A lack of preparedness for college-level coursework has been shown to negatively impact student success rates in STEM. Remedial instruction has been the most widespread approach to helping at-risk students attain college-level competencies; however, studies have shown that remediation has had null or negative impacts on degree completion for students placed into these courses. This study examines two decades worth of data from one institution to evaluate the efficacy of course pathway diversification as an alternative model to traditional remediation on general chemistry students' firstand second-semester outcomes. In this approach, students with low mathematics placement exam scores take a separate lecture offering of general chemistry I with a corequisite support course (GCI-S) that is offered in parallel with the mainstream course (GCI-M). The course content across these offerings is the same, and successful students in either course are rejoined in a common general chemistry II course (GCII) in the subsequent semester. Our results indicate that first-semester outcomes for at-risk students have improved markedly since the inception of GCI-S relative to non-at-risk students. However, these improvements are not as apparent in GCII. Additionally, while the achievement gap in first-semester general chemistry outcomes between GCI-S and GCI-M students has improved, corresponding achievement gaps in GCII have worsened. We discuss the implications of our findings in ways that might guide the efforts of others in better supporting our most vulnerable students in chemistry.
Inferring gene co-expression networks is a useful process for understanding gene regulation and pathway activity. The networks are usually undirected graphs where genes are represented as nodes and an edge represents a significant co-expression relationship. When expression data of multiple (p) genes in multiple (K) conditions (e.g., treatments, tissues, strains) are available, joint estimation of networks harnessing shared information across them can significantly increase the power of analysis. In addition, examining condition-specific patterns of co-expression can provide insights into the underlying cellular processes activated in a particular condition. Condition adaptive fused graphical lasso (CFGL) is an existing method that incorporates condition specificity in a fused graphical lasso (FGL) model for estimating multiple co-expression networks. However, with computational complexity of O(p2K log K), the current implementation of CFGL is prohibitively slow even for a moderate number of genes and can only be used for a maximum of three conditions. In this paper, we propose a faster alternative of CFGL named rapid condition adaptive fused graphical lasso (RCFGL). In RCFGL, we incorporate the condition specificity into another popular model for joint network estimation, known as fused multiple graphical lasso (FMGL). We use a more efficient algorithm in the iterative steps compared to CFGL, enabling faster computation with complexity of O(p2K) and making it easily generalizable for more than three conditions. We also present a novel screening rule to determine if the full network estimation problem can be broken down into estimation of smaller disjoint sub-networks, thereby reducing the complexity further. We demonstrate the computational advantage and superior performance of our method compared to two non-condition adaptive methods, FGL and FMGL, and one condition adaptive method, CFGL in both simulation study and real data analysis. We used RCFGL to jointly estimate the gene co-expression networks in different brain regions (conditions) using a cohort of heterogeneous stock rats. We also provide an accommodating C and Python based package that implements RCFGL.
Inferring gene co-expression networks is a useful process for understanding gene regulation and pathway activity. The networks are usually undirected graphs where genes are represented as nodes and an edge represents a significant co-expression relationship. When gene-expression data from multiple conditions (e.g., treatments, tissues, strains) are available, joint estimation of networks harnessing shared information across them can significantly increase the power of analysis. In addition, examining condition-specific patterns of co-expression can provide insights into the underlying cellular processes activated in a particular condition. Condition adaptive fused graphical lasso (CFGL) is an existing method that incorporates condition specificity in a fused graphical lasso (FGL) model for estimating multiple co-expression networks. However, the current implementation of CFGL is prohibitively slow even for a moderate number of genes and can only be used for a maximum of three conditions. In this paper, we propose a fast alternative of CFGL known as rapid condition adaptive fused graphical lasso (RCFGL). In RCFGL, we incorporate the condition specificity into another popular model for joint network estimation, known as fused multiple graphical lasso (FMGL). We use a more efficient algorithm in the iterative steps compared to CFGL, enabling faster computation and making it easily generalizable for more than three conditions. We also present a novel screening rule to determine if the full network estimation problem can be broken down into estimation of smaller disjoint sub-networks, thereby reducing the complexity further. We demonstrate the computational advantage and superior performance of our method compared to two non-condition adaptive methods, FGL and FMGL, and one condition adaptive method, CFGL in several simulation scenarios. We use RCFGL to jointly estimate the gene co-expression networks of different brain regions (conditions) using a cohort of heterogeneous stock rats. We also provide an accommodating C and Python based package that implements RCFGL.
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