Raman chemometric urinalysis (Rametrix™) was used to analyze 235 urine specimens from healthy individuals. The purpose of this study was to establish the “range of normal” for Raman spectra of urine specimens from healthy individuals. Ultimately, spectra falling outside of this range will be correlated with kidney and urinary tract disease. Rametrix™ analysis includes direct comparisons of Raman spectra but also principal component analysis (PCA), discriminant analysis of principal components (DAPC) models, multivariate statistics, and it is available through GitHub as the Rametrix™ LITE Toolbox for MATLAB®. Results showed consistently overlapping Raman spectra of urine specimens with significantly larger variances in Raman shifts, found by PCA, corresponding to urea, creatinine, and glucose concentrations. A 2-way ANOVA test found that age of the urine specimen donor was statistically significant (p < 0.001) and donor sex (female or male identification) was less so (p = 0.0526). With DAPC models and blind leave-one-out build/test routines using the Rametrix™ PRO Toolbox (also available through GitHub), an accuracy of 71% (sensitivity = 72%; specificity = 70%) was obtained when predicting whether a urine specimen from a healthy unknown individual was from a female or male donor. Finally, from female and male donors (n = 4) who contributed first morning void urine specimens each day for 30 days, the co-occurrence of menstruation was found statistically insignificant to Rametrix™ results (p = 0.695). In addition, Rametrix™ PRO was able to link urine specimens with the individual donor with an average of 78% accuracy. Taken together, this study established the range of Raman spectra that could be expected when obtaining urine specimens from healthy individuals and analyzed by Rametrix™ and provides the methodology for linking results with donor characteristics.

Bladder cancer (BCA) is relatively common and potentially recurrent/progressive disease. It is also costly to detect, treat, and control. Definitive diagnosis is made by examination of urine sediment, imaging, direct visualization (cystoscopy), and invasive biopsy of suspect bladder lesions. There are currently no widely-used BCA-specific biomarker urine screening tests for early BCA or for following patients during/after therapy. Urine metabolomic screening for biomarkers is costly and generally unavailable for clinical use. In response, we developed Raman spectroscopy-based chemometric urinalysis (Rametrix™) as a direct liquid urine screening method for detecting complex molecular signatures in urine associated with BCA and other genitourinary tract pathologies. In particular, the Rametrix TM screen used principal components (PCs) of urine Raman spectra to build discriminant analysis models that indicate the presence/absence of disease. The number of PCs included was varied, and all models were cross-validated by leave-one-out analysis. In Study 1 reported here, we tested the Rametrix™ screen using urine specimens from 56 consented patients from a urology clinic. This proof-of-concept study contained 17 urine specimens with active BCA (BCA-positive), 32 urine specimens from patients with other genitourinary tract pathologies, seven specimens from healthy patients, and the urinalysis control Surine TM. Using a model built with 22 PCs, BCA was detected with 80.4% accuracy, 82.4% sensitivity, 79.5% specificity, 63.6% positive predictive value (PPV), and 91.2% negative predictive value (NPV). Based on the number of PCs included, we found the Rametrix TM screen could be fine-tuned for either high sensitivity or specificity. In other studies reported here, Rametrix TM was also able to differentiate between urine specimens from patients with BCA and other genitourinary pathologies and those obtained from patients with end-stage kidney disease (ESKD). While larger studies are needed to improve Rametrix TM models and demonstrate clinical relevance, this study demonstrates the ability of the Rametrix TM screen to differentiate urine of

Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these studies. Motivated from two real-life examples, we present in this paper a function-on-function regression model that can be used to analyze such kind of functional data. Our estimator of the 2D coefficient function is the optimizer of a form of penalized least squares where the penalty enforces a certain level of smoothness on the estimator. Our first result is the Representer Theorem which states that the exact optimizer of the penalized least squares actually resides in a data-adaptive finite dimensional subspace although the optimization problem is defined on a function space of infinite dimensions. This theorem then allows us an easy incorporation of the Gaussian quadrature into the optimization of the penalized least squares, which can be carried out through standard numerical procedures. We also show that our estimator achieves the minimax convergence rate in mean prediction under the framework of function-on-function regression. Extensive simulation studies demonstrate the numerical advantages of our method over the existing ones, where a sparse functional data extension is also introduced. The proposed method is then applied to our motivating examples of the benchmark Canadian weather data and a histone regulation study.

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In some survival analysis of medical studies, there are often long-term survivors who can be considered as permanently cured. The goals in these studies are to estimate the noncured probability of the whole population and the hazard rate of the susceptible subpopulation. When covariates are present as often happens in practice, to understand covariate effects on the noncured probability and hazard rate is of equal importance. The existing methods are limited to parametric and semiparametric models. We propose a two-component mixture cure rate model with nonparametric forms for both the cure probability and the hazard rate function. Identifiability of the model is guaranteed by an additive assumption that allows no time-covariate interactions in the logarithm of hazard rate. Estimation is carried out by an expectation-maximization algorithm on maximizing a penalized likelihood. For inferential purpose, we apply the Louis formula to obtain point-wise confidence intervals for noncured probability and hazard rate. Asymptotic convergence rates of our function estimates are established. We then evaluate the proposed method by extensive simulations. We analyze the survival data from a melanoma study and find interesting patterns for this study.