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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.
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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
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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, 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 125
Confidence limits, Poisson 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, 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 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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