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Meta-analysis

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Title: Meta-analysis


1
Meta-analysis
2
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 the
findings (Glass 1976)
3
When is meta-analysis useful?
  • Recurrent issues
  • Small effect sizes e.g. average r in ecology and
    evolution is often lower than 0.20 (Møller
    Jennions 2002)
  • Studies on small and/or highly variable sample
    size
  • Debated theories
  • Møller AP, Jennions MD. 2002. How much variation
    can be explained by ecologists and evolutionary
    biologists? Oecologia 132 492-500

4
Benefits of Meta-Analysis An Example using a
funnel plot
5
Benefits of meta-analysis
  • Gives the general effect of a given phenomenon
    (e.g. the effect of group size on fitness in
    primates Majolo et al 2008)
  • It controls for variance in the data by using
    effect size
  • Effect size a statistical measure portraying the
    degree to which a given event is present in a
    sample (Cohen, 1969). The type of measure is
    called the effect, and its magnitude is
    considered an effect size
  • The effect size of a meta-analysis is greater
    than the effect sizes of the single studies on
    which its based
  • Majolo B, de Bortoli Vizioli a, Schino G (2008)
    Costs and benefits of group living in primates
    group size effects on behaviour and demography.
    Anim Behav 761235-1247

6
Steps to run a meta-analysis
  • Select research question highly studied but
    debated topic?
  • Select criteria for data to be included in your
    dataset (very important to avoid biases!)
  • Collect data from previous studies (published or
    not)
  • Calculate effect size (chosen based on type of
    data available, e.g. means, standard deviations,
    correlation coefficients, and so on)
  • Statistics necessary for chosen effect size can
    be obtained from various sources, e.g. p value,
    F, t, chi-square
  • Calculate variance of your dataset
  • Run analysis with dedicated software (e.g. STATA)

7
Problems of meta-analysis
  • Meta-analysis is usually run on published studies
    and thus the researcher has limited power on data
    availability or experimental design
  • Usually required a minimum of 25 studies (sample
    points) but often meta-analyses have been
    published with smaller sample sizes
  • Meta-analysis is run at the within-study level
    effect size is calculated for each study (so each
    study has to have, e.g., data on a control and an
    experimental group)
  • Publication bias the tendency to publish studies
    only with significant results may bias data used
    in a meta-analysis
  • Test for publication bias need to be performed to
    make sure this factor does not affect results
    (e.g. Beggs or Eggers test)

8
Reading material (available in the library)
  • Hedges L.V. Olkin I. (1985). Statistical
    methods for meta-analysis. Academic Press
  • Stangl D.K. Berry D.A. (2000). Meta-analysis in
    medicine and health policy. E-Book

9
Generalised Linear Mixed Models (GLMMs)
10
Some recurrent problems
  • Data are often clustered or hierarchically
    structured, e.g.
  • Children are nested within schools
  • Subjects come from different populations / study
    sites / cultures
  • Several (repeated) observations are collected on
    the same individual
  • We need to take these clusters into account

11
An example of the relationship between exercise
and blood pressure Missing important
information?
12
Same example as previous slide (relationship
between exercise and blood pressure) but this
time we look at individual scores
13
Some problems with (RM) ANOVAs - 1
  • Missing values a subject is excluded from the
    analysis if one datum is missing
  • Not possible to include covariates on each
    time/condition measurement this is a problem as
    often various factors change across conditions
    (e.g. age)
  • Needs equal spacing among conditions (e.g. time
    1, time 2, time 3)
  • Developmental trajectories difficult to model
    (e.g. growth curves)

14
Some problems with (RM) ANOVAs - 2
  • Differences in individual behaviour not
    detectable, so we may miss important information
  • Not easy to analyse more complex designs
  • individuals nested within families or groups
  • students nested in class, classes nested in
    schools, schools nested in countries...
  • Only available for continuous and normal
    distributed data

15
For example Factors affecting reconciliation in
macaques (Majolo et al 2009)
Aggressor_ID Victim_ID Aggression_type Context Reconciliation
A B Threat Social Yes
A C Bite Feeding No
C A Bite Feeding Yes
D C Threat Social No
A B Bite Feeding No
B A Threat Feeding Yes
Majolo B., Ventura R. Koyama N.F. (2009a). A
statistical modelling approach to the occurrence
and timing of reconciliation in wild Japanese
macaques. Ethology, 115 152-166.
16
GLMMs - 1
  • Solve most (all) of the problems encountered with
    ANOVAs
  • DV can be continuous or dichotomous
  • Individual ID can be incorporated (as a random
    factor) and controlled for (thus we can have
    multiple observations on the same subject without
    the risk of sample inflation)
  • Different fixed factors and covariates can be
    added for each condition or observation time
  • Missing data do not result in sample reduction

17
GLMMs - 2
  • Random factors variables from which you want to
    obtain a more general result from your dataset
  • E.g. You have to control for your subject IDs but
    you want to generalise your finding to the whole
    study population
  • Fixed factors variables for which you are
    interested in their specific effect on the DV
  • E.g. Gender (male vs female) or treatment
    conditions are fixed factors (you cannot
    generalise their effects on the DV to more
    treatments or sex)

18
GLMMs - 3
  • Model selection may be used to choose the model
    with the best fit
  • One measure frequently used is the Akaike
    Information Criterion (AIC)
  • A lower AIC corresponds to a better fit of the
    model

19
Same example as before Factors affecting
reconciliation in macaques (Majolo et al 2009)
Aggressor_ID Victim_ID Aggression_type Context Reconciliation
A B Threat Social Yes
A C Bite Feeding No
C A Bite Feeding Yes
D C Threat Social No
A B Bite Feeding No
B A Threat Feeding Yes
Majolo B., Ventura R. Koyama N.F. (2009a). A
statistical modelling approach to the occurrence
and timing of reconciliation in wild Japanese
macaques. Ethology, 115 152-166.
20
Reading material (available in the library)
  • Ho R. (2006). Handbook of Univariate and
    Multivariate Data Analysis and Interpretation
    with SPSS. Chapman Hall.
  • Tabachnick B.G. Fidell L.S. (2001). Using
    multivariate statistics. Allyn Bacon.
  • West B., Welch K.B. Galecki A.T. (2006). Linear
    Mixed Models A Practical Guide Using Statistical
    Software. Chapman Hall.
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