RT-PCR Algorithm Reverse Engineering & Statistical Redesign

Role: Data Scientist — algorithm analysis & redesign (6-person Data Science team)  ·  Period: 2021.10 – 2023.04  ·  Stack: Matlab, Python, mechanistic + statistical modeling, joint parameter estimation, residual analysis

Reverse-engineered an undocumented legacy Matlab algorithm (10+ correction stages, 50+ empirical parameters) and designed a statistically rigorous replacement.

• Legacy pain — the deterministic rule stack grew exponentially with each new noise pattern; stage-by-stage sequential correction accumulated systematic bias with non-linear interactions, making sensitivity analysis impossible.
• Design constraint — regulatory clearance demanded explainability, so I reframed the problem as a mechanistic + statistical hybrid rather than a deep-learning black box.

Highlights

• 80% of the legacy algorithm’s logic and dependencies interpreted and documented — decision-tree visualizations of the branching structure and a detailed technical spec for the Data Engineering team’s C++ port.
• Joint-estimation hybrid model — a composite of three preprocessing functions with an RT-PCR-kinetics logistic sigmoid, fit by estimating all parameters simultaneously. Sequential (backfitting) estimation accumulates per-stage bias; joint estimation removes it structurally.
• Explicit statistical modeling of the residuals — Gaussian-error assumption with white-noise checks, closed-form analytic gradients for stability and speed, and constrained optimization over physically valid parameter ranges.
• Unified quantification and calling — Ct values and positive/negative calls come from the same statistical model, folding curve-fitting, quantification, and calling into a single estimation problem.
• (Organizational constraint) the redesign was not adopted at the team-lead level — a lesson in balancing technical excellence against organizational buy-in. The statistical signal-processing and curve-fitting experience carried forward into the later PCR baseline correction work.

Approach

Phase 1 recovers the legacy logic; Phase 2 reformulates it as a single statistical model whose parameters map to interpretable curve features (slope, inflection, plateau) for regulatory justification.

flowchart TB
    L[Undocumented legacy Matlab<br/>10+ stages, 50+ params] --> RE[Reverse engineering<br/>80% interpreted + documented]
    RE --> SPEC[Decision-tree spec<br/>for C++ port]
    RE --> HY[Mechanistic + statistical<br/>hybrid composite function]
    HY --> JE[Joint parameter estimation<br/>vs. sequential backfitting]
    JE --> OUT[Systematic bias removed<br/>+ interpretable parameters]