The name is absent

2. Let I be the current step number. Remove fcθ ^l'' values from the right end of the original Y_i and estimate Δ^ based on
this trimmed set of n — fc∩ ^-1^ values: {Yi,..., Y ɔ/-1 _;}. Construct the next set of centered values

^{v                  v ,     ,} п—Kq '^j

γV=Y_i-∆W, i = l,...,n

and estimate feθŋ using the chosen estimator for k₀ applied to the set of values Y_i^l∖

3. Increment I and repeat step 2 until an iteration L where = fcθ^b-1∖ Assign this common value to be the estimated
value fc₀. Note that in this iteration it will also be true that ʌ(ɪə = Δ^^l-1∖

4. Augment (that is, “fill”) the dataset Y with the ко imputed symmetric values

y∕ = 2∆W-y_n._j+1, j = l,...,k₀

and imputed standard errors

σ*=σ_n-j₊ι, j = l,...,k₀

Estimate the “trimmed and filled” value of Δ using the chosen meta-analysis method applied to the full augmented dataset
{y₁,...,y_n,y₁*,...,κ≈}.

Conceptually, this algorithm starts with the observed data, iteratively trims (that is, removes) extreme positive studies from
the dataset until the remaining studies do not show detectable deviation from symmetry, fills (that is, imputes into the original
dataset) studies that are left-side mirrored reflections (about the center of the trimmed data) of the trimmed studies and, finally,
repeats the meta-analysis on the filled dataset to get “trimmed and filled” estimates. Each filled study is assigned the same
standard error as the trimmed study it reflects in order to maintain symmetry within the filled dataset.

Example

The method is illustrated with an example from the literature that examines the association between Chlamydia trachomatis
and oral contraceptive use derived from 29 case-control studies (Cottingham and Hunter 1992). Analysis of these data with the
publication bias tests of Begg and Mazumdar (p = 0.115) and Egger et al. (p = 0.016), as provided in metabias, suggests
that publication bias may affect the data. To examine the potential impact of publication bias on the interpretation of the data,
metatrim is invoked as follows:

. metatrim Iogor varlogor, reffeet funnel var

The random-effects model and display of the optional funnel graph are requested via options ref feet and funnel. Option var
is required because the data were provided as log-odds ratios and variances. By default, the linear estimator, L₀, is used to
estimate fc₀, as no other estimator was requested. metatrim provides the following output:

Test for heterogeneity: Q= 37.034 on 28 degrees of freedom (p= 0.118)

Moment-based estimate of between studies variance = 0.021

Trimming estimator: Linear

Meta-analysis type: Random-effects model

Filled

Meta-analysis

Test for heterogeneity: Q= 49.412 on 35 degrees of freedom (p= 0.054)

Moment-based estimate of between studies variance = 0.031

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