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Mean Cumulative Function (MCF) For Recurrent Events

Mean Cumulative Function (MCF) For Recurrent Events. (Only what I learned so far.). Outline. Background What is MCF? How to estimate MCF? Plot of MCF Compare two MCFs. Coronary Artery Disease. Coronary Artery Bypass Graft (CABG) Surgery. Percutaneous Coronary Intervention (PCI).

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Mean Cumulative Function (MCF) For Recurrent Events

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  1. Mean Cumulative Function (MCF) For Recurrent Events (Only what I learned so far.)

  2. Outline • Background • What is MCF? • How to estimate MCF? • Plot of MCF • Compare two MCFs

  3. Coronary Artery Disease

  4. Coronary Artery Bypass Graft (CABG) Surgery

  5. Percutaneous Coronary Intervention (PCI)

  6. Limitations associated with PCI: Restenosis • The treated vessel becomes blocked again. • Usually occurs within 6 months after the initial procedure • Balloon angioplasty alone: 40% • Stenting: 25% • In-stent restenosis • Scar tissue overgrow and obstruct the blood flow • Typically within 3 to 6 months • Brachytherapy • Drug elute stent

  7. Recurrent events • A sample units can undergo repeated events, such as repairs of products, recurrences of tumors, and restenosis of coronary artery in our case.

  8. Analysis of recurrent events • Time-to-first event • simple and easy to interpret. • conventional survival analysis method • ignores information hence inefficient • Wei, Lin Weissfeld (WLW) marginal model event number is used as a stratification variable; separate model per stratum • Prentice, Williams and Peterson (PWP) conditional method: ‘at-risk process’ for jth event only becomes 1 after the (j - 1)th event • Andersen and Gill (AG) method: ‘at-risk process’ remains at 1 until unit is censored • Wayne Nelson: Mean cumulative function (MCF)

  9. What is MCF? • Product reliability analysis • When a repairable system fails, it is repaired and placed back in service. As a repairable system ages, it accumulates a history of repairs and costs of repairs. • At a particular age t, there is a population distribution of cumulative cost (or number) of repairs; the distribution has a mean M(t), called the Mean Cumulative Function (MCF) for the cost (or number) of repairs.

  10. How to estimate MCF?

  11. How to estimate MCF? Calculation of MCF for Artificial Data System Repair Histories for Artificial data

  12. Transmission data MCF and 95% confidence limits

  13. Using SAS for MCF estimation • RELIABILITY procedure • nonparametric estimates of population MCF and its 95% confidence interval • plot the estimated MCF for the number of repairs or the cost of repairs • estimates of the difference of two MCFs and confidence intervals • plot the difference of two MCFs and confidence intervals.

  14. Using SAS for MCF estimation symbol c=blue v=plus; proc reliability data=valve; unitid id; mcfplot days*value(-1) / cframe = ligr ccensor = megr; inset / cfill = ywh ; run;

  15. S-plus for MCF • SPLIDA (S-PLUS Life Data Analysis) • By W. Q. Meeker

  16. References • Nelson, Wayne (2003), Recurrent-Events Data Analysis for Repairs, Disease Episodes, and Other Applications, ASA SIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, PA. • Nelson, W. (1995), "Confidence Limits for Recurrence Data--Applied to Cost or Number of Product Repairs," Technometrics, 37, 147 -157.

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