tau2h: Calculating Heterogeneity Variance
In nshi-stat/pimeta: Prediction Intervals for Random-Effects Meta-Analysis

Description Usage Arguments Details Value References Examples

Returns a heterogeneity variance estimate and its confidence interval.

1
2
3

tau2h(y, se, maxiter = 100, method = c("DL", "VC", "PM", "HM", "HS",
  "ML", "REML", "AREML", "SJ", "SJ2", "EB", "BM"), methodci = c(NA, "ML",
  "REML"), alpha = 0.05)

`y`	the effect size estimates vector
`se`	the within studies standard errors vector
`maxiter`	the maximum number of iterations
`method`	the calculation method for heterogeneity variance (default = "DL"). `DL`: DerSimonian–Laird estimator (DerSimonian & Laird, 1986). `VC`: Variance component type estimator (Hedges, 1983). `PM`: Paule–Mandel estimator (Paule & Mandel, 1982). `HM`: Hartung–Makambi estimator (Hartung & Makambi, 2003). `HS`: Hunter–Schmidt estimator (Hunter & Schmidt, 2004). This estimator has negative bias (Viechtbauer, 2005). `ML`: Maximum likelihood (ML) estimator (e.g., DerSimonian & Laird, 1986). `REML`: Restricted maximum likelihood (REML) estimator (e.g., DerSimonian & Laird, 1986). `AREML`: Approximate restricted maximum likelihood estimator (Thompson & Sharp, 1999). `SJ`: Sidik–Jonkman estimator (Sidik & Jonkman, 2005). `SJ2`: Sidik–Jonkman improved estimator (Sidik & Jonkman, 2007). `EB`: Empirical Bayes estimator (Morris, 1983). `BM`: Bayes modal estimator (Chung, et al., 2013).
`methodci`	the calculation method for a confidence interval of heterogeneity variance (default = NA). `NA`: a confidence interval will not be calculated. `ML`: Wald confidence interval with a ML estimator (Biggerstaff & Tweedie, 1997). `REML`: Wald confidence interval with a REML estimator (Biggerstaff & Tweedie, 1997).
`alpha`	the alpha level of the confidence interval

Excellent reviews of heterogeneity variance estimation have been published (Sidik & Jonkman, 2007; Veroniki, et al., 2016; Langan, et al., 2018).

tau2h: the estimate for τ^2.
lci, uci: the lower and upper confidence limits \hat{τ}^2_l and \hat{τ}^2_u.

Sidik, K., and Jonkman, J. N. (2007). A comparison of heterogeneity variance estimators in combining results of studies. Stat Med. 26(9): 1964-1981. https://doi.org/10.1002/sim.2688.

Veroniki, A. A., Jackson, D., Viechtbauer, W., Bender, R., Bowden, J., Knapp, G., Kuss, O., Higgins, J. P. T., Langan, D., and Salanti, J. (2016). Methods to estimate the between-study variance and its uncertainty in meta-analysis. Res Syn Meth. 7(1): 55-79. https://doi.org/10.1002/jrsm.1164.

Langan, D., Higgins, J. P. T., Jackson, D., Bowden, J., Veroniki, A. A., Kontopantelis, E., Viechtbauer, W., and Simmonds, M. (2018). A comparison of heterogeneity variance estimators in simulated random-effects meta-analyses. Res Syn Meth. In press. https://doi.org/10.1002/jrsm.1316.

DerSimonian, R., and Laird, N. (1986). Meta-analysis in clinical trials. Control Clin Trials. 7(3): 177-188. https://doi.org/10.1016/0197-2456(86)90046-2.

Hedges, L. V. (1983). A random effects model for effect sizes. Psychol Bull. 93(2): 388-395. https://doi.org/10.1037/0033-2909.93.2.388.

Paule, R. C., and Mandel, K. H. (1982). Consensus values and weighting factors. J Res Natl Inst Stand Techno. 87(5): 377-385. https://doi.org/10.6028/jres.087.022.

Hartung, J., and Makambi, K. H. (2003). Reducing the number of unjustified significant results in meta-analysis. Commun Stat Simul Comput. 32(4): 1179-1190. https://doi.org/10.1081/SAC-120023884.

Hunter, J. E., and Schmidt, F. L. (2004). Methods of Meta-Analysis: Correcting Error and Bias in Research Findings. 2nd edition. Sage Publications, Inc.

Viechtbauer, W. (2005). Bias and efficiency of meta-analytic variance estimators in the random-effects model. J Educ Behav Stat. 30(3): 261-293. https://doi.org/10.3102/10769986030003261.

Thompson, S. G., and Sharp, S. J. (1999). Explaining heterogeneity in meta-analysis: a comparison of methods. Stat Med. 18(20): 2693-2708. https://doi.org/10.1002/(SICI)1097-0258(19991030)18:20<2693::AID-SIM235>3.0.CO;2-V.

Sidik, K., and Jonkman, J. N. (2005). Simple heterogeneity variance estimation for meta-analysis. J R Stat Soc Ser C Appl Stat. 54(2): 367-384. https://doi.org/10.1111/j.1467-9876.2005.00489.x.

Morris, C. N. (1983). Parametric empirical Bayes inference: theory and applications. J Am Stat Assoc. 78(381): 47-55. https://doi.org/10.1080/01621459.1983.10477920.

Chung, Y. L., Rabe-Hesketh, S., and Choi, I-H. (2013). Avoiding zero between-study variance estimates in random-effects meta-analysis. Stat Med. 32(23): 4071-4089. https://doi.org/10.1002/sim.5821.

Biggerstaff, B. J., and Tweedie, R. L. (1997). Incorporating variability in estimates of heterogeneity in the random effects model in meta-analysis. Stat Med. 16(7): 753-768. https://doi.org/10.1002/(SICI)1097-0258(19970415)16:7<753::AID-SIM494>3.0.CO;2-G.