Methods for Summarizing the Evidence: Meta-Analyses and Pooled Analyses Donna Spiegelman, Sc.D. Departments of Epidemiology and Biostatistics Harvard School of Public Health

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 Citrus Fruits Vegetables< Green Veg Carrots 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 reviews Montori 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

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

Random Effects  Studies allowed to have different underlying or true effects  Allows variation between studies as well as within studies

Random Effects Model

Random Effects Model, continued

Test for Heterogeneity

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

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 + β 1 GENDER s + β 2 CURRENT s + β 2 PAST s + b s + ε s GENDER s = 1 if study s is male; 0 if female CURRENT s = 1 if study s has current smokers only, 0 otherwise PAST s = 1 if study s has past smokers only, 0 otherwise H 0 : β 1 = 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 R 2 (to be defined) CV = / Ι β Ι, with S=ranging from 7 to 33 12

Analysis of between-studies heterogeneity  Explored maximum likelihood methods for estimation of and testing H 0 : =0 (i.e. no between-studies heterogeneity) ML methods have power roughly equivalent to D&L’s, but assume b s ~N (0, ) and ε s ~ N [ 0, Var s ( β s ) ] LRT for H 0 : = 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 14 ^

Quantification of heterogeneity CV B = /  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 CV B, R 2 (Identical to I 2 (Higgins et al., 2006)) 1 ^

* Parametric bootstrap version of the test. † Odds ratio = 2. ‡ WLS, weighted least squares; LRT, likelihood ratio test. § R 2, proportion of the total variance due to between-study variance: /(( + (S x Var(  ))). Power of Test of Heterogeneity 13

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 fruits0.94 ( ) <0.001 Total vegetables0.75 ( )<0.001 Gandini, 2000

Fruits and Vegetables and Breast Cancer Meta-Analysis: Sensitivity Analysis # of RR Significance Studies of factors Study design Case-control Cohort Validated FFQ Yes60.85 No 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-planned Retrospectively-planned meta-analysis of individual patient data Established in

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 Cohort Netherlands 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 Units Example: Vitamin A, Carotene  Units:  g retinol equivalents  g 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: 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 (ref) 1.00 (ref) ( ) 0.99 ( ) ( ) 0.97 ( ) ( ) 0.96 ( ) p for trend p for hetero Quartile Total Fruits Total Vegetables RR (95% CI) RR (95% CI) Smith-Warner, et al. 2001

Contrast to Vegetable and Breast Cancer Meta-Analysis: Results RR (95% CI)p for het high vs low Total fruits0.94 ( ) <0.001 Total vegetables0.75 ( )<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 Citrus Fruits All Vegetables< Green Veg Carrots WCRF/AICR 1997

CONTRAST TO 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

Pooled Multivariate Relative Risks of Breast Cancer and Botanically Defined Fruit and Vegetable Groups and Individual Foods RR (95% CI) Cruciferae0.96 ( ) Leguminosae0.97 ( ) Rutaceae0.99 ( ) Carrots0.95 ( ) Potatoes1.03 ( ) Apples0.96 ( ) Increment=100 g/d Smith-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 ( ) Postmeno ( )0.80 Total vegetables Premeno ( ) Postmeno ( )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 projects Ritz J, Demidenko E, Spiegelman D Journal of Statistical Planning and Inference, 2008; 138:  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 one 4

Multivariate Pooling -Let β s = β + b s + e s + +, s = 1,… s studies dim ( β)= p model covariates E( b s ) = E (e s ) = 0, Var(b s ) = Σ B, Var(e s ) = Cov ( β s ) pxp 5 -If Σ B and Cov ( β s ) are not diagonal, more efficient estimates of β can be obtained -Weighted estimating equation ideas are used -Test statistics for H 0: Σ B = 0 and major submatrices are given assuming normality in b s and e s and asymptotically ^ ^ ^

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Results From Smith-Warner, et al “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 fat86% 81% 93% 84% Mono-unsaturated fat76% 72% 36% 32% Poly-unsaturated fat91% 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) MLEEE

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 17

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 , 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

Multivariate 1 Adjusted Relative Risks (RR) and 95% Confidence Intervals (CI) for Ovarian Cancer According to Lactose Intake (>30g/day compared to <10g/day) by Study

Data and SAS Program to analyze Lactose and Ovarian Cancer – Pooling Project

SAS Output for Analysis of Lactose Data

SAS Output: Random effects regression model

SAS Output: Fixed effects regression model

Prospectively Planned Prospectively 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  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) 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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