Sergio Uribe

# Meta-Analysis Course Materials

Below you can find the course materials (this website will be updated during the course with new materials). Please download the files to your computer (right-click on the link to a file and select “Save Link/Target As” to download a file to your computer). This website is temporary and will not be available after the course is over.

## Lecture Slides

## Exercises

## Datasets

## Code from Lectures

## Solution for Exercises

## Code for Exercises

## Literature

Chalmers, I., Hedges, L. V., & Cooper, H. (2002). A brief history of research synthesis. Evaluation and the Health Professions, 25(1), 12-37.

Durlak, J. A., & Lipsey, M. W. (1991). A practitioner's guide to meta-analysis. American Journal of Community Psychology, 19(3), 291-332.

LaValley, M. (1997). A consumer's guide to meta-analysis. Arthritis Care and Research, 10(3), 208-213.

Colditz, G. A., Brewer, T. F., Berkey, C. S., Wilson, M. E., Burdick, E., Fineberg, H. V., & Mosteller, F. (1994). Efficacy of BCG vaccine in the prevention of tuberculosis: Meta-analysis of the published literature. Journal of the American Medical Association, 271(9), 698-702.

Normand, S. T. (1999). Meta-analysis: Formulating, evaluating, combining, and reporting. Statistics in Medicine, 18(3), 321-359.

Riley, R. D., Higgins, J. P. T., & Deeks, J. J. (2011). Interpretation of random effects meta-analyses. British Medical Journal, 342, d549.

Laird, N. M., & Mosteller, F. (1990). Some statistical methods for combining experimental results. International Journal of Technology Assessment in Health Care, 6(1), 5-30.

Viechtbauer, W. (2007). Accounting for heterogeneity via random-effects models and moderator analyses in meta-analysis. Zeitschrift für Psychologie / Journal of Psychology, 215(2), 104-121.

Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1-48.

# Meta-Analysis Course

## General Information

## Course Description

Researchers trying to summarize the constantly growing body of research in the social, health, and natural sciences are increasingly using a technique called meta-analysis. Meta-analysis encompasses an entire array of statistical methods for aggregating and comparing the results from related studies in a systematic manner. For example, meta-analysis is frequently used to determine whether a particular treatment or intervention is actually effective overall and whether the effectiveness of the treatment or intervention depends on certain study and/or subject characteristics (so-called moderator variables). The focus of this course will be on current methods and techniques for analyzing meta-analytic data.

We will start out with a short overview of the entire meta-analytic process (consisting of seven steps: problem formulation, literature search, information gathering, quality evaluation, analysis, interpretation of findings, and presentation of results). Next, we will examine how the results from a study can be summarized with various effect size or outcome measures. We will then delve into equal-, fixed-, and random/mixed-effects models for combining the observed outcomes and for examining whether the outcomes depend on one or more moderator variables. The use of so-called meta-regression models will be emphasized in this context. Model diagnostics and methods for sensitivity analyses will be covered as well.

A major problem that may distort the results of a meta-analysis is publication bias (the fact that the published literature may not be representative of all the research that has been conducted on a particular topic). Therefore, current methods for detecting and dealing with publication bias will be discussed next. Finally, time permitting (and depending on the interests of the participants), we will examine missing data issues, sequential/cumulative methods in the context of meta-analysis, meta-analytic techniques using individual subject data, multilevel and multivariate models, methods for dealing with dependent/correlated outcomes, and Bayesian approaches to meta-analysis.

The course consists of a mixture of lectures, hands-on tutorials, and computer exercises to cover not only the theoretical background, but also provide practical experience with analyzing real meta-analytic datasets. Emphasis throughout the course is on the application of the various methods and the interpretation of the results obtained (supplementary references can be provided to those interested in the mathematical/statistical details).

## Course Schedule

Note: Despite the level of detail, this schedule is tentative. The starting and ending times of the course are definite, but everything in between is subject to change. Also, breaks are not explicitly indicated in the schedule below, but are planned in throughout the days.

# Meta-analisis

Es una técnica de análisis de datos que permite combinar cuantitativamente los resultados de distintos estudios. En 1989, Gene V. Glass acuño el término al combinar los estudios de 375 estudios de psicoterapia.

## Indicaciones

1. Distintos estudios acerca de un mismo tratamiento dan distintos resultados
2. Se desea conocer con mayor precisión el efecto de una intervención: aumentar el tamaño muestral
3. Se desea hacer análisis de subgrupos

## Funciones del meta-analisis

1. Identifica heterogeneidad entre estudios
2. Identifica sesgos de publicación
3. Cuando es apropiado, provee una medida de efecto promedio
4. Aumenta el poder estadístico y precisión para detectar un efecto
5. Prueba, refina y genera hipótesis
6. Reduce la subjetividad entre comparaciones de estudios utilizando métodos sistemáticos y explícitos para compararlos
7. Identifica vacios en el conocimiento y propone futuros estudios
8. Analiza el efecto de estudios previos en el conocimiento o actitud clínica

## Etapas de un meta-análisis

1. Pregunta de investigación
2. Protocolo, con
   1. bases de datos
   2. estrategias de búsqueda
   3. términos claves
   4. criterios de inclusión y exclusión
   5. criterios para la evaluación de calidad
   6. criterios para la extracción de datos
   7. criterios para la síntesis de datos

## Análisis

### Sesgo de publicación Funnel plot: muy utilizado Egger's regression test: estudios pequeños tienden a tener mayores tamaños de efecto que los esperados, lo que implica que estudios pequeños con pequeños tamaños de efecto tienden a no ser publicados. Begg's rank correlation

### Medida de efecto #### Binaria Odds ratio Risk Ratio Risk difference #### Continua Promedio Effect size: cualquier medida de efecto

### Modelo fijo o aleatorio Los datos se pueden analizar asumiendo que se incluyeron todos los estudios disponibles, por lo que las diferencias entre estudios se debe a la diferencia de efectividad del tratamiento, y esto es el modelo de efectos fijos. Se puede asumir por otro lado que los estudios incluidos representan a la mayoría de los estudios pero que podrían haber algunos no incluidos. Por esto, las diferencias de efecto entre estudios se podrían deber a otros factores. Este modelo se llama de efectos aleatorios.

¿Cuándo elegir uno u otro? Esto tiene impacto solo para el análisis de medidas binarias. Si deseamos saber el efecto de una intervención en distintos estudios con una población homogénea, el modelo fijo es apropiado. Para las medidas continuas, usualmente no hay diferencias entre uno u otro y generalmente se reportan los resultados de ambos modelos. #### Resultados ##### Binarias ##### Continuas

Ver http://www.edii.uclm.es/~useR-2013/Tutorials/kovalchik/kovalchik_meta_tutorial.pdf

## Tipos de modelos Common practice is to report both fixed and random effects model results.

### Fixed → Same mean ES, zero between-study variance.

The FE model is a description of the studies.

Same mean ES, known variance

Y = θ + ei,

e ∼ N(0, Vi).

### Random → Different mean ES, between-study variance

The RE model regards the studies as a sample of a larger universe of studies.

The RE model can be used to infer what would likely happen if a new study were performed, the FE model cannot.

Y = θ + θ + ei

θ ∼ N(0,τ 2 ),

e ∼ N(0, Vi ).

### Mixed → Study-level regression for mean ES (Meta-Regression)

Y = β′xi+ θi + ei θi ∼ N(0,τ2) ei ∼ N(0, Vi ).

xi = study covariates