PMC:539276 / 30438-35366 JSONTXT

{"project":"2_test","denotations":[{"id":"15588297-12606952-8294866","span":{"begin":577,"end":579},"obj":"12606952"},{"id":"15588297-12704611-8294867","span":{"begin":1283,"end":1285},"obj":"12704611"},{"id":"15588297-12704611-8294868","span":{"begin":1471,"end":1473},"obj":"12704611"},{"id":"15588297-14757357-8294869","span":{"begin":1951,"end":1953},"obj":"14757357"}],"text":"Conclusions\nThe LOWESS method has recently been applied in other applications for the biological sciences. Comparative genomic hybridization (CGH) is a molecular cytogenetic method of screening a tumor for genetic changes. The alterations are classified as DNA gains and losses and they reveal a characteristic pattern that includes mutations at chromosomal and subchromosomal levels. Our proposed optimized scheme is directly applicable to the application of calibrating CGH microarray experiments, as well as for data analysis aspects. For example, the work of Clark et al. [36] utilized the LOWESS method for identifying the regions where gene copy numbers were aberrantly high or low in prostate cancer using CGH microarray technology. The parameter f was chosen arbitrarily and its value was not reported in the study. Consequently, reproduction and verification of these results may be diffcult. For instance, some of the important biological findings, such as start and end points of amplifications and deletions, may be adversely affected by different choices of f.\nIn addition to CGH analysis, LOWESS has found application in case-control studies where logistic regression has been used to model the relationship between binary responses and continuous predictor variables [37]. In these types of studies one may use LOWESS to remove systematic trends that contaminate the laboratory measurements of predictor variables. The analysis reported by Borkowf et al. [37] clearly shows that different choices of f result in noticeably different correction effects and the optimization method proposed here may be suitable for enhancing such a study. Adaptations to the cost function may be utilized to handle this type of data. In addition, analysis of other types of scatterplot data by utilizing the LOWESS method with an arbitrary choice for the bandwidth parameter is undoubtedly susceptible to varied interpretations or errant conclusions [38,39].\nAnother result of this optimized calibration study is that we uncovered a better understanding of choosing the parameter d in the weighted polynomial fit. A higher-order (d \u003e 2), weighted polynomial is rarely needed based on the argument that such an assumption is, to a certain extent, over-fitting the data. From the findings of our study, we find that it is better to use a linear estimate based on minimizing the estimate errors across (A, M)-scatterplots. Consequently, different choices of d resulted in different optimized values for f. The reason is that for the higher-order polynomial, it is beneficial in general to retain a larger fraction of the values of A for the weight function in computing the polynomial coeffcients. It is very important to carefully select f since ultimately, the bandwidth is a function of the polynomial order.\nHere, we also reaffirmed the idea that the quality filtering of ratios and spots is a necessary step that should precede all experimental microarray data handling procedures, whether it is scatterplot-based normalization or any other normalization method, since errant ratios would surely have a deleterious affect on the calibration. For instance, in the BT-474 data, the first replicate slide had poor ratio quality for a handful of genes. Calibration without considering or removing these errant spots resulted in less reliable results. This study addresses the issue of locating sources of experimental error for print-tips that have high sensitivity for the parameter f . For one, print-tips are physically different and they are considered to have different types of errors introduced based on these properties. In the formulation of normalization, it is imperative to address such subtle issues when choosing and implementing any algorithm.\nThe systematic choice of the parameters in the LOWESS algorithm has not been previously addressed in the microarray literature and the method proposed here may be utilized in different microarray platforms. Such a treatment is also important for a wide variety of applications that employ scatterplot-based regression. The findings of this study illustrate that by choosing different values of f for the LOWESS algorithm results in noticeably different normalization results. This proposed method requires the calibration step to clearly state the assumptions used for within-slide normalization. Our optimization algorithm is more systematic than simply choosing an arbitrary parameter value or through trial and error techniques since the optimized approach relies on the actual underlying structure of the data. We also stress that such an optimization algorithm may also be utilized for other studies in addition to DNA microarray normalization treatments. Proper changes need to be made to Eq. (5) to reflect the ideal model for the data captured in the function ψk,i(·), but in some studies, such a function may be satisfactorily determined or estimated from the data."}