Methods for Summarizing the Evidence: Meta-Analyses and Pooled Analyses
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Transcript of Methods for Summarizing the Evidence: Meta-Analyses and Pooled Analyses
Methods for Summarizing the Evidence:
Meta-Analyses and Pooled Analyses
Donna Spiegelman, Sc.D.Departments of Epidemiology and
BiostatisticsHarvard School of Public [email protected]
Methods for Summarizing the Evidence
Narrative review
Meta-analysis of published data Pooled analysis of primary data (meta-
analysis of individual data)• Retrospectively planned• Prospectively planned
Narrative Review
Fruits, Vegetables and Breast Cancer: Summary of Case-Control Studies
Total number of studies: 12
Studies showing a statistically significant protective association: 8 (67%)
Studies showing no statistically significant protective association: 4 (33%)
WCRF/AICR 1997
Specific Fruits and Vegetables and Breast Cancer: Summary of Case-Control Studies
# of % of Total Food Group studies risk null risk
Fruits 4 75 0 25
Citrus Fruits 3 33 0 66
Vegetables <3 -- -- --
Green Veg. 6 83 17 0
Carrots 4 75 25 0
WCRF/AICR 1997
Fruits, Vegetables and Breast Cancer: Conclusion of Narrative Review
A large amount of evidence has accumulated regarding vegetable and fruit consumption and the risk of breast cancer. Almost all of the data from epidemiological studies show either decreased risk with higher intakes or no relationship; the evidence is more abundant and consistent for vegetables, particularly green vegetables, than for fruits.
Diets high in vegetables and fruits probably decrease the risk of breast cancer.
WCRF/AICR 1997
Narrative Review
Strengths• Short timeframe• Inexpensive
Limitations• Provide qualitative summary only frequently
tabulate results• Subjective• Selective inclusion of studies• May be influenced by publication bias
Publication Bias: Funnel Plots
Sterne 2001
Where Can Publication Bias Occur?
Project dropped when preliminary analyses suggest results are negative
Authors do not submit negative study Results reported in small, non-indexed journal Editor rejects manuscript Reviewers reject manuscript Author does not resubmit rejected manuscript Journal delays publication of negative study Results not reported by news, policy makers,
or narrative reviewsMontori 2000
Meta-Analyses
Rationale for Combining Studies
“Many of the groups…are far too small to allow of any definite opinion being formed at all, having regard to the size of the probable error involved.”
Pearson, 1904
Definition
“Meta-analysis refers to the analysis of analyses…the statistical analysis of a large collection of analysis results from individual studies for the purpose of integrating findings. It connotes a rigorous alternative to the casual, narrative discussions of research studies which typify our attempts to make sense of the rapidly expanding literature…”
Glass, 1976
Meta-Analyses: # of Publications by Year
010002000300040005000
1986 1991 1996 2001Year of Publication
Why conduct a meta-analysis?
Summarize published literature• A more objective summary of literature than narrative
review• Estimate average effect from all available studies
Increase statistical power more precise estimate of effect size
Identify between study heterogeneity
Identify research needs
Outline for Conducting Meta-Analyses
Objective, hypothesis
Define outcome, exposure, population
Study inclusion criteria
Search strategy
Data extraction
Quality assessment
Statistical analysis
Meta-Analyses: Study Sources
Published literature
• citation indexes
• abstract databases
• reference lists
• contact with authors
Unpublished literature
Uncompleted research reports
Work in progress
Meta-Analyses: Data Extraction
Publication year
Performing year
Study design
Characteristics of study population (n, age, sex)
Geographical setting
Assessment procedures
Risk estimate and variance
Covariates
Meta-Analyses: Quality Assessment
Study components• Study design• Outcome measurement• Exposure measurement• Response rate/follow-up rate
Analytic strategy• Adjustment for confounding
Quality of reporting
Meta-Analyses: Statistical Analyses
Define analytic strategy
Investigate between study heterogeneity
Decide whether results can be combined
Estimate summary effect, if appropriate
Conduct sensitivity analysis• Stratification• Meta-regression analyses
Fixed Effects
Assumes that all studies are estimating the same true effect
Variability only from sampling of people within each study
Precision depends mainly on study size
Fixed Effects Model
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Studies allowed to have different underlying or true effects
Allows variation between studies as well as within studies
Random Effects Model , , . . . ,
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Test for Heterogeneity
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Fixed Effects vs Random Effects Model
Random effects generally yield larger variances and CI • Why? Incorporate
If heterogeneity between studies is large,
will dominate the weights and all studies will be weighted more equally
Model weight for large studies less in random vs fixed effects model
2B
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Sources of Between Study Heterogeneity
Different study designs
Different incidence rates among unexposed
Different length of follow-up
Different distributions of effect modifiers
Different statistical methods/models used
Different sources of bias
Study quality
Meta-Analyses: Sensitivity Analyses
Exclude studies with particular heterogeneous results
Conduct separate analyses based on• Study design• Geographic location• Time period• Study quality
Meta-regression (Stram, Biometrics, 1996)
Purpose: to identify heterogeneity of effects by covariates that are constant within study (e.g. gender, smoking status)
Model: β s = β 0 + β1 GENDERs + β2 CURRENTs
+ β2 PASTs + bs + εs
GENDERs = 1 if studys is male; 0 if femaleCURRENTs = 1 if studys has current smokers only, 0 otherwise PASTs = 1 if studys has past smokers only, 0 otherwise
H0: β1 = 0 no effect-modification by gender
Standard method for mixed effects models can be used to test hypotheses and estimate parameters
^
Analysis of between-studies heterogeneity p-value for test for heterogeneity is a function of the
power of the pooled analysis to detect between-studies differences. This power is believed to be low.
• a simulation study was conducted and published (Takkouche, Cardoso-Suárez, Spiegelman, AJE, 1999) which investigated the power of several old and some newly developed test statistics to detect heterogeneity of different plausible magnitudes, as quantified by CV and R2 (to be defined)
• CV = /Ι β Ι , with S=ranging from 7 to 33
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2B
Analysis of between-studies heterogeneity Explored maximum likelihood methods for estimation of and testing H0: =0 (i.e. no between-studies
heterogeneity)
• ML methods have power roughly equivalent to D&L’s, but assume bs ~N (0, ) and εs ~ N [ 0, Vars ( βs ) ]
• LRT for H0: = 0 has no known asymptotic distribution because hypothesis is on the boundary of the parameter space
• A simulation-based bootstrap approach for constructing the empirical distribution function of the test statistic was developed
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Quantification of heterogeneity CVB = /β• between-studies variance expressed relative to the magnitude of
the overall association • if the association is small, CV 'blows up’
proportion of the variance of the pooled estimate due to between-studies variation
• Useful for when β is near 0 as well as when it is far from it • Heterogeneity is evaluated relative to within-studies contribution
to the variance, and can appear large if the participating studies yield precise estimates
Further experience with these measures will give us more insight as to their relative merits
Confidence intervals for CVB, R2 (Identical to I2 (Higgins et al., 2006))
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14.38 25.90 38.12
7.85
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14.68 25.97 37.81
15.32 24.92 37.94
RI = 0.5 S = 7 S = 20 S = 40
37.54 70.56 90.88
27.14 64.11 88.61
27.60 58.54 79.76
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38.50 68.62 91.14
RI = 0.75 S = 7 S = 20 S = 40
77.66 98.66
100.00
70.21 97.51 99.93
58.84 93.64 99.64
78.31 99.12 99.94
75.02 98.34 99.94
* Parametric bootstrap version of the test.
† Odds ratio = 2.‡ WLS, weighted least squares; LRT, likelihood ratio test. § R2, proportion of the total variance due to between-study variance: /(( + (S x Var())).
Power of Test of Heterogeneity
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2B 2
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Fruit & Vegetable and Breast Cancer Meta-Analysis
Objective: analyze published results that explore the relationship between breast cancer risk and the consumption of fruits and vegetables
Search strategy
• MEDLINE search of studies published January 1982 – April 1997
• Review of reference lists Gandini, 2000
Fruit & Vegetable and Breast Cancer Meta-Analysis: Inclusion Criteria
Relative risks and confidence intervals reported or could be estimated• Comparisons: tertiles, quartiles, quintiles
Studies were independent Diet assessed by food frequency
questionnaire Populations were homogeneous, not limited
to specific subgroup
Gandini, 2000
Fruit & Vegetable and Breast Cancer Meta-Analysis: Data Extraction and Analysis
Selected risk estimate for total fruits and total vegetables, when possible• Otherwise, selected nutrient dense food
Extracted the most adjusted relative risk comparing the highest vs. lowest intake • Comparisons: tertiles, quartiles, quintiles
Used random effects model to calculate summary estimate
Sensitivity analyses
Gandini, 2000
Fruit and Vegetable and Breast Cancer Meta-Analysis: Results
RR (95% CI) p for het high vs low
Total fruits 0.94 (0.79-1.11) <0.001
Total vegetables 0.75 (0.66-0.85) <0.001
Gandini, 2000
Fruits and Vegetables and Breast Cancer Meta-Analysis: Sensitivity Analysis
# of RR Significance Studies of factors
Study design Case-control 14 0.71Cohort 3 0.73 0.30
Validated FFQYes 6 0.85No 11 0.66 0.13
Gandini, 2000
Fruits and Vegetables and Breast Cancer: Conclusion of Meta-Analysis
The quantitative analysis of the published studies…suggests a moderate protective effect for high consumption of vegetables… For fruit intake, study results were less clear. Only two studies show a significant protective effect of high fruit intake for breast cancer.
This analysis confirms the association between intake of vegetables and, to a lesser extent, fruits and breast cancer risk from published sources.
Gandini, 2000
Limitations of Meta-Analyses
Heterogeneity across studies Difficult to evaluate dose-response
associations Difficult to examine population subgroups Errors in original work cannot be checked Errors in data extraction Limited by quality of the studies included May be influenced by publication bias
Pooled Analyses
Outline for Conducting Pooled Analyses
• Search strategy
• Study inclusion criteria
• Obtain primary data
• Prepare data for pooled analysis
• Estimate study-specific effects
• Examine whether results are heterogeneous
• Estimate pooled result
• Conduct sensitivity analyses
Friedenreich 1993
Pooling Project of Prospective Studies of Diet and Cancer
• Collaborative project to re-analyze the primary data in multiple cohort studies using standardized analytic criteria to generate summary estimates
• Retrospectively-plannedRetrospectively-planned meta-analysis of individual patient data
• Established in 1991
• http://www.hsph.harvard.edu/poolingproject/about.html
Pooling Project of Prospective Studies of Diet and Cancer: Inclusion Criteria
Prospective study with a publication on diet and cancer
Usual dietary intake assessed
Validation study of diet assessment method
Minimum number of cases specific for each cancer site examined
Sweden Mammography
CohortNetherlands Cohort Study
New York State Cohort
Iowa Women’s Health Study
Canadian National Breast Screening Study
Cohort Studies in the Pooling Project of Prospective Studies of Diet and Cancer
Cancer Prevention Study II Nutrition Cohort
Adventist Health Study
Alpha-Tocopherol Beta-Carotene Cancer Prevention Study
New York University
Women’s Health Study Health Professionals
Follow-up Study, Nurses’ Health Study, Women’s Health Study, Nurses’
Health Study II
Breast Cancer Detection Demonstration Project
ORDET
Total=948,983
CA Teacher’s Study
Analytic Strategy
Study-specific analyses
Data collection Pooling
Nutrients
Food groups
Foods
Non-dietary risk factors
Main effect
Population subgroups
Effect modification
Annual meeting
Pooling Project: Data Management
Receive primary data–Different media–Different formats
Check data follow-up with investigators Apply exclusion criteria Calculate energy-adjusted nutrient intakes Create standardized name and format for
each variable
Pooling Project: Data Checks Dates
• Questionnaire return• Follow-up time• Diagnosis• Death
Non-dietary variables• Frequency distributions, means• Consistency checks
–Parity and age at first birth–Smoking status and # cigarettes
Nutrients and foods: means, range
Data Management: Inconsistent UnitsExample: Vitamin A, Carotene
Units:g retinol equivalentsg • International units
How determine units• Original data sheets• Published values• Correspondence
Data Management: Standardizing Food Data
Created standardized name for each food on the FFQs (range: 46-276 items)
• Multiple foods on same line
• “Other” categories Standardized quantity information as grams/d
• For some studies, calculated gram intakes by frequency * portion size * gram weight
Defined food groups
Pooling Project: Foods
Food Std Name Std Serv
Orange juice juior 6 oz
Orange or grapefruit juice juici 6 oz
Oranges orang one
Oranges, grapefruits cifru average
Oranges, orange juice orang one orange
Oranges, tangerines orang one
Oranges, tangerines, grapefruit cifru average
Pooling Project: Primary Analysis Programs
Read data• Study name, exposure, covariates
Data management Analysis - Cox proportional hazards model
(SAS, Epicure)• Continuous• Categorical• Splines• Interactions
Pooling Project: Primary Analysis Programs, cont’d
Output for each study
• File with number of cases and covariates included in the model
• File identifying whether any of the relative risks > 10
• For quantile analyses, file with the mean, range and number of cases for each quantile
• Data set with beta, variance, covariance, likelihood for each variable
Pooling Project: Pooling Programs
Read study-specific output data sets Calculate summary relative risk by using random
effects model
• Weight studies by the inverse of their variance
• Test for between studies heterogeneity
• Test for effect modification by sex Output table
Pooling Project: Analytic Strategy for Breast Cancer Analyses
Analysis• Cohorts analyzed using Cox proportional
hazards model• Canadian National Breast Screening Study is a
nested case-control study with a 1:2 ratio of cases:controls
• Netherlands Cohort Study is a case-cohort study–Subcohort: 1812 women
Pooling Project: Exposures Total fruits
• Fruits, excluding fruit juice
• Fruit juice
Total vegetables
Total fruits and vegetables
Botanical groups
Specific foods
Pooled Multivariate Relative Risks for Breast Cancer and Fruits and Vegetables
1 1.00 (ref) 1.00 (ref)
2 0.94 (0.87-1.01) 0.99 (0.90-1.08)
3 0.92 (0.86-0.99) 0.97 (0.90-1.05)
4 0.93 (0.86-1.00) 0.96 (0.89-1.04)
p for trend 0.08 0.54
p for hetero. 0.94 0.73
Quartile Total Fruits Total Vegetables RR (95% CI) RR (95% CI)
Smith-Warner, et al. 2001
Contrast toVegetable and Breast Cancer Meta-Analysis: Results
RR (95% CI) p for het high vs low
Total fruits 0.94 (0.79-1.11) <0.001
Total vegetables 0.75 (0.66-0.85) <0.001
Gandini, 2000
Specific Fruits and Vegetables and Breast Cancer: Summary of Case-Control Studies
# of % of Total Food Group studies risk null risk
All Fruits 4 75 0 25
Citrus Fruits 3 33 0 66
All Vegetables <3 -- -- --
Green Veg. 6 83 17 0
Carrots 4 75 25 0
WCRF/AICR 1997
CONTRAST TOFruits, Vegetables and Breast Cancer:
Conclusion of Narrative ReviewA large amount of evidence has accumulated regarding vegetable and fruit consumption and the risk of breast cancer. Almost all of the data from epidemiological studies show either decreased risk with higher intakes or no relationship; the evidence is more abundant and consistent for vegetables, particularly green vegetables, than for fruits.
Diets high in vegetables and fruits probably decrease the risk of breast cancer.
WCRF/AICR 1997
Pooled Multivariate Relative Risks of Breast Cancer and Botanically Defined Fruit and Vegetable Groups and Individual Foods
RR (95% CI)
Cruciferae 0.96 (0.87-1.06)
Leguminosae 0.97 (0.87-1.08)
Rutaceae 0.99 (0.97-1.01)
Carrots 0.95 (0.81-1.12)
Potatoes 1.03 (0.98-1.08)
Apples 0.96 (0.92-1.01)
Increment=100 g/dSmith-Warner 2001
Pooled Multivariate Relative Risks of Breast Cancer and F & V by Menopausal Status
Multi RR (95% CI) p-for - (increment=100 g/d) interaction
Total fruits Premeno. 0.98 (0.94-1.02) Postmeno. 0.99 (0.98-1.01) 0.80
Total vegetables Premeno. 0.99 (0.93-1.06) Postmeno. 1.00 (0.97-1.02) 0.54
Smith-Warner, et al. 2001
Pooling Study-Specific Results vs. Combining Primary Data into One Dataset
Difficult to distinguish population-specific differences in true intake from artifactual differences due to differences in dietary assessment methods• exception: when the unit of measurement
is standard (e.g. alcohol, body mass index)
Pooling allows for study-specific differences in the adjustment for confounders
Multivariate meta-analysis for data consortia, individual patient meta-analysis, and pooling
projectsRitz J, Demidenko E, Spiegelman D
Journal of Statistical Planning and Inference, 2008; 138: 1919-1933
Maximum likelihood and estimating equations metnods for combining results from multiple studies in pooling projects
The univariate meta-analysis model is generalized to a multivariate method, and eficiency advantages are investigated
The test for heterogeneity is generalized to a multivariate one4
Multivariate Pooling-Let βs = β + bs + es + + , s = 1,… s studies
dim (β)= p model covariates E(bs) = E (es) = 0, Var(bs) = ΣB, Var(es) = Cov (βs)
pxp
5
-If ΣB and Cov (βs) are not diagonal, more efficient estimates of β can be obtained
-Weighted estimating equation ideas are used
-Test statistics for H0: ΣB = 0and major submatrices are given assuming normality in bs and es
and asymptotically
^
^
^
6
ResultsFrom Smith-Warner, et al. 2001
“Types of dietary fat and breast cancer: a pooled analysis of cohort studies”
ARE ( compared to corresponding univariate estimate)
p=3 p=18* p=3 p=18*Saturated fat 86% 81% 93% 84%Mono-unsaturated fat 76% 72% 36% 32%Poly-unsaturated fat 91% 88% 1.35% 1.21%
*Using estimates adjusted for total energy, % protein intake, bmi, parity x age at first birth, height (4 levels), dietary fiber (4 quintiles)
MLE EE
Measurement error correction for pooled estimates
Measurement error correction study-specific estimate using the measurement error model developed from each study's validation data
Pool measurement error corrected β's in the usual way -- note that pooled variance will reflect additional uncertainty in the study-specific measurement error corrected estimates
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Pooled Analyses vs. Meta-Analyses
Strengths• Increased standardization• Can examine rare exposures• Can analyze population subgroups• Reduce publication bias
Limitations• Expensive• Time-consuming• Requires close cooperation with many
investigators• Errors in study design multiplied (prospective)
Another example: Dairy intake and ovarian cancer incidence (Genkinger et al., 2005)
• From pooling project of prospective studies of diet and cancer
• 12 studies, 2,087 epithelial ov ca, 560,035 women
• Located in North America and Europe• Follow-up between 1976-2002, of between 7
to 20 years• Studies had to have 50 or more cases to be
included (range 52 to 315)
Daily Mean Intakes of Dairy Nutrients and Foods by Cohort Study in the Ovarian Cancer Analyses in the Pooling Project
Table 1. Daily Mean Intakes of Dairy Nutrients and Foods by Cohort Study in the Ovarian Cancer Analyses in the Pooling Project of Prospective Studies of Diet and Cancer
Mean (SD) Intake3 Cohort1
Follow-up Years
Baseline Cohort Size2
Number of Cases
Dietary Calcium (mg/day)
Total Calcium4 (mg/day)
Lactose (g/day)
Dietary Vitamin D (IU/day)
Total Vitamin
D4 (IU/day)
Total Milk
(g/day) 5
Hard Cheese
(g/day) 5
Yogurt (g/day) 5
AHS 1976-1988 18,402 53 832 (124) 878 (139) 18 (14) --- --- 419 (349) 8 (8) --- BCDDP 1987-1999 32,885 142 862 (369) 1186 (2979) 19 (14) 206 (122) 341 (279) 260 (269) 13 (20) --- CNBSS 1980-2000 56,837 223 672 (252) --- 8 (7) --- --- 199 (198) 22 (23) 29 (60) CPS II 1992-2001 60,796 233 888 (381) 1140 (585) 18 (14) 197 (119) 343 (259) 269 (269) 6 (12) 44 (71) IWHS 1986-2001 28,486 208 748 (285) 1029 (483) 15 (11) 223 (111) 382 (292) 275 (265) 11 (13) 12 (39) NLCS 1986-1995 62,412 208 869 (261) --- 14 (8) --- --- 187 (153) 23 (18) 52 (56) NYSC 1980-1987 22,550 77 828 (209) 873 (220) 15 (9) 203 (68) 371 (227) 137 (87) --- --- NYU 1985-1998 12,401 65 810 (307) 867 (317) 14 (11) --- --- 202 (243) 17 (22) 38 (61) NHS80 1980-1986 80,195 120 722 (298) 731 (310) 14 (11) 167 (107) 279 (262) 215 (241) 14 (15) 21 (54) NHS86 1986-2000 59,538 315 718 (254) 1056 (492) 13 (10) 182 (100) 319 (243) 221 (230) 13 (13) 28 (55) NHS II 1991-2000 91,502 52 787 (271) 910 (381) 16 (11) 223 (109) 351 (231) 268 (255) 12 (12) 31 (55) SMC 1987-2003 61,103 287 913 (256) --- 16 (10) 199 (130) --- 156 (130) 27 (19) 104 (108) WHS 1993-2002 32,466 104 729 (258) 940 (442) 14 (10) 217 (104) 324 (216) 215 (222) 9 (11) 36 (64)
1 AHS=Adventist Health Study, BCDDP=Breast Cancer Detection Demonstration Project, CNBSS=Canadian National Breas t Screening Study, CPS II=Cancer Prevention Study II Nutrition Cohort, IWHS=Iowa Women’s Health Study, NLCS=Netherlands Cohort Study, NYSC=New York State Cohort, NYU=New York University Women’s Health Study, NHS80=Nurses’ Health Study (part a), NHS86=Nurses’ Health Study (part b), NHS II=Nurses’ Health Study II, SMC=Sweden Mammography cohort, WHS=Womens’ Health Study 2 Baseline cohort size determined after specific exclusions (i.e., prior cancer diagnosis other than non -melanoma skin cancer at baseline, had a bilateral oophorectomy prior to baseline, or if they had loge-transformed energy intakes beyond three standard deviations from the study-specific loge-transformed mean energy intake of the population ) 3 Studies which have a --- did not estimate that nutrient or did not ask on their questionnaire about the consumption of that food item 4 Total calcium and vitamin D includes dietary and supplemental sources.
Multivariate1 Adjusted Relative Risks (RR) and 95% Confidence Intervals (CI)
for Ovarian Cancer According to Lactose Intake (>30g/day compared to <10g/day)
by Study
F ig u r e 2 . M u lt iv a r ia te 1 A d ju s te d R e la t iv e R is k s (R R ) a n d 9 5 % C o n f id e n c e I n te r v a ls (C I ) fo r O v a r ia n C a n c e r A c c o r d in g to L a c to s e I n ta k e (> 3 0 g /d a y c o m p a r e d to < 1 0 g /d a y ) b y S tu d y
R e la tiv e Ris k.2 .5 1 2 5
C o m b i n e d
W o m e n 's H e a l th S tu d y
N u rse s' H e a l th S t u d y 1 9 8 0
N u rse s' H e a l th S tu d y I I
N e th e r l a n d s C o h o rt S tu d y
S w e d e n M a m m o g ra p h y C o h o rt
N u rse s' H e a l th S t u d y 1 9 8 6
Io w a W o m e n 's H e a l t h S tu d y
C a n c e r P re v e n t i o n S tu d y I I
B re a st C a n c e r D e m o n st ra t i o n D e te c t i o n P ro g ra m
N e w Y o rk U n i v e rsi t y W o m e n 's H e a l th S tu d y
N e w Y o rk S ta t e C o h o rt
C a n a d i a n N a t i o n a l B re a st S c re e n i n g S tu d y
A d v e n t i st H e a l t h S tu d y
1 M u ltiv a r ia te re la t iv e r isk s w e re a d ju s te d fo r a g e a t m e n a rc h e (< 1 3 , 1 3 , > 1 3 y e a r s ) , m e n o p a u sa l s ta tu s a t b a se l in e , o ra l c o n tra c e p tiv e u se (e v e r , n e v e r ) , h o r m o n e re p la c e m e n t th e ra p y u s e a m o n g p o s t- m e n o p a u s a l w o m e n ( n e v e r , p a s t , c u r re n t) , p a r ity (0 , 1 , 2 , > 2 ) , b o d y m a ss in d e x (< 2 3 , 2 3 -2 4 .9 , 2 5 -2 9 .9 , > 3 0 k g /m 2 ) , s m o k in g s ta tu s (n e v e r , p a s t, c u r r e n t) , p h y s ic a l a c tiv ity ( lo w , m e d iu m , h ig h ) , a n d e n e rg y in ta k e (c o n tin u o u s ly ) , m o d e le d id e n t ic a lly a c ro s s s tu d ie s . . E u n y o u n g p a p e r [T h e b la c k s q u a re s a n d h o r iz o n ta l l in e s c o r re sp o n d to th e s tu d y -sp e c i f ic re la t iv e r is k s a n d 9 5 % c o n f id e n c e in te rv a ls fo r > 3 0 g /d a y la c to s e in ta k e . T h e a re a o f th e b la c k s q u a re s re f le c ts th e s tu d y -sp e c i f ic w e ig h ts ( in v e rse o f th e v a r ia n c e ) , w h ic h is re la te d to s a m p le s iz e a n d in ta k e v a r ia t io n . T h e d ia m o n d re p re s e n ts th e p o o le d m u l tiv a r ia te re la t iv e r is k a n d 9 5 % c o n f id e n c e in te rv a l. T h e d a s h e d lin e re p re se n ts th e p o o le d m u lt iv a r ia te re la tiv e r is k . ]
Data and SAS Program to analyze Lactose and Ovarian Cancer – Pooling Project
AHS 0.496 1.23 BCDDP 0.873 1.46 CNBSS 0.659 2.76 CPS2 1.033 1.48 IWHS 1.225 1.95 NLCS 1.568 3.32 NYS 0.767 3.53 NYU 0.787 2.69 NHSa 1.619 2.90 NHSb 1.240 1.90 NHSII 1.573 3.51 SMC 1.346 2.07 WHS 1.699 3.23 options ps=58 ls=120 nodate nonumber; %include "newmeta.mac"; data dat; *infile "no_conf.dat" lrecl=2000; infile "lactose.dat" lrecl=2000; input study $ beta ub; beta = log(beta); var = ((log(ub)-beta)/1.96)**2; w=1/var; %meta(beta = beta, var = var, data = _last_, labels=study, wt=1,name='pooling project -- lactose and ov ca',modlab=1, out=metaout); proc mixed data=dat; class study; model beta = /s; random study/s; repeated; weight w; parms (0) (1) / eqcons=2; proc mixed data=dat; class study; model beta = /s; random study/s; repeated; weight w; parms (0) (1) / eqcons=1 to 2;
SAS Output for Analysis of Lactose Data The SAS System Meta-Analysis for variable : 'pooling project -- lactose and ov ca' Model : 1 Weight used for Odds Ratios etc., is 1 Inverse-variance weighted average of estimates ----------------------------------------------------------------------------------------------- Pooled Lower Upper Z-score for Chi-sq Estimate S.E. 95% CL 95% CL H0: OR=1 Prob ----------------------------------------------------------------------------------------------- Beta 0.164614 0.082208 0.003487 0.325741 2.002423 0.045239 OR 1.178938 1.003494 1.385057 ----------------------------------------------------------------------------------------------- Test of heterogeneity ======================= Q : 10.550490 df : 12 Prob : 0.567783 ======================= Estimate of among-study variability = 0 Weighted average of estimates using the DerSimonian and Laird random effects model ----------------------------------------------------------------------------------------------- Pooled Lower Upper Z-score for Chi-sq Estimate S.E. 95% CL 95% CL H0: OR=1 Prob ----------------------------------------------------------------------------------------------- Beta 0.164614 0.082208 0.003487 0.325741 2.002423 0.045239 OR 1.178938 1.003494 1.385057 ----------------------------------------------------------------------------------------------- Input data: ========================================================================================================== Label Beta Variance OR Lower 95% Upper 95% Fixed wt Random wt ========================================================================================================== AHS -0.701179 0.214706 0.496000 0.200013 1.230000 0.03 0.03 BCDDP -0.135820 0.068841 0.873000 0.522006 1.460000 0.10 0.10 CNBSS -0.417032 0.533990 0.659000 0.157348 2.760000 0.01 0.01 CPS2 0.032467 0.033656 1.033000 0.721006 1.480000 0.20 0.20 IWHS 0.202941 0.056258 1.225000 0.769551 1.950000 0.12 0.12 NLCS 0.449801 0.146487 1.568000 0.740549 3.320000 0.05 0.05 NYS -0.265268 0.606623 0.767000 0.166654 3.530000 0.01 0.01 NYU -0.239527 0.393224 0.787000 0.230249 2.690000 0.02 0.02 NHSa 0.481809 0.088446 1.619000 0.903849 2.900000 0.08 0.08 NHSb 0.215111 0.047405 1.240000 0.809263 1.900000 0.14 0.14 NHSII 0.452985 0.167695 1.573000 0.704937 3.510000 0.04 0.04 SMC 0.297137 0.048223 1.346000 0.875225 2.070000 0.14 0.14 WHS 0.530040 0.107438 1.699000 0.893685 3.230000 0.06 0.06 ==========================================================================================================
SAS Output: Random effects regression model The SAS System The Mixed Procedure Model Information Data Set WORK.DAT Dependent Variable beta Weight Variable w Covariance Structure Variance Components Estimation Method REML Residual Variance Method Parameter Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values study 13 AHS BCDDP CNBSS CPS2 IWHS NHSII NHSa NHSb NLCS NYS NYU SMC WHS Dimensions Covariance Parameters 2 Columns in X 1 Columns in Z 13 Subjects 1 Max Obs Per Subject 13 Observations Used 13 Observations Not Used 0 Total Observations 13 Parameter Search CovP1 CovP2 Res Log Like -2 Res Log Like 0 1.0000 -5.3070 10.6140 Iteration History Iteration Evaluations -2 Res Log Like Criterion 1 1 10.61404477 0.00000000 Convergence criteria met.
SAS Output: Random effects regression model The SAS System The Mixed Procedure Covariance Parameter Estimates Cov Parm Estimate study 0 Residual 1.0000 Fit Statistics -2 Res Log Likelihood 10.6 AIC (smaller is better) 10.6 AICC (smaller is better) 10.6 BIC (smaller is better) 10.6 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 0 0.00 1.0000 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 0.1646 0.08221 12 2.00 0.0684
SAS Output: Fixed effects regression model
fixed effects model The Mixed Procedure Model Information Data Set WORK.DAT Dependent Variable beta Weight Variable w Covariance Structure Variance Components Estimation Method REML Residual Variance Method Parameter Fixed Effects SE Method Model-Based Degrees of Freedom Method Containment Class Level Information Class Levels Values study 13 AHS BCDDP CNBSS CPS2 IWHS NHSII NHSa NHSb NLCS NYS NYU SMC WHS Dimensions Covariance Parameters 2 Columns in X 1 Columns in Z 13 Subjects 1 Max Obs Per Subject 13 Observations Used 13 Observations Not Used 0 Total Observations 13 Parameter Search CovP1 CovP2 Res Log Like -2 Res Log Like 0 1.0000 -5.3070 10.6140 Iteration History Iteration Evaluations -2 Res Log Like Criterion 1 1 10.61404477 0.00000000 Convergence criteria met.
SAS Output: Fixed effects regression model The SAS System The Mixed Procedure Covariance Parameter Estimates Cov Parm Estimate study 0 Residual 1.0000 Fit Statistics -2 Res Log Likelihood 10.6 AIC (smaller is better) 10.6 AICC (smaller is better) 10.6 BIC (smaller is better) 10.6 PARMS Model Likelihood Ratio Test DF Chi-Square Pr > ChiSq 0 0.00 1.0000 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 0.1646 0.08221 12 2.00 0.0684
Prospectively PlannedProspectively Planned Pooled Analyses
Protocol standardized across studies for
• hypotheses
• data collection methods
• definition of variables
• analyses
European Prospective Investigation into Cancer and Nutrition (EPIC): Study Design
Multicenter prospective study• 22 centers in 9 countries• Initiated 1993-1998
Objective:• Improve scientific knowledge on nutritional
factors involved in diet• Provide scientific bases for public health
interventions Baseline cohort: 484,042
Riboli 2001
EPIC: Study Design, cont’d
Measures• Questionnaires• Anthropometry• Blood samples (n=387,256)
Outcomes• Cancer registry (n=6)• Combination (n=3)
–Health insurance records–Cancer and pathology registries–Active followup
• Mortality registries (n=9)
Riboli 2001
EPIC: Diet Assessment Methods
Self-administered questionnaire (n=7 countries)• 300-350 foods
Interviewer-administered questionnaire (n=2 centers)• Similar to self-administered questionnaire
Food frequency questionnaire + 7-day diet record (n=2 centers)
24-hr recall from 8-10% random sample from each cohort
Riboli 2001
Why Are Pooled Analyses Time-Consuming?
Data management Add updated case information Errors found in data Individual study wants to publish their findings
prior to submitting pooled results Manuscript review Signature sheets
“Pooling decreases the variation caused by random error (increasing the sample size) but does not eliminate any bias (systematic error)”.
Blettner 1999
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