This document outlines the concepts and methods of multiple-treatments meta-analysis (MTM). MTM allows for the simultaneous comparison of multiple interventions for a condition by combining both direct and indirect evidence from randomized controlled trials. Key advantages of MTM include the ability to rank treatments, comprehensively use all available data, and compare interventions not directly compared in trials. The document discusses MTM approaches using frequentist meta-regression and Bayesian statistics.
Title:
A Meta-Analysis of Adventure Therapy Outcomes and Moderators
Abstract:
This presentation reports on a meta-analytic review of 197 studies of adventure therapy participant outcomes (2,908 effect sizes, 206 unique samples). The short-term effect size for adventure therapy was moderate (g = .47) and larger than for alternative (.14) and no treatment (.08) comparison groups. There was little change during the lead-up (.09) and follow-up periods (.03) for adventure therapy, indicating long-term maintenance of the short-term gains. The short-term adventure therapy outcomes were significant for seven out of the eight outcome categories, with the strongest effects for clinical and self-concept measures, and the smallest effects for spirituality/morality. The only significant moderator of outcomes was a positive relationship with participant age.
References:
Bowen, D. J., & Neill, J. T. (2013). A meta-analysis of adventure therapy outcomes and moderators. The Open Psychology Journal, 6, 28-53. doi: 10.2174/1874350120130802001
Bowen, D. J., & Neill, J. T. (2013). A meta-analysis of adventure therapy outcomes and moderators: Pre-post adventure therapy age-based benchmarks for outcome categories. Retrieved from http://www.danielbowen.com.au/meta-analysis
For more information, see: http://www.danielbowen.com.au/meta-analysis
the role of Cochrane collaboration and specifically the menstrual disorder & subfertility group is illustrated . simple explanation how to use cochrane reviews is done.
Title:
A Meta-Analysis of Adventure Therapy Outcomes and Moderators
Abstract:
This presentation reports on a meta-analytic review of 197 studies of adventure therapy participant outcomes (2,908 effect sizes, 206 unique samples). The short-term effect size for adventure therapy was moderate (g = .47) and larger than for alternative (.14) and no treatment (.08) comparison groups. There was little change during the lead-up (.09) and follow-up periods (.03) for adventure therapy, indicating long-term maintenance of the short-term gains. The short-term adventure therapy outcomes were significant for seven out of the eight outcome categories, with the strongest effects for clinical and self-concept measures, and the smallest effects for spirituality/morality. The only significant moderator of outcomes was a positive relationship with participant age.
References:
Bowen, D. J., & Neill, J. T. (2013). A meta-analysis of adventure therapy outcomes and moderators. The Open Psychology Journal, 6, 28-53. doi: 10.2174/1874350120130802001
Bowen, D. J., & Neill, J. T. (2013). A meta-analysis of adventure therapy outcomes and moderators: Pre-post adventure therapy age-based benchmarks for outcome categories. Retrieved from http://www.danielbowen.com.au/meta-analysis
For more information, see: http://www.danielbowen.com.au/meta-analysis
the role of Cochrane collaboration and specifically the menstrual disorder & subfertility group is illustrated . simple explanation how to use cochrane reviews is done.
Avoid overfitting in precision medicine: How to use cross-validation to relia...Nicole Krämer
The identification of patient subgroups who may derive benefit from a treatment is of crucial importance in precision medicine. Many different algorithms have been proposed and studied in the literature.
We illustrate that many of these algorithms overfit in the sense that the treatment benefit for the identified patients is substantially overestimated. Further, we show that with cross-validation, it is possible to obtain more realistic estimates.
This presentation is aimed at presenting the issues associated with subgroup analyses in clinical trials: the different types of subgroup analyses and the statistical issues associated with the conduct of subgroup analyses.
Young Tom Selleck: A Journey Through His Early Years and Rise to Stardomgreendigital
Introduction
When one thinks of Hollywood legends, Tom Selleck is a name that comes to mind. Known for his charming smile, rugged good looks. and the iconic mustache that has become synonymous with his persona. Tom Selleck has had a prolific career spanning decades. But, the journey of young Tom Selleck, from his early years to becoming a household name. is a story filled with determination, talent, and a touch of luck. This article delves into young Tom Selleck's life, background, early struggles. and pivotal moments that led to his rise in Hollywood.
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Early Life and Background
Family Roots and Childhood
Thomas William Selleck was born in Detroit, Michigan, on January 29, 1945. He was the second of four children in a close-knit family. His father, Robert Dean Selleck, was a real estate investor and executive. while his mother, Martha Selleck, was a homemaker. The Selleck family relocated to Sherman Oaks, California. when Tom was a child, setting the stage for his future in the entertainment industry.
Education and Early Interests
Growing up, young Tom Selleck was an active and athletic child. He attended Grant High School in Van Nuys, California. where he excelled in sports, particularly basketball. His tall and athletic build made him a standout player, and he earned a basketball scholarship to the University of Southern California (U.S.C.). While at U.S.C., Selleck studied business administration. but his interests shifted toward acting.
Discovery of Acting Passion
Tom Selleck's journey into acting was serendipitous. During his time at U.S.C., a drama coach encouraged him to try acting. This nudge led him to join the Hills Playhouse, where he began honing his craft. Transitioning from an aspiring athlete to an actor took time. but young Tom Selleck became drawn to the performance world.
Early Career Struggles
Breaking Into the Industry
The path to stardom was a challenging one for young Tom Selleck. Like many aspiring actors, he faced many rejections and struggled to find steady work. A series of minor roles and guest appearances on television shows marked his early career. In 1965, he debuted on the syndicated show "The Dating Game." which gave him some exposure but did not lead to immediate success.
The Commercial Breakthrough
During the late 1960s and early 1970s, Selleck began appearing in television commercials. His rugged good looks and charismatic presence made him a popular brand choice. He starred in advertisements for Pepsi-Cola, Revlon, and Close-Up toothpaste. These commercials provided financial stability and helped him gain visibility in the industry.
Struggling Actor in Hollywood
Despite his success in commercials. breaking into large acting roles remained a challenge for young Tom Selleck. He auditioned and took on small parts in T.V. shows and movies. Some of his early television appearances included roles in popular series like Lancer, The F.B.I., and Bracken's World. But, it would take a
240529_Teleprotection Global Market Report 2024.pdfMadhura TBRC
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growth rate (CAGR) of 26.0%.
From the Editor's Desk: 115th Father's day Celebration - When we see Father's day in Hindu context, Nanda Baba is the most vivid figure which comes to the mind. Nanda Baba who was the foster father of Lord Krishna is known to provide love, care and affection to Lord Krishna and Balarama along with his wife Yashoda; Letter’s to the Editor: Mother's Day - Mother is a precious life for their children. Mother is life breath for her children. Mother's lap is the world happiness whose debt can never be paid.
Meet Dinah Mattingly – Larry Bird’s Partner in Life and Loveget joys
Get an intimate look at Dinah Mattingly’s life alongside NBA icon Larry Bird. From their humble beginnings to their life today, discover the love and partnership that have defined their relationship.
Matt Rife Cancels Shows Due to Health Concerns, Reschedules Tour Dates.pdfAzura Everhart
Matt Rife's comedy tour took an unexpected turn. He had to cancel his Bloomington show due to a last-minute medical emergency. Fans in Chicago will also have to wait a bit longer for their laughs, as his shows there are postponed. Rife apologized and assured fans he'd be back on stage soon.
https://www.theurbancrews.com/celeb/matt-rife-cancels-bloomington-show/
_7 OTT App Builders to Support the Development of Your Video Applications_.pdfMega P
Due to their ability to produce engaging content more quickly, over-the-top (OTT) app builders have made the process of creating video applications more accessible. The invitation to explore these platforms emphasizes how over-the-top (OTT) applications hold the potential to transform digital entertainment.
Experience the thrill of Progressive Puzzle Adventures, like Scavenger Hunt Games and Escape Room Activities combined Solve Treasure Hunt Puzzles online.
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Modern Radio Frequency Access Control Systems: The Key to Efficiency and SafetyAITIX LLC
Today's fast-paced environment worries companies of all sizes about efficiency and security. Businesses are constantly looking for new and better solutions to solve their problems, whether it's data security or facility access. RFID for access control technologies have revolutionized this.
Skeem Saam in June 2024 available on ForumIsaac More
Monday, June 3, 2024 - Episode 241: Sergeant Rathebe nabs a top scammer in Turfloop. Meikie is furious at her uncle's reaction to the truth about Ntswaki.
Tuesday, June 4, 2024 - Episode 242: Babeile uncovers the truth behind Rathebe’s latest actions. Leeto's announcement shocks his employees, and Ntswaki’s ordeal haunts her family.
Wednesday, June 5, 2024 - Episode 243: Rathebe blocks Babeile from investigating further. Melita warns Eunice to stay clear of Mr. Kgomo.
Thursday, June 6, 2024 - Episode 244: Tbose surrenders to the police while an intruder meddles in his affairs. Rathebe's secret mission faces a setback.
Friday, June 7, 2024 - Episode 245: Rathebe’s antics reach Kganyago. Tbose dodges a bullet, but a nightmare looms. Mr. Kgomo accuses Melita of witchcraft.
Monday, June 10, 2024 - Episode 246: Ntswaki struggles on her first day back at school. Babeile is stunned by Rathebe’s romance with Bullet Mabuza.
Tuesday, June 11, 2024 - Episode 247: An unexpected turn halts Rathebe’s investigation. The press discovers Mr. Kgomo’s affair with a young employee.
Wednesday, June 12, 2024 - Episode 248: Rathebe chases a criminal, resorting to gunfire. Turf High is rife with tension and transfer threats.
Thursday, June 13, 2024 - Episode 249: Rathebe traps Kganyago. John warns Toby to stop harassing Ntswaki.
Friday, June 14, 2024 - Episode 250: Babeile is cleared to investigate Rathebe. Melita gains Mr. Kgomo’s trust, and Jacobeth devises a financial solution.
Monday, June 17, 2024 - Episode 251: Rathebe feels the pressure as Babeile closes in. Mr. Kgomo and Eunice clash. Jacobeth risks her safety in pursuit of Kganyago.
Tuesday, June 18, 2024 - Episode 252: Bullet Mabuza retaliates against Jacobeth. Pitsi inadvertently reveals his parents’ plans. Nkosi is shocked by Khwezi’s decision on LJ’s future.
Wednesday, June 19, 2024 - Episode 253: Jacobeth is ensnared in deceit. Evelyn is stressed over Toby’s case, and Letetswe reveals shocking academic results.
Thursday, June 20, 2024 - Episode 254: Elizabeth learns Jacobeth is in Mpumalanga. Kganyago's past is exposed, and Lehasa discovers his son is in KZN.
Friday, June 21, 2024 - Episode 255: Elizabeth confirms Jacobeth’s dubious activities in Mpumalanga. Rathebe lies about her relationship with Bullet, and Jacobeth faces theft accusations.
Monday, June 24, 2024 - Episode 256: Rathebe spies on Kganyago. Lehasa plans to retrieve his son from KZN, fearing what awaits.
Tuesday, June 25, 2024 - Episode 257: MaNtuli fears for Kwaito’s safety in Mpumalanga. Mr. Kgomo and Melita reconcile.
Wednesday, June 26, 2024 - Episode 258: Kganyago makes a bold escape. Elizabeth receives a shocking message from Kwaito. Mrs. Khoza defends her husband against scam accusations.
Thursday, June 27, 2024 - Episode 259: Babeile's skillful arrest changes the game. Tbose and Kwaito face a hostage crisis.
Friday, June 28, 2024 - Episode 260: Two women face the reality of being scammed. Turf is rocked by breaking
Tom Selleck Net Worth: A Comprehensive Analysisgreendigital
Over several decades, Tom Selleck, a name synonymous with charisma. From his iconic role as Thomas Magnum in the television series "Magnum, P.I." to his enduring presence in "Blue Bloods," Selleck has captivated audiences with his versatility and charm. As a result, "Tom Selleck net worth" has become a topic of great interest among fans. and financial enthusiasts alike. This article delves deep into Tom Selleck's wealth, exploring his career, assets, endorsements. and business ventures that contribute to his impressive economic standing.
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Early Life and Career Beginnings
The Foundation of Tom Selleck's Wealth
Born on January 29, 1945, in Detroit, Michigan, Tom Selleck grew up in Sherman Oaks, California. His journey towards building a large net worth began with humble origins. , Selleck pursued a business administration degree at the University of Southern California (USC) on a basketball scholarship. But, his interest shifted towards acting. leading him to study at the Hills Playhouse under Milton Katselas.
Minor roles in television and films marked Selleck's early career. He appeared in commercials and took on small parts in T.V. series such as "The Dating Game" and "Lancer." These initial steps, although modest. laid the groundwork for his future success and the growth of Tom Selleck net worth. Breakthrough with "Magnum, P.I."
The Role that Defined Tom Selleck's Career
Tom Selleck's breakthrough came with the role of Thomas Magnum in the CBS television series "Magnum, P.I." (1980-1988). This role made him a household name and boosted his net worth. The series' popularity resulted in Selleck earning large salaries. leading to financial stability and increased recognition in Hollywood.
"Magnum P.I." garnered high ratings and critical acclaim during its run. Selleck's portrayal of the charming and resourceful private investigator resonated with audiences. making him one of the most beloved television actors of the 1980s. The success of "Magnum P.I." played a pivotal role in shaping Tom Selleck net worth, establishing him as a major star.
Film Career and Diversification
Expanding Tom Selleck's Financial Portfolio
While "Magnum, P.I." was a cornerstone of Selleck's career, he did not limit himself to television. He ventured into films, further enhancing Tom Selleck net worth. His filmography includes notable movies such as "Three Men and a Baby" (1987). which became the highest-grossing film of the year, and its sequel, "Three Men and a Little Lady" (1990). These box office successes contributed to his wealth.
Selleck's versatility allowed him to transition between genres. from comedies like "Mr. Baseball" (1992) to westerns such as "Quigley Down Under" (1990). This diversification showcased his acting range. and provided many income streams, reinforcing Tom Selleck net worth.
Television Resurgence with "Blue Bloods"
Sustaining Wealth through Consistent Success
In 2010, Tom Selleck began starring as Frank Reagan i
Scandal! Teasers June 2024 on etv Forum.co.zaIsaac More
Monday, 3 June 2024
Episode 47
A friend is compelled to expose a manipulative scheme to prevent another from making a grave mistake. In a frantic bid to save Jojo, Phakamile agrees to a meeting that unbeknownst to her, will seal her fate.
Tuesday, 4 June 2024
Episode 48
A mother, with her son's best interests at heart, finds him unready to heed her advice. Motshabi finds herself in an unmanageable situation, sinking fast like in quicksand.
Wednesday, 5 June 2024
Episode 49
A woman fabricates a diabolical lie to cover up an indiscretion. Overwhelmed by guilt, she makes a spontaneous confession that could be devastating to another heart.
Thursday, 6 June 2024
Episode 50
Linda unwittingly discloses damning information. Nhlamulo and Vuvu try to guide their friend towards the right decision.
Friday, 7 June 2024
Episode 51
Jojo's life continues to spiral out of control. Dintle weaves a web of lies to conceal that she is not as successful as everyone believes.
Monday, 10 June 2024
Episode 52
A heated confrontation between lovers leads to a devastating admission of guilt. Dintle's desperation takes a new turn, leaving her with dwindling options.
Tuesday, 11 June 2024
Episode 53
Unable to resort to violence, Taps issues a verbal threat, leaving Mdala unsettled. A sister must explain her life choices to regain her brother's trust.
Wednesday, 12 June 2024
Episode 54
Winnie makes a very troubling discovery. Taps follows through on his threat, leaving a woman reeling. Layla, oblivious to the truth, offers an incentive.
Thursday, 13 June 2024
Episode 55
A nosy relative arrives just in time to thwart a man's fatal decision. Dintle manipulates Khanyi to tug at Mo's heartstrings and get what she wants.
Friday, 14 June 2024
Episode 56
Tlhogi is shocked by Mdala's reaction following the revelation of their indiscretion. Jojo is in disbelief when the punishment for his crime is revealed.
Monday, 17 June 2024
Episode 57
A woman reprimands another to stay in her lane, leading to a damning revelation. A man decides to leave his broken life behind.
Tuesday, 18 June 2024
Episode 58
Nhlamulo learns that due to his actions, his worst fears have come true. Caiphus' extravagant promises to suppliers get him into trouble with Ndu.
Wednesday, 19 June 2024
Episode 59
A woman manages to kill two birds with one stone. Business doom looms over Chillax. A sobering incident makes a woman realize how far she's fallen.
Thursday, 20 June 2024
Episode 60
Taps' offer to help Nhlamulo comes with hidden motives. Caiphus' new ideas for Chillax have MaHilda excited. A blast from the past recognizes Dintle, not for her newfound fame.
Friday, 21 June 2024
Episode 61
Taps is hungry for revenge and finds a rope to hang Mdala with. Chillax's new job opportunity elicits mixed reactions from the public. Roommates' initial meeting starts off on the wrong foot.
Monday, 24 June 2024
Episode 62
Taps seizes new information and recruits someone on the inside. Mary's new job
2. Outline – Part I
• Concept
• Simple indirect comparison
• Advantages of the methods
• MTM using frequentist meta-regression
• Presentation of results
• The notion of Inconsistency
3. Outline – Part II
• Bayesian MTM model
• Comparison of models
4. Evidence Based Medicine
Levels of evidence For Therapy, Prevention, Aetiology and Harm
Randomized Controlled trials (RCTs)
Meta-analysis of RCTs
Two
interventions
Centre for Evidence Based Medicine, University of Oxford
Cohort studies, Case-control studies
• Backbone: meta-analysis
• Rigorous statistical models
• Clinical practice guidelines
– NICE, WHO, The Cochrane Collaboration, HuGENet
5. Fluoxetine: 28€ Venlafaxine:111€ Sertaline: 76 €
“Although Mirtazapine is likely to have a faster onset of
action than Sertraline and Paroxetine no significant
differences were observed...”
“Venlafaxine tends to have a
favorable trend in response rates
compared with duloxetine”
“…statistically significant differences in
terms of efficacy …. between
Fluoxetine and Venlafaxine, but the
clinical meaning of these differences is
uncertain…”
“…meta-analysis
highlighted a trend
in favour of
Sertraline over
other Fluoxetine”
12 new generation antidepressants
19 meta-analyses published in the last two years
13. Indirect comparison
A B C
• We can obtain an indirect estimate for A vs B from
RCTs comparing A vs C and B vs C:
MDAB = MDAC – MDBC
Var(MDAB) = Var(MDAC) + Var(MDBC)
16. Simple exercise: prevented mean caries
Comparison MD CIs
Placebo vs Toothpaste -0.34 (-0.41, -0.28)
Placebo vs Gel -0.19 (-0.30, -0.10)
How to compare Gel to Toothpaste?
Estimate indirect MD and a 95% CI
Toothpaste Gel Placebo
17. Flash back to stats…
Each estimate has uncertainty as conveyed by the
variance, the standard error and the 95% CI
Variance=SE2
95% CI (Low CI, High CI): x-1.96·SE to x+1.96·SE :
SE=(High CI – Low CI)/3.92
18. Pen and paper (and calculator!) exercise!
Indirect MDGvsT= MDPvsT – MDPvsG
Indirect MDGvsT = -0.34 – (-0.19)= -0.15
Variance Indirect MDGvsT = Variance MDPvsT + Variance MDPvsG
Variance MDPvsT = ((high CI –low CI)/3.92)2
Variance MDPvsT= ((-0.28– (-0.41))/3.92)2 =0.0011
Variance MDGvsT= ((-0.10– (-0.30))/3.92)2 =0.0026
Variance Indirect MDGvsT = 0.0011+0.0026=0.0037
SE Indirect MDGvsT = sqrt(0.0037)=0.061
95% CI for Indirect MDGvsT = (-0.15 – 1.96·0.061, -0.15 + 1.96·0.061)
95% CI for Indirect MDGvsT = (-0.27, -0.03)
20. Combining direct and indirect evidence
• Inverse variance method
• Each estimate is ‘weighted’ by the inverse of the
variance
• Then a common (pooled) result is obtained!
IndirectDirect
Indirect
Indirect
Direct
Direct
MDMD
var
1
var
1
var
1
var
1
MDpooled
21. You can do this with any measure... lnOR, lnRR, RD, mean difference, HR, Peto’s lnOR
etc…
Indirect MDGvsT = - 0.15
Variance Indirect MDGvsT = 0.0037
Direct MDGvsT = 0.04
Variance Direct MDGvsT = 0.011
Pooled MDGvsT= -0.14
037.0
1
011.0
1
15.0
0037.0
1
04.0
011.0
1
MDpooled
23. sertraline
citalopram
fluoxetine
Lancet 2009 Cipriani, Fukurawa, Salanti et al
Network of experimental comparisons
LORSF
v1
LORFC
v2
LORSC
Var(LORSC)
Combine the direct estimate
with the indirect estimate
using IV methods
Get a combined LOR!
v4<v3
LORSF
v4
Combined
LORSC
v3
Indirect estimation
LORSC = LORSF - LORCF
Var(LORSC) = v1+ v2
33. Advantages of MTM
– Ranking of many treatments for the same
condition (see later)
– Comprehensive use of all available data
(indirect evidence)
– Comparison of interventions which haven’t
been directly compared in any experiment
34. Bevacizumab
Fluorouracil and leucovorin
Fluorouracil and
leucovorin+bevacizumab
Fluorouracil and
leucovorin+irinotecan
Fluorouracil and
leucovorin+
irinotecan+bevacizumab
Fluorouracil and
leucovorin+irinotecan
+oxaliplatinFluorouracil+leucovorin+oxaliplatin
Fluorouracil and leucovorin +
oxaliplatin + bevacizumab
Irinotecan
Irinotecan + oxaliplatin
Oxaliplatin
Colorectal Cancer
Golfinopoulos V, Salanti G, Pavlidis N, Ioannidis JP: Survival and disease-progression benefits with treatment regimens for advanced colorectal cancer: a meta-analysis. Lancet Oncol
2007, 8: 898-911.
35. Advantages of MTM
– Ranking of many treatments for the same
condition (see later)
– Comprehensive use of all available data
(indirect evidence)
– Comparison of interventions which haven’t
been directly compared in any experiment
– Improved precision for each comparison
37. Why use Bayesian statistics for
meta-analysis?
• Natural approach for accumulating data
• Repeated updating of meta-analyses fine:
posterior should always reflect latest beliefs
• People naturally think as Bayesians:
they have degrees of belief about the effects of
treatment, which change when they see new data
• Probability statements about true effects of
treatment easier to understand than confidence
intervals and p -values
38. Why use Bayesian statistics for
MTM?
• Bayesian approach is easier to account for
correlations induced by multi-arm trials
• Estimation of predictive intervals is straightforward
• Estimation of ranking probabilities is straightforward
• MTM with two-arm trials only
(or ignoring the correlations)
Easy with frequentist meta-regression
42. • We observe yi in each study (e.g. the log(OR))
• Meta-regression using the treatments as
‘covariates’
• AC, AB, BC studies, chose C as reference
Meta-regression
• The AC studies have (1,0), the BC studies (0,1) [basic]
• AB studies have (1,-1) [functional]
yi = C (Treati=A) + BC (Treati=B)
43. Parametrisation of the network
t-PA
Angioplasty
Acc t-PA
Anistreplase
Retaplase
Streptokinase
Choose basic parameters
Write all other contrasts
as linear functions of the
basic parameters to build
the design matrix
LOR for death in treatments for MI
45. X),,,,(Y EDCBA
LOR for death in treatments for MI
Matrix of all
observations
Vector of
LogOR
yi= μA t-PA μB Anistreplasei μC Accelerated t-PAi μD Angioplastyi μE Reteplasei
Design
matrix
Random
effects
matrix
)V,X(N~Y μ ))τ(diag,(N~ 2
∆ 0
Variance-covariance
matrix (for the
observed LOR)
47. What’s the problem with multi-arm trials?
• We need to take into account the correlations between
the estimates that come from the same study
• A B C
yi
BC
yi
AC
• The random effects (θi
BC, θi
AC) that refer to the same trial
are correlated as well
• You have to built in the correlation matrix for the
observed effects, and the correlation matrix for the
random effects
)V,X(N~Y μ ))τ(diag,(N~ 2
∆ 0
48. Study No. arms # Data Contrast
i=1 T1=2 1 y1,1, v1,1 AB
i=2 T2=2 1 y2,1, v2,1 AC
i=3 T3=2 1 y3,1, v3,1 BC
i=4 T4=3 2
y4,1, v4,1
y4,2, v4,2
cov(y4,1, y4,2)
AB
AC
Hypothetical example
Basic parameters: AB and AC
49. 1,1 1,11,1
2,1 2,12,1
3,1 3,13,1
4,1 4,14,1
4,2 4,2 4,2
1 0
0 1
1 1
1 0
0 1
AB
AC
y
y
y
y
y
Meta-regression
Study No. arms # Data Contrast
i=1 T1=2 1 y1,1, v1,1 AB
i=2 T2=2 1 y2,1, v2,1 AC
i=3 T3=2 1 y3,1, v3,1 BC
i=4
T4=3 2
y4,1, v4,1
y4,2, v4,2
cov(y4,1, y4,2)
AB
AC
50. 1,1 1,11,1
2,1 2,12,1
3,1 3,13,1
4,1 4,14,1
4,2 4,2 4,2
1 0
0 1
1 1
1 0
0 1
AB
AC
y
y
y
y
y
Study No. arms # Data Contrast
i=1 T1=2 1 y1,1, v1,1 AB
i=2 T2=2 1 y2,1, v2,1 AC
i=3 T3=2 1 y3,1, v3,1 BC
i=4
T4=3 2
y4,1, v4,1
y4,2, v4,2
cov(y4,1, y4,2)
AB
AC
Take into account correlation
in observations
1,11,1
2,12,1
3,13,1
4,1 4,1 4,24,1
4,2 4,1 4,2 4,2
0 0 0 00
0 0 0 00
0 0 0 0~ ,0
0 0 0 cov ,0
0 0 0 0 cov ,
v
v
vN
v y y
y y v
52. How to fit such a model?
• MLwiN
• SAS, R
• STATA using metan
53. Ranking measures from MTM
• With many treatments judgments based
on pairwise effect sizes are difficult to
make
• Example: Antidepressants
54.
55. Ranking measures from MTM
• With many treatments judgments based
on pairwise effect sizes are difficult to
make
• Example: Antidepressants
• Example: Antiplatelet regimens for serious
vascular events
56. Aspirin vs Placebo
Thienopyridines vs Aspirin
Thienopyridines vs Placebo
0.5 1 1.5 2
0.32
0.03
<0.01
Aspirin+Dipyridamole vs Aspirin+Thienopyridines
Aspirin+Dipyridamole vs Aspirin
Aspirin+Dipyridamole vs Placebo
Aspirin+Dipyridamole vs Thienopyridines
0
Aspirin+Thienopyridines vs Aspirin
Aspirin+Thienopyridines vs Placebo
Aspirin+Thienopyridines vs Thienopyridines0.23
0.05
<0.01
0.19
<0.01
<0.01
P-value Comparison
Odds Ratio for serious vascular event
Favors first treatment Favors second treatment
Serious vascular events with antiplatelet regimens
57. Probabilities instead of effect sizes
• Estimate for each treatment the
probability to be the best
• This is straightforward within a Bayesian
framework
58. %
probability
A B C D
j=1 0.25 0.50 0.25 0.00
j=2 0.50 0.75 0.75 0.00
j=3 0.75 1.00 1.00 0.25
j=4 1.00 1.00 1.00 1.00
59. %
probability
A B C D
j=1 0.25 0.50 0.25 0.00
j=2 0.25 0.25 0.50 0.00
j=3 0.25 0.25 0.25 0.25
j=4 0.25 0 0 0.75
i the treatment
j the rank
60. Rank of paroxetine
Probability
2 4 6 8 10 12
0.00.20.40.6
Rank of sertraline
2 4 6 8 10 12
0.00.20.40.6
Rank of citalopram
2 4 6 8 10 12
0.00.20.40.6
Rank of escitalopram
2 4 6 8 10 12
0.00.20.40.6
Rank of fluoxetine
Probability
2 4 6 8 10 12
0.00.20.40.6
Rank of fluvoxamine
2 4 6 8 10 12
0.00.20.40.6
Rank of milnacipran
2 4 6 8 10 12
0.00.20.40.6
Rank of venlafaxine
2 4 6 8 10 12
0.00.20.40.6
Rank of reboxetine
Probability
2 4 6 8 10 12
0.00.20.40.6
Rank of bupropion
2 4 6 8 10 12
0.00.20.40.6
Rank of mirtazapine
2 4 6 8 10 12
0.00.20.40.6
Rank of duloxetine
2 4 6 8 10 12
0.00.20.40.6
Ranking for efficacy (solid line) and acceptability (dotted line). Ranking: probability to be the best treatment, to be the second
best, the third best and so on, among the 12 comparisons).
61. %
probability
A B C D
j=1 0.25 0.50 0.25 0.00
j=2 0.50 0.75 0.75 0.00
j=3 0.75 1.00 1.00 0.25
j=4 1.00 1.00 1.00 1.00
The areas under the
cumulative curves for the
four treatments of the
example above are
A=0.5
B=0.75
C=0.67
D=0.08
i the treatment
j the rank
Rank of A
CumulativeProbability
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.00.20.40.60.81.0
Rank of B
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.00.20.40.60.81.0
Rank of C
CumulativeProbability
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.00.20.40.60.81.0
Rank of D
1.0 1.5 2.0 2.5 3.0 3.5 4.0
0.00.20.40.60.81.0
62. Preliminary results for ranking 12 antidepressants
Rank of paroxetine
CumulativeProbability
2 4 6 8 10 12
Rank of sertraline
2 4 6 8 10 12
Rank of reboxetine
CumulativeProbability
2 4 6 8 10 12
020406080100
Rank of mirtazapine
2 4 6 8 10 12
35% 77%
1%
92%
020406080100
020406080100020406080100
A comprehensive ranking measure
Compared to an imaginary antidepressant which is ‘always the best’, mirtazapine reaches up to
92% of its potential!
63.
64. • What is inconsistency?
• How it manifests itself?
Inconsistency
65. Inconsistency
Direct t-PA vs Angioplasty= 0.41 (0.36)
0.02 (0.03)
- 0.48 (0.43)
Calculate a difference
between direct and
indirect estimates
t-PA
Angioplasty
Streptokinase
LOR (SE) for MI
Indirect t-PA vs Angioplasty = 0.46 (0.18)
Inconsistency in the loop = 0.05
66. Inconsistency - Heterogeneity
• Heterogeneity: ‘excessive’ discrepancy among
study-specific effects
• Inconsistency: it is the excessive discrepancy
among source-specific effects (direct and
indirect)
68. • In 3 cases out of 44 there was an important
discrepancy between direct/indirect effect.
• Direction of the discrepancy is inconsistent
Glenny et al HTA 2005
Inconsistency
Empirical Evidence
69. Placebo
Toothpaste
Gel
Direct SMD(TvsG) = 0.04
Indirect SMD(TvsG) = – 0.15
IF= 0.11
P-Gel
P-Toothpaste
I cannot learn about Toothpaste versus Gel through Placebo!
Compare Fluoride treatments in preventing dental caries
What can cause inconsistency?
Inappropriate common comparator
70. Screening for lung cancer
Baker & Kramer, BMC Meth 2002
Chest X-ray
Standard
Spiral CT
A new therapy (possibly unreported in the trials) decreases the mortality but in
different rates for the three screening methods
Percent receiving new therapy
Mortality
30 70
Trial 1:
Chest X-ray=
Standard
Trial 2:
Spiral-CT=
Standard
New Trial:
Spiral-CT <
Chest X-ray
100
What can cause inconsistency?
Confounding by trial characteristics
71. age
Effectiveness
Alfacalcidol +Ca
Calcitriol + Ca
Ca
What can cause inconsistency?
Confounding by trial characteristics
Vitamin D for Osteoporosis-related fractures, Richy et al Calcif Tissue 2005, 76;276
Vitamin D +Ca
Different characteristics across comparisons may cause inconsistency
72. • There is not confounding by trial characteristics that are
related to both the comparison being made and the
magnitude of treatment difference
• The trials in two different comparisons are exchangeable
(other than interventions being compared)
• Equivalent to the assumption ‘the unobserved
treatment is missing at random’
– Is this plausible?
– Selection of the comparator is not often random!
Assumptions of MTM
73. • Check the distribution of important
characteristics per treatment comparison
– Usually unobserved….
– Time (of randomization, of recruitment) might be
associated with changes to the background risk that
may violate the assumptions of MTM
• Get a taste by looking for inconsistency in
closed loops
Inconsistency
Detecting
74. No. studies T G R V P Fup Baseline Year Water F
(yes/no)
69 2.6 11.8 1968 0.2
13 2.3 3.8 1973 0.2
30 2.4 5.9 1973 0.1
3 2.3 2.7 1983 0
3 2.7 NA 1968 0.66
6 2.8 14.7 1969 0
1 2 0.9 1978 0
1 1 NA 1977 0
1 3 7.4 1991 NA
4 2.5 7.6 1981 0.33
Compare the characteristics!
Salanti G, Marinho V, Higgins JP: A case study of multiple-treatments meta-analysis demonstrates that covariates
should be considered. J Clin Epidemiol 2009, 62: 857-864.
75. • Check the distribution of important characteristics per
treatment comparison
– Usually unobserved….
– Time (of randomization, of recruitment) might be associated with
changes to the background risk that may violate the assumptions of MTM
• Get a taste by looking for inconsistency in closed loops
• Fit a model that relaxes consistency
– Add an extra ‘random effect’ per loop (Lu & Ades JASA 2005)
Inconsistency
Detecting
77. -1.0 0.0 0.5 1.0 1.5 2.0
Closed loops
NGV
NGR
NRV
PDG
PDV
PDR
DGV
DGR
DRV
PGV
PGR
PRV
GRV
AGRV
PDGV
PDGR
PDRV
DGRV
PGRV
PDGRV
Evaluation of concordance within closed loops
Estimates with 95% confidence intervals
R routine in http://www.dhe.med.uoi.gr/software.htm
Salanti G, Marinho V, Higgins JP: A case study of multiple-treatments meta-analysis demonstrates that covariates should be
considered. J Clin Epidemiol 2009, 62: 857-864.
78. • Check the distribution of important characteristics per
treatment comparison
– Usually unobserved….
– Time (of randomization, of recruitment) might be associated with
changes to the background risk that may violate the assumptions of MTM
• Get a taste by looking for inconsistency in closed loops
• Fit a model that relaxes consistency
– Add an extra ‘random effect’ per loop (Lu & Ades JASA 2005)
Inconsistency
Detecting
80. References
1. Baker SG, Kramer BS: The transitive fallacy for randomized trials: if A bests B and B bests C in separate trials, is A
better than C? BMC Med Res Methodol 2002, 2: 13.
2. Caldwell DM, Ades AE, Higgins JP: Simultaneous comparison of multiple treatments: combining direct and indirect
evidence. BMJ 2005, 331: 897-900.
3. Cipriani A, Furukawa TA, Salanti G, Geddes JR, Higgins JP, Churchill R et al.: Comparative efficacy and acceptability of 12
new-generation antidepressants: a multiple-treatments meta-analysis. Lancet 2009, 373: 746-758.
4. Cooper NJ, Sutton AJ, Lu G, Khunti K: Mixed comparison of stroke prevention treatments in individuals with
nonrheumatic atrial fibrillation. Arch Intern Med 2006, 166: 1269-1275.
5. Golfinopoulos V, Salanti G, Pavlidis N, Ioannidis JP: Survival and disease-progression benefits with treatment regimens
for advanced colorectal cancer: a meta-analysis. Lancet Oncol 2007, 8: 898-911.
6. Heres S, Davis J, Maino K, Jetzinger E, Kissling W, Leucht S: Why olanzapine beats risperidone, risperidone beats
quetiapine, and quetiapine beats olanzapine: an exploratory analysis of head-to-head comparison studies of second-
generation antipsychotics. Am J Psychiatry 2006, 163: 185-194.
7. Jansen JP, Crawford B, Bergman G, Stam W: Bayesian Meta-Analysis of Multiple Treatment Comparisons: An
Introduction to Mixed Treatment Comparisons. Value Health 2008.
8. Lu G, Ades AE: Assessing Evidence Inconsistency in Mixed Treatment Comparisons. Journal of American Statistical
Association 2006, 101: 447-459.
9. Lu G, Ades AE: Combination of direct and indirect evidence in mixed treatment comparisons. Stat Med 2004, 23: 3105-
3124.
10. Salanti G, Higgins JP, Ades AE, Ioannidis JP: Evaluation of networks of randomized trials. Stat Methods Med Res 2008,
17: 279-301.
11. Salanti G, Marinho V, Higgins JP: A case study of multiple-treatments meta-analysis demonstrates that covariates
should be considered. J Clin Epidemiol 2009, 62: 857-864.
12. Song F, Harvey I, Lilford R: Adjusted indirect comparison may be less biased than direct comparison for evaluating
new pharmaceutical interventions. J Clin Epidemiol 2008, 61: 455-463.
13. Sutton A, Ades AE, Cooper N, Abrams K: Use of indirect and mixed treatment comparisons for technology assessment.
Pharmacoeconomics 2008, 26: 753-767.
14. Welton NJ, Cooper NJ, Ades AE, Lu G, Sutton AJ: Mixed treatment comparison with multiple outcomes reported
inconsistently across trials: Evaluation of antivirals for treatment of influenza A and B. Stat Med 2008, 29: 5620-5639.