Survival Analysis Without Life Data

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Survival Analysis Without Life Data
It's not the figures themselves," she said
finally, "it's what you do with them that
matters." Lamia Gurdleneck

• SF ASA Chapter CSU EB StatisticsOct. 16, 2006
• Larry George

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Survivor Function is PLife gt t

• Survival analysis is a branch of statistics which
  deals with death in biological organisms and
  failure in mechanical systems. This topic is
  called reliability theory or reliability analysis
  in engineering, and duration analysis or duration
  modeling in economics. (Wikipedia)
• reliability function (durability?)
• ccdf
• Whos interested in survival analysis? Why?

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Outline

• People say life data are necessary. Not always!
• Motivations the IBM way, Apple lit. search, TP
  and ergodicity, shopping time survey
• Methods npmle and nplse, missing data, queuing
  theory, renewals, stages
• Examples AIDS, SARS, bird flu, ICDs
  (pacemakers), and AEDs
• Questions limitations, data, kill controls?
• Progress in artificial stupidity

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People say life data are necessary

• estimation requires detailed individual patient
  data on the time from admission (or illness
  onset) to death or full recovery. Yu et al.
  SARS
• For device failures, the year of device implant
  was not known. An individual patients
  riskcould not be sufficiently evaluated in this
  study, such as device model and years since
  implant. Maisel ICD
• Accurate assessment of actual device performance
  is not possible based on limitations of the
  post-marketing surveillance system for medical
  devices. Estes AED
• "The data required to provide an expected
  replacement profile actuarial rates are not
  automatically available at this time thus, the
  expansion of this theory actuarial forecast
  into full practical applications" Krupp
• as well as the failure to maintain life cycle
  part and labor histories at the end item level,
  makes it difficult to apply standard economic
  useful life models RAND M1 Tanks

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Life data (grouped)

• Suppose all you had was shipped and returns
  counts (bottom line)?

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Ships and Returns Counts are Sufficient Statistics

• Ships ? nj births, sales, installed base,
  survivors
• Returns ? Rj deaths, recoveries, complaints,
  failures, repairs, spares sales
• GAAP requires ships and returns counts, without
  id
• Theyre population data www.who.int,
  www.fda.gov/cdrh/ maude.html

• n1

• R1

• n2

• R2

Time
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AFR is calendar-specific, not age-specific

• giving guns to children. Mensing

• AFRj ? Rj/Snk (sum over k 1,2,,j)
• Maisel published AFRj in JAMA for FDA pacemaker
  and AED advisories, not failures
• AFRs are averages. Age-specific reliability,
  broom charts, forecasts, and SPC tell more,
  better, sooner
• Good news can compute ships and returns counts
  from AFRj and installed base nj

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AED advisory rates per 100 AED device years
Maisel
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Cdf of time from release to FDA advisories (ICDs)

• Weighted average 3 years

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Methods npmle and nplse

• Nonparametric gt no need to defend unwarranted,
  mathematically convenient assumptions
• nplse Harris and Rattner, Oscarsson and
  Hallberg, and George
• npmle George and Agrawal, 1973
• Apple story lit. search with 1 hit, my own article

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Npmle Mt/G/?

• Estimate distribution of time in store, without
  tracking individuals, from arrival times and
  departure times
• Light traffic gt FIFO gt departure arrival
  random sample of iid times in store
• Heavier traffic gt probability of FIFO, second in
  is first out, and so on, as a function of cdf of
  time in store
• Steady state no info

lG(t)
l
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Missing data, renewals

• Often early ships returns counts are unknown
• The data are archived Apple
• We dont even know our own inventory LILCO,
  http//www.lipower.org/company/relipability.html
• TP and ergodic story
• M88A1 production started in 1977, data from 1990s

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M88A1 annual actuarial rate of engine rebuilds

• 160,000 each plus labor

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Biostatistical examples

• AIDS case forecasts (Harris and Rattner) from
  case counts without identification
• Actuarial forecast from HIV-gtAIDS-to-death
• SARS and bird flu country comparisons from
  www.who.int data and CFR
• Yu used time from case admission to death or
  recovery
• WHO data are cumulative case counts
• Pacemaker ICD (Medtronic)
• Age at failure vs. ships and returns

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CA AIDS
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SARS Weekly Actuarial Death Rate Estimates

• Data from http//www.who.int/csr/sars/country/en/i
  ndex.html and Yu et al., HKU

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Bird flu survivor functions

• Data from http//www.who.int/csr/disease/avian_inf
  luenza/en/index.html

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Pacemakers and AEDs

• ISO 5841-22000(E) requires names and dates
• Implants for surgery -- Cardiac pacemakers --
  Part 2 Reporting of clinical performance of
  populations of pulse generators or leads Annex
  B, actuarial analysis
• Many ICDs dont have serial numbers! Required,
  now
• www.hrsonline.org/UploadDocs/HRS_Device-Performanc
  e-Recommendations-Apr06.pdf
• Follow-up by name, date, and ???

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ICDs and FDA advisories

• Survival function estimates
• ICD broom charts. Why no improvement?

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7271 GEM DR
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7271 GEM DR nplse Broom Charts for electrical
failures

• Sell-through time?

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7271 GEM DR nplse broom charts for battery
failures
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Marquis andMaximo

• Improvement?

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Discussion

• A sine qua non of scientific publication is,
  publish information so that anyone with the time
  and inclination could reproduce the results.
  biostatistician
• FDA time-to-advisories? (shown earlier) Why does
  it take so long?
• Ships and returns are sufficient. When to use?
• Could we do more with data? What data? SPC on
  returns. Want early warning?
• Why kill controls?

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Ships and returns counts may be all you can get

• Population estimates have no sample uncertainty
• Variation may be because of nonstationary
  reliability from different calendar intervals
• Automotive aftermarket ships and returns require
  1/1000 the data as storing by VIN, part number,
  dates
• Ships and returns counts protect privacy
• Avoid errors
• Auto dealers complain long and bitterly about
  having to enter VIN, part numbers, repairs, and
  mileage every time they fix something

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Do more with data

• Look around for data. GAAP requires it. HRS wants
  ages. What should FDA do?
• Broom charts?
• SPC on returns?
• Early warning?

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Why kill controls?

• Were lucky to get 100 people with some of the
  diseases were testing drugs for and we have to
  divide them into matched control and treatment
  groups. Abbott clinical trials statistician
• R. A. Fisher said so, but he was doing
  agricultural experiments
• Why not use population estimate of untreated
  group?
• Limitation of M/G/? in steady state
• Works for epidemics, transplants, pacemakers, AEDs

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Progress in Artificial Stupidity
The very powerful and the very stupid have one
thing in common. They don't alter their views to
fit the facts. They alter the facts to fit the
views, which can be uncomfortable if you happen
to be one of the facts that needs altering. Dr.
Who

• http//www2.hawaii.edu/bergen/bush.html Bush
  state stereotypes
• www.fieldreliability.com/ASRI.htm
• Broken down by sex
• www.fieldreliability.com/VirtStat.htm
• Weibull DoA statistics. What MTBF would you like?
• Terminate SPRT at time of fixed sample test
• If at first you dont succeed, try again
• How often do you beat your wife?
• Changing cdfs after a while

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References

• Alison P. Galvani, Xiudong Lei, and Nicholas P.
  Jewell, "Temporal Stability and Geographic
  Variation in Cumulative Case Fatality Rates and
  Average Doubling Times of SARS Epidemics" (June
  2003). U.C. Berkeley Division of Biostatistics
  Working Paper Series. Working Paper 133,
  http//www.bepress.com/ucbbiostat/paper133
• Gregor Raley and Dan Raimooni, The Further
  Undoing of Lamia Gurdleneck, Applied Probability
  Newsletter, TIMS-ORSA, April 1986
• Grunkemeien, GL, JL Dobbs and A Starr,
  Statistical analysis of pacemaker follow-up
  data. Rate stability and reliability,
  Circulation 197653241-244
• Karr, A. F. et al., A framework for evaluation
  the utility of data altered to protect
  confidentiality, The Am. Statistician, Aug.
  2006, Vol. 60, No. 3, pp. 224-232
• Maisel, William H MD, MPH, Safety issues
  involving medical devices, JAMA Aug24/31, 2005,
  Vol. 294, No. 8, pp. 955-958
• Maisel, William H MD, MPH, Pacemaker and ICD
  generator reliability. Meta-analysis of device
  registries, JAMA, 20062951929-1934
• Mark Estes III, N. A. MD, Automated external
  defibrillators-device reliability and clinical
  benefits, JAMA, August 9, 2006, Vol. 296, No. 6,
  pp. 700-702
• US FDA manufacturer and user facility device
  experience db (MAUDE), www.fda.gov/cdrh/maude.html
  
• Draft recommendations report by the Heart Rhythm
  Society task force on device performance policies
  and guidelines, www.hrsonline.org/uploadDocs/RS_De
  vice-Performance-Recommendations-Apr06.pdf
• Shah, Jignesh S. MD and William H. Maisel, MD,
  MPH, Recalls and safety alerts affecting AEDs,
  JAMA, August 9, 2006, Vol. 296, No. 6, pp.
  655-660
• Yu, Philip L. H., Jennifer S. K. Chan, and Wing
  K. Fung, Statistical Exploration from SARS, The
  Am. Statistician, Feb. 2006, Vil. 60, No. 1, pp.
  81-91