Using Bonferroni, BIC and AIC to assess evidence for alternative biological pathways: covariate selection for the multilevel Embryo-Uterus model

Background: IVF treatments for infertility involve the transfer of multiple embryos in any one treatment cycle. When data is available on individual embryos the outcomes of each embryo are only partially observed, as treatment outcome (live birth) is assessed at the patient level. Two-level Embryo-Uterus (EU) models have been developed which assume a biologically plausible mechanism and assume that effects are mediated directly through the embryo (E) and also through the uterine environment (U), represented by two sub-models. This approach potentially allows inference as to the association of patient variables with outcome. However, when the variable is measured at the patient level either additional decisions have to be made in the modelling process as to in which sub-model the variable should be included or some model selection algorithm has to be invoked. These uncertainties have limited the practical application of these models. Methods: We have conducted simulation studies based around realistic parameter values of situations where a putative patient-level variable is being considered for inclusion in an EU model and/or the mechanistic interpretation from the sub-model assignment is of interest. Firstly we explore various strategies for inference for a variable of interest where the sub-model is either pre-specified or considered unknown. Secondly we explore the use of information criteria to select the appropriate sub-model and the strength of evidence for that assignment. These are demonstrated in a reanalysis of a previously published dataset. Results: In the absence of prior evidence for potential prognostic factors measured at the patient level, two single degree-of-freedom likelihood ratio tests with a Bonferroni correction including the variable of interest in first the E then the U sub-model performs well as a statistical test for association with outcome. For model building the information criteria can be used, but large differences are required (greater than or similar to 6) to provide reasonable evidence of submodel assignment. Previous interpretations have been over-optimistic. Conclusions: These results suggest simple strategies and should enable these models to be used more confidently in practical applications.