Eden Malka – Biostatistics Labs

Project Summary

Week 1 – Data Exploration and Mapping

We began by processing raw sequencing reads into genomic bins and mapping them to reference regions. We explored variability in coverage and examined GC-content bias patterns using descriptive statistics and visual tools. This stage built the foundation for understanding systematic bias in sequencing data.

Week 2 – Statistical Modeling of GC Bias

We developed regression models to describe the relationship between read coverage and GC content. Both Weighted Least Squares (WLS) and Cubic Spline regression were fitted to estimate the smooth function f(GC) representing expected coverage as a function of GC content. This established the baseline for normalization and later CNV detection.

Week 5 – Model Comparison and Residual Analysis

This lab focused on comparing performance across different bin resolutions (1K, 2.5K, 5K, and 10K). We evaluated bias–variance trade-offs using MAE, Median Absolute Error, and residual analysis. Models included LOESS and Cubic Spline corrections. The results guided the choice of optimal bin size for robust CNV detection.

Week 6 – Model Refinement and Simulation Design

This stage bridged empirical modeling and theoretical simulation. We refined the spline-based correction model and introduced Poisson regression, modeling coverage as Y_k ~ Poisson(Λ_k), where Λ_k = f(GC_k) + ε_k. Different estimation strategies were explored — MLE, Method of Moments, and MAD — for the variance parameter σ². The analysis also examined UnderSpread and OverSpread behavior using Cubic vs. Natural Splines, forming the basis for the later simulation study.

Week 7 – Data Cleaning and Copy Number Estimation

Using the cleaned coverage data (2.5K-bin resolution), we applied spline-based correction to compute copy number estimates (aᵢ). Outlier filtering via LOESS residuals and IQR trimming improved normalization accuracy. The resulting aᵢ distribution confirmed diploid coverage near 1 and identified local CNV deviations.

Week 8 – Simulation and Model Validation

The final lab implemented a Poisson-based simulation framework to mimic GC-dependent sequencing bias. We estimated the Poisson variance parameter (σ), generated synthetic datasets with realistic coverage variability, and compared them to observed data using RMSE between fitted and true f(GC) curves. This simulation validated the reliability and interpretability of the modeling approach.

Final Presentation – Comprehensive CNV Analysis

The final presentation summarized the complete CNV detection pipeline developed throughout the semester. We compared the performance of Model B, Model C, and Model D, each representing a variation in GC-correction and residual filtering using LOESS and Cubic Spline functions. Key evaluation criteria included the proportion of bins retained after IQR-based outlier filtering, Mean Absolute Error, and the stability of coverage across genomic regions (e.g., 26.5M–28.5M). The analysis demonstrated that combining GC correction with adaptive smoothing (Spline + LOESS) provided the most consistent and biologically interpretable results. This final stage integrated all prior modeling, simulation, and correction steps into a cohesive and validated CNV detection workflow.

Summary

Across all stages, we integrated statistical reasoning, computational modeling, and visualization in R to analyze and correct sequencing coverage data. Each lab reflected a deeper layer of insight — from exploratory analysis to model fitting, correction, and simulation — culminating in a reproducible CNV detection pipeline grounded in sound biostatistical principles.

📊 Created by Eden Malka, Salome Baranes, and Omer Abuhatzira – 2025