The term "multivariate" is used incorrectly, see Hidalgo B, Goodman M. Multivariate or multivariable regression? Am J Public Health 2013;103:1-3.
The terminology used by the authors includes terms with clear definitions only in experimental studies. For example, primary and secondary outcomes play important roles in strategies for addressing multiplicity issues in confirmatory trials, but the presented study is not confirmatory, and adverse events usually refer to all unfavourable events, temporally but not causally, associated with an investigated product or procedure. I recommend clarifying the definitions of such terms to avoid misunderstanding.
The manuscript presents an observational study, but it seems to be based on trial-related terminology including terms such as "efficacy", "primary outcome" and "serious adverse events". These terms have clear definitions in randomised trials but not in observational studies. For example, an adverse event is generally known as any untoward medical occurrence that has a temporal but not necessarily causal relation to the studied treatment. The subgroup of adverse events that are causally related to the treatment are usually described as treatment-related adverse events, and if they cause death, are life-threatening, or leads to hospital treatment, they are usually described as serious treatment-related adverse events. While treatment-related adverse events may be registered in an observational database, I doubt that temporally related adverse events are can be identified or even defined, in a retrospective study. Primary and secondary outcomes usually play important roles in strategies for addressing multiplicity issues in confirmatory trials, but multiplicity issues are hardly relevant in observational studies, see e.g. Bender R, Lange S. Adjusting for multiple testing: when and how? J Clin Epidemiol 2001; 54: 343–349. As for efficacy, see Ernst E, Pittler MH. Efficacy or effectiveness? J Int Med 2006;260:488–490.
The ICMJE recommends avoiding 'nontechnical uses of technical terms in statistics, such as “random” (which implies a randomizing device), “normal,” “significant,” “correlations,” and “sample.”'.