates 2. In examining trends, an appropriate standard is one that reflects the average structure of the population over the time period 3. The standard should be similar to the population of interest 4. It should not change frequently (all historic data would need to be recomputed) Choi, 1999. Am J Epi 5. It should be used consistently to ensure comparability of rates

Suggested standard population Age (years) <1 year 1 – 4 5 – 9 10 -14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85 - 89 90 + Total Standard population, Canada 1991 Population Numbers Version 1 Version 2 401, 731 403, 061 1, 551, 438 1, 550, 285 1, 952, 910 1, 953, 045 1, 912, 988 1, 913, 115 1, 925, 926 1, 926, 090 2, 108, 995 2, 109, 452 2, 528, 685 2, 529, 239 2, 597, 980 2, 598, 289 2, 344, 684 2, 344, 872 2, 138, 771 2, 138, 891 1, 674, 125 1, 674, 153 1, 339, 856 1, 339, 902 1, 238, 381 1, 238, 441 1, 190, 172 1, 190, 217 1, 084, 556 1, 084, 588 834, 014 834, 024 622, 230 622, 221 382, 310 382, 303 192, 414 192, 410 95, 466 95, 467 28, 117, 632 28, 120, 065 % of Total Version 1 Version 2 1. 43% 5. 52% 5. 51% 6. 95% 6. 80% 6. 85% 7. 50% 8. 99% 9. 24% 8. 34% 7. 61% 5. 95% 4. 77% 4. 76% 4. 40% 4. 23% 3. 86% 2. 97% 2. 21% 1. 36% 0. 68% 0. 34% 1 1

Age versus Age/Sex Ø Ø Adjusts for underlying differences in age and sex distribution simultaneously Disadvantage n n with so many stratum, numbers are spread thin Rates are NOT COMPARABLE to those that are agestandardized

Age/sex standardization: Sample calculation ( 1 1, 800, 000 9, 500 * ) + ( 4 10, 500 * 2, 200, 000 ) = 1027. 6

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)

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)

Age categories US NCI (19) M & M (13) US NCHS (11) <1 1 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 55 - 59 60 - 64 65 - 69 70 - 74 75 - 79 80 - 84 85+ <1 1 - 4 5 - 9 10 - 14 15 - 19 20 - 24 <1 1 - 4 25 - 34 35 - 44 45 - 54 55 - 64 65 - 74 75 - 84 85+ 5 - 14 15 - 24

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

All cause age-specific mortality rates, Ontario 2001

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

Variance estimates “There 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.

Variance estimates 1. Based on binomial distribution 1. 2. 3. Based on Poisson distribution Based on Gamma distribution 1. 4. Better for small numbers Based on Chi-square 1. 5. Spiegelman, Lilienfeld NCHS, Statistics Canada (for vital events) Not great when <100 events Seer. Stat With adjustment for non-independent events 1. Carriere & Roos, Stukel

Based on Binomial distribution ∑ Pi ∑Pi 2 * 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 Poisson approximation ∑ Pi ∑Pi 2 2 * ri di 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 ∑ Pi ∑Pi 2 * di 2 pi 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

Other issues Ø How to treat cells with 0 values Ø When NOT to standardize Ø Ø 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

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

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