Download A guided tour of research study design and statistics II

A guided tour of
research study design and statistics II
Mustafa Soomro
Consultant psychiatrist
St James Hospital, Portsmouth
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Plan
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Systematic Review and Meta-analysis
Economic evaluation
Survival analysis
Factor analysis
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Systematic Review
and Meta-Analysis
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Systematic Review
and Meta-Analysis
• Definitions
– SR: Objective review of all available relevant
studies using standard methods of SR
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Formulating focussed question
Comprehensive searching
Using objective study selection criteria
Quality assessment of studies
Qualitative or quantitative synthesis of data from
included studies
– MA: Quantitative synthesis of data from
included studies
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Meta-analysis
• Quantitative synthesis or pooling of results
from several similar studies
• Steps involved in meta-analysis
– Data extraction from individual studies
– Analysing heterogeneity
– Pooling of results using appropriate statistical
methods (fixed vs. random effects [the
DerSimonian-Laird] model)
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Data needed for meta-analysis
• For continuous outcome you need:
– Mean change and SD of the mean change
within treatment and within control groups
– Number of individuals in treatment and control
group
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Data needed for meta-analysis
• For dichotomous outcome you need:
– Events in treatment group and events in
control group
– Number of individuals in treatment group and
in control group
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Publication bias and
funnel plot test
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Publication bias
and funnel plot test
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Graphical exploration of statistical heterogeneity
L’ Abbe Plot
Y axis= the event rate in the experimental (intervention) group
and X axis= the event rate in the control group
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Graphical exploration of statistical heterogeneity
– Forest plot
• Forest plot (visual test)
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Assessing statistical heterogeneity
• Cochran’s Q test (chi square test):
• Q has low power when the number of studies is small; Q
has too much power as if the number of studies is large
(Higgins et al. 2003);
• Gives you chi square statistic and p value; with small
number of trials p should be fixed at 0.1
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Q forms part of the DerSimonian-Laird random effects pooling method (DerSimonian
and Laird 1985).
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Assessing statistical heterogeneity
• I² statistic:
– the percentage of variation across
studies that is due to heterogeneity
rather than chance (Higgins and
Thompson, 2002; Higgins et al., 2003).
– I² = 100% x (Q-df)/Q.
– Unlike Q it does not inherently depend
upon the number of studies considered.
• A confidence interval for I² is constructed using either i) the iterative non-central chisquared distribution method of Hedges and Piggott (2001); or ii) the test-based method
of Higgins and Thompson (2002).
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Assessing statistical heterogeneity
• I² statistic: interpretation of
– 0% to 40%: might not be important;
– 30% to 60%: may represent moderate
heterogeneity*;
– 50% to 90%: may represent substantial
heterogeneity*;
– 75% to 100%: considerable heterogeneity*.
• *The importance of the observed value of ‘I square’ depends
on (i) magnitude and direction of effects and (ii) strength of
evidence for heterogeneity (e.g. P value from the chi-squared
test, or a confidence interval for ‘I square’).
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Forest plot for dichotomous data
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Forest plot for continuous data
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When heterogeneity is present
• To pool or not pool that is the question.
– To pool using random effects model
– Not to pool
– And investigate heterogeneity
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Investigating heterogeneity
• Meta-regression
• Subgroup analysis
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Economic analysis / evaluation
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Methods of economic evaluation
• Cost Minimisation
– Intervention with less cost (£s) [input] is selected (used when
outcome [output] of two interventions are considered as
broadly similar)
• Cost effectiveness
– Cost (£s) [input] for each intervention for the same
magnitude of improvement on a particular outcome scale
[output]. Less costly option would be more cost effective
• Cost Utility
– Cost (£s) [input] for each intervention in terms of life utility
units (QUALYS or QOL or DALYS)
• Cost benefit
– Cost (£s) [input] for each intervention as input; and different
types of outputs are translated into monetary terms (£s).
• Cost consequences:
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– Cost (£s) [input] input; and output are natural units like days
Economic evaluation - CEAC
• Cost effectiveness
acceptability curve:
– Y = probability that
an intervention is
cost-effective
compared with the
alternative
– X = for a range of λ
(Willingness to
Pay) values.
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Survival time / event history /
time to vent analysis
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Survival time analysis
Type of data:
Any outcome that is dichotomous occurs
once during follow up
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Survival time analysis
• Survival rate does not provide time to event
information (it only gives rate towards the end of a
period e.g. 5 year survival rate)
• Time to event data provide more detailed information
of probability of survival at any given point.
• However time to event data are often censored –
therefore require special consideration in terms of
analysis
• Censored data refer to incomplete data.
– Examples of incomplete data are:
• individuals still alive (no event) at end of study
• individual lost to follow up or left study before the end
• event not recorded properly
– Data in above examples are right censored
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Censored data
• Censored data
– Suppose a set of components are being monitored to
see how long they last. If the monitoring stops before all
the components have broken, then the information
concerning the lifetimes of the unbroken components
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has been censored
Survival time analysis
• Life tables and survival curve analysis (KM survival
curve)
– Calculates probabilities of survival at any point during follow up
period
– Censored data are removed before probabilities are calculated
– Probability of survival at particular point is conditional probability at
that point (Kirkwood 1988, p118; Altman 1991, p368)
• Log rank test (compares two curves)
• Cox regression analysis (estimates of hazard ratio
controlling for confounders)
– Hazard ratio (HR) is the ratio of hazard rates for group1 to group2
over the same time period
• Hazard rate is the ratio of number of events within the group to total
number within the group, over a given time period
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Survival time analysis – life table
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Survival time analysis – KM curves
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Survival time analysis –
KM curve details
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Exploratory factor analysis
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Exploratory factor analysis
Principal (common) factor analysis and
principal component analysis
• Basic idea:
– Multiple variable correlation is used to extract
underlying dimensions (i.e. groups of
variables which correlate highly with one
another).
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Exploratory factor analysis
Principal (common) factor analysis and
principal component analysis
• Principal (common) factor analysis:
uses common variance (correlationfocussed method) only to find out
underlying dimensions composed of
common variances only (this approach is
used in SEM). This accounts for only
common variance between variables.
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Exploratory factor analysis
• Principal component analysis: uses
both common and unique variances
between variables (variance-focussed
method) to find out underlying
dimensions; used for data reduction. This
accounts for all variance between
variables.
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Exploratory factor analysis
• Factor loading: correlation coefficient between a
variable and a factor (this is also interpreted as
regression coefficient predicting variable from
factor).
• Communality: communality measures the
proportion of variance of a given variable explained
by all the factors jointly.
• Eigenvalue: The eigenvalue for a given factor
measures the amount of variance in all the
variables, which is accounted for by that factor.
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Exploratory factor analysis
• How many factors to extract: all factors
with eigenvalue greater than 1
– Or using scree plot [factors x axis and
eigenvalues y axis], thus all factors before the
point of inflexion would be selected
• Factor rotation is carried out to maximise
factor loadings (to help in interpretation of
factors). Varimax (orthogonal) rotation is
most common method; other is oblique
rotation
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