introduction
play

Introduction Outline how to investigate heterogeneity Give - PDF document

Jan 31, 2023 •436 likes •660 views

4/13/2012 Interpreting Heterogeneity in Meta Analyses of Clinical Trials Steven A. Julious University of Sheffield Steven A. Julious 1 Introduction Outline how to investigate heterogeneity Give statistical test Highlight graphical

  1. 4/13/2012 Interpreting Heterogeneity in Meta Analyses of Clinical Trials Steven A. Julious University of Sheffield Steven A. Julious 1 Introduction • Outline how to investigate heterogeneity • Give statistical test • Highlight graphical methods • Use worked examples throughout Steven A. Julious 2 1

  2. 4/13/2012 Assessing Statistical Assumptions Steven A. Julious 3 Statistical Tests • The test of homogeneity of the treatment effect across studies is based on the statistic k � 2 ( ) ˆ ˆ Q = θ − θ w i i = i 1 Steven A. Julious 4 2

  3. 4/13/2012 The Residuals from a Meta Analysis • The weighted residuals from fitting a fixed-effects meta-analysis are given by ˆ ˆ = ( θ − θ ) q w i i i • Under the standard fixed-effects meta-analysis the standardised weighted residuals are ˆ ˆ θ − θ ( ) w i i ′ = q i k � − 1 w w i i i = 1 5 Steven A. Julious 5 Assessing the Residuals • The standardised residuals should follow a standard Normal distribution • Under the standard random-effects meta-analysis the weighted residuals and standardised weighted residuals would be ˆ w θ calculated from same equations by replacing and with i * w ˆ * θ and i Steven A. Julious 6 3

  4. 4/13/2012 Assessing the Residuals q ′ • A Normal probability plot of the q or may be used to i i check the distributional assumptions of the meta-analysis model Steven A. Julious Steven A. Julious 7 7 Multi-Centre Trials v Meta Analysis • A multi-centre trial may be analysed in the same way as a meta-analysis • That is by treating centres as studies. • Multi-centre trials can be analysed using an overall model which includes the terms centre and treatment. • Homogeneity of treatment effects across centres can be undertaken by fitting a treatment by centre interaction to obtain an estimate of treatment effect with its variance for each centre. • The standardised residual can be calculated replacing the w’s with the inverse of the variance. Steven A. Julious 8 8 4

  5. 4/13/2012 Worked Example Paroxetine in Adults Steven A. Julious 9 Meta analysis of 23 Paroxetine Trials Steven A. Julious 10 5

  6. 4/13/2012 Paroxetine Trials • The treatment effect is measured by the difference in mean HAMD between Paroxetine and placebo. • There seems to be some evidence of heterogeneity in treatment effect though most of the heterogeneity seems to be in the smaller trials • The fixed effect meta-analysis gave an overall mean difference of 2.91 with a 95% confidence interval of (2.66 to 3.17). • The test of homogeneity gives a P-value of <0.001 (chi- squared of 170.23 on 22 degrees of freedom). • The overall mean difference from the random effects meta- analysis is 3.36 with 95% confidence interval of (2.59 to 4.12) Steven A. Julious 11 Steven A. Julious 11 Fixed Effects Steven A. Julious 12 6

  7. 4/13/2012 q ′ Histogram of i 13 q ′ Normality Probability Plot for i Estimating the Mean and Variance from the Data 14 7

  8. 4/13/2012 q ′ Normal Probability Plot for Setting i the Mean and Variance to be 0 and 1 Respectively 15 Assessment of Homogeneity of Treatment Effects with Normality Assumption of Fixed Effects Meta-analysis Normal probability plot estimating the mean and variance from the data Histogram Normal probability plot setting the mean and variance to be 0 and 1 respectively 16 8

  9. 4/13/2012 Random Effects Steven A. Julious 17 q ′ Histogram of i 18 9

  10. 4/13/2012 Normality Probability Plot for q ′ i Estimating the Mean and Variance from the Data 19 q ′ Normal Probability Plot for setting i the Mean and Variance to be 0 and 1 Respectively Steven A. Julious 20 10

  11. 4/13/2012 Assessment of Homogeneity of Treatment Rffects with Normality Assumption of Random Effects meta-Analysis Normal probability plot estimating the mean and variance from the data Histogram Normal probability plot setting the mean and variance to be 0 and 1 respectively 21 Summary of Results so Far • There seems to be deviation from the assumptions for a fixed effects meta analysis although the data do seem to take a Normal form • The assumptions seem to hold better for a random effects meta analysis • If a fixed effects analysis was the primary analysis then the results would need to be interpreted with care • The diagnostics so far although easy to produce in most statistics packages but have limitations • Could an assessment of outliers better be made? Steven A. Julious 22 22 11

  12. 4/13/2012 Confidence Bands for the Normal Probability Plots • Confidence bands for the Normal probability plots can be constructed to assist in interpretation • For the Normal probability line confidence bands can be calculate – Using Normal approximation (using the Friendly macro) – Using simulation • For the observed data a confidence band can be calculated – Using bootstrapping Steven A. Julious 23 Simulation Envelopes 1. Simulate a value for the estimated treatment effect from w − 1 study i from a N(0, ), for i = 1,…, k . i q ′ 2. Perform the fixed-effects meta-analysis and calculate the i q ′ 3. Order the from smallest to largest i 4. Repeat 1. to 3. a number of times, for example 1,000 5. For each i, calculate the 2.5 th and 97.5 percentile of the 1,000 values, to give the 95% lower and upper bounds for all points Steven A. Julious 24 24 12

  13. 4/13/2012 Bootstrapping 1. From the observed data pairs ( θ , w − 1 ), i = 1,…,k, take a i i random sample with replacement of size k 2. Perform the fixed-effects meta-analysis and calculate q ′ the i q ′ 3. Order the from smallest to largest i 4. Repeat 1. to 3. a number of times, for example 1,000. 5. For each i, calculate the 2.5 th and 97.5 percentile of the 1,000 values, to give the 95% lower and upper bounds for all points 25 Steven A. Julious 25 Fixed Effects Steven A. Julious 26 13

  14. 4/13/2012 Normal Approximation, Estimating the Expected Values with the Mean and Variance from the Data Steven A. Julious 27 Normal Approximation, Estimating the Expected Values from N(0,1) Steven A. Julious 28 14

  15. 4/13/2012 Simulated Envelopes Steven A. Julious 29 Bootstrap Envelopes Steven A. Julious 30 15

  16. 4/13/2012 Comparison of Plots Normal using data Normal using N(0,1) Simulation using N(0,1) Simulation 31 Random Effects Steven A. Julious 32 16

  17. 4/13/2012 Normal Approximation, Estimating the Expected Values with the Mean and Variance from the Data Steven A. Julious 33 Normal Approximation, Estimating the Expected Values from N(0,1) 34 17

  18. 4/13/2012 Simulated Envelopes An outlying study? 35 Bootstrap Envelopes 36 18

  19. 4/13/2012 Comparison of Plots Normal using N(0,1) Normal using data Bootstrapping Simulation using N(0,1) Steven A. Julious 37 Summary of Results so Far (Again) • The additional analyses confirm the original analysis • The bands are wider at the extremes of the range • For this example bootstrapping has wide bands at one end • Allows for an assessment of outliers Steven A. Julious 38 38 19

  20. 4/13/2012 What if the Treatment Effects Differ Study to Study? • Find explanation – Investigate baseline imbalances – Look at subgroups • Are there any possible explanations? Steven A. Julious 39 Summary of Meta Analysis • Gave overview of how to investigate heterogeneity in a meta analysis • Recommended not to rely on statistical tests to assess heterogeneity • Described graphical approaches to assess heterogeneity Steven A. Julious 40 20

  21. 4/13/2012 Steven A. Julious 41 21

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION

INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION

TRAINING COURSE ON SOCIAL PROTECTION &amp; FORMALIZATION TRINIDAD AND TOBAGO MARCH 15, 2017 INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION INTRODUCTION Design of the NIS Assistance from the

547 views • 23 slides
INTRODUCTION Introduction 2/42 INTRODUCTION Alternations I am giving bread to the

INTRODUCTION Introduction 2/42 INTRODUCTION Alternations I am giving bread to the

Patterns of variation in the expression of case and agreement Andrs Brny Leiden University Centre for Linguistics 9 November 2019, BaSIS Workshop a.barany@hum.leidenuniv.nl INTRODUCTION Introduction 2/42 INTRODUCTION

1.37k views • 42 slides
Introduction Introduction Introduction Introduction Outline Motivation Failures

Introduction Introduction Introduction Introduction Outline Motivation Failures

Introduction Introduction Introduction Introduction Outline Motivation Failures Definition and concepts Process and product properties Principles SE Approaches Motivation Software and the economy The economies of

1.03k views • 49 slides
Introduction Introduction Introduction Nationwide Cause for Concern 1

Introduction Introduction Introduction Nationwide Cause for Concern 1

Introduction Introduction Introduction Nationwide Cause for Concern 1 https://www.cdc.gov/std/stats17/infographic.htm Introduction Epidemiology in Western Colorado CPHE Surveillance Data Report, May 2018 Chlamydia Epidemiology in Western

977 views • 39 slides
DAQ introduction Purpose of this talk : (1) Introduction for those who have not been in every

DAQ introduction Purpose of this talk : (1) Introduction for those who have not been in every

DAQ introduction Purpose of this talk : (1) Introduction for those who have not been in every meeting (2) Some ideas of diagrams for section 7.1 (Introduction) of TP. Giles Barr 25 Jan 2018, Pembroke College On DUNE, the reality is there is a

474 views • 10 slides
INTRODUCTION cf. Schneider, Chapter 1 INTRODUCTION THEY ARE OUT TO GET YOU INTRODUCTION WHAT

INTRODUCTION cf. Schneider, Chapter 1 INTRODUCTION THEY ARE OUT TO GET YOU INTRODUCTION WHAT

ADVANCED COMPUTER SECURITY INTRODUCTION cf. Schneider, Chapter 1 INTRODUCTION THEY ARE OUT TO GET YOU INTRODUCTION WHAT IS SECURITY? A systems security policies describe What the system is supposed to do Store and provide access

479 views • 16 slides
Overview Introduction to SMIL Introduction to W3C and XML Introduction to SMIL

Overview Introduction to SMIL Introduction to W3C and XML Introduction to SMIL

Overview Introduction to SMIL Introduction to W3C and XML Introduction to SMIL Writing a SMIL file Adding Media Objects Martin Halvey Clipping media files January 2008 Timing and Synchronising Layout World Wide

387 views • 14 slides
14 Introduction Introduction Bad guys can put malware into Example: hosts

14 Introduction Introduction Bad guys can put malware into Example: hosts

Introduction Introduction source Encapsulation ISO/OSI reference model message M application segment H t H t M transport network datagram H n H n H t M presentation: allow applications to frame link H l H n H t M interpret

583 views • 4 slides
Previous Lecture Introduction to SMIL 2 Introduction to W3C and XML Introduction to SMIL

Previous Lecture Introduction to SMIL 2 Introduction to W3C and XML Introduction to SMIL

Previous Lecture Introduction to SMIL 2 Introduction to W3C and XML Introduction to SMIL Writing a SMIL file Adding Media Objects Martin Halvey Clipping media files January 2008 Timing and Synchronising Layout

322 views • 8 slides
Lecture 1 Andreas Habegger Introduction Zynq Introduction Zynq Introduction Zynq PS vs. PL

Lecture 1 Andreas Habegger Introduction Zynq Introduction Zynq Introduction Zynq PS vs. PL

Introduction Zynq Lecture 1 Andreas Habegger Introduction Zynq Introduction Zynq Introduction Zynq PS vs. PL Processing System Processor Peripherals Data Buses AXI Bus Conclusion BTE5380 - Embedded Systems Octobre 2014 Andreas Habegger

1.81k views • 30 slides
2018.06 01 SMILE5 Introduction S E 5 02 Alpha Cloud M I L 03 Company Introduction 04

2018.06 01 SMILE5 Introduction S E 5 02 Alpha Cloud M I L 03 Company Introduction 04

2018.06 01 SMILE5 Introduction S E 5 02 Alpha Cloud M I L 03 Company Introduction 04 Project References S E 5 PART.1 SMILE5 Introduction M I L Introduction STORION-SMILE5 Residential Energy Storage System Inverter 5kW Output Input

1.06k views • 25 slides
Introduction to CICS Course introduction Course introduction What is CICS? What is an

Introduction to CICS Course introduction Course introduction What is CICS? What is an

Introduction to CICS Course introduction Course introduction What is CICS? What is an application server? Why use an application server? Course introduction Services provided by CICS How CICS applications are defined Scaling CICS to meet

1.84k views • 146 slides
Network Visualization Introduction Presented by Shahed Introduction Introduction Basic

Network Visualization Introduction Presented by Shahed Introduction Introduction Basic

Network Visualization Introduction Presented by Shahed Introduction Introduction Basic building blocks Node Links (relationship between nodes) Spatial information Network data

584 views • 9 slides
Introduction Introduction (1) Main argument of the paper: universities are not only

Introduction Introduction (1) Main argument of the paper: universities are not only

Le jugement des pairs comme outil de management des universits Peer-review as a management tool Christine Musselin (CSO, Sciences Po et CNRS) Avril 2013, Lirrsistible ascension du capitalisme acadmique Introduction Introduction (1)

590 views • 28 slides
Introduction Introduction to storage and to storage and filesystems filesystems Introduction

Introduction Introduction to storage and to storage and filesystems filesystems Introduction

Moreno Baricevic Gilberto Daz Axel Kohlmeyer Stefano Cozzini ULA ICTP CNR-IOM DEMOCRITOS Merida, VENEZUELA Trieste, ITALY Trieste, ITALY Introduction Introduction to storage and to storage and filesystems filesystems Introduction

1.19k views • 51 slides
JABLOTRON JA-100 introduction November 2011 Introduction Todays goals First introduction of

JABLOTRON JA-100 introduction November 2011 Introduction Todays goals First introduction of

JABLOTRON JA-100 introduction November 2011 Introduction Todays goals First introduction of the brand new JA-100 alarm system Visions Basic architecture System components Setting Help us with final validations You are the FIRST ones

1.69k views • 111 slides
CSE P 527 Computational Biology 3: BLAST, Alignment score significance; PCR and DNA sequencing

CSE P 527 Computational Biology 3: BLAST, Alignment score significance; PCR and DNA sequencing

CSE P 527 Computational Biology 3: BLAST, Alignment score significance; PCR and DNA sequencing 1 Outline BLAST Scoring Weekly Bio Interlude: PCR &amp; Sequencing 2 BLAST: Basic Local Alignment Search Tool Altschul, Gish, Miller, Myers,

706 views • 44 slides
Statistics and Data Analysis Probability Ling-Chieh Kung Department of Information Management

Statistics and Data Analysis Probability Ling-Chieh Kung Department of Information Management

Random variables Expectation and variances Continuous distributions Normal distribution Statistics and Data Analysis Probability Ling-Chieh Kung Department of Information Management National Taiwan University Probability 1 / 41 Ling-Chieh

538 views • 41 slides
Introduction to Data Science: Statistical X i = {0, 1} x 1 , x 2 , x 3 , , x 100 x 1 , x 2 , x

Introduction to Data Science: Statistical X i = {0, 1} x 1 , x 2 , x 3 , , x 100 x 1 , x 2 , x

Why Stats? Why Probability? Why Probability? Variation, randomness and stochasticity Variation, randomness and stochasticity Variation, randomness and stochasticity One nal word Why Probability? Why Probability? Why Probability? Why

1.32k views • 89 slides
Anticipating Visual Representations from Unlabeled Data Carl Vondrick, Hamed Pirsiavash, Antonio

Anticipating Visual Representations from Unlabeled Data Carl Vondrick, Hamed Pirsiavash, Antonio

Anticipating Visual Representations from Unlabeled Data Carl Vondrick, Hamed Pirsiavash, Antonio Torralba Overview Problem Key Insight Methods Experiments Problem: Predict future actions and objects Image from Vondrick

396 views • 27 slides
Calibrating Survey Weights in Stata Jeff Pitblado StataCorp LLC 2018 Nordic and Baltic Stata

Calibrating Survey Weights in Stata Jeff Pitblado StataCorp LLC 2018 Nordic and Baltic Stata

Calibrating Survey Weights in Stata Jeff Pitblado StataCorp LLC 2018 Nordic and Baltic Stata Users Group Meeting Oslo, Norway Outline Motivation Methods Syntax Stata Example Summary Motivation Survey data analysis We collect data from a

575 views • 35 slides
Lecture 14 Covariance Functions 3/08/2018 1 More on Covariance Functions 2 Nugget Covariance

Lecture 14 Covariance Functions 3/08/2018 1 More on Covariance Functions 2 Nugget Covariance

Lecture 14 Covariance Functions 3/08/2018 1 More on Covariance Functions 2 Nugget Covariance 3 ( , ) = 2 1 {=0} where = | | 2 1.00 1 0.75 draw 0 Draw 1 C

563 views • 35 slides
Using to Facilitate Quantitative Reasoning in Science May Lee

Using to Facilitate Quantitative Reasoning in Science May Lee

Using to Facilitate Quantitative Reasoning in Science May Lee Elizabeth Schultheis Melissa Kjelvik Michigan State University Facilitated Discussion NaBonal Numeracy Network Wells Hall A116 11:30 am

446 views • 17 slides
Combining Crowd and AI to scale professional-quality translation Joo Graa CTO The Internet,

Combining Crowd and AI to scale professional-quality translation Joo Graa CTO The Internet,

Combining Crowd and AI to scale professional-quality translation Joo Graa CTO The Internet, 1997 80% English The Internet, 2017 30% English 20% Chinese 8% 6% Spanish 5% Japanese 4% Portuguese 3% German

1.14k views • 99 slides

More recommend