metahet {altmeta} | R Documentation |
Meta-Analysis Heterogeneity Measures
Description
Calculates various between-study heterogeneity measures in meta-analysis, including the conventional measures (e.g., ) and the alternative measures (e.g.,
) which are robust to outlying studies; p-values of various tests are also calculated.
Usage
metahet(y, s2, data, n.resam = 1000)
Arguments
y |
a numeric vector specifying the observed effect sizes in the collected studies; they are assumed to be normally distributed. |
s2 |
a numeric vector specifying the within-study variances. |
data |
an optional data frame containing the meta-analysis dataset. If |
n.resam |
a positive integer specifying the number of resampling iterations for calculating p-values of test statistics and 95% confidence interval of heterogeneity measures. |
Details
Suppose that a meta-analysis collects studies. The observed effect size in study
is
and its within-study variance is
. Also, the inverse-variance weight is
. The fixed-effect estimate of overall effect size is
. The conventional test statistic for heterogeneity is
Based on the statistic, the method-of-moments estimate of the between-study variance
is (DerSimonian and Laird, 1986)
Also, the and
statistics (Higgins and Thompson, 2002; Higgins et al., 2003) are widely used in practice because they do not depend on the number of collected studies
and the effect size scale; these two statistics are defined as
Specifically, the statistic reflects the ratio of the standard deviation of the underlying mean from a random-effects meta-analysis compared to the standard deviation from a fixed-effect meta-analysis; the
statistic describes the proportion of total variance across studies that is due to heterogeneity rather than sampling error.
Outliers are frequently present in meta-analyses, and they may have great impact on the above heterogeneity measures. Alternatively, to be more robust to outliers, the test statistic may be modified as (Lin et al., 2017):
Based on the statistic, the method-of-moments estimate of the between-study variance
is defined as the solution to
If no positive solution exists to the equation above, set . The counterparts of the
and
statistics are defined as
To further improve the robustness of heterogeneity assessment, the weighted mean in the statistic may be replaced by the weighted median
, which is the solution to
with respect to
. The new test statistic is
Based on , the new estimator of the between-study variance
is the solution to
The counterparts of the and
statistics are
Value
This function returns a list containing p-values of various heterogeneity tests and various heterogeneity measures with 95% confidence intervals. Specifically, the components include:
p.Q |
p-value of the |
p.Q.theo |
p-value of the |
p.Qr |
p-value of the |
p.Qm |
p-value of the |
Q |
the |
ci.Q |
95% CI of the |
tau2.DL |
DerSimonian–Laird estimate of the between-study variance. |
ci.tau2.DL |
95% CI of the between-study variance based on the DerSimonian–Laird method. |
H |
the |
ci.H |
95% CI of the |
I2 |
the |
ci.I2 |
95% CI of the |
Qr |
the |
ci.Qr |
95% CI of the |
tau2.r |
the between-study variance estimate based on the |
ci.tau2.r |
95% CI of the between-study variance based on the |
Hr |
the |
ci.Hr |
95% CI of the |
Ir2 |
the |
ci.Ir2 |
95% CI of the |
Qm |
the |
ci.Qm |
95% CI of the |
tau2.m |
the between-study variance estimate based on the |
ci.tau2.m |
95% CI of the between-study variance based on the |
Hm |
the |
ci.Hm |
95% CI of the |
Im2 |
the |
ci.Im2 |
95% CI of the |
References
DerSimonian R, Laird N (1986). "Meta-analysis in clinical trials." Controlled Clinical Trials, 7(3), 177–188. <doi: 10.1016/0197-2456(86)90046-2>
Higgins JPT, Thompson SG (2002). "Quantifying heterogeneity in a meta-analysis." Statistics in Medicine, 21(11), 1539–1558. <doi: 10.1002/sim.1186>
Higgins JPT, Thompson SG, Deeks JJ, Altman DG (2003). "Measuring inconsistency in meta-analyses." BMJ, 327(7414), 557–560. <doi: 10.1136/bmj.327.7414.557>
Lin L, Chu H, Hodges JS (2017). "Alternative measures of between-study heterogeneity in meta-analysis: reducing the impact of outlying studies." Biometrics, 73(1), 156–166. <doi: 10.1111/biom.12543>
Examples
data("dat.aex")
set.seed(1234)
metahet(y, s2, dat.aex, 100)
metahet(y, s2, dat.aex, 1000)
data("dat.hipfrac")
set.seed(1234)
metahet(y, s2, dat.hipfrac, 100)
metahet(y, s2, dat.hipfrac, 1000)