Biomarker discovery and development requires measurement reproducibility studies in addition to case-control studies. Parallel pursuit of reproducibility studies is especially important for emerging technologies such as protein biomarkers based on time-of-flight mass spectrometry, the case considered in this paper. For parallel studies, a way to improve reproducibility prior to identification of protein species is necessary. One approach is use of functional principal components analysis (PCA) as the basis for assessing measurement reproducibility. Reproducibility studies involve repeated measurement of a reference material such as a human serum standard. Measurement in our example is by SELDI-TOF (surface-enhanced laser desorption and ionization time-of-flight) mass spectrometry. Reproducibility is defined in reference to a source of variation, which in our example is associated with a type of commercially available protein biochip. We obtained spectra for 8 spots on each 11 chips. Two spectra are generally more alike when obtained from the same chip rather than different chips. Thus, our experiment indicates potential improvements from reducing variation in chip manufacture and chip handling during measurement. Our analysis involves careful registration of the spectra and characterization of the spectral differences. As shown by our example, a metrological analysis may enhance case-control studies by guiding optimization of the measurements underlying the biomarker.
Under the assumption that deep-water ocean noise is a superposition of uncorrelated plane waves, the covariance can be expressed in terms of the noise directivity. We propose a simple directivity function that agrees with experimental results and use it to study the covariance for the case of vertical receiving points. We investigate covariance versus spacing for zero time delay and various directivities and bandwidths. When almost all of the noise arrives from the horizontal, the zero-delay covariance is always positive; when most of the noise arrives from overhead, it is negative for some spacings. We present contours of constant covariance as a function of spacing and time delay for various directivities and a narrow frequency band. We also examine covariance for single-frequency noise. Vertical noise with steering towards the vertical and horizontal noise with steering towards the horizontal are found to give the same covadance values. We examine maximum covariance over time delay and also that delay for which maximum covariance occurs. Numerous comparisons are made between our predictions and published experimental results. Finally, covariance for horizontal receiving points is considered.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.