This repository documents our semester-long work in the Biostatistics Laboratory course, focusing on statistical modeling of genomic coverage, GC-content bias correction, and simulation-based validation.
The project gradually builds a full CNV (Copy Number Variation) analysis pipeline using real and simulated sequencing data.
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.
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.
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.
This stage bridged empirical modeling and theoretical simulation.
We refined the spline-based correction model and introduced Poisson regression, modeling coverage as
Different estimation strategies were explored — MLE, Method of Moments, and MAD — for the variance parameter
The analysis also examined UnderSpread and OverSpread behavior using Cubic vs. Natural Splines, forming the basis for the later simulation study.
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.
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.
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.
This figure summarizes regional spline fits across four genomic segments, showing both training and test sets.
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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 © All rights reserved.