Computationally Efficient Kalman Filter Approaches for Fitting Smoothing Splines

Smoothing spline models have shown to be effective in various fields (e.g., engineering and biomedical sciences) for understanding complex signals from noisy data. As nonparametric models, smoothing spline ANOVA (Analysis Of variance) models do not fix the structure of the regression function, leading to more flexible model estimates (e.g., linear or nonlinear estimates). The functional ANOVA decomposition of the regression function estimates offers interpretable results that describe the relationship between the outcome variable, and the main and interaction effects of different covariates/predictors. However, smoothing spline ANOVA (SS-ANOVA) models suffer from high computational costs, with a computational complexity of ON3 for N observations. Various numerical approaches can address this problem. In this chapter, we focus on the introduction to a state space representation of SS-ANOVA models. The estimation algorithms based on the Kalman filter are implemented within the SS-ANOVA framework using the state space representation, reducing the computational costs significantly

Inter-Platform comparability of microarrays in acute lymphoblastic leukemia

BACKGROUND: Acute lymphoblastic leukemia (ALL) is the most common pediatric malignancy and has been the poster-child for improved therapeutics in cancer, with life time disease-free survival (LTDFS) rates improving from <10% in 1970 to >80% today. There are numerous known genetic prognostic variables in ALL, which include T cell ALL, the hyperdiploid karyotype and the translocations: t(12;21)[TEL-AML1], t(4;11)[MLL-AF4], t(9;22)[BCR-ABL], and t(1;19)[E2A-PBX]. ALL has been studied at the molecular level through expression profiling resulting in un-validated expression correlates of these prognostic indices. To date, the great wealth of expression data, which has been generated in disparate institutions, representing an extremely large cohort of samples has not been combined to validate any of these analyses. The majority of this data has been generated on the Affymetrix platform, potentially making data integration and validation on independent sample sets a possibility. Unfortunately, because the array platform has been evolving over the past several years the arrays themselves have different probe sets, making direct comparisons difficult. To test the comparability between different array platforms, we have accumulated all Affymetrix ALL array data that is available in the public domain, as well as two sets of cDNA array data. In addition, we have supplemented this data pool by profiling additional diagnostic pediatric ALL samples in our lab. Lists of genes that are differentially expressed in the six major subclasses of ALL have previously been reported in the literature as possible predictors of the subclass. RESULTS: We validated the predictability of these gene lists on all of the independent datasets accumulated from various labs and generated on various array platforms, by blindly distinguishing the prognostic genetic variables of ALL. Cross-generation array validation was used successfully with high sensitivity and high specificity of gene predictors for prognostic variables. We have also been able to validate the gene predictors with high accuracy using an independent dataset generated on cDNA arrays. CONCLUSION: Interarray comparisons such as this one will further enhance the ability to integrate data from several generations of microarray experiments and will help to break down barriers to the assimilation of existing datasets into a comprehensive data pool

Statistical methods for assays with limits of detection: Serum bile acid as a differentiator between patients with normal colons, adenomas, and colorectal cancer

In analytic chemistry a detection limit (DL) is the lowest measurable amount of an analyte that can be distinguished from a blank; many biomedical measurement technologies exhibit this property. From a statistical perspective, these data present inferential challenges because instead of precise measures, one only has information that the value is somewhere between 0 and the DL (below detection limit, BDL). Substitution of BDL values, with 0 or the DL can lead to biased parameter estimates and a loss of statistical power. Statistical methods that make adjustments when dealing with these types of data, often called left-censored data, are available in many commercial statistical packages. Despite this availability, the use of these methods is still not widespread in biomedical literature. We have reviewed the statistical approaches of dealing with BDL values, and used simulations to examine the performance of the commonly used substitution methods and the most widely available statistical methods. We have illustrated these methods using a study undertaken at the Vanderbilt-Ingram Cancer Center, to examine the serum bile acid levels in patients with colorectal cancer and adenoma. We have found that the modern methods for BDL values identify disease-related differences that are often missed, with statistically naive approaches

Combined benefit of prediction and treatment: a criterion for evaluating clinical prediction models.

Clinical treatment decisions rely on prognostic evaluation of a patient's future health outcomes. Thus, predictive models under different treatment options are key factors for making good decisions. While many criteria exist for judging the statistical quality of a prediction model, few are available to measure its clinical utility. As a consequence, we may find that the addition of a clinical covariate or biomarker improves the statistical quality of the model, but has little effect on its clinical usefulness. We focus on the setting where a treatment decision may reduce a patient's risk of a poor outcome, but also comes at a cost; this may be monetary, inconvenience, or the potential side effects. This setting is exemplified by cancer chemoprevention, or the use of statins to reduce the risk of cardiovascular disease. We propose a novel approach to assessing a prediction model using a formal decision analytic framework. We combine the predictive model's ability to discriminate good from poor outcome with the net benefit afforded by treatment. In this framework, reduced risk is balanced against the cost of treatment. The relative cost-benefit of treatment provides a useful index to assist patient decisions. This index also identifies the relevant clinical risk regions where predictive improvement is needed. Our approach is illustrated using data from a colorectal adenoma chemoprevention trial

Restaurant Inspection Scores and Foodborne Disease

Restaurants in the United States are regularly inspected by health departments, but few data exist regarding the effect of restaurant inspections on food safety. We examined statewide inspection records from January 1993 through April 2000. Data were available from 167,574 restaurant inspections. From 1993 to 2000, mean scores rose steadily from 80.2 to 83.8. Mean inspection scores of individual inspectors were 69–92. None of the 12 most commonly cited violations were critical food safety hazards. Establishments scoring <60 had a mean improvement of 16 points on subsequent inspections. Mean scores of restaurants experiencing foodborne disease outbreaks did not differ from restaurants with no reported outbreaks. A variety of factors influence the uniformity of restaurant inspections. The restaurant inspection system should be examined to identify ways to ensure food safety