st: Inconsistent tau^2 estimates from metareg

[Rebecca Boehm <boehm@musc.edu>]

Hello all,

I recently completed a meta-analysis on 11 studies. I found that the max 
likelihood (ml) and restricted max likelihood (reml) estimators of tau^2 
consistently produced widely different p-values for covariates when 
compared to the method of moments (mm) estimator. They usually estimated 
tau^2 to be zero when hetergeneity was present in the data. An example:

Meta-analysis regression                               No of studies =   11
                                                      tau^2 method 
reml
                                                      tau^2 estimate = 
5.0e-0

> 5
Successive values of tau^2 differ by less than 10^-4 :convergence achieved
---------------------------------------------------------------------------
---
            |      Coef.   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
-------------+-------------------------------------------------------------
---
    minedum |   .1938276   .0465574     4.16   0.000     .1025768 
.2850783
      _cons |     .16374   .0228645     7.16   0.000     .1189265 
.2085535
---------------------------------------------------------------------------
---

. metareg log_RR minedum, wsse( Standard_Error) bsest(mm)

Meta-analysis regression                               No of studies =   11
                                                      tau^2 method      mm
                                                      tau^2 estimate = 
.0515

---------------------------------------------------------------------------
---
            |      Coef.   Std. Err.      z    P>|z|     [95% Conf. 
Interval]
-------------+-------------------------------------------------------------
---
    minedum |   .1229214   .1912227     0.64   0.520    -.2518682 
.4977111
      _cons |   .3722394   .1603357     2.32   0.020     .0579871 
.6864916
---------------------------------------------------------------------------
---

Does anyone have some insight as to why the ML estimates of tau^2 are often 
going to zero despite strong heterogeneity?

Thank you very much,
Becky Boehm
Ph.D student - biostatistics
Department of Biometry and Epidemiology
Medical University of South Carolina

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