*! version 1.0.0 metaLong for Stata 14.1

ml_meta — Longitudinal Meta-Analysis with Robust Variance Estimation

Syntax

ml_meta yi vi [if] [in] ,
study(varname)
time(varname)
[options]

Description

ml_meta fits a random-effects meta-analytic model at each unique time point
in a long-format dataset. The pooled estimate uses DerSimonian-Laird tau2 and
inverse-variance random-effects weights. Standard errors are cluster-robust
(Huber-White sandwich), clustered by study.

Options

study(varname) — Study (cluster) identifier variable. Required.

time(varname) — Numeric follow-up time variable. Required.

alpha() — Significance level for CIs and p-values. Default 0.05.

mink() — Minimum number of studies required to fit a model
at a given time point. Default 2.

nosmallsample — Use z-based (Wald) inference instead of t(k-1).
By default, the t(k-1) distribution is used as a small-sample correction.

saving() — Save results dataset to filename.

replace — Allow overwriting an existing saving() file.

Returned values (r-class)

The following are stored in r():

r(meta) — Matrix with one row per time point.
Columns: time k theta se df t_stat p_val ci_lb ci_ub tau2.

r(alpha) — Significance level used.

r(n_times) — Number of time points.

Saved dataset variables

time Follow-up time

k Number of studies

theta Pooled effect (RE)

se Cluster-robust standard error

df Degrees of freedom

t_stat t-statistic

p_val Two-sided p-value

ci_lb Lower confidence bound

ci_ub Upper confidence bound

tau2 DL between-study variance

sig 1 if significant at alpha

Statistical method

At each time point t:

(1) Fixed-effects weights: wi = 1/vi.

(2) Q statistic: Q = sum(wi*(yi - theta_FE)^2).

(3) DL tau2: max(0, (Q - (k-1)) / c) where c = sum(wi) - sum(wi^2)/sum(wi).

(4) RE weights: wi_RE = 1/(vi + tau2).

(5) Pooled estimate: intercept from
regress yi [aw=wi_RE] if t==tt, vce(cluster study).

(6) Inference: t(k-1) distribution (small-sample default).

Example

. sim_longmeta, k(20) times(0 6 12 24) seed(42) clear

. ml_meta yi vi, study(study) time(time) saving(meta_res) replace

. use meta_res, clear

. list

References

Hedges, L.V., Tipton, E., & Johnson, M.C. (2010).
Research Synthesis Methods, 1(1), 39-65.

Tipton, E. (2015). Psychological Methods, 20(3), 375-393.