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									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                  1       6/13/2012
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.


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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
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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]

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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]

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Typical report
(almost daily)




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Survivor function
                              SARS Survivor Function Estimates

            1



          0.98
                                                                  npmle S(t) 17 weeks
                                                                  npmle S(t) 14 weeks
          0.96                                                    npmle S(t) 10 weeks
                                                                  npmle S(t) 6 weeks
                                                                  nplse S(t) 17 weeks
          0.94                                                    nplse S(t) 14 weeks
                                                                  nplse S(t) 10 weeks
                                                                  nplse S(t) 6 weeks
          0.92



           0.9
                 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
                      Time From Infection to Death, Weeks




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Weekly death rates
                                Weekly SARS Death Rate
                        as a Function of Weeks Since Case Report

          0.05


          0.04


          0.03                                                     nplse 17 weeks
                                                                   nplse 14 weeks
                                                                   nplse 10 weeks
          0.02
                                                                   nplse 6 weeks


          0.01


            0
                 0        5          10           15     20
                              Weekly Death Rate



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Recovery (Survivor) function
                           SARS Recovery Time Survivor Function

           1

          0.9
          0.8

          0.7

          0.6                                                    nplse S(t) 17 weeks
                                                                 nplse S(t) 14 weeks
          0.5
                                                                 nplse S(t) 10 weeks
          0.4                                                    nplse S(t) 6 weeks
          0.3

          0.2
          0.1

           0
                0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
                     Time from Infection to Recovery, Weeks




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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

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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.
                                                                 11

     1, pp 81-91, 2006
Problem Solving Tools                                                                     6/13/2012

								
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