metaoutliers {altmeta}

Outlier Detection in Meta-Analysis

Description

Calculates the standardized residual for each study in meta-analysis using the methods desribed in Chapter 12 in Hedges and Olkin (1985) and Viechtbauer and Cheung (2010). A study is considered as an outlier if its standardized residual is greater than 3 in absolute magnitude.

Usage

metaoutliers(y, s2, data, model)

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 data is specified, the previous arguments, y and s2, should be specified as their corresponding column names in data.

model

a character string specified as either "FE" or "RE". If model = "FE", this function uses the outlier detection procedure for the fixed-effect meta-analysis desribed in Chapter 12 in Hedges and Olkin (1985); If model = "RE", the procedure for the random-effects meta-analysis desribed in Viechtbauer and Cheung (2010) is used. See Details for the two approaches. If the argument model is not specified, this function sets model = "FE" if I_r^2 < 30\% and sets model = "RE" if I_r^2 \geq 30\%.

Details

Suppose that a meta-analysis collects n studies. The observed effect size in study i is y_i and its within-study variance is s^{2}_{i}. Also, the inverse-variance weight is w_i = 1 / s^{2}_{i}.

Chapter 12 in Hedges and Olkin (1985) describes the outlier detection procedure for the fixed-effect meta-analysis (model = "FE"). Using the studies except study i, the pooled estimate of the overall effect size is \bar{\mu}_{(-i)} = \sum_{j \neq i} w_j y_j / \sum_{j \neq i} w_j. The residual of study i is e_{i} = y_i - \bar{\mu}_{(-i)}. The variance of e_{i} is v_{i} = s_{i}^{2} + (\sum_{j \neq i} w_{j})^{-1}, so the standardized residual of study i is \epsilon_{i} = e_{i} / \sqrt{v_{i}}.

Viechtbauer and Cheung (2010) describes the outlier detection procedure for the random-effects meta-analysis (model = "RE"). Using the studies except study i, let the method-of-moments estimate of the between-study variance be \hat{\tau}_{(-i)}^{2}. The pooled estimate of the overall effect size is \bar{\mu}_{(-i)} = \sum_{j \neq i} \tilde{w}_{(-i)j} y_j / \sum_{j \neq i} \tilde{w}_{(-i)j}, where \tilde{w}_{(-i)j} = 1/(s_{j}^{2} + \hat{\tau}_{(-i)}^{2}). The residual of study i is e_{i} = y_i - \bar{\mu}_{(-i)}, and its variance is v_{i} = s_{i}^2 + \hat{\tau}_{(-i)}^{2} + (\sum_{j \neq i} \tilde{w}_{(-i)j})^{-1}. Then, the standardized residual of study i is \epsilon_{i} = e_{i} / \sqrt{v_{i}}.

Value

This functions returns a list which contains standardized residuals and identified outliers. A study is considered as an outlier if its standardized residual is greater than 3 in absolute magnitude.

References

Hedges LV, Olkin I (1985). Statistical Method for Meta-Analysis. Academic Press, Orlando, FL.

Viechtbauer W, Cheung MWL (2010). "Outlier and influence diagnostics for meta-analysis." Research Synthesis Methods, 1(2), 112–125. <doi: 10.1002/jrsm.11>

Examples

data("dat.aex")
metaoutliers(y, s2, dat.aex, model = "FE")
metaoutliers(y, s2, dat.aex, model = "RE")

data("dat.hipfrac")
metaoutliers(y, s2, dat.hipfrac)