4. Issues in Trial Monitoring
|
|
- Sheena McDaniel
- 6 years ago
- Views:
Transcription
1 4. Issues in Trial Monitoring 4.1 Elements of Trial Monitoring Monitoring trial process and quality Infrastructure requirements and DSMBs 4.2 Interim analyses: group sequential trial design 4.3 Group sequential design families 4.4 Frequentist evaluation of sequential trials 4.5 On the use of stochastic curtailment What is stochastic curtailment? (a) Stopping decisions based on conditional power (b) Stopping decisions based on predictive power Example: sepsis trial 4.6 Implementing a monitoring plan 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 1
2 4.5 On the use of stochastic curtailment: What is it? Consider the sepsis trial: Suppose you observe a 5% higher mortality rate with antibody treatment at the first interim analysis (ˆθ = 0.05). You are considering stopping for lack of effect. It might seem relevant to ask: if I were to continue, would I change my mind? More formally, what is the probability of reversing the current decision: P θ (ˆθ J < d J ˆθ 1 = 0.05)? This is a form of power. If it is small, then you should stop. The probability of changing your mind based on the data is known as stochastic curtailment. There are two types of approaches: (a) Conditional power: Power based on some relevant value for θ. (b) Predictive power: Mean power integrated over a posterior distribution for θ Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
3 4.5(a) Conditional power (Example): Recall the sepsis trial: According to the monitoring plan, the trial would stop for benefit if ˆθ J < d J = at N J = 1700 patients. If ˆθ 1 = 0.05, then what is the chance (power) that ˆθ J < d J? If we observe ˆθj = x, then the increment between the jth and Jth analysis is normally distributed: N J ˆθJ N j x N [(N J N j )θ, (N J N j )V ] where V = = Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 3
4 4.5(a) Conditional power (Example): It follows that: P θ (ˆθ J < d J ˆθ j = x) < α N J d J N jx (N J N j )θ) < z α (NJ N j )V ] x > N 1 j [N J d J (N J N j )θ z α NJ N j That is, we would be very unlikely (probability less than α) to reverse a futility decision if ˆθ j > d j where: ] d j = N 1 j [N J d J (N J N j )θ z α NJ N j 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 4
5 4.5(a) Conditional power (Example): Suppose in the sepsis trial we used the following stopping criteria: Final critical value is d J = Decide futility as long as the power for changing our mind is smaller than 10% (z α = 1.28). Calculate this power under θ = 2 d J = The following futility stopping criteria result from the above calculations: d 1 = d 2 = d 3 = d 4 = Notice the degree conservatism. Is it ethical? 5 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
6 4.5(a) Conditional power (Example): Suppose we instead use zα = 0; i.e., a 50% chance of changing our mind. Then: d 1 = d 2 = d 3 = d 4 = Notice the degree conservatism. Is it ethical? Do these stopping rules look familiar? Is it reasonable to use z α = 0? 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 6
7 4.5(a) Conditional power (design family): It is instructive to construct a conditional futility design family in the standardized scale: V/NJ Standardized mean: δ = θ θ 0 Standardized statistic: ˆδj N (δ, 1 Decision criteria: Π j ) δ j > d j Decide for superiority δ j < a j Decide for lack of superiority Let d J = a J = G. 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 7
8 4.5(a) Conditional power (design family): Conditional power decision rules: Stop for efficacy if P δ=0 (ˆδ J < G δ j = d j ) = α, which implies d j = (G + z 1 α 1 Πj )Π 1 j Stop for futility if P δ=δ+ (ˆδ J > G δ j = a j ) = α, which implies: a j = 2G (G + z 1 α 1 Πj )Π 1 j As in other families, G can be selected to control operating characteristics (see R-code in file lctsec4-5.r). 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 8
9 4.5(a) Conditional power (design family): Example: Suppose Π j = 0.25, 0.5, 0.75, 1.0. The values of G satisfying: are: J P (ˆδ j > d j δ = 0) = (type I error) j=1 J P (ˆδ j < a j δ = 2G) = (type II error) j=1 Values of d j for selected α Π j α = 0.10 α = 0.35 α = Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
10 4.5(a) Conditional power (design family): Stopping boundaries: CF.10 CF.35 CF.50 Difference in Means Sample size Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
11 4.5(a) Conditional power (design family): Sample Size: Average Sample Size 75th percentile Sample Size CF.10 CF.35 CF.50 Sample Size CF.10 CF.35 CF Difference in Means Difference in Means 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 11
12 4.5(a) Conditional power (design family): Power: CF.10 CF.35 CF.50 Power (Upper) Theta Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
13 4.5(a) Conditional power (Sepsis example) Comparing inference at lower (efficacy) boundary: Design: DSMB2 Bias-adjusted inference IA (N) a j ˆδj 95% CI p-value 1 (N = 425) (-0.228, ) (N = 850) (-0.132, ) (N = 1275) (-0.097, ) (N = 1700) (-0.086, ) Design: Conditional Futility (α = 0.1): Bias-adjusted inference IA (N) a j ˆδj 95% CI p-value 1 (N = 425) (-0.319, ) (N = 850) (-0.168, ) (N = 1275) (-0.114, ) (N = 1700) (-0.085, ) Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
14 4.5(a) Conditional power (Sepsis example) Comparing inference at upper (futility) boundary: Design: DSMB2 Bias-adjusted inference IA (N) d j ˆδj 95% CI p-value 1 (N = 425) ( 0.003, 0.141) (N = 850) (-0.060, 0.044) (N = 1275) (-0.079, 0.010) (N = 1700) (-0.086, ) Design: Conditional Futility (α = 0.1): Bias-adjusted inference IA (N) d j ˆδj 95% CI p-value 1 (N = 425) ( 0.096, 0.234) (N = 850) (-0.022, 0.083) (N = 1275) (-0.060, 0.028) (N = 1700) (-0.085, ) Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18
15 4.5(a) Conditional power (Summary) When compared with an O Brien-Fleming design, the conditional power family has the following characteristics: Nearly identical power Much lower stopping probability at early interim analyses Much larger ASN (loss of efficiency) Extreme conservatism in making any early decision Resulting questions: Is it ethical to continue in the presence of overwhelming evidence of harm (or benefit)? Does conditional power obfuscate the essential clinical/scientific issues in deciding whether to terminate a trial? 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 15
16 4.5(a) Conditional power (Summary) Note: There are fixes for the problems with conditional power: Calculate conditional power under a different value of δ; e.g.,: Calculate P δ=δ+ /2(ˆδ J < G ˆδ j = d j) instead of P δ=0 (ˆδ J < G ˆδ j = d j). Calculate P δ=δ+ /2(ˆδ J > G ˆδ j = a j) instead of P δ=δ+ (ˆδ J > G ˆδ j = a j). Calculate conditional power under the MLE ˆδj : Calculate P δ=ˆδj (ˆδ J < G ˆδ j = d j) instead of P δ=0 (ˆδ J < G ˆδ j = d j). Calculate P δ=ˆδj (ˆδ J > G ˆδ j = a j) instead of P δ=δ+ (ˆδ J > G ˆδ j = a j). (Consider predictive power.) 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 16
17 4.5(b) Predictive power Conditional power relied on a specific choice for δ: Efficacy: Pδ=0 (ˆδ J < G ˆδ j = d j ). Futility: P δ=δ+ (ˆδ J > G ˆδ j = a j ). Predictive power integrates over a posterior distribution for δ: Let λ0 (δ) denote a prior distribution for δ Let λ(δ ˆδ j ) denote the posterior distribution of δ at the jth interim analysis. Predictive probability: P (ˆδ J > G ˆδ j ) = P δ=u (ˆδ J > G ˆδ j )λ(u ˆδ j )du u Decision criteria can be defined based on the magnitude of the predictive probability. 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 17
18 4.5 Concluding remarks There are foundational issues with both conditional and predictive power. Neither frequentist nor Bayesian foundations construct inference around the probability of changing our mind (see paper). Underlying principles illustrated with this discussion of stochastic curtailment: All designs can be expressed as conditions on the observed estimate. Always consider statistical inference on the boundary when evaluating stopping criteria. 4. Trial Monitoring 4.5 Stochastic Curtailment 3 April / 18 18
Bios 6649: Clinical Trials - Statistical Design and Monitoring
Bios 6649: Clinical Trials - Statistical Design and Monitoring Spring Semester 2015 John M. Kittelson Department of Biostatistics & Informatics Colorado School of Public Health University of Colorado Denver
More informationSequential Monitoring of Clinical Trials Session 4 - Bayesian Evaluation of Group Sequential Designs
Sequential Monitoring of Clinical Trials Session 4 - Bayesian Evaluation of Group Sequential Designs Presented August 8-10, 2012 Daniel L. Gillen Department of Statistics University of California, Irvine
More informationOptimising Group Sequential Designs. Decision Theory, Dynamic Programming. and Optimal Stopping
: Decision Theory, Dynamic Programming and Optimal Stopping Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj InSPiRe Conference on Methodology
More informationInterim Monitoring of Clinical Trials: Decision Theory, Dynamic Programming. and Optimal Stopping
Interim Monitoring of Clinical Trials: Decision Theory, Dynamic Programming and Optimal Stopping Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj
More informationPubh 8482: Sequential Analysis
Pubh 8482: Sequential Analysis Joseph S. Koopmeiners Division of Biostatistics University of Minnesota Week 8 P-values When reporting results, we usually report p-values in place of reporting whether or
More informationGroup Sequential Designs: Theory, Computation and Optimisation
Group Sequential Designs: Theory, Computation and Optimisation Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj 8th International Conference
More informationBios 6648: Design & conduct of clinical research
Bis 6648: Design & cnduct f clinical research Sectin 3 - Essential principle 3.1 Masking (blinding) 3.2 Treatment allcatin (randmizatin) 3.3 Study quality cntrl : Interim decisin and grup sequential :
More informationPubh 8482: Sequential Analysis
Pubh 8482: Sequential Analysis Joseph S. Koopmeiners Division of Biostatistics University of Minnesota Week 7 Course Summary To this point, we have discussed group sequential testing focusing on Maintaining
More informationPubh 8482: Sequential Analysis
Pubh 8482: Sequential Analysis Joseph S. Koopmeiners Division of Biostatistics University of Minnesota Week 10 Class Summary Last time... We began our discussion of adaptive clinical trials Specifically,
More informationAn Adaptive Futility Monitoring Method with Time-Varying Conditional Power Boundary
An Adaptive Futility Monitoring Method with Time-Varying Conditional Power Boundary Ying Zhang and William R. Clarke Department of Biostatistics, University of Iowa 200 Hawkins Dr. C-22 GH, Iowa City,
More informationBios 6649: Clinical Trials - Statistical Design and Monitoring
Bios 6649: Clinical Trials - Statistical Design and Monitoring Spring Semester 2015 John M. Kittelson Department of Biostatistics & Informatics Colorado School of Public Health University of Colorado Denver
More informationTesting a secondary endpoint after a group sequential test. Chris Jennison. 9th Annual Adaptive Designs in Clinical Trials
Testing a secondary endpoint after a group sequential test Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj 9th Annual Adaptive Designs in
More informationThe Design of Group Sequential Clinical Trials that Test Multiple Endpoints
The Design of Group Sequential Clinical Trials that Test Multiple Endpoints Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj Bruce Turnbull
More informationEstimation in Flexible Adaptive Designs
Estimation in Flexible Adaptive Designs Werner Brannath Section of Medical Statistics Core Unit for Medical Statistics and Informatics Medical University of Vienna BBS and EFSPI Scientific Seminar on Adaptive
More informationStatistical Aspects of Futility Analyses. Kevin J Carroll. nd 2013
Statistical Aspects of Futility Analyses Kevin J Carroll March Spring 222013 nd 2013 1 Contents Introduction The Problem in Statistical Terms Defining Futility Three Common Futility Rules The Maths An
More informationBios 6649: Clinical Trials - Statistical Design and Monitoring
Bios 6649: Clinical Trials - Statistical Design and Monitoring Spring Semester 2015 John M. Kittelson Department of Biostatistics & nformatics Colorado School of Public Health University of Colorado Denver
More informationGroup Sequential Tests for Delayed Responses. Christopher Jennison. Lisa Hampson. Workshop on Special Topics on Sequential Methodology
Group Sequential Tests for Delayed Responses Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj Lisa Hampson Department of Mathematics and Statistics,
More informationOverrunning in Clinical Trials: a Methodological Review
Overrunning in Clinical Trials: a Methodological Review Dario Gregori Unit of Biostatistics, Epidemiology and Public Health Department of Cardiac, Thoracic and Vascular Sciences dario.gregori@unipd.it
More informationTwo-Phase, Three-Stage Adaptive Designs in Clinical Trials
Japanese Journal of Biometrics Vol. 35, No. 2, 69 93 (2014) Preliminary Report Two-Phase, Three-Stage Adaptive Designs in Clinical Trials Hiroyuki Uesaka 1, Toshihiko Morikawa 2 and Akiko Kada 3 1 The
More informationThe Design of a Survival Study
The Design of a Survival Study The design of survival studies are usually based on the logrank test, and sometimes assumes the exponential distribution. As in standard designs, the power depends on The
More informationSAMPLE SIZE RE-ESTIMATION FOR ADAPTIVE SEQUENTIAL DESIGN IN CLINICAL TRIALS
Journal of Biopharmaceutical Statistics, 18: 1184 1196, 2008 Copyright Taylor & Francis Group, LLC ISSN: 1054-3406 print/1520-5711 online DOI: 10.1080/10543400802369053 SAMPLE SIZE RE-ESTIMATION FOR ADAPTIVE
More informationGroup Sequential Tests for Delayed Responses
Group Sequential Tests for Delayed Responses Lisa Hampson Department of Mathematics and Statistics, Lancaster University, UK Chris Jennison Department of Mathematical Sciences, University of Bath, UK Read
More informationTopic 12 Overview of Estimation
Topic 12 Overview of Estimation Classical Statistics 1 / 9 Outline Introduction Parameter Estimation Classical Statistics Densities and Likelihoods 2 / 9 Introduction In the simplest possible terms, the
More informationCOS513 LECTURE 8 STATISTICAL CONCEPTS
COS513 LECTURE 8 STATISTICAL CONCEPTS NIKOLAI SLAVOV AND ANKUR PARIKH 1. MAKING MEANINGFUL STATEMENTS FROM JOINT PROBABILITY DISTRIBUTIONS. A graphical model (GM) represents a family of probability distributions
More informationBayesian inference for multivariate extreme value distributions
Bayesian inference for multivariate extreme value distributions Sebastian Engelke Clément Dombry, Marco Oesting Toronto, Fields Institute, May 4th, 2016 Main motivation For a parametric model Z F θ of
More informationType I error rate control in adaptive designs for confirmatory clinical trials with treatment selection at interim
Type I error rate control in adaptive designs for confirmatory clinical trials with treatment selection at interim Frank Bretz Statistical Methodology, Novartis Joint work with Martin Posch (Medical University
More informationCHL 5225H Advanced Statistical Methods for Clinical Trials: Multiplicity
CHL 5225H Advanced Statistical Methods for Clinical Trials: Multiplicity Prof. Kevin E. Thorpe Dept. of Public Health Sciences University of Toronto Objectives 1. Be able to distinguish among the various
More informationMonitoring clinical trial outcomes with delayed response: incorporating pipeline data in group sequential designs. Christopher Jennison
Monitoring clinical trial outcomes with delayed response: incorporating pipeline data in group sequential designs Christopher Jennison Department of Mathematical Sciences, University of Bath http://people.bath.ac.uk/mascj
More informationChapter 8 - Statistical intervals for a single sample
Chapter 8 - Statistical intervals for a single sample 8-1 Introduction In statistics, no quantity estimated from data is known for certain. All estimated quantities have probability distributions of their
More informationOptimal group sequential designs for simultaneous testing of superiority and non-inferiority
Optimal group sequential designs for simultaneous testing of superiority and non-inferiority Fredrik Öhrn AstraZeneca R & D Mölndal, SE-431 83 Mölndal, Sweden and Christopher Jennison Department of Mathematical
More informationBiometrika Trust. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika.
Biometrika Trust Discrete Sequential Boundaries for Clinical Trials Author(s): K. K. Gordon Lan and David L. DeMets Reviewed work(s): Source: Biometrika, Vol. 70, No. 3 (Dec., 1983), pp. 659-663 Published
More informationc Copyright 2014 Navneet R. Hakhu
c Copyright 04 Navneet R. Hakhu Unconditional Exact Tests for Binomial Proportions in the Group Sequential Setting Navneet R. Hakhu A thesis submitted in partial fulfillment of the requirements for the
More informationStatistical considerations for a trial of Ebola virus disease therapeutics
Design Statistical considerations for a trial of Ebola virus disease therapeutics CLINICAL TRIALS Clinical Trials 216, Vol. 13(1) 39 48 Ó The Author(s) 216 Reprints and permissions: sagepub.co.u/journalspermissions.nav
More informationUse of frequentist and Bayesian approaches for extrapolating from adult efficacy data to design and interpret confirmatory trials in children
Use of frequentist and Bayesian approaches for extrapolating from adult efficacy data to design and interpret confirmatory trials in children Lisa Hampson, Franz Koenig and Martin Posch Department of Mathematics
More informationComparing Adaptive Designs and the. Classical Group Sequential Approach. to Clinical Trial Design
Comparing Adaptive Designs and the Classical Group Sequential Approach to Clinical Trial Design Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj
More informationMultiple Testing in Group Sequential Clinical Trials
Multiple Testing in Group Sequential Clinical Trials Tian Zhao Supervisor: Michael Baron Department of Mathematical Sciences University of Texas at Dallas txz122@utdallas.edu 7/2/213 1 Sequential statistics
More informationCalculation of Efficacy and Futiltiy Boundaries using GrpSeqBnds (Version 2.3)
Calculation of Efficacy and Futiltiy Boundaries using GrpSeqBnds (Version 2.3) Grant Izmirlian March 26, 2018 1 Introduction The function GrpSeqBnds computes efficacy and futility boundaries given the
More informationPubh 8482: Sequential Analysis
Pubh 8482: Sequential Analysis Joseph S. Koopmeiners Division of Biostatistics University of Minnesota Week 12 Review So far... We have discussed the role of phase III clinical trials in drug development
More informationQuantitative Understanding in Biology 1.7 Bayesian Methods
Quantitative Understanding in Biology 1.7 Bayesian Methods Jason Banfelder October 25th, 2018 1 Introduction So far, most of the methods we ve looked at fall under the heading of classical, or frequentist
More informationFrequentist-Bayesian Model Comparisons: A Simple Example
Frequentist-Bayesian Model Comparisons: A Simple Example Consider data that consist of a signal y with additive noise: Data vector (N elements): D = y + n The additive noise n has zero mean and diagonal
More information6.4 Type I and Type II Errors
6.4 Type I and Type II Errors Ulrich Hoensch Friday, March 22, 2013 Null and Alternative Hypothesis Neyman-Pearson Approach to Statistical Inference: A statistical test (also known as a hypothesis test)
More informationPart III. A Decision-Theoretic Approach and Bayesian testing
Part III A Decision-Theoretic Approach and Bayesian testing 1 Chapter 10 Bayesian Inference as a Decision Problem The decision-theoretic framework starts with the following situation. We would like to
More informationPower assessment in group sequential design with multiple biomarker subgroups for multiplicity problem
Power assessment in group sequential design with multiple biomarker subgroups for multiplicity problem Lei Yang, Ph.D. Statistical Scientist, Roche (China) Holding Ltd. Aug 30 th 2018, Shanghai Jiao Tong
More informationThe SEQDESIGN Procedure
SAS/STAT 9.2 User s Guide, Second Edition The SEQDESIGN Procedure (Book Excerpt) This document is an individual chapter from the SAS/STAT 9.2 User s Guide, Second Edition. The correct bibliographic citation
More informationBayesian Inference. STA 121: Regression Analysis Artin Armagan
Bayesian Inference STA 121: Regression Analysis Artin Armagan Bayes Rule...s! Reverend Thomas Bayes Posterior Prior p(θ y) = p(y θ)p(θ)/p(y) Likelihood - Sampling Distribution Normalizing Constant: p(y
More informationConstrained Boundary Monitoring for Group Sequential Clinical Trials
UW Biostatistics Working Paper Series 4-25-2003 Constrained Boundary Monitoring for Group Sequential Clinical Trials Bart E. Burington University of Washington Scott S. Emerson University of Washington,
More informationComparison of Different Methods of Sample Size Re-estimation for Therapeutic Equivalence (TE) Studies Protecting the Overall Type 1 Error
Comparison of Different Methods of Sample Size Re-estimation for Therapeutic Equivalence (TE) Studies Protecting the Overall Type 1 Error by Diane Potvin Outline 1. Therapeutic Equivalence Designs 2. Objectives
More informationGroup-Sequential Tests for One Proportion in a Fleming Design
Chapter 126 Group-Sequential Tests for One Proportion in a Fleming Design Introduction This procedure computes power and sample size for the single-arm group-sequential (multiple-stage) designs of Fleming
More informationLikelihood and Fairness in Multidimensional Item Response Theory
Likelihood and Fairness in Multidimensional Item Response Theory or What I Thought About On My Holidays Giles Hooker and Matthew Finkelman Cornell University, February 27, 2008 Item Response Theory Educational
More informationAdaptive designs beyond p-value combination methods. Ekkehard Glimm, Novartis Pharma EAST user group meeting Basel, 31 May 2013
Adaptive designs beyond p-value combination methods Ekkehard Glimm, Novartis Pharma EAST user group meeting Basel, 31 May 2013 Outline Introduction Combination-p-value method and conditional error function
More informationModule 22: Bayesian Methods Lecture 9 A: Default prior selection
Module 22: Bayesian Methods Lecture 9 A: Default prior selection Peter Hoff Departments of Statistics and Biostatistics University of Washington Outline Jeffreys prior Unit information priors Empirical
More informationTheory of Maximum Likelihood Estimation. Konstantin Kashin
Gov 2001 Section 5: Theory of Maximum Likelihood Estimation Konstantin Kashin February 28, 2013 Outline Introduction Likelihood Examples of MLE Variance of MLE Asymptotic Properties What is Statistical
More informationHybrid Bayesian-frequentist approaches for small sample trial design: examples and discussion on concepts.
Hybrid Bayesian-frequentist approaches for small sample trial design: examples and discussion on concepts. Stavros Nikolakopoulos Kit Roes UMC Utrecht Outline Comfortable or not with hybrid Bayesian-frequentist
More informationSTATS 200: Introduction to Statistical Inference. Lecture 29: Course review
STATS 200: Introduction to Statistical Inference Lecture 29: Course review Course review We started in Lecture 1 with a fundamental assumption: Data is a realization of a random process. The goal throughout
More informationInterval estimation. October 3, Basic ideas CLT and CI CI for a population mean CI for a population proportion CI for a Normal mean
Interval estimation October 3, 2018 STAT 151 Class 7 Slide 1 Pandemic data Treatment outcome, X, from n = 100 patients in a pandemic: 1 = recovered and 0 = not recovered 1 1 1 0 0 0 1 1 1 0 0 1 0 1 0 0
More informationTime Series and Dynamic Models
Time Series and Dynamic Models Section 1 Intro to Bayesian Inference Carlos M. Carvalho The University of Texas at Austin 1 Outline 1 1. Foundations of Bayesian Statistics 2. Bayesian Estimation 3. The
More informationClinical Trials. Olli Saarela. September 18, Dalla Lana School of Public Health University of Toronto.
Introduction to Dalla Lana School of Public Health University of Toronto olli.saarela@utoronto.ca September 18, 2014 38-1 : a review 38-2 Evidence Ideal: to advance the knowledge-base of clinical medicine,
More informationAn extrapolation framework to specify requirements for drug development in children
An framework to specify requirements for drug development in children Martin Posch joint work with Gerald Hlavin Franz König Christoph Male Peter Bauer Medical University of Vienna Clinical Trials in Small
More informationStatistics: Learning models from data
DS-GA 1002 Lecture notes 5 October 19, 2015 Statistics: Learning models from data Learning models from data that are assumed to be generated probabilistically from a certain unknown distribution is a crucial
More informationHypothesis Test. The opposite of the null hypothesis, called an alternative hypothesis, becomes
Neyman-Pearson paradigm. Suppose that a researcher is interested in whether the new drug works. The process of determining whether the outcome of the experiment points to yes or no is called hypothesis
More informationMS&E 226: Small Data
MS&E 226: Small Data Lecture 12: Frequentist properties of estimators (v4) Ramesh Johari ramesh.johari@stanford.edu 1 / 39 Frequentist inference 2 / 39 Thinking like a frequentist Suppose that for some
More informationDART_LAB Tutorial Section 5: Adaptive Inflation
DART_LAB Tutorial Section 5: Adaptive Inflation UCAR 14 The National Center for Atmospheric Research is sponsored by the National Science Foundation. Any opinions, findings and conclusions or recommendations
More informationTwo-stage Adaptive Randomization for Delayed Response in Clinical Trials
Two-stage Adaptive Randomization for Delayed Response in Clinical Trials Guosheng Yin Department of Statistics and Actuarial Science The University of Hong Kong Joint work with J. Xu PSI and RSS Journal
More informationAdaptive Designs: Why, How and When?
Adaptive Designs: Why, How and When? Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj ISBS Conference Shanghai, July 2008 1 Adaptive designs:
More informationDetermination of sample size for two stage sequential designs in bioequivalence studies under 2x2 crossover design
Science Journal of Clinical Medicine 2014; 3(5): 82-90 Published online September 30, 2014 (http://www.sciencepublishinggroup.com/j/sjcm) doi: 10.11648/j.sjcm.20140305.12 ISSN: 2327-2724 (Print); ISSN:
More informationInverse Sampling for McNemar s Test
International Journal of Statistics and Probability; Vol. 6, No. 1; January 27 ISSN 1927-7032 E-ISSN 1927-7040 Published by Canadian Center of Science and Education Inverse Sampling for McNemar s Test
More informationLECTURE 5 NOTES. n t. t Γ(a)Γ(b) pt+a 1 (1 p) n t+b 1. The marginal density of t is. Γ(t + a)γ(n t + b) Γ(n + a + b)
LECTURE 5 NOTES 1. Bayesian point estimators. In the conventional (frequentist) approach to statistical inference, the parameter θ Θ is considered a fixed quantity. In the Bayesian approach, it is considered
More informationSparse Linear Models (10/7/13)
STA56: Probabilistic machine learning Sparse Linear Models (0/7/) Lecturer: Barbara Engelhardt Scribes: Jiaji Huang, Xin Jiang, Albert Oh Sparsity Sparsity has been a hot topic in statistics and machine
More informationParadoxical Results in Multidimensional Item Response Theory
UNC, December 6, 2010 Paradoxical Results in Multidimensional Item Response Theory Giles Hooker and Matthew Finkelman UNC, December 6, 2010 1 / 49 Item Response Theory Educational Testing Traditional model
More informationMonitoring clinical trial outcomes with delayed response: Incorporating pipeline data in group sequential and adaptive designs. Christopher Jennison
Monitoring clinical trial outcomes with delayed response: Incorporating pipeline data in group sequential and adaptive designs Christopher Jennison Department of Mathematical Sciences, University of Bath,
More informationEffect of investigator bias on the significance level of the Wilcoxon rank-sum test
Biostatistics 000, 1, 1,pp. 107 111 Printed in Great Britain Effect of investigator bias on the significance level of the Wilcoxon rank-sum test PAUL DELUCCA Biometrician, Merck & Co., Inc., 1 Walnut Grove
More informationFrequentist Statistics and Hypothesis Testing Spring
Frequentist Statistics and Hypothesis Testing 18.05 Spring 2018 http://xkcd.com/539/ Agenda Introduction to the frequentist way of life. What is a statistic? NHST ingredients; rejection regions Simple
More informationINTERIM MONITORING AND CONDITIONAL POWER IN CLINICAL TRIALS. by Yanjie Ren BS, Southeast University, Nanjing, China, 2013
INTERIM MONITORING AND CONDITIONAL POWER IN CLINICAL TRIALS by Yanjie Ren BS, Southeast University, Nanjing, China, 2013 Submitted to the Graduate Faculty of the Graduate School of Public Health in partial
More informationData Mining Chapter 4: Data Analysis and Uncertainty Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University
Data Mining Chapter 4: Data Analysis and Uncertainty Fall 2011 Ming Li Department of Computer Science and Technology Nanjing University Why uncertainty? Why should data mining care about uncertainty? We
More informationarxiv: v2 [stat.me] 25 Feb 2011
arxiv:112.588v2 [stat.me] 25 Feb 211 Estimation of the relative risk following group sequential procedure based upon the weighted log-rank statistic Grant Izmirlian National Cancer Institute; Executive
More informationPlay-the-winner rule in clinical trials: Models for adaptative designs and Bayesian methods
Play-the-winner rule in clinical trials: Models for adaptative designs and Bayesian methods Bruno Lecoutre and Khadija Elqasyr ERIS, Laboratoire de Mathématiques Raphael Salem, UMR 6085, C.N.R.S. et Université
More informationAdaptive Trial Designs
Adaptive Trial Designs Wenjing Zheng, Ph.D. Methods Core Seminar Center for AIDS Prevention Studies University of California, San Francisco Nov. 17 th, 2015 Trial Design! Ethical:!eg.! Safety!! Efficacy!
More informationMathematical Statistics
Mathematical Statistics MAS 713 Chapter 8 Previous lecture: 1 Bayesian Inference 2 Decision theory 3 Bayesian Vs. Frequentist 4 Loss functions 5 Conjugate priors Any questions? Mathematical Statistics
More informationBIOS 312: Precision of Statistical Inference
and Power/Sample Size and Standard Errors BIOS 312: of Statistical Inference Chris Slaughter Department of Biostatistics, Vanderbilt University School of Medicine January 3, 2013 Outline Overview and Power/Sample
More informationStatistics - Lecture One. Outline. Charlotte Wickham 1. Basic ideas about estimation
Statistics - Lecture One Charlotte Wickham wickham@stat.berkeley.edu http://www.stat.berkeley.edu/~wickham/ Outline 1. Basic ideas about estimation 2. Method of Moments 3. Maximum Likelihood 4. Confidence
More informationF & B Approaches to a simple model
A6523 Signal Modeling, Statistical Inference and Data Mining in Astrophysics Spring 215 http://www.astro.cornell.edu/~cordes/a6523 Lecture 11 Applications: Model comparison Challenges in large-scale surveys
More informationEarly Stopping in Randomized Clinical Trials
T. van Hees Early Stopping in Randomized Clinical Trials Bachelor Thesis Thesis Supervisor: prof. dr. R. D. Gill 29 August 2014 Mathematical Institute, Leiden University Contents 1 Introduction 1 1.1
More informationPubh 8482: Sequential Analysis
Pubh 8482: Sequential Analysis Joseph S. Koopmeiners Division of Biostatistics University of Minnesota Week 5 Course Summary So far, we have discussed Group sequential procedures for two-sided tests Group
More informationPreliminary Statistics Lecture 2: Probability Theory (Outline) prelimsoas.webs.com
1 School of Oriental and African Studies September 2015 Department of Economics Preliminary Statistics Lecture 2: Probability Theory (Outline) prelimsoas.webs.com Gujarati D. Basic Econometrics, Appendix
More informationSAS/STAT 15.1 User s Guide The SEQDESIGN Procedure
SAS/STAT 15.1 User s Guide The SEQDESIGN Procedure This document is an individual chapter from SAS/STAT 15.1 User s Guide. The correct bibliographic citation for this manual is as follows: SAS Institute
More informationHigh-throughput Testing
High-throughput Testing Noah Simon and Richard Simon July 2016 1 / 29 Testing vs Prediction On each of n patients measure y i - single binary outcome (eg. progression after a year, PCR) x i - p-vector
More informationExam 2 Practice Questions, 18.05, Spring 2014
Exam 2 Practice Questions, 18.05, Spring 2014 Note: This is a set of practice problems for exam 2. The actual exam will be much shorter. Within each section we ve arranged the problems roughly in order
More informationOn the Inefficiency of the Adaptive Design for Monitoring Clinical Trials
On the Inefficiency of the Adaptive Design for Monitoring Clinical Trials Anastasios A. Tsiatis and Cyrus Mehta http://www.stat.ncsu.edu/ tsiatis/ Inefficiency of Adaptive Designs 1 OUTLINE OF TOPICS Hypothesis
More informationSTAT 499/962 Topics in Statistics Bayesian Inference and Decision Theory Jan 2018, Handout 01
STAT 499/962 Topics in Statistics Bayesian Inference and Decision Theory Jan 2018, Handout 01 Nasser Sadeghkhani a.sadeghkhani@queensu.ca There are two main schools to statistical inference: 1-frequentist
More informationPubH 7470: STATISTICS FOR TRANSLATIONAL & CLINICAL RESEARCH
PubH 7470: STATISTICS FOR TRANSLATIONAL & CLINICAL RESEARCH The First Step: SAMPLE SIZE DETERMINATION THE ULTIMATE GOAL The most important, ultimate step of any of clinical research is to do draw inferences;
More informationFoundations of Statistical Inference
Foundations of Statistical Inference Julien Berestycki Department of Statistics University of Oxford MT 2016 Julien Berestycki (University of Oxford) SB2a MT 2016 1 / 20 Lecture 6 : Bayesian Inference
More informationDefinition 3.1 A statistical hypothesis is a statement about the unknown values of the parameters of the population distribution.
Hypothesis Testing Definition 3.1 A statistical hypothesis is a statement about the unknown values of the parameters of the population distribution. Suppose the family of population distributions is indexed
More informationHypothesis Testing. Part I. James J. Heckman University of Chicago. Econ 312 This draft, April 20, 2006
Hypothesis Testing Part I James J. Heckman University of Chicago Econ 312 This draft, April 20, 2006 1 1 A Brief Review of Hypothesis Testing and Its Uses values and pure significance tests (R.A. Fisher)
More informationarxiv: v1 [stat.me] 5 Nov 2017
Biometrics 99, 1 24 December 2010 DOI: 10.1111/j.1541-0420.2005.00454.x Likelihood Based Study Designs for Time-to-Event Endpoints arxiv:1711.01527v1 [stat.me] 5 Nov 2017 Jeffrey D. Blume Department of
More information(1) Introduction to Bayesian statistics
Spring, 2018 A motivating example Student 1 will write down a number and then flip a coin If the flip is heads, they will honestly tell student 2 if the number is even or odd If the flip is tails, they
More informationTechnical Manual. 1 Introduction. 1.1 Version. 1.2 Developer
Technical Manual 1 Introduction 1 2 TraditionalSampleSize module: Analytical calculations in fixed-sample trials 3 3 TraditionalSimulations module: Simulation-based calculations in fixed-sample trials
More informationInterval Estimation. Chapter 9
Chapter 9 Interval Estimation 9.1 Introduction Definition 9.1.1 An interval estimate of a real-values parameter θ is any pair of functions, L(x 1,..., x n ) and U(x 1,..., x n ), of a sample that satisfy
More informationSample size re-estimation in clinical trials. Dealing with those unknowns. Chris Jennison. University of Kyoto, January 2018
Sample Size Re-estimation in Clinical Trials: Dealing with those unknowns Christopher Jennison Department of Mathematical Sciences, University of Bath, UK http://people.bath.ac.uk/mascj University of Kyoto,
More informationGrundlagen der Künstlichen Intelligenz
Grundlagen der Künstlichen Intelligenz Uncertainty & Probabilities & Bandits Daniel Hennes 16.11.2017 (WS 2017/18) University Stuttgart - IPVS - Machine Learning & Robotics 1 Today Uncertainty Probability
More information