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SARS Survivor Function Estimation from Cumulative Reports (Draft March 14, 2006)

It's not the figures themselves," she said finally, "it's what you do with them that matters." Lamia Gurdleneck. SARS Survivor Function Estimation from Cumulative Reports (Draft March 14, 2006). Larry George. Vision Statement.

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SARS Survivor Function Estimation from Cumulative Reports (Draft March 14, 2006)

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  1. It's not the figures themselves," she said finally, "it's what you do with them that matters." Lamia Gurdleneck SARS Survivor Function Estimation from Cumulative Reports (Draft March 14, 2006) Larry George Problem Solving Tools

  2. Vision Statement • Cumulative case and death counts are statistically sufficient to estimate nonparametric survivor functions of transient stochastic processes. Such estimates would benefit biostatistics and reliability statistics. Problem Solving Tools

  3. Goal and Objective • State the desired goal • Help the WHO and biostatisticians with epidemiological statistics • State the desired objective • Spread the use of survival analysis without life data, to save computer storage requirements and money, reduce errors, improve credibility, and obtain more precise actuarial forecasts, without privacy violation • Such estimates would benefit biostatistics with statistical confidence limits on forecasts and regional differences in survivor functions Problem Solving Tools

  4. Today’s Situation • Statisticians believe random samples of death times are required for survival analysis • “The WHO did not describe the estimation method and just mentioned that this estimation requires detailed individual patient data on the time from admission (or illness onset) to death or full recovery.” [Yu et al] • “…we also used a version of the Kaplan-Meier survival curve, adapted to allow for two types of outcome (death and discharge).” ”We thank David R. Cox for developing a suitable nonparametric method for estimation of the case fatality rate.” [Donnelly et al] Problem Solving Tools

  5. Counterexample • SARS data from www.who.int/csr/sars/country/en/ • Daily cases, deaths, some recoveries • Grouped by week and country • Used the total for all countries • Make nonparametric maximum likelihood and least squares estimators of survivor functions • Npmle [George and Agrawal, George 1999] • Nplse [Oscarsson and Hallberg; Harris, Rattner, and Sutton; George 1995] Problem Solving Tools

  6. Typical report (almost daily) Problem Solving Tools

  7. Survivor function Problem Solving Tools

  8. Weekly death rates Problem Solving Tools

  9. Recovery (Survivor) function Problem Solving Tools

  10. Recommendations • Use nonparametric estimates of age-or-time-specific survivor and actuarial rate functions from case, death, and recovery reports • Make actuarial forecasts of deaths and recoveries • Estimate CFR, survival and recovery time distributions, and estimate confidence limits • Test hypotheses about country differences, treatments, and so on Problem Solving Tools

  11. References • Donnelly, Christl A., et al., “Epidemiological determinants of spread of causal agent of SARS in Hong Kong,” http://image, thelancet.com/extras/03art4453web.pdf • George, L. L. and A. Agrawal, “Estimation of a Hidden Service Distribution of an M/G/ Service System,” Naval Research Logistics Quarterly, pp. 549-555, September, 1973, Vol. 20, No. 3. • Ibid., “Field Reliability Estimation Without Life Data,” ASA SPES Newsletter, Dec. 1999, pp 13-16 http://web.utk.edu/~asaqp/newsletters/1299newsletter.pdf • Ibid., “Apply Field Reliability to Service and Spares,” QC95 Conference, ASQC Santa Clara Valley, April 1995 • Harris, Carl M.; Rattner, Edward; Sutton, Clifton. Forecasting the extent of the HIV/AIDS epidemic. Socio-Economic Planning Sciences, Vol. 26, No. 3, Jul 1992. 149-68 pp. Elmsford, New York/Oxford, England. • Oscarsson P and Hallberg Ö, “EriView 2000 -A Tool For The Analysis Of Field Statistics”, Proc. ESREL 97, Lisbon, June 1997, ISBN 0-08-042835-5 • Yu, Philip L. H. et al., “Statistical exploration from SARS,” Amer. Statistician, vol. 60, No. 1, pp 81-91, 2006 Problem Solving Tools

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