# A Two-Step Algorithm for Handling Block-Wise Missing Data in Multi-Omics
## 5 Discussion  
In this study, we adopted the methodological approach outlined in [6] and expanded it to accommodate multi-class classification. We introduced an efficient method for estimating feature and source parameters by alternating between regularization and constraint penalties, which has been implemented in the bm R package, accessible at [[https://github.com/sergibaena-miret/Block-Wise-Missing](https://github.com/sergibaena-miret/Block-Wise-Missing)]([https://github.com/sergibaena-miret/Block-Wise-Missing](https://github.com/sergibaena-miret/Block-Wise-Missing)), accessed date 16 February 2025. To showcase the effectiveness of the two-stage algorithm in managing block-wise missing data in omics studies, we applied it to two multi-omics datasets: breast cancer [15] and exposome data [19]. The breast cancer dataset serves as a case study where the cross-entropy loss is crucial, as the outcome variable to predict is the cancer subtype (Basal, Her2, LumA, and LumB). The predictors in this dataset are divided into three blocks: mRNA, miRNA, and DNAm. This dataset allowed us to assess the effectiveness of our approach in handling various scenarios of block-wise missing data. The metrics used indicated satisfactory performance across all cases. However, in instances where a significant portion of blocks were missing (around 30%), accuracy metrics showed a slight decrease in performance. One strategy for dealing with missing data is to exclude observations with missing data from the analysis,  
Figure 5: Scatter plots of predicted values versus true values in several block-wise missing scenarios in exposure data. which is clearly inefficient. In this context, we emphasize the comparison between our profile-based approach and the strategy relying solely on complete data. The profile-based approach has proven superior in all scenarios. On the other hand, the exposome dataset is used as a case study in which the mean squared error is applied as the loss function since the target variable to be predicted is a numerical variable: the z-score body mass index at 6-11 years. The dataset consists of five blocks: Covariates, Chemical exposures, Indoor air, Lifestyles, and Outdoor exposures. Just like the breast cancer dataset, the exposome dataset assesses the performance of our approach using the same block-wise missing scenarios as those in the breast cancer dataset. The metrics applied demonstrate competitive performance in all scenarios. Although performance showed a slight decrease in the scenario with the highest percentage (30% or more) of missing blocks. Despite these good results, scalability issues could be a concern. The presence of various profiles increases computational complexity, and even with modern computing power, processing high-dimensional data can be time-consuming. This is particularly relevant as the size and complexity of omics datasets continue to grow. Future work should focus on optimizing the algorithm for scalability, potentially through parallel computing or more efficient data handling techniques, to ensure its applicability to larger datasets without compromising performance. Additionally, sensitivity analysis was performed to assess the model's robustness by varying the proportions of missingness across different percentages of missing data. Cross-validation was also conducted in [6] for binary classification and regression approaches. Future research should include comprehensive sensitivity analyses to further explore the model's reliability and robustness under diverse conditions, such as different random seeds and varying noise levels, while continuing to compare its performance to other approaches such as imputation or the removal of missing data, to ensure its effectiveness and adaptability in handling incomplete datasets.