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SMRs, PMRs and Survival Measures

SMRs, PMRs and Survival Measures. Principles of Epidemiology Lecture 3 Dona Schneider , PhD, MPH, FACE. REVIEW: Adjusted Rates are Created Through Standardization. Standardization: The process by which you derive a summary figure to compare health outcomes of groups

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SMRs, PMRs and Survival Measures

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  1. SMRs, PMRs and Survival Measures Principles of Epidemiology Lecture 3 Dona Schneider, PhD, MPH, FACE

  2. REVIEW: Adjusted Rates are Created Through Standardization • Standardization: • The process by which you derive a summary figure to compare health outcomes of groups • The process can be used for mortality, natality, or morbidity data

  3. Standardization Examples • Direct Method requires • Age-specific rates in the sample population • The age of each case • The population-at-risk for each age group in the sample • Age structure (percentage of cases in each age group) of a standard population • Summary figure is an AGE-ADJUSTED RATE

  4. Standardization: Age Adjustment (cont.) • Indirect method requires • Age structure of the sample population at risk • Total cases in the sample population (not ages of cases) • Age-specific rates for a standard population • Summary figure is a STANDARDIZED MORTALITY RATIO (SMR)

  5. Indirect Standardization • Instead of a standard population structure, you utilize a standard rate to adjust your sample • Indirect standardization does not require that you know the stratum-specific rates of your cases • The summary measure is the SMR or standardized mortality/morbidity ratio SMR = ObservedX 100 Expected

  6. Indirect Standardization (cont.) • An SMR of 100 or 100% means no difference between the number of outcomes in the sample population and that which would be expected in the standard population

  7. Example: SMR for Male Farmers, England and Wales, 1951 Expected Number of Deaths for Farmers and Farm Managers per 1,000,000 Age Group Number of Farmers and Farm Managers (Census, 1951) Standard Death Rates per 1,000,000 (All Causes of Death) Total expected deaths per year: 2,083 (1) (2) (3) = (1) X (2) 20-24 7,989 1,383 11 25-34 37,030 1,594 59 35-44 60,838 2,868 174 45-54 68,687 8,212 564 55-64 55,565 22,953 1,275 SMR = 1,464X 100= 70.3% 2,083 Total observed deaths per year: 1,464

  8. In 1951, male farmers in England and Wales had a mortality rate 30 percent lower than the comparably-aged general population.

  9. SMR for Tuberculosis for White Miners Ages 20 to 59 Years, United States, 1950 Expected Deaths From TBC in White Miners if They Had the Same Risk as the General Population Observed Deaths from TBC in White Miners Death Rate (per 100,000) for TBC in Males in the General Population Age (yr) Estimated Population of White Miners (1) (2) (3) = (1) X (2) (4) 20-24 74,598 12.26 9.14 10 25-29 85,077 16.12 13.71 20 30-34 80,845 21.54 17.41 22 35-44 148,870 33.96 50.55 98 45-54 102,649 56.82 58.32 174 55-59 42,494 75.23 31.96 112 Totals 181.09 436 SMR = Observed / Expected X 100 SMR (for 20–59 yr olds) = 436 / 181.09 X 100 = 241%

  10. In the United States in 1950, white miners ages 20 to 59 years died of tuberculosis almost 2.5 times as often as comparably-aged males in the general population

  11. Calculation of stratum or age-specific and total SMRs SMR = O/E X100 = 179/88.15 X 100 = 203% • Individuals in a cohort may contribute different amounts of risk due to length of exposure (person-years) Study Cohort Reference Population Rate per 1,000 Number or outdomes of interest (Obs) Person-Years in TOTAL cohort Age (yr) Exp SMR = (1) / (4) (1) (2) (3) (4) = (2) X (3) 40-49 6 1,200 2.5 3.00 2.00 50-59 27 2,340 6.1 14.27 1.89 98 3,750 12.4 46.50 2.11 60-69 70-79 48 975 25.0 24.38 1.97 179 88.15 2.03 Total

  12. Workers in this cohort were twice as likely to have the outcome of interest as the general population • Those ages 60-69 had the highest age-specific SMR • Those ages 50-59 had the lowest age-specific SMR

  13. SMR’s (con’t) • Sometimes exposures change over time and individuals may have different amounts of exposure when they are in a cohort over multiple years • Example: Over a period of years, the manufacturing process of product X changed. The occupational cohort involved in the processes had 58deaths (we do not know their ages). Was this more or less than would be expected in the general population? • Stratify the cohort by known exposure periods

  14. Age Group Person-years in Cohort US White Male CA Deaths (per 100,000) Exp. Cancer Deaths 1948-1952 15-24 1,250 9.9 0.1 25-34 3,423 17.7 0.6 35-44 3,275 44.5 1.5 45-54 2,028 150.8 3.1 55-64 1,144 409.4 4.7 1953-1957 15-24 544 11.2 0.1 25-34 3,702 17.5 .06 35-44 4,382 44.2 1.9 45-54 2,968 157.7 4.7 55-64 1,552 432.0 6.7 1958-1963 15-24 4 10.3 0.0 25-34 2,206 18.8 0.4 35-44 4,737 46.3 2.2 45-54 4,114 164.1 6.8 55-64 2,098 450.9 9.5 TOTAL 42.9 SMR = observed/expected x 100% = 58 / 42.9 x 100% = 135%

  15. Persons in this cohort had the outcome 35% more often than would be expected in the general population.We could not calculate age-specific SMRs without the ages of the cases.If we have the ages of cases:

  16. Person-years 1970-74 1975-79 1980-84 Age 20-24 1000 500 200 25-29 1000 1500 1000 30-34 500 500 1500 Observed Deaths Age 20-24 2 1 0 25-29 3 4 2 30-34 0 1 2 S Obs = 15 Population rates(per 1,000) Age 20-24 1.8 1.8 1.6 25-29 1.7 1.5 1.5 30-34 1.9 1.8 1.7 Expected deaths = population rates x person-years / 1000 Age 20-24 1.8 0.9 0.3 25-29 1.7 2.3 1.5 30-34 0.9 0.9 2.6 S Exp = 12.9 SMR = S Obs / S Exp X 100 = 15 / 12.9 X 100 = 116%

  17. From these data you can compute • A total SMR (116%) • Age-specific SMRs (age 20-25, SMR = 100%) • Time period SMRs (1970-1974, SMR = 114%) • Age-specific and time period SMRs (age 20-24, 1970-74, SMR = 111%)

  18. SMRs • Expecta Healthy worker effect • Occupational studies should have SMRs < 100 • Workers tend to be healthier than the general population which comprises both healthy and unhealthy individuals • You cannot compare SMRs between studies -- only to the standard population

  19. Advantages Disadvantages Comparison of Rates Actual Summary rates Difficult to interpret because of differences in population structures Crude Readily calculable Controls for homogeneous subgroups Specific Cumbersome if there are many subgroups Provides detailed information No summary figure Adjusted Provides a summary figure Fictional rate Controls confounders Magnitude depends on population standard Permits group comparison Hides subgroup differences

  20. In Summary: One type of rate is not necessarily more important than another. Which you choose depends on the information sought. Crude rates are often used to estimate the burden of disease and to plan health services. To compare rates among subpopulations or for various causes, specific rates are preferred. To compare the health of entire populations, adjusted rates are preferred because they allow for comparison of populations with different demographic structures.

  21. CDC Wonder http://wonder.cdc.gov/

  22. Additional Outcome Measures • Proportionate Mortality Ratio • Proportionate Mortality Rate • Case Fatality Rate • Years of Potential Life Lost • Measures of Survival

  23. Additional Outcome Measures • Proportionate Mortality Ratio • The ratio of observed/expected deaths (in terms of proportions of deaths in the standard population) x 100 • PMRs are explained similarly to SMRs • 100% = no difference between groups

  24. 1950-54 1955-59 1960-64 20-24 10 5 2 25-29 10 15 10 30-34 5 5 15 20-24 2 1 0 25-29 3 4 2 30-34 0 1 2 S =15 Population Proportion of Cancer Deaths 20-24 0.07 0.07 0.07 25-29 0.09 0.10 0.10 30-34 0.11 0.12 0.12 Expected deaths due to cancer = Population proportion x all deaths in sample 20-24 0.7 0.4 0.1 25-29 0.9 1.5 1.0 30-34 0.6 0.6 1.8 S =7.6 All Deaths Computing a PMR Cancer Deaths observed expected PMR = Observed/Expected x 100 = (15/7.6) x 100 = 197%

  25. PMR = 197%The study population has twice the proportion of cancer deaths as the standard population.

  26. CHD Proportionate Mortality Rate

  27. Ten Leading Causes of Death, 25-44 Years, All Races, Both Sexes, United States, 1991 (Population 82,438,000) Number Cause of Death Rank Order Proportionate mortality rate (%) Cause-specific death rate per 100,000 1 26,526 18.0 32.2 Accidents and adverse effects 2 Malignant neoplasms 22,228 15.0 27.0 3 HIV infection 21,747 14.7 26.4 Diseases of the heart 4 15,822 10.7 19.2 Homicide and legal intervention 5 12,372 8.4 15.0 14.9 6 Suicide 12,281 8.3 Chronic liver disease and cirrhosis 7 3.0 5.4 4,449 8 4.1 Cerebrovascular diseases 3,343 2.3 9 Diabetes mellitus 2,211 1.5 2.7 10 2,203 1.5 2.7 Pneumonia and influenza All causes 147,750 100

  28. Comparing Mortality and Case-Fatality Rates • Assume a 1995 population of 100,000 people where 20 contract disease X and 18 people die from the disease. One remains stricken and one recovers. What is the mortality rate and what is the case-fatality rate for disease X? • Mortality rate from disease X 18 / 100,000 = .00018 = .018% • Case-fatality rate from disease X 18 / 20 = .9 = 90%

  29. Years of Potential Life Lost • Death occurring in a particular individual at an early age results in a greater loss of that individual’s productivity than if that same individual lived to an average life span. • By convention, YPLL (or PYLL) is based on a life expectancy of 75 years • YPLL can be calculated for individual or group data

  30. Example: Individual data method • A person who died at age 20 would contribute 55 potential years of life lost (75-20=55 YPLL) • Deaths in individuals 75 years or older are excluded • The rate is obtained by dividing total potential years of life lost by the total population less than 75 years of age.

  31. Individual Age at Death (Years) YPLL Contributed (75-age) 1 6 months 74.5 2 55 20 3 15 60 4 85* xx 5 60 15 Sum xxx 169.5 *excluded YPLL from Disease X = 169.5 / 4 = 42.4 per person

  32. Example: Age Group MethodIn a population of 12,975,615, what is the rate of YPLL for 2000? • Obtain the ages at the time of death for each case (column 1) Exclude those over age 75 • Calculate the mean age for each age group (column 2) • Subtract the mean age from 75 (column 3) • Calculate stratum-specific YPLL by multiplying column 1 by column 3 • Sum the stratum-specific YPLL • Divide by the total population for the ages selected

  33. # Deaths(1) Age 75-mean(3) YPPL(1)x(3) Mean Age at Death(2) Age <1 4 0.5 74.5 298.0 1-4 28 3.0 72.0 2016.0 5-9 52 7.5 67.5 3510.0 10-14 64 12.5 62.5 4000.0 15-19 315 17.5 57.5 18112.5 20-24 410 22.5 52.5 21525.0 25-29 308 27.5 47.5 14630.0 30-34 243 32.5 42.5 10327.5 35-39 171 37.5 37.5 6412.5 40-44 131 42.5 32.5 4257.5 45-49 116 47.5 27.5 3190.0 50-54 85 52.5 22.5 1912.5 55-59 85 57.5 17.5 1487.5 60-64 86 62.5 12.5 1075.0 65-69 64 67.5 7.5 480.0 70-74 70 72.5 2.5 175.0 xxx xxx xxx 93,234.0 Rate of YPLL per 1,000 persons = 93,234.0/12,975,615 = 7.2 per 1,000 in 2000

  34. Measuring Survival • Five-year survival • Not a magical number • May be subject to LEAD TIME BIAS • Cannot evaluate new therapies

  35. Measuring Survival (cont.) • Life Tables (assume no change in treatment over the time of observation) • Used to calculate probability of surviving fixed segments of time • Allow each case to contribute to data analysis regardless of the time segment in which they are enrolled • The probability of surviving 5 years is the product of surviving each year (p.89)

  36. Measuring Survival (cont.) • Kaplan-Meier • Time periods are not predetermined but are set by the death or diagnosis of a case • Withdrawls and those lost to follow-up are removed from the analysis • Typically used for small numbers of cases

  37. Measuring Survival (cont.) • Median Survival • The time that half the population survives • Not effected by outliers like the mean • Can calculate the median survival time when half rather than all the cases die

  38. Measuring Survival (cont.) • Relative survival rate • Compares survival from a given disease to a comparable group who do not have the disease Relative Survival Rate (%) = Observed/Expected x 100

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