An example comparing effect of increased dosage of statins on mycardial infarction.
In conclusive evidence.
Cannon et al 2006
Hypothesis: Genetic risk score for obesity has more effect on inactive people
GRS=n∑i=1risk alleles
The goal of meta analyses is to contextualize the results of any study in the context
of all the other studies
Statistical Significance
Clinical importance of the effect
Consistency of effects
Consider Ahmed et al.
X- axis : Sample size
Y- axis :statistical power
Fisher's method: Sum of minus log-transformed P-values where larger Fisher score reflects stronger aggregated differential expression evidence.
p=−2×k∑i=1 ln (pi)
p=−2×k∑i=1 ln (1−pi)
Zi=Φ−1(1−pi)
Φ is the standard normal cumulative distribution function.
∑ki=1 Zi√k
it allows including weights for the studies. In this case, the statistic is
minP: min
maxP: \begin{equation} \mathit{\max}\ \left({p}_1,{p}_2,\dots, {p}_i,\dots, {p}_k\right) \end{equation}
FEM combines the effect size across K studies by assuming a simple linear model with an underlying true effect size plus a random error in each study
\begin{equation} \overline{T_{.}}=\frac{\varSigma{\omega}_i{T}_i}{\varSigma{\omega}_i} \end{equation}
REM extends FEM by allowing random effects for the inter-study heterogeneity in the model.
\begin{equation} {\overline{T_{.}}}^{\ast }=\frac{\sum_{i=1}^k\ {\omega}_i^{\ast }{T}_i}{\sum_{i=1}^k\ {\omega}_i^{\ast }} \end{equation}
\omega are the different weights assigned to each study, that is, the inverse within-study variance V\Big({T}_i\Big) and \begin{equation} {\omega}_i=\frac{1}{V\left({T}_i\right)} \end{equation}
The statistic that represents the total variance, Q, is defined as (Cochran's Q) which is computed by summing the squared deviations of each study's estimate from the overall meta-analytic estimate
\begin{equation} Q=\sum_{i=1}^k\ {\omega}_i\left({T}_i-\overline{T_{.}}\right) \end{equation}
where T_i is the observed effect, ωi is the calculated weights for the FEM and T_i⎯ \widehat{T}.is the combined effect calculated for the FEM
A test for heterogeneity examines the null hypothesis that all studies are evaluating the same effect. The usual test statistic , weighting each study's contribution in the same manner as in the meta-analysis.
P values are obtained by comparing the statistic with a \chi^2 distribution with k-1 degrees of freedom (where k is the number of studies).
I2 = 100×(Q - df)/Q, where Q is Cochran's heterogeneity statistic and df the degrees of freedom$
\begin{equation} {RP}_g=\prod_i^k r_{ig} \end{equation}
\begin{equation} {RS}_g=\sum_i^K {r}_{ig} \end{equation}
Vertical Integration
Horizontal integration techniques cross studies on the same variables
Detect/validate deferentially expressed genes
Detect/validate deferentially regulated pathways
Detect/ co-expression network
Meta analyses based on pathways
MetaPath: Meta analyses based on pathways
Gene level, Pathway level or a hybrid approach.
Differential co-expression (DC) refers to the change in gene–gene correlations between two conditions (e.g. cases and controls).
The differential correlation relationship could arise from meaningful biological sources as well as uncorrected technical biases
Unwanted batch effect, or mixture of tissues could potentially contribute to co-expression relationships
Differential co-expression may be confirmed across multiple datasets via meta-analyses to increase the detection power and stability.
Disambiguation
Here we are not discussing Network meta-analysis (NMA) which extends principles of meta-analysis to the evaluation of multiple treatments in a single analysis.
*Basic DC module detection
Differential Coexpression based on phenotype
DC supermodule assembly
Bioinformatics. 2017 Apr 15; 33(8): 1121–1129.
An example comparing effect of increased dosage of statins on mycardial infarction.
In conclusive evidence.
Cannon et al 2006
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