Functional principal component analysis for functional data with detection limits

When measurements fall below or above a detection threshold, the resulting data are missing not at random (MNAR), posing challenges for statistical analysis. For example, in longitudinal biomarker studies, observations may be subject to detection limits. Functional principal component analysis (FPCA) is commonly used method for dimension reduction of dense and sparse data measured along a continuum, but standard approaches typically ignore MNAR mechanisms by imputing detection limit values, leading to biased estimates of principal components and scores. Building on recent work by Liu and Houwing-Duistermaat (2022, 2023), who proposed estimators for the mean and covariance functions under detection limits, we extend FPCA to accommodate functional data affected by such limits. We derive the asymptotic properties of the resulting estimators and assess their performance through simulations, comparing them to standard methods. Finally, we illustrate our approach using longitudinal biomarker data subject to detection limits. Our method yields more accurate estimates of functional principal components and scores, enhancing the reliability of functional data analysis in the presence of detection limits.