Negative binomial additive models

The generalized additive model is extended to handle negative binomial responses. The extension is complicated by the fact that the negative binomial distribution has two parameters and is not in the exponential family. The methodology is applied to data involving DNA adduct counts and smoking variables among ex-smokers with lung cancer. A more detailed investigation is made of the parametric relationship between the number of adducts and years since quitting while retaining a smooth relationship between adducts and the other covariates.     

Fitting semiparametric additive hazards models using standard statistical software

The Cox proportional hazards model has become the standard in biomedical studies, particularly for settings in which the estimation covariate effects (as opposed to prediction) is the primary objective. In spite of the obvious flexibility of this approach and its wide applicability, the model is not usually chosen for its fit to the data, but by convention and for reasons of convenience. It is quite possible that the covariates add to, rather than multiply the baseline hazard, making an additive hazards model a more suitable choice. Typically, proportionality is assumed, with the potential for additive covariate effects not evaluated or even seriously considered. Contributing to this phenomenon is the fact that many popular software packages (e.g., SAS, S-PLUS/R) have standard procedures to fit the Cox model (e.g., proc phreg, coxph), but as of yet no analogous procedures to fit its additive analog, the Lin and Ying (1994) semiparametric additive hazards model. In this article, we establish the connections between the Lin and Ying (1994) model and both Cox and least squares regression. We demonstrate how SAS's phreg and reg procedures may be used to fit the additive hazards model, after some straightforward data manipulations. We then apply the additive hazards model to examine the relationship between Model for End-stage Liver Disease (MELD) score and mortality among patients wait-listed for liver transplantation.     

Quantile regression improves models of lake eutrophication with implications for ecosystem‐specific management

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Additive partial linear models with measurement errors

We consider statistical inference for additive partial linearmodels when the linear covariate is measured with error. Wepropose attenuation-to-correction and simulation-extrapolation,simex, estimators of the parameter of interest. It is shownthat the first resulting estimator is asymptotically normaland requires no undersmoothing. This is an advantage of ourestimator over existing backfitting-based estimators for semiparametricadditive models which require undersmoothing of the nonparametriccomponent in order for the estimator of the parametric componentto be root-n consistent. This feature stems from a decreaseof the bias of the resulting estimator, which is appropriatelyderived using a profile procedure. A similar characteristicin semiparametric partially linear models was obtained by Wanget al. (2005). We also discuss the asymptotics of the proposedsimex approach. Finite-sample performance of the proposed estimatorsis assessed by simulation experiments. The proposed methodsare applied to a dataset from a semen study.     

Correct and logical inference on efficacy in subgroups and their mixture for binary outcomes

Targeted therapies are becoming more common. In targeted therapy development, suppose its companion diagnostic test divides patients into a marker‐positive subgroup and its complementary marker‐negative subgroup. To find the right patient population for the therapy to target, inference on efficacy in the marker‐positive and marker‐negative subgroups as well as efficacy in the overall mixture population are all of interest. Depending on the type of clinical endpoints, inference on mixture population can be nontrivial and commonly used efficacy measures may not be suitable for a mixture population. Correlations among estimates of efficacy in the marker‐positive, marker‐negative, and overall mixture population play a crucial role in using an earlier phase study to inform on the design of a confirmatory study (e.g., determination of sample size). This article first shows that when the clinical endpoint is binary (such as respond or not), odds ratio is inappropriate as an efficacy measure in this setting, but relative response (RR) is appropriate. We show a safe way of calculating estimated correlations is to consider mixing subgroup response probabilities within each treatment arm first, and then derive the joint distribution of RR estimates. We also show, if one calculates RR within each subgroup first, how wrong the correlations can be if the Delta method derivation fails to take randomness of estimating the mixing coefficient into account.     

Decision Tree-PLS (DT-PLS) algorithm for the development of process: Specific local prediction models

This work presents a novel multivariate statistical algorithm, Decision Tree-PLS (DT-PLS), to improve the prediction and understanding of dynamic processes based on local partial least square regression (PLSR) models for characteristic process groups defined based on Decision Tree (DT) analysis. The DT-PLS algorithm is successfully applied to two different cell culture data sets, one obtained from bioreactors of 3.5 L lab scale and the other obtained from the 15 ml ambr microbioreactor system. Substantial improvement in the predictive capabilities of the model can be achieved based on the localization compared to the classical PLSR approach, which is implemented in the commercially available packages. Additionally, the differences in the model parameters of the local models suggest that the governing process variables vary for the different process regimes indicating the different states of the cell under different process conditions.     

A probabilistic framework for microarray data analysis: Fundamental probability models and statistical inference

Gene expression studies generate large quantities of data with the defining characteristic that the number of genes (whose expression profiles are to be determined) exceed the number of available replicates by several orders of magnitude. Standard spot-by-spot analysis still seeks to extract useful information for each gene on the basis of the number of available replicates, and thus plays to the weakness of microarrays. On the other hand, because of the data volume, treating the entire data set as an ensemble, and developing theoretical distributions for these ensembles provides a framework that plays instead to the strength of microarrays. We present theoretical results that under reasonable assumptions, the distribution of microarray intensities follows the Gamma model, with the biological interpretations of the model parameters emerging naturally. We subsequently establish that for each microarray data set, the fractional intensities can be represented as a mixture of Beta densities, and develop a procedure for using these results to draw statistical inference regarding differential gene expression. We illustrate the results with experimental data from gene expression studies on Deinococcus radiodurans following DNA damage using cDNA microarrays.     

Segmented linear regression models applied to the analysis of data from a cross-sectional growth experiment

Several different methods of analysis are applied to data consisting of weight measurements, taken at specified post-treatment times, of harvested thyroids from rats given one of four treatments. Previous studies of this type of data indicated that the growth is initially rapid, and that a second phase of less rapid growth is followed by a final phase in which little additional growth occurs. The data are further characterized by increasing variance through time. The primary purpose of the analysis is to study the effect of the treatments at the end of the study period. One-way analysis of variance tests among groups are performed on each day, but the results are not particularly helpful. However, results from two-way analyses of variance (over subsets of days and groups) are consistent with the three phase model and accordingly indicate significant group differences during each. Finally, maximum likelihood methods are used to fit a three part segmented linear regression model.     

Chemometric methods for simultaneous quantification of lactic,malic and fumaric acids

Lactic, fumaric and malic acids are commonly used in food and pharmaceutical industries. During microbial production of these compounds, it is important to determine their concentrations in the fermentation broth with a rapid and sensitive method. Spectrophotometry is commonly used. However, UV‐spectral overlap between these organic acids makes it difficult to determine each of them individually from the mixture. In order to overcome this problem, statistical methods, namely principal component regression (PCR) and partial least squares‐1 methods, were tested and compared with conventional HPLC techniques. The absorbance data matrix was obtained by measuring the absorbances of 21 ternary mixtures of lactic, fumaric and malic acids in a wavelength range of 210–260 nm. Calibration and validation were performed by using the data obtained in a mixture of these organic acids. The prediction abilities of the methods were tested by applying them to fermentation broths. The precision of the PCR method was better than that of the partial least squares‐1 method. In the PCR method, the correlation coefficients between actual and predicted concentrations of the organic acids were calculated as 0.970 for lactic acid and 0.996 for fumaric acid in fermentation broths. The concentration of malic acid was not detected due to its low concentration in samples. These results show that the PCR method can be applied for simultaneous determination of lactic, fumaric and malic acids in fermentation broths.     

Penalized discriminant methods for the classification of tumors from gene expression data

Due to the advent of high-throughput microarray technology, it has become possible to develop molecular classification systems for various types of cancer. In this article, we propose a methodology using regularized regression models for the classification of tumors in microarray experiments. The performances of principal components, partial least squares, and ridge regression models are studied; these regression procedures are adapted to the classification setting using the optimal scoring algorithm. We also develop a procedure for ranking genes based on the fitted regression models. The proposed methodologies are applied to two microarray studies in cancer.     

Chemometrics-assisted simple UV-spectroscopic determination of carbamazepine in human serum and comparison with reference methods

In the present report, carbamazepine is determined on serum samples of real patients by a procedure completely assisted by chemometric tools. First, a response surface methodology based on a mixture design was applied in order to select the best conditions for the extraction step. Finally, partial least squares multivariate calibration (PLS-1) was applied to second-derivative UV spectra, eliminating a shift baseline effect that originated in the extraction procedure. The performance assessment included: (a) a three-level precision study, (b) a recovery study analyzing spiked samples, and (c) a method comparison with high-performance liquid chromatography (HPLC) and fluorescence polarization immunoassay (FPIA) applied on real patient samples. The obtained results show the potentiality of the presently studied methodology for the monitoring of patients treated with this anticonvulsant.     

Airborne hyperspectral data predict Ellenberg indicator values for nutrient and moisture availability in dry grazed grasslands within a local agricultural landscape

Species-based ecological indices, such as Ellenberg indicators, reflect plant habitat preferences and can be used to describe local environment conditions. One disadvantage of using vegetation data as a substitute for environmental data is the fact that extensive floristic sampling can usually only be carried out at a plot scale within limited geographical areas. Remotely sensed data have the potential to provide information on fine-scale vegetation properties over large areas. In the present study, we examine whether airborne hyperspectral remote sensing can be used to predict Ellenberg nutrient (N) and moisture (M) values in plots in dry grazed grasslands within a local agricultural landscape in southern Sweden. We compare the prediction accuracy of three categories of model: (I) models based on predefined vegetation indices (VIs), (II) models based on waveband-selected VIs, and (III) models based on the full set of hyperspectral wavebands. We also identify the optimal combination of wavebands for the prediction of Ellenberg values. The floristic composition of 104 (4 m × 4 m grassland) plots on the Baltic island of Öland was surveyed in the field, and the vascular plant species recorded in the plots were assigned Ellenberg indicator values for N and M. A community-weighted mean value was calculated for N (mN) and M (mM) within each plot. Hyperspectral data were extracted from an 8 m × 8 m pixel window centred on each plot. The relationship between field-observed and predicted mean Ellenberg values was significant for all three categories of prediction models. The performance of the category II and III models was comparable, and they gave lower prediction errors and higher R² values than the category I models for both mN and mM. Visible and near-infrared wavebands were important for the prediction of both mN and mM, and shortwave infrared wavebands were also important for the prediction of mM. We conclude that airborne hyperspectral remote sensing can detect spectral differences in vegetation between grassland plots characterised by different mean Ellenberg N and M values, and that remote sensing technology can potentially be used to survey fine-scale variation in environmental conditions within a local agricultural landscape.