Meta analysis using Glimmix

[G_Le_Teuff]

Dear Lvm,

I read a second time the paper you cited above (Meta-analysis with linear and Nonlinear multilevel models using proc mixed and proc nlmixed). The authors used a proc mixed based on log(OR) with weight statement and compare the results using a proc nlmixed with a random effect. In the SAS code of proc nlmixed, I did not seen how they fixed the within-study variance. Very strange ! because the variance function, here, is mu(1-mu)/n for a proportion. Have you some idea about it !

[lvm]

I think your last posting gets at the critical point. Using the NLMIXED code (or equivalent now in GLIMMIX for this example), the within-study variance is automatically determined based on the specified distribution. One does not fix the within-study variance. If the data have a Poisson distribution, the variance is determined by the mean (by definition); i.e., the variance is completely known, and there is no reason to fix it in each study. The software takes care of this. This is why the approach you are taking is difficult -- you are specifying a discrete distribution (NB or Poisson), but you want to fix the within-study variances at something other than what is defined for those discrete distributions. You are essentially getting a overdispersed distribution scenario, where the degree of overdispersion (or possibly underdispersion) varies with the study. I attemped one workaround, where you take into account the internal variance structure (determined by the software), and then rescaled it to achieve YOUR fixed variances. However, I think you would be better off using the normal approximations, because this is easier to control the within-study variances.

[G_Le_Teuff]

Thank. It's clearer. But based on the paper for log ddd ratios (normal data) and binomial data, is Poisson with internal residual variance determined by software (wihout weight statement) a correct and reasonable approach for incidence rate and gives results similar to the normal distribution with variance of log incidence.

[G_Le_Teuff]

I am thinking that my confusion come from the 2 following responses  : y= (#event / Person-year) and y=#event. In your last post, you propose the model

proc glimmix data=count_data;

class study;

model LOGtox =  / offset=logPA2 solution;  

random intercept   / subject=study ; * to test heterogeneity between study;

weight inv_varln; * weight = inverse variance;

parms (1) (1) / hold=2;

run;

But I have an approximation of the variance of tox/person-year or log(tox/person-year). So I have to peform a model where the response is log(tox/person-year) and delete the offset.

proc glimmix data=count_data;

class study;

model LOG(tox/person-years) =  / solution;  

random intercept   / subject=study ; * to test heterogeneity between study;

weight inv_varln; * weight = inverse variance;

parms (1) (1) / hold=2;

run;

In my last posts I was wondering whether I have to consider the denominator of the response (offset) in the function variance determined by the software or whether the software takes into account only the numerator of incidence rate i.e #events.