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Nelson W.B. — Recurrent events data analysis for product repairs, disease recurrences, and other applications
Nelson W.B. — Recurrent events data analysis for product repairs, disease recurrences, and other applications

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Название: Recurrent events data analysis for product repairs, disease recurrences, and other applications

Автор: Nelson W.B.

Аннотация:

Survival data consist of a single event for each population unit, namely, end of life, which is modeled with a life distribution. In contrast, many applications involve repeated-events data, where a unit may accumulate any number of events over time. Examples include the number and cost of repairs of products, the number and treatment costs of recurrent disease episodes in patients, and the number of childbirths to statisticians. This applied book provides practitioners with basic nonparametric methods for such data, particularly the plot of the estimate of the population mean cumulative function (MCF), which yields most of the information sought.

Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications is the first book to present a simple, unified theory that includes data on costs or other "values" of discrete events, not just the number of events. It surveys computer programs that calculate and plot the MCF estimate with confidence limits, shows their output, and explains how to interpret such plots. Many such calculations can be easily done with a pocket calculator or spreadsheet program. Also, the book introduces basic Poisson and Cox regression models and parametric models, including homogeneous and nonhomogeneous Poisson processes and renewal processes.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 164

Добавлена в каталог: 21.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Actuarial adjustment      82
Age data, distinct      70
Age data, exact      3—11
Age data, interval      11—13
Age, censoring      4
Age, definition      4 20
Analysis longitudinal      133
Antibiotics      58
Application      1
Application, AIDS      53
Application, air conditioner      33 76 124—127 134
Application, appliances      2
Application, automotive      1
Application, aviation      2
Application, bladder tumor      5—8 55 112 134
Application, blood analyzer      29
Application, braking grid      112
Application, business      2
Application, CGD      58 77 118
Application, childbirth      12 31 79 81 86 90 118
Application, childbirth, to men      80
Application, childbirth, to women      87
Application, circuit breaker      58 77
Application, compressor      10 46 129
Application, computers      1
Application, criminology      2
Application, defrost control      79 87 135
Application, economics      2
Application, electric power      1
Application, electronics      1
Application, fan motor      43 66 77
Application, fan motor costs      8—10 44
Application, gearbox      91 135
Application, gearbox costs      93
Application, heat pump      8 10
Application, Internet customers      10
Application, locomotives      14 56
Application, marketing      2 10
Application, medical equipment      2
Application, medicine      2
Application, military      1
Application, power plant      14
Application, Proschan      33 76 124—127 134
Application, refrigerators      87
Application, reliability      1
Application, social sciences      2
Application, subway car      16 97
Application, traction motor      16 90 97 102 103 106 108
Application, transmission      4—5 37 55 60 76 110
Application, transportation      1
Application, trucks      42
Application, tumor      40 61 76 90
Application, turbines      18 28
Application, valve seats      56
Approximation, $\chi^{2}$      116
Approximation, normal      71
Assumptions, confidence limits      70
Assumptions, confidence limits for a difference of two MCFs      118
Assumptions, dubious      74
Assumptions, MCF estimate      51
Assumptions, naive confidence limits      86
Assumptions, not assumed      26 74
Assumptions, not used      53
Assumptions, unverified      40
Assumptions, verified      51 60
Autocorrelation      71
Availability      14 30
Availability, average      31
Availability, instantaneous      31
Bad as old      20
Bathtub      29
Bias      53
Bias, unknown      36
Birth process      122
Births      see "Application childbirth"
Bladder tumors      see "Application bladder
Blood analyzer      see "Application blood
Bonferroni inequality      115
Bootstrap      75
Burn-in      29
Cause and effect      108
Censoring      4
Censoring, adjustment      82
Censoring, age      4 69
Censoring, ages unknown      42
Censoring, complex      75
Censoring, conditional      65
Censoring, estimate ages      42
Censoring, informative      25 52 76 133
Censoring, interval age data      82
Censoring, left      10—11 46—49
Censoring, left and gaps      118
Censoring, noninformative      52 133
Censoring, nonrandom      25 52
Censoring, nonrandom, example      52
Censoring, property of the data      26 99
Censoring, random      52 54 70 74
Censoring, right      3—10 37—43 70
Censoring, times      128
Censoring, unknown ages      42
CGD      58
Childbirth      see "Application childbirth"
Chronic granulomatous disease      see "Application CGD"
Coefficients      132
Coefficients, estimate      132
Coefficients, random      134
Compare MCFs      32 109—119
Compare MCFs, analysis-of-variance      115
Compare MCFs, bladder tumor      112
Compare MCFs, breaking grids      112
Compare MCFs, CGD      118
Compare MCFs, childbirth      79 118
Compare MCFs, entire MCFs      116—117
Compare MCFs, entire range      109
Compare MCFs, issues      118
Compare MCFs, K samples      117
Compare MCFs, multivariate      117
Compare MCFs, naive      119
Compare MCFs, nonparametric      116
Compare MCFs, parametric      116 117
Compare MCFs, plots      110 112 116
Compare MCFs, pointwise      109
Compare MCFs, Poisson rates      127
Compare MCFs, simple theory      109
Compare MCFs, theory      118
Compare MCFs, transmissions      110
Competing risks      108
Confidence bands      63 118
Confidence intervals, simultaneous      115
Confidence limits, approximate      63 83
Confidence limits, assumptions      68—76
Confidence limits, bootstrap      75 83
Confidence limits, conservative      68
Confidence limits, correct for interval data      83
Confidence limits, difference of two MCFs      110
Confidence limits, interval age data      83—87
Confidence limits, jackknife      75
Confidence limits, MCF      59—77
Confidence limits, motivation      60
Confidence limits, naive      83 129 see
Confidence limits, naive assumptions      86
Confidence limits, naive for interval age data      83 85
Confidence limits, negative      67 75
Confidence limits, Nelson      59—64 75
Confidence limits, normal approximation      60
Confidence limits, pointwise      63 110
Confidence limits, Poisson      64
Confidence limits, Poisson $\chi^{2}$      125
Confidence limits, Poisson $\lambda$      125
Confidence limits, Poisson approximation      67
Confidence limits, Poisson normal      125
Confidence limits, positive      75
Confidence limits, properties      61
Confidence limits, resampling      75
Confidence limits, simultaneous      63 110
Confidence limits, staircase      67
Confidence limits, steps for naive      84
Confidence limits, theory      68—76
Confidence limits, too narrow      83
Confidence limits, two-sided      60
Correlation      71
Correlation, mix of events      99
Corticosteroids      58
Costs, definition      21
Costs, fan motor      8—10 43
Costs, gearbox      93
Costs, incremental      69 73
Costs, negative      10
Costs, prorated      133
Costs, statistically independent      74
Costs, treatment      31
Costs, ultimate      31
Costs, warranty      133
Counting process      132
Counts, sums of      124
Covariance      71
Covariance, matrix      134
Covariance, population      71 73
Covariates      132 134
Covariates, time-varying      132
COW      14
Cox model      132
Cox model, estimate      132
Cox regression relationship      132
Cox regression relationship for a cumulative hazard function      132
Cox regression relationship for an MCF      132
Crack growth      14
Crow-AMSAA model      129
Cumulative distribution function      28
Cumulative hazard function      28
Cumulative history function      5
DATA      see also "Applications"
Data, childbirth      12
Data, cost      10 82
Data, errors      21
Data, exact age      35—58
Data, gap      11
Data, grouped ages      79
Data, inspection      15
Data, interval age      79—95
Data, interval tabulation      83
Data, intervals differ      80
Data, intervals in common      80
Data, life      100
Data, longitudinal      133
Data, multivariate      10
Data, peculiar      35
Data, Proschan      33 55 see Proschan"
Data, survival      28
Data, value      10
Defect growth      14 49
Dependent increments      54
Dependent increments, example      74
Design life      5 101 104
Difference of MCF estimates      110 see
Difference of MCF estimates, all pairwise      115
Disease      see also "Application tumor
Disease, episodes      5
Display      9
Display, compressor      10
Display, interval data      12
Display, mix of events      16
Display, time-event      4 16 34
Distribution, $\chi^{2}$      125
Distribution, continuous      26
Distribution, density      26
Distribution, discrete      26
Distribution, exponential      33
Distribution, F      126
Distribution, joint      99
Distribution, life      28 130
Distribution, multivariate      134
Distribution, multivariate normal      134
Distribution, normal      71
Distribution, normal cdf      124
Distribution, Poisson      71
Distribution, population      26
Distribution, renewal      130
Distribution, sampling      71
downtime      20
Error      21
Error, measurement      21
Error, reporting      21 108
Estimate, actuarial      82
Estimate, Poisson $\lambda$      124
Estimate, pooled      134
Events      see also "Recurrences"
Events, charts      5
Events, combined      97
Events, definition      19
Events, discrete      3
Events, eliminated      16 97
Events, group of      16 79 99
Events, mix of types      15—18 97—108
Events, separate      97
Events, statistically dependent      108
Events, statistically independent      108
events, types      15—18 25
Events, types combined      103 105
Events, types definition      98
Events, value      24
Exact ages      3—11
Excel      46 49 67 86 98
Failure modes, combined      16 97
Failure modes, dependent      18
Failure modes, eliminated      16 97
Failure modes, group of      16 97
Failure modes, independent competing      100
Failure modes, individual      16
Failure modes, separate      97
Failure modes, statistically dependent      54
Failure modes, statistically independent      54
Failure rate      27 see
Failure rate, decreasing      130
Failure rate, pooled      130
Failure, definition      19
Failure, degradation      19
Failure, intermittent      19
Failure, unreported      19
FLEET      53
gaps      10—11 46—49
Good as new      20
Group of events      16
Grouping into age intervals      12
Growth of defect      49
Hazard function      27 28
Hazard function, cumulative      28
History function      5
History function for cost      9
History function for cost of recurrences      24
History function for number      9
History function for number of recurrences      23
History function, continuous      13 24
History function, independent      54
History function, mix of events      98
History function, population      23—25
History function, staircase      26
History function, terminated      21 25
History function, vector      98
Homogeneous Poisson process      see "Poisson process"
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