Bloomberg School BIO 651 - lecture 27 (29 pages)

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lecture 27



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lecture 27

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Pages:
29
School:
Johns Hopkins Bloomberg School of Public Health
Course:
Bio 651 - Simpson’s (perceived) paradox
Simpson’s (perceived) paradox Documents

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Lecture 27 Brian Caffo Table of contents Outline The Poisson distribution Poisson approximation to the binomial Person time analysis Exact tests Time to event modeling Lecture 27 Brian Caffo Department of Biostatistics Johns Hopkins Bloomberg School of Public Health Johns Hopkins University December 19 2007 Lecture 27 Table of contents Brian Caffo Table of contents Outline 1 Table of contents The Poisson distribution Poisson approximation to the binomial 2 Outline 3 The Poisson distribution Person time analysis Exact tests Time to event modeling 4 Poisson approximation to the binomial 5 Person time analysis 6 Exact tests 7 Time to event modeling Lecture 27 Outline Brian Caffo Table of contents Outline The Poisson distribution Poisson approximation to the binomial Person time analysis Exact tests Time to event modeling 1 Poisson distribution 2 Tests of hypothesis for a single Poisson mean 3 Comparing multiple Poisson means 4 Likelihood equivalence with exponential model Lecture 27 Pump failure data Brian Caffo Table of contents Outline The Poisson distribution Poisson approximation to the binomial Pump Failures Time 1 5 94 32 2 1 15 72 3 5 62 88 4 14 125 76 5 3 5 24 Pump Failures Time 6 19 31 44 7 1 1 05 8 1 1 05 9 4 2 10 10 22 10 48 Person time analysis Exact tests Time to event modeling From Casella and Robert Monte Carlo Statistical Methods first edition Lecture 27 The Poisson distribution Brian Caffo Table of contents Outline The Poisson distribution Poisson approximation to the binomial Used to model counts The Poisson mass function is P X x Person time analysis Exact tests Time to event modeling x e x for x 0 1 The mean of this distribution is The variance of this distribution is Notice that x ranges from 0 to Lecture 27 Brian Caffo Table of contents Some uses for the Poisson distribution Outline The Poisson distribution Poisson approximation to the binomial Person time analysis Exact tests Time to event modeling Modeling event time data Modeling radioactive



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