[R-sig-ME] Duplicating meta-regression results from PROC MIXED with lmer

[Viechtbauer Wolfgang (STAT)]

I now had a chance to run these models myself. 

Here are the data that I used (study is a factor and the first column is the # of TB cases and the second the # of non-TB cases).

                group ablati syear study
 [1,]   4   119     1     44    48     1
 [2,]   6   300     1     55    49     2
 [3,]   3   228     1     42    60     3
 [4,]  62 13536     1     52    77     4
 [5,]  33  5036     1     13    73     5
 [6,] 180  1361     1     44    53     6
 [7,]   8  2537     1     19    73     7
 [8,] 505 87886     1     13    80     8
 [9,]  29  7470     1     27    68     9
[10,]  17  1699     1     42    61    10
[11,] 186 50448     1     18    74    11
[12,]   5  2493     1     33    69    12
[13,]  27 16886     1     33    76    13
[14,]  11   128     0     44    48     1
[15,]  29   274     0     55    49     2
[16,]  11   209     0     42    60     3
[17,] 248 12619     0     52    77     4
[18,]  47  5761     0     13    73     5
[19,] 372  1079     0     44    53     6
[20,]  10   619     0     19    73     7
[21,] 499 87892     0     13    80     8
[22,]  45  7232     0     27    68     9
[23,]  65  1600     0     42    61    10
[24,] 141 27197     0     18    74    11
[25,]   3  2338     0     33    69    12
[26,]  29 17825     0     33    76    13

If you want results that are essentially those from the paper, you should use:

lmer(y ~ group + ablati:group + syear:group + study + (group - 1| study), family=binomial)

The estimate of tau^2 is then essentially zero and:

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  -2.426859   0.269031  -9.021  < 2e-16 ***
group         0.548365   0.493131   1.112  0.26613    
study2        0.131173   0.320457   0.409  0.68230    
...
study13      -3.716989   0.301366 -12.334  < 2e-16 ***
group:ablati -0.034185   0.003948  -8.659  < 2e-16 ***
group:syear  -0.001770   0.005753  -0.308  0.75838    

This matches up quite nicely with the results from the "usual" approach.

An alternative would be to add study as a random instead of a fixed effect. Then the main effects for absolute latitude and study year can also be added to the model:

lmer(y ~ group + ablati + ablati:group + syear + syear:group + (group | study), family=binomial)

Then the estimate of tau^2 is 0.00045553, still pretty much zero, and:

Fixed effects:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)   1.699707   2.386607   0.712  0.47635    
group         0.514024   0.497863   1.032  0.30186    
ablati        0.024016   0.021007   1.143  0.25294    
syear        -0.099948   0.027955  -3.575  0.00035 ***
group:ablati -0.034332   0.003991  -8.601  < 2e-16 ***
group:syear  -0.001488   0.005811  -0.256  0.79787    

which is still quite close.

Best,

-- 
Wolfgang Viechtbauer
 Department of Methodology and Statistics
 University of Maastricht, The Netherlands
 http://www.wvbauer.com/