Jonathan J Shuster PhD shusterjufledu University of Florida College of Medicine 1 PreTalk Questions Are you familiar with MetaAnalysis Have been the Statistician on a MA Have you written one or more methods papers on MA ID: 779408
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Slide1
Meta-Analysis of Clinical Trials: Effects- or Studies-at-Random?
Jonathan J Shuster, PhD shusterj@ufl.eduUniversity of FloridaCollege of Medicine
1
Slide2Pre-Talk Questions
Are you familiar with Meta-Analysis?
Have been the Statistician on a MA?
Have you written one or more methods papers on MA?
Have you analyzed Sample Survey data?
2
Slide3What is MA?
The science of putting together a complete set of independent completed studies on a question (such as treatment difference) to make an informed overall inference.
3
Slide4Two Key Events in MA History
4
Pearson K (1904).
"Report on certain enteric fever inoculation
statistics"
.
BMJ.
2
(2288): 1243–1246.
doi
:
10.1136/bmj.2.2288.1243
.
PMC
2355479
.
PMID
20761760
.
(First
known
medical meta-analysis)
Glass G. V (1976). "Primary, secondary, and meta-analysis
of research". Educational Researcher.
5
(10): 3–8. )
Founded
name
of field for MA
Slide5The Bad News/Good News
Bad News:
You will need to toss anything you have learned about estimating the main effect size in Random Effects Meta-Analysis. The “tried and true” is very dangerous to public health.
Good News:
Using survey sampling methods, everything you need to estimate the main effect size can be derived from Ratio Estimates (two Means, two standard deviations, and one correlation coefficient).
5
Slide63
Slide7Unbelievable but Rigorously True
Despite hundreds of thousands of publications, the State of the Art in Meta-analysis will be shown to be in total disarray.
Current mainstream methods are fraught with risk to public health and should be avoided
This talk will not only demonstrate the amazing truth of the above two statements, but we will provide unified rigorous methods.
7
Slide8Outline for Today’s Session
Goals and Limitations of Session
The “Evidence Pyramid”
Definition of Meta-Analysis (facts and myths)
The Universally Used Models for fixed and random effects.
Effects vs. Studies at Random
Interaction between Effect Size and Design
Examples and Conclusions
8
Slide9Goals and Limitations
Goal: How to analyze the data for “Effect Size” in a Collection of Studies.
Secondary Goal: How to assess Heterogeneity of Studies
Limitation: We are not getting at design of a MA. See the Cochrane Handbook for advice on that
Limitation: We will not address “Publication Bias”. There is no statistical tool including Egger’s Test that can do this.
9
Slide10Typical Evidence Pyramid
10
Slide11Meta-Analysis of Clinical Trials
Collection of Independent Completed Randomized Trials
All “Eligible” Trials Included
Typically Treatment vs. Control
Same (or Comparable) Endpoints
Main Goal: Estimate the Global “Effect Size”
11
Slide12Ex: Rosiglitazone
Nissen-Wolski (2007 NEJM)
Type II Diabetes
48 Randomized Trials of Rosiglitazone
Outcome: Myocardial InfarctionResult: Estimated OR=1.43 (95% CI 1.03-1.98) P=0.03
12
Slide13Rosiglitazone Fate (2007)
Virtual Ban on New prescriptions
Near immediate closure of two huge trials to new patients
Glaxo-Smith-Kline (GSK) sales of drug drops by $2 Billion per year
Lawsuits against GSK cost company $100s of millions
Without the MA, this would almost certainly never have occurred.
13
Slide14Effects-at-Random
14
Slide15Fixed Effects vs. Effects at Random
Fixed: All selections of Effect Sizes in Hat have same value.
Effects-at-Random: Potential Selections are drawn at random from a single “Hat”. One is drawn with replacement for each study
15
Slide16Effects-at-Random Model
Θ
j
= θ + ε
j
with E(ε
j
)=0
Θ
j
is the true value of the effect size for study #j. θ is the unweighted mean true effect size in the Hat.
The estimate of the effect size for study #j,
j
is Unbiased” for Θ
j
given study index j.
Bayes and Frequentist methods both rely on this.
Comments?????
16
Slide17Each
j
is Unbiased for θ
E(
j
)=E[E(
j
)|j]
=E(Θ
j
) Conditional unbiasedness
=E(θ + ε
j
) (From model)
= θ E(ε
j
) =0 from model
17
Slide18Weights and Optimal Weights
The frequentist estimate of θ is
=Σ W
j
j
where Σ W
j
=1
The Weights W
j
are optimized to minimize the variance of the estimates by taking them inversely proportional to the variances of
j
.
Are the W
j
fixed or Random variables????
18
Slide19Throw Pairs [W
j ,
j
] into our hat to randomly Re-index the j’s.
These are now exchangeable.
19
Slide20Is Estimate Unbiased?
=Σ W
j
j
did this change after shuffle?
Cov(W
j
,
j
)=E(W
j
j
)-E(W
j
)E(
j
)
=E(W
j
j
)- θ /M where M=Number of Studies
Hence E(
)=E(Σ W
j
j
)= θ +
M Cov(W
j
,
j
)
is guaranteed to be unbiased if and only if
Cov(W
j
,
j
)=0
Only uniform weights ( W
j
=1/M) guarantee unbiasedness
20
Slide21What impact this discovery has had on MA Practice?
Disappointingly little
I published this dagger in 2010 in Statistics in Medicine, but it has been virtually ignored.
For Equal Weighting, targeting the unweighted sample mean with weights 1/M is Correct, but
other target parameters
may be better.
The classical model is a danger to science
Wrong conclusions can easily be attributed to inappropriate statistical analysis
21
Slide22Can we diagnose the Interaction?
22
Slide23Issues
Can never prove beyond a reasonable doubt that Cov=0.
Therefore you cannot infer you came down the right branch, and error properties from after the branch may be different from error properties you must look at (from before the branch).
The next two slides paint a scary picture (Actual Highly Cited Journal of the American Medical Association Paper)
23
Slide24Neto: Original Data
24
Slide25Neto: Double Num and Den
25
Slide26Effects-at-Random (Conclusion)
Virtually all Random-Effects methods (Bayes or Frequentist) use this
Cannot disprove interaction between design and effect size (Required to be absent)
Society must stop using methods that rely on Effects-at-Random
New texts and software are needed
Past meta-analysis that have impacted public health need to be redone
26
Slide27Analogy: Mainstream Historical Analysis is
Wrong
A. Would you reject an Unmatched Analysis of a Matched Pair Experiment?
Why?
27
Slide28Analogy: Mainstream Historical Analysis is
Wrong (2)
B. Would you reject a Mainstream Random Effects Analysis because of potential within Pair (i.e. Weight and Estimate) Correlation,
Cov(W
j
,
j
)≠ 0?
If A is wrong, B is wrong!!!! Pairs are likely correlated
28
Slide29Is there a Solution?
Survey Sampling paves the way for us.
Use “Studies-at-Random” and classical cluster sampling methods.
Solution is simple
Handles interaction easilyUnlike Effects-at-random, whether or not there is interaction, the target parameter is well defined
29
Slide30Studies-at-Random
Analogy to Clinical Trials Inference
We have large conceptual “Hat” of completed Past, Present, and Future Patients
Studies on a Research question. We take a conceptual random sample of Patients
Studies
and infer what the global effect size is in the total Patient
Study
population.
30
Slide31Why this Formulation Works
In the inference, Studies are complete and the inference is directed to a totality of studies
Within Study Variation is Irrelevant in this set-up as the Individual Study Population and Sample are Identical
This set-up recognizes that Sample Sizes are Random Variables (Effects-at-Random does not)
Physical Interpretations of Effect Sizes are Simple, and work whether there is Interaction or Not.
31
Slide32Generality
Studies-at-Random can accommodate any population of Studies
Effects-at-Random is a constrained subset of the totality of populations, needing
Θj = θ + ε
j
with E(ε
j
)=0
32
Slide33Ratio Estimation in Survey Sampling
33
Slide34Ratio Estimation (Digression)
Let (Y
j
, Z
j
) be M iid random vectors with mean (μ
y ,
μ
z
).
If the (Y
j
, Z
j
)
are non-negative
, Log (
/
) has an asymptotic t-distribution with M-2 degrees of freedom, with mean Log(μ
y /
μ
z
) and asymptotic variance
V
2
= {( σ
y
/ μ
y
)
2
+ ( σ
z
/μ
z
)
2
-2 ρ ( σ
y
/μ
y
) (σ
z
/μ
z
)}/M , σ
y
, σ
z
and ρ are the standard deviations of Y and Z and the correlation between Y and Z.
2
is obtained by replacing the parameters by their sample moments.
34
Slide35Why T not Z?
Asymptotic Normal and asymptotic T with M-2 df are asymptotically equivalent. T (M-2 df ) worked far better for low event binomials based on nearly 40,000 random effect scenarios, each with 100,000 replications. M ranged from 5-20.
This is the largest vetting of a method under general conditions ever.
All we use is the Central Limit Theorem and the Delta Method
35
Slide36Test and Confidence Interval
T=[Log (
/
)- Log (
μ
y
/μ
z
) ]/
P-value=2Probt(-|T|) , where Probt is the cumulative central T-distribution with M-2 df (Number of studies -2)
Endpoints of 100(1-α) Confidence Interval
EXP[Log (
/
) +/-
T(M-2, α/2)] i.e.
CI is [(
/
) exp(-
T(M-2, α/2)] to
[(
/
) exp(
T(M-2, α/2)]
36
Slide37Ratios (Accommodates Negatives)
(
/
) has an asymptotic t-distribution with M-2 degrees of freedom with mean (μ
y
/μ
z
) and asymptotic variance
V
2
= {( σ
y
/ μ
z
)
2
+ (μ
y
σ
z
/μ
z
2
)
2
-2 ρ (μ
y
σ
y
σ
z
/
/
μ
z
3
)}/M
2
is obtained by replacing the parameters by their sample moments.
37
Slide38Population Parameter vs. Estimate
=Σ
Y
j
/ Σ
Z
j
(Summed over sample studies)
θ
=Σ
Y
j
/ Σ
Z
j
(Summed over total population)
Parameter is projected ratio of means
Natural Inference
38
Slide39Honest Assessment
Methods that use Effects-at-Random have no idea what they are estimating in the presence of true interaction between study design and outcomes.
Studies-at-random have this very easy to understand target parameter.
39
Slide40Five application scenarios
1. Estimating a single mean or proportion
2. Estimating global difference in means or proportion from randomized trials
3. Estimating global relative risk from randomized trials
4. Estimating global hazard ratios from randomized clinical trials
5. Repeated measures Bland-Altman studies
40
Slide41Application 1 (of 5): Overall Mean or Proportion
=Σ
N
j
j
/ Σ
N
j
Numerator Y
j
= N
j
j
j
is the study j mean of proportion
N
j
is the study j sample size
Denominator Z
j
= N
j
If non-Negative, prefer logs
41
Slide42Targeted Parameter: Overall Mean or Proportion
We are trying to estimate the mean or proportion for all patients in the Urn of Studies.
42
Slide43Application 2: Clinical Trials, difference in Means or Proportions
=Σ N
j
j
/ Σ N
j
.
Numerator Y
j
= N
j
j
.
j
is the study difference in means or proportions (Treatment #2 minus Treatment #1)
N
j
is the combined study j sample size
Denominator Z
j
= N
j
Cannot use Logs: Numerator can be
negative
43
Slide44Difference in Means or Proportions
=[Σ
N
j
j2
/ Σ
N
j
]-
[Σ
N
j
j1
/ Σ
N
j
]
jk
=Mean for Study j, Treatment #k. This is the mean difference projected for Treatment 2 –that of Treatment 1 if all subjects had Received Treatment #2(#1) respectively.
44
Slide45Application 3: Relative Risk
=
Σ
N
j
j2
/
Σ
N
j
j1
Σ
N
j
jk
(Summed over the entire Population) is the projected total number of events for study j, treatment #k if all patients received Treatment #j.
θ
=
Σ
N
j
j2
/
Σ
N
j
j1
Summed over the pop
n
45
Slide46Roles of the Numerator and Denominator in Ratio
Numerator Y
j
=N
j
j2
Denominator Z
j
=N
j
j1
46
Slide47Relative Risk
is the projected risk ratio in the sample if all received Rx #2 to all receive Rx#1, and estimates
θ
, its population counterpart
Use the log version here since there are no negatives.
Note that zero event studies and/or arms are not problems
47
Slide48What the Mainstream Does
Estimates individual Study Log Relative Risks, and uses within study estimates of variance, which are unreliable, especially when event rates are low
2011 Cochrane Handbook: Warns against using inverse variance methods (including DerSimonian-Laird=DL) when event rates are low. Says there is no software available to handle it properly.
Thousands of applications of DL for low events since.
Interaction slaughters this method even if events not low
48
Slide49Classical RR or Method(2)
Low Events: Throw out zero event studies (we do not)
Low Events: Use continuity corrections for “one zero arm studies” (Shuster-Guo-Skylar 2012 shows this does not help much against poor variance estimation. It is low events not just no events.)
Log and Antilog transforms on the individual relative risk estimates: Cause more bias.
We use logs and antilogs, but it is of the summary estimates not individual study estimates. Our methods in the end directly estimate the target parameter.
No interpretation of target parameter if interaction exists.
49
Slide50Application 4: Hazard Ratios
Same as Relative Risk Methods except Total Time on Test Replaces Total Sample Size for each Study.
We do not assume proportional hazards due to the definition of the population of events per person years at risk, and the ratio for Treatment 2:Treatment 1.
50
Slide51Application 5:Can a non-invasive measure replace an Invasive one?
Bland-Altman pioneered this. “Bland and Altman” has over 13,000 PubMed hits, and over 130,000 Google Scholar hits.
Why is this potentially a meta-analysis?
51
Slide52Why a meta-analysis?
Subjects play the role of study.
BA started with one observation per study and graphically defined the “Limits of Agreement” as the mean deviation (Non-invasive-Invasive) +/- 1.96 standard deviations.
Later, they established a fixed effects extension (all subjects have the same personal mean difference and personal standard deviation, and all observations are independent.)
52
Slide53Meta-analysis Population and Sample (Bland-Altman)
We have a target population of past present and future patients with complete data
The goal is to estimate the mean-square error in the population: The average squared deviation of all measurements in the population.
The observed patients’ deviation data are complete (known without error)
53
Slide54Why are current methods not enough?
We want to allow for random effects (each subject has his/her own personal mean deviation)
We do not believe that we have independence of observations within patients
We believe that “Limits of Agreement” (Mean +/- 2SD) do not make sense as the means vary personally, so there is no common mean to use.
Meta-Analysis gives us a very good answer.
54
Slide55We have converted this to an estimation of a single mean
=Σ
N
j
j
/ Σ
N
j
(Summed over sample)
j
is the mean squared deviation (Non-invasive minus invasive) for subject j over subject j’s observations.
Handles, but does not require repeated measures or within patient independence.
The target population parameter is
θ
=Σ
N
j
j
/ Σ
N
j
(Summed over the target Pop)
55
Slide56Why mean-square error (MSE)?
Takes both bias and sampling error into account.
No new theory required, (Means in a meta-analysis)
Absolute Bias and variance can be studied in a like way. For variance, patients contributing one observation cannot be used.
MSE provides point and interval estimates, so we can assess if replacement of the invasive test is warranted.
56
Slide57Describing Heterogeneity
57
Slide58Between Study Variance
This is very simple in Studies-at-Random
V
b
2= Σ W j
( y
j
–y*)
2
.
y
j
is the estimated mean for study j
W
j
= N
j
/ Σ N
j
.
y*= Σ W
j
y
j
is the point estimate of the overall mean.
Interpretation: Replace all study data with the study mean and calculate the resulting variance in the total sample. (Descriptive Statistic)
58
Slide59Obstacles to Getting Things Right
43 Years of Malpractice (1976-2019)
59
Slide60Establishment Clout
Short Courses by the Insiders ($1795 for three days)
Software from the Insiders (Comprehensive Meta-Analysis, $795 for one site for two years);RevMan 5 (Default for the Cochrane Collaborative)
DerSimonian-Laird paper (over 24,000 Google Scholar citations, over 1,000 PubMed hits)
Egger’s Test (over 23,000 Google Scholar citations, over 1,200 PubMed hits)
60
Slide61Conflict of Interest (Advice that Applies beyond Meta-Analysis)
If you submit a paper that challenges the establishment’s way of doing business, you reviewers are almost certainly insiders or scholars whose own analyses as consultants have relied heavily on the establishment’s methods.
If you say these methods are seriously flawed, expect pushback. But in your cover letter bring up the potential conflict to the editor and suggest possible non-conflicted reviewers.
61
Slide62Ex: Testosterone Replacement Therapy and Cardiac Events
Xu
et al. (2013) Conduct a Meta-Analysis of demonstrating an Elevated Cardiac Risk for men receiving this treatment
Veteran’s Administration bans nearly all prescriptions
Our team, Borst, Shuster, Zou et al. (2014) reanalyze data and overturn scientific basis
VA lifts ban
Therapy now thought to be modestly beneficial to Cardiac health
62
Slide63Slide64Potential Reanalysis Impact
Shuster, Guo, Skylar (2012) and Shuster-Walker (2016) reviewed 31 highly cited MA, and 7 had major discrepancies with the published analysis (23%), overturning their evidence basis.
64
Slide65Recommended Application
M<5 Studies (No Random effects MA)
M=5-20 Studies: Except for Binomials, issue Caution about: asymptotics not vetted. (Same is true about all competitors, as all simulations presumed Effects-at-Random)
M>20 Studies. No problems. CLT converges quickly
Vetting of
non
-binomials M=5-20 will need Supercomputers and Outside Funding.
65
Slide66Irrefutable Fact Charts
Studes-at-Random
Effects-at_Random
Asymptotic in # of Studies
Yes
Yes
Asymptotic in Patients per Study
No
Yes
66
Slide67Irrefutable Fact Charts
Studies-at-Random
Approximation
T (M-2 df)
Normal
Interaction with Weights
No Problem
Causes major potential bias
67
Slide68Irrefutable Fact Charts
Studies-at-Random
Effects-at-Random
Physical interpretation of Outcome
Yes
No
Presumes weights are Random Variables
Yes
No
68
Slide69Irrefutable Fact Charts
Studies-at-Random
Effects-at-Random
Needs within Study variance
No
Yes
Analysis Based on Study-Specific Transform and Back Transform
No
Often
69
Slide70Irrefutable Fact Charts
Studies-at-Random
Effects-at-Random
Unified application for different types of Data
(Incorporates mix of Designs)
Yes (Ratio Estimates)
No
Extensive Past Use
No
Yes
70
Slide71My Personal History 1
Shuster, Jones, Salmon (2007): Low events
Unweighted sample mean proportions (
1
,
2
)
is unbiased for “Classical Model” (P1, P2) , the global proportions in the classical model.
This makes
2
/
1
nonparametrically and asymptotically optimal for the Relative Risk P2/ P1
Removes worries about estimating study-specific odds ratios or relative risk.
71
Slide72My Personal History 2
Shuster 2010
Unweighted and Patient-weighted Estimates of Means (Ratio Estimates)
UW=Σ
j
/M WT=
Σ
N
j
j
/
Σ
N
j
.
M=# of studies in MA and N
j
= Number of pts on Study j
72
Slide73My Personal History 2(Con’d)
Proved UW is the only nonparametrically unbiased estimator of the true mean of the “Classical Model”
Physical interpretation of what each is estimating?
73
Slide74My Personal History 3
Shuster: Review of 2011 Cochrane Handbook
Main New Contribution. Completely discredits cause-effect link in Egger’s Test for Publication Bias. “Offending associations” are natural and expected w/o such bias.
Irony: Researchers measure “Study Quality” and remove studies they deem as “Poor quality”. Then they conduct Egger’s Test for publication bias!
My Recommendation: Use Intent-to-treat
74
Slide75My Personal History 4
Shuster-Guo-Skylar (2012) Low-Event Binomials
Showed classical inverse variance methods do a terrible job at estimating within study standard errors, even w/o zero event arms within studies.
Developed patient weighted non-parametric estimates of relative risk
Most comprehensive vetting of any method of meta-analysis paper (Nearly 40,000 scenarios of low # of studies (5-20), 100,000 simulations each
75
Slide76Personal History 4 (concluded)
Demonstrated T-approximation (M-2 df) is far superior to the Normal Approximation
Demonstrated that when effects-at-random is valid, Studies at Random is far superior to Unweighted (much narrower confidence limits)
76
Slide77Personal History 5
Shuster-Walker 2016
Follow-up to Personal History 4
Reviewed 13 highly cited recent low-event Meta-Analysis papers (18 low event-rate analyses) published in the Journal of the American Medical Association.
Five analyses had major qualitative or quantitative disparities with patient-weighted relative risk analysis.
77
Slide78My Personal History 6
Shuster (2019?)
Submitted paper (+/- corresponds to this talk)
Initially rejected without any proof that anything in the content was untrue. Editor recognized this and invited a resubmission.
Conclusion of paper states that “Business as Usual (Effects-at-Random)” is tantamount to
malpractice
when it comes to random effects meta-analysis.
78
Slide79Might vs. Right
79
Slide80Thank You
Questions????
80
Slide81Personal Key Reference History
1: Shuster JJ, Jones LS, Salmon DA. (2007) Fixed vs random effects meta-analysis in rare event studies: the rosiglitazone link with myocardial infarction and cardiac death.
Stat Med
. Oct 30;26(24):4375-85. PubMed PMID: 17768699.
2. Shuster JJ. (2010) Empirical vs natural weighting in random effects meta-analysis.
Stat Med
. May 30;29(12):1259-65. doi: 10.1002/sim.3607. PubMed PMID:19475538; PubMed Central PMCID: PMC3697007.
3. Shuster JJ. (2011) Review: Cochrane handbook for systematic review of interventions, Version 5.1.0 oublished 3/2011, Julian Higgins and Sally Green, Editors.
Research Synthesis Methods
, 2, 126-130.
81
Slide82Personal Key Reference History (2)
4. Shuster JJ, Guo JD, Skyler JS. (2012) Meta-analysis of safety for low event-rate binomial trials.
Res Synth Methods
. Mar;3(1):30-50. doi: 10.1002/jrsm.1039. PubMed PMID: 24339834; PubMed Central PMCID: PMC3856441.
5. Shuster JJ, Walker MA. (2016) Low-event-rate meta-analyses of clinical trials: implementing good practices.
Stat Med.
Jun 30;35(14):2467-78. doi:10.1002/sim.6844. Epub 2016 Jan 5. PubMed PMID: 26728099; PubMed Central PMCID:PMC4891219.
82
Slide83Key “Push-Back” attempt vs. Shuster(2)(Unweighted)
Laird N, Fitzmaurice G, Ding X. (2010) Comments on 'Empirical vs natural weighting in random effects meta-analysis'
. Stat Med.
May 30;
29(12)
:1266-7; discussion 1272-81. doi: 10.1002/sim.3657. PubMed PMID: 20499329.
Waksman JA. (2010)Comments on 'Empirical vs natural weighting in random effects meta-analysis'.
Stat Med.
2010 May 30;
29(12)
:1268-9; discussion 1272-81. doi: 10.1002/sim.3692. PubMed PMID: 20499330.
Thompson SG, Higgins JP. (2010) Comments on 'Empirical vs natural weighting in random effects meta-analysis'.
Stat Med.
May 30;
29(12):
1270-1; discussion 1272-81. doi: 10.1002/sim.3718. PubMed PMID: 20499331.
83
Slide84Our “Quashing” Response
Shuster JJ, Hatton RC, Hendeles L, Winterstein AG.(2010)Reply to discussion of 'Empirical vs natural weighting in random effects meta-analysis'.
Stat Med.
May 30;
29(12): 1272-81. doi: 10.1002/sim.3718. PubMed PMID: 20499332
Non-recognition of Weights as major random variables (despite random permutation of indices)
Non-recognition of fact that only unbiased estimate of the model parameter (unweighted mean) is the unweighted observed mean (model true of false)
84
Slide85The Big Two References
DerSimonian R, Laird N. (1986)Meta-analysis in clinical trials.
Control Clin Trials.
1986 Sep;
7(3):177-88. PubMed PMID: 3802833.Egger M, Davey Smith G, Schneider M, Minder C. (1997) Bias in meta-analysis detected by a simple, graphical test.
BMJ.
Sep 13;
315(
7109):629-34. PubMed PMID: 9310563; PubMed Central PMCID: PMC2127453.
85
Slide86Medical Applications Used
Neto AS, Cardosa SO, Manetta JA, et al. (2012)
Association Between Use of Lung-Protective Ventilation With Lower Tidal Volumes and Clinical Outcomes Among Patients Without Acute Respiratory Distress Syndrome: A Meta-analysis
. JAMA.
308(16)
:1651-1659
Borst SE, Shuster JJ, Zou B, Ye F, Jia H, Wokhlu A, Yarrow JF. (2014) Cardiovascular risks and elevation of serum DHT vary by route of testosterone administration: a systematic review and meta-analysis. BMC Med. Nov 27;12:211. doi: 10.1186/s12916-014-0211-5. Review. PubMed PMID: 25428524; PubMed Central PMCID:PMC4245724.
86
Slide87Medical Applications Used (2)
Nissen SE, Wolski K. Effect of rosiglitazone on the risk of myocardial infarction and death from cardiovascular causes.
NEJ Med.
2007 Jun 14;
356(24):2457-71. Epub 2007 May 21. Erratum in: N Engl J Med. 2007 Jul 5;357(1):100. PubMed PMID: 17517853.
87
Slide88Medical Applications Used(3)
Xu L, Freeman G, Cowling BJ, Schooling CM. Testosterone therapy and cardiovascular events among men: a systematic review and meta-analysis of placebo-controlled randomized trials.
BMC Med.
2013 Apr
18;11:108. doi:10.1186/1741-7015-11-108. PubMed PMID: 23597181; PubMed Central PMCID:PMC3648456.
88
Slide89Bland-Altman Repeated Measures Reference
Bland JM, Altman DG.
Agreement between methods of measurement with multiple observations per individual
.
Journal of Biopharmaceutical Statistics
2007;
17 (4)
: 571-582.
89