Joint modelling of binary longitudinal outcomes in using random effects approach

[Innocent Mboya]

Hi everyone,
I would like to jointly model two binary repeated outcomes in STATA using the random effects approach. The measurements are repeated within a single cluster (ID).
How can I implement this model in STATA?

[Innocent Mboya]

Got a solution. You can implement these models using gsem function in Stata.

[Mike Lacy]

For those of us who are less knowledgeable, could you post an explanation of 1) why it's not possible or desirable to do this with -melogit-, since on the surface it sounds less complicated than some things described in the manual entry for -melogit-; and 2) how you set it up with -gsem-. Having an explanation here might help out some future user.

[Innocent Mboya]

Hello Mike,
I am sorry I did not see this timely.
To my understanding, the -melogit- function (with an alternative and a more flexible function using -meglm-) in Stata are specifically designed to handle mixed effects models, such as in situations where one has repeated/ clustered observations. For my case, though used for preliminary analyses of two binary events separately, the two events could not be jointly modelled using either -melogit- or -meglm-. I would be happy to learn how the joint distribution of the two events can be manually specified using -melogit- or -meglm-.

Nevertheless, I learned that -gsem- package has a lot more flexibilities of modelling even the mixed-effects even the joint model, which was the interest in my work. In my joint model analysis, the two equations (for the two binary events) were specified as follows;

gsem (y1 <- var1 var2 ... var_n M1(cluster_var), latent(M1) family(binomial) link(logit) ///
(y2 <- var1 var2 ... var_n M2(cluster_var), latent(M2) family(binomial) link(logit)), ///
covstruct(M1[cluster_var] M2[cluster_var], exch) intpoints(10) vce(robust)

Using -gsem-, I was also able to fit a "Two-level multinomial logistic model with separate but correlated random effects" as described in the Stata Manual such as in Example 41g from page 427 [1]. The paper corresponding to these analyses is available here [2].

1. Stata Press 2017. Structural Equation Modeling Reference Manual. Available from: Structural Equation Modeling Reference Manual, Release 17.
2. Mboya, I.B., Mahande, M.J., Obure, J. and Mwambi, H.G., 2021. Joint Modeling of Singleton Preterm Birth and Perinatal Death Using Birth Registry Cohort Data in Northern Tanzania. Frontiers in Pediatrics, p.1327.