PCP-LOD

PCP-LOD decomposes environmental exposure matrices into low-rank and sparse components to identify underlying exposure patterns and extreme events while accounting for concentrations below the limit of detection, nonnegativity, and missing data.

Key Features:

• Decomposition of exposure mixtures: Decomposes observed concentration matrices into a low-rank matrix capturing consistent patterns across pollutants and a sparse matrix isolating unique or extreme exposure events.
• Handling special data characteristics: Explicitly accommodates nonnegative data, missing values, and concentrations below the limit of detection (LOD).
• Performance evaluation via simulation: Assessed using simulations with varying proportions of LOD values and different noise structures, consistently recovering the true number of patterns and outperforming traditional principal component analysis (PCA) in accuracy and predictive error.
• Application to NHANES persistent organic pollutants: Applied to 21 persistent organic pollutants (POPs) measured in 1,000 U.S. adults from the 2001–2002 NHANES, identifying a rank-three underlying structure and flagging 6% of values as extreme events.
• Pattern characterization: Uses singular value decomposition on the estimated low-rank matrix to characterize exposure patterns, including comprehensive exposure to all POPs and groupings by chemical structure and toxicity.

Scientific Applications:

• Exposure pattern identification: Extracts interpretable multidimensional exposure patterns from complex environmental mixture data.
• Extreme event detection: Isolates sparse extreme exposures for downstream assessment of outliers and unusual events.
• Population-level exposure characterization: Produces pattern summaries suitable for evaluating sources of exposure and potential impacts on public health and epidemiologic analyses.

Methodology:

Adapts robust principal component pursuit (PCP) to decompose exposure matrices into low-rank and sparse components while accommodating nonnegativity, missing values, and values below the LOD; applies singular value decomposition to the estimated low-rank matrix; performance assessed via simulations with varied LOD proportions and noise structures.