The purpose of ‘metaKIN’ is to assist users in efficiently specifying metaSEM models.
To install metaKIN run the following code:
#install.packages("remotes")
remotes::install_github("conig/metaKIN")This packages is a wrapper around the metaSEM package. It does not perform any calculations itself, but rather converts your instructions into metaSEM syntax. Resultant models are returned along with formatted output. The full model call is reproducible so users can scrutinise intermediate steps.
Functions are built around meta3 and tssem1 and tssem2
metaKIN will automatically load metaSEM (upon which it heavily depends).
To run a metaSEM model, you need an effect size, corresponding sampling variance, and information about how effect sizes are clustered.
We’ll use the Bornmann07 dataset included in metaSEM. This meta-analysis sought to determine whether women were more or less likely than men to have their grant proposals approved.
library(metaKIN)## meta�[1m�[31mKIN�[39m�[22m 0.3.0
## Under active development.
## Report bugs: https://github.com/conig/metaKIN/issues
dat <- metaSEM::Bornmann07
m0 <- meta3L(
y = logOR,
v = v,
cluster = Cluster,
data = dat
)
summary(m0)##
## Call:
## meta3L(y = logOR, v = v, cluster = Cluster, data = dat)
##
## 95% confidence intervals: z statistic approximation (robust=FALSE)
## Coefficients:
## Estimate Std.Error lbound ubound z value Pr(>|z|)
## Intercept -0.1007784 0.0401327 -0.1794371 -0.0221198 -2.5111 0.01203 *
## Tau2_2 0.0037965 0.0027210 -0.0015367 0.0091297 1.3952 0.16295
## Tau2_3 0.0141352 0.0091445 -0.0037877 0.0320580 1.5458 0.12216
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Q statistic on the homogeneity of effect sizes: 221.2809
## Degrees of freedom of the Q statistic: 65
## P value of the Q statistic: 0
##
## Heterogeneity indices (based on the estimated Tau2):
## Estimate
## I2_2 (Typical v: Q statistic) 0.1568
## I2_3 (Typical v: Q statistic) 0.5839
##
## Number of studies (or clusters): 21
## Number of observed statistics: 66
## Number of estimated parameters: 3
## Degrees of freedom: 63
## -2 log likelihood: 25.80256
## OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
## Other values may indicate problems.)
The baseline model shows us the pooled log-odds of women having their proposals approved relative to men. The intercept shows that for included studies, the pooled log-odds for relative approval was -0.1 [95%CI -.18, -.02]. That women were less likely to have their prosals approved.
I2_2 shows the proportion of heterogeneity within cluster. I2_3 shows the heterogeneity between studies.
There was more heterogeneity between clusters than within clusters
metaSEM allows users to test for the effect of moderators. To do this, a categorical moderator (e.g. Proposal type) must be converted to a matrix (often by encoding dummy variable).
In metaKIN this process can be done automatically. Just provide the baseline model and a variable or equation you wish to moderate by.
moderation_object = m0 |>
moderate("Proposal type" = Type)
moderation_object## Moderation results:
##
## I2(2): 15.7%
## I2(3): 58.4%
## ---------------------------------------
## moderation k n R2_2 R2_3 p.value
## ---------------------------------------
## 1 Proposal type 21 66 0.07 0.79 0.004*
## ---------------------------------------
## All models converged.
The p-value demonstrates that the baseline model is significantly improved by including gender as a moderator.
To get the specific values we can call summary on this object. Additionally, we can request a transformation to something which is easier to interpret than log-odds.
summary(moderation_object,
transf = exp,
transf_name = "OR [95% CI]")## Moderation results
## -----------------------------------------------------------------------------
## Moderation k n OR [95% CI] Estimate SE p R2(2) R2(3) LRT_p
## -----------------------------------------------------------------------------
## Baseline 21 66 0.90 [0.84, 0.98] -0.10 0.04 0.012
## Proposal type 21 66 6.93 79.43 0.004
## Intercept 0.99 [0.92, 1.07] -0.01 0.04 0.86
## Fellowship 11 26 0.82 [0.74, 0.91] -0.20 0.05 < 0.001
## -----------------------------------------------------------------------------
We can see that females were less likely to get fellowships than males, but about as likely to get other kinds of grants.
If we want to add more moderators we just throw them into the moderation function as argument separated by commas. These models are estimated separately.
moderation_object2 <- m0 |>
moderate(Type, Discipline, Country)
moderation_object2## Moderation results:
##
## I2(2): 15.7%
## I2(3): 58.4%
## ------------------------------------
## moderation k n R2_2 R2_3 p.value
## ------------------------------------
## 1 Type 21 66 0.07 0.79 0.004*
## 2 Discipline 21 66 0.00 0.50 0.13
## 3 Country 21 66 0.12 0.66 0.020*
## ------------------------------------
## All models converged.
We can see that including the moderator matrix for type and country improved the baseline model’s fit, but discipline did not.
We can then format this table with another function
summary(moderation_object2,
transf = exp,
transf_name = "OR [95% CI]")## Moderation results
## --------------------------------------------------------------------------------------------
## Moderation k n OR [95% CI] Estimate SE p R2(2) R2(3) LRT_p
## --------------------------------------------------------------------------------------------
## Baseline 21 66 0.90 [0.84, 0.98] -0.10 0.04 0.012
## Type 21 66 6.93 79.43 0.004
## Intercept 0.99 [0.92, 1.07] -0.01 0.04 0.86
## Fellowship 11 26 0.82 [0.74, 0.91] -0.20 0.05 < 0.001
## Discipline 21 66 0.00 49.75 0.13
## Intercept 0.98 [0.84, 1.13] -0.02 0.08 0.75
## Life sciences/biology 12 26 0.89 [0.76, 1.05] -0.12 0.08 0.16
## Social sciences/humanities 5 13 0.80 [0.64, 1.00] -0.23 0.11 0.047
## Multidisciplinary 5 13 1.01 [0.83, 1.23] 0.01 0.10 0.93
## Country 21 66 12.09 66.06 0.020
## Intercept 1.00 [0.89, 1.13] 0.00 0.06 0.97
## Canada 1 3 0.87 [0.69, 1.10] -0.13 0.12 0.26
## Australia 5 13 0.98 [0.79, 1.21] -0.02 0.11 0.83
## United Kingdom 4 10 1.06 [0.87, 1.28] 0.05 0.10 0.59
## Europe 7 28 0.80 [0.69, 0.93] -0.22 0.07 0.003
## --------------------------------------------------------------------------------------------
By default, the intercept is calculated for all matrices which represents the first level (for models including factors). The other levels show the distance from the reference level. We can check what the reference level for country is by looking at the first factor level:
levels(dat$Country)[1]## [1] "United States"
If we do not want intercepts we can specify that in the formula, like in regular regression equations:
moderation_object2.noint <- m0 |>
moderate(Type = ~ Type - 1,
Discipline = ~ Discipline - 1,
Country = ~ Country - 1)
moderation_object2.noint## Moderation results:
##
## I2(2): 15.7%
## I2(3): 58.4%
## ------------------------------------
## moderation k n R2_2 R2_3 p.value
## ------------------------------------
## 1 Type 21 66 0.07 0.79 0.004*
## 2 Discipline 21 66 0.00 0.50 0.13
## 3 Country 21 66 0.12 0.66 0.020*
## ------------------------------------
## All models converged.
This doesn’t change model fit. But it does change how the model is displayed. Now you can see all the levels; but there is no longer a reference level, so each estimate is absolute (e.g. the coefficient for Australia no longer describes the difference between Australia and USA.)
summary(moderation_object2.noint,
transf = exp,
transf_name = "OR [95% CI]")## Moderation results
## --------------------------------------------------------------------------------------------
## Moderation k n OR [95% CI] Estimate SE p R2(2) R2(3) LRT_p
## --------------------------------------------------------------------------------------------
## Baseline 21 66 0.90 [0.84, 0.98] -0.10 0.04 0.012
## Type 21 66 6.93 79.43 0.004
## Grant 13 40 0.99 [0.92, 1.07] -0.01 0.04 0.86
## Fellowship 11 26 0.82 [0.76, 0.88] -0.20 0.04 < 0.001
## Discipline 21 66 0.00 49.75 0.13
## Physical sciences 5 14 0.98 [0.84, 1.13] -0.02 0.08 0.75
## Life sciences/biology 12 26 0.87 [0.80, 0.95] -0.14 0.04 0.001
## Social sciences/humanities 5 13 0.78 [0.64, 0.95] -0.25 0.10 0.013
## Multidisciplinary 5 13 0.99 [0.87, 1.12] -0.01 0.06 0.82
## Country 21 66 12.09 66.06 0.020
## United States 4 12 1.00 [0.89, 1.13] 0.00 0.06 0.97
## Canada 1 3 0.88 [0.72, 1.07] -0.13 0.10 0.20
## Australia 5 13 0.98 [0.82, 1.17] -0.02 0.09 0.82
## United Kingdom 4 10 1.06 [0.91, 1.24] 0.06 0.08 0.48
## Europe 7 28 0.80 [0.73, 0.89] -0.22 0.05 < 0.001
## --------------------------------------------------------------------------------------------
A method is provided to convert moderated tables to paragraph descriptions which can be rendered in rmarkdown.
report(moderation_object2, rmarkdown = FALSE)[1] “Twenty-one studies (including sixty-six effect sizes) reported
data which could be pooled. Inspecting the Q statistic revealed
significant heterogeneity
For those who use {papaja}, a method is included for apa_table()
moderation_object2 |>
format_nicely() |>
papaja::apa_table(caption = "Moderation table created with apa\\_table",
landscape = TRUE,
escape = FALSE)
To make a forest plot you need to have author in one column, and year in another. In the Bornmann07 dataset this information is in the same column so we need to split it using regex.
dat$study_year <- stringr::str_extract(dat$Study, "[0-9]{1,4}")
dat$study_author <- gsub("\\s.*","",dat$Study)plot(
moderation_object,
author = "study_author",
year = "study_year",
transf = exp,
xlab = "OR"
)
Author and year were automatically detected by looking for clues like “et al”. But you can also manually specify them.
A function is provided to create a funnel plot from metaSEM models. Data can be aggregated to cluster for ease of interpretation. Trim and fill can be employed using an argument.
moderation_object2 |>
funnel_plot(density = TRUE, xlab = "lnOR",
aggregate = TRUE, trimfill = TRUE)