# Estimates of Survival and Mortality from Successive, Cross-Sectional Surveys David W. Smith, Ph.D., M.P.H. Consultant Stephanie L. McFall, Ph.D. Institute.

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Estimates of Survival and Mortality from Successive, Cross-Sectional Surveys David W. Smith, Ph.D., M.P.H. Consultant Stephanie L. McFall, Ph.D. Institute for Social and Economic Research University of Essex Benjamin S. Bradshaw, Ph.D. University of Texas School of Public Health

Background Death rates among people with chronic conditions are necessary to understand the burden of disease and identify public health goals Estimates of such death rates are not readily available because chronic conditions are not identified on death certificates unless they are a cause of death

Background Populations with chronic conditions are identified in surveys and totals can be estimated These are used to estimate prevalence and other characteristics Can estimate incidence rates when age at onset or diagnosis is also obtained

Estimate survival using methods that demographers have used with successive population censuses (United Nations, 1967) Estimate an initial subpopulation size Estimate the surviving subpopulation size several years later Survival Estimation Method

Count a population size at first census, denoted P 1, usually for men or women and a specific age interval, e.g., men aged 25 to 44 Count the population of survivors at the next census k years later, denoted SP 2, e.g., if 10 years later, men aged 35 to 54, Compute the survival ratio for k years, SR k = SP 2 /P 1, and use it to compute an annual death rate, q = 1 - SR k 1/k Census Method to Estimate Survival

Estimate a population size, P 1, and its variance from an initial survey, taken in the past, e.g., men with diabetes, Estimate the population size of survivors, SP 2, and its variance, from a second survey taken k years later This requires determining presence of diabetes at both the second survey and the first survey, and asking age of onset at the second survey Survey Method to Estimate Survival

Survey Estimate Formulas Estimate the survival ratio for k years, SR k = SP 2 /P 1 Estimate the variance and standard error of SR k, using the standard method for a ratio estimate: Var(SR k ) = (SR k ) 2 * (Var(P 1 )/P 1 2 + Var(SP 2 )/SP 2 2 ) se(SR k ) = Var(SR k ) 1/2 Note that P 1 and SP 2 are independent

Estimate a survival rate for 1 year, SR 1 = SR k 1/k Estimate its standard error using delta method (see Smith, McFall, Bradshaw 2010) Estimate a death rate for 1 year, q = 1 – SR 1 The standard error of q, se(q) = se(SR 1 ) Annual Estimates of Death Rates

Sponsored by the Centers for Disease Control and Prevention (CDC) since 1980s (Holtzman 2003, CDC web site) Designed to produce state and local health information, with national estimates when pooled Telephone sample and interview BRFSS obtains information about chronic conditions to estimate prevalence: diabetes, high cholesterol, asthma, arthritis, etc United States Example: Behavioral Risk Factor Surveillance System

Two Chronic Disease Questions Standard: Have you ever been told by a physician that you have diabetes? (Questions to exclude gestational diabetes) Optional: How old were you when you were first told you have diabetes? (Used by all states except Oregon and Illinois in 2001 to 2003)

Survival Estimates for the Diabetic Population The sizes of the diabetic populations ages 18-94, by sex, using pooled samples for 1996-1998, P 1 The sizes of the surviving diabetic populations, ages 23-99, by sex, using pooled samples in 2001-2003, SP 2 Survival ratios for five years, SR 5, and derived statistics

Survival of the Diabetic Population of the US from 1996-8 to 2001-3 All : 81.1% (se: 1.3%) of diabetics aged 18- 94 survived five years Annual death rate: 41.1/1000 (se: 3.2) Women: 78.5% (se: 1.7%) survived five years Annual Death Rate: 48.1/1000 (se: 4.1) Men: 84.7% (se: 2.1%) survived five years Annual death rate: 32.8 /1000 ( se = 4.9)

Evaluation of Survival using Survey Linked Mortality Records National Health Interview Survey of CDC Household sample with personal interviews for national estimates Linked interviews to three sources of death: death certificates, Medicare, Social Security Sampled in 1997-2001, followed five years Survival and death rates use standard survey analysis methods

Five Year Survival Rates of Diabetics, Using Two Methods BRFSS NHIS Both 81.4 (1.3) 83.4 (0.4) Males 84.7 (2.1) 82.6 (0.6) Females 78.5 (1.7) 84.1 (0.6) Five year survival rates (%) and standard errors, in brackets, are shown using two surveys and two methods.

Health Survey for England Repeated, cross-sectional surveys Annual since 1991 Purpose - to assess and monitor health trends Interview and examination Multistage stratified probability sample of addresses »Households are sampled and eligible members interviewed »Often, all adults and 2 children per household interviewed

Health Survey for England: Design Core content, e.g., Self rated health, smoking, drinking, height and weight Special topics - cardiovascular disease; physical activity; accidents, lung function Boost samples used – children and young people, mothers, ethnic minority, elderly, people in care homes

Health Survey for England: Diabetes Questions Were you told by a doctor that you had diabetes? (Questions to exclude gestational diabetes) Approximately how old were you when you were first told by a doctor that you had diabetes? »Asked in 2003 through 2006, 2009, and 2010 »Adult sample sizes range from 4,600 to 15,000

Conclusion Repeated cross-sectional surveys can be used to estimate survival and mortality for important chronic conditions The statistical methods are already well- developed The age of onset or diagnosis must be obtained, at least in the later of two surveys Sample sizes must be large enough to estimate the initial number of people with a chronic condition

Recommendation Always ask about age of onset of any chronic condition or habit – The cost is minimal and both incidence and mortality can be estimated

Bibliography BRFSS Web site: www.cdc.gov/brfss/ Holtzman D. (2003). Analysis and interpretations of data from the US Behavioral Risk Factor Surveillance System. In: D. V. McQueen, & P. Puska (Eds.), Global Behavioral Risk Factor Surveillance. (pp. 35-46). New York: Kluwer Academic/Plenum Publishers. Smith D. W., McFall S. L., Bradshaw B. S. (2010). Estimates of Survival and Mortality from Successive Cross-Sectional Surveys. University of Essex, ISER Working Paper Series: 2010-12. Accessed at http://www.iser.essex.ac.uk/publications/working- papers/iser, 1 May, 2010. United Nations (1967). Methods of Estimating Basic Demographic Measures from Incomplete Data. New York: United Nations.

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