Predicting patient survival from microarray data by accelerated failure time modeling using partial least squares and LASSO

We consider the problem of predicting survival times of cancer patients from the gene expression profiles of their tumor samples via linear regression modeling of log-transformed failure times. The partial least squares (PLS) and least absolute shrinkage and selection operator (LASSO) methodologies are used for this purpose where we first modify the data to account for censoring. Three approaches of handling right censored data-reweighting, mean imputation, and multiple imputation-are considered. Their performances are examined in a detailed simulation study and compared with that of full data PLS and LASSO had there been no censoring. A major objective of this article is to investigate the performances of PLS and LASSO in the context of microarray data where the number of covariates is very large and there are extremely few samples. We demonstrate that LASSO outperforms PLS in terms of prediction error when the list of covariates includes a moderate to large percentage of useless or noise variables; otherwise, PLS may outperform LASSO. For a moderate sample size (100 with 10,000 covariates), LASSO performed better than a no covariate model (or noise-based prediction). The mean imputation method appears to best track the performance of the full data PLS or LASSO. The mean imputation scheme is used on an existing data set on lung cancer. This reanalysis using the mean imputed PLS and LASSO identifies a number of genes that were known to be related to cancer or tumor activities from previous studies.     

Bayesian meta-analysis models for microarray data: a comparative study

Background

With the growing abundance of microarray data, statistical methods are increasingly needed to integrate results across studies. Two common approaches for meta-analysis of microarrays include either combining gene expression measures across studies or combining summaries such as p-values, probabilities or ranks. Here, we compare two Bayesian meta-analysis models that are analogous to these methods.

Results

Two Bayesian meta-analysis models for microarray data have recently been introduced. The first model combines standardized gene expression measures across studies into an overall mean, accounting for inter-study variability, while the second combines probabilities of differential expression without combining expression values. Both models produce the gene-specific posterior probability of differential expression, which is the basis for inference. Since the standardized expression integration model includes inter-study variability, it may improve accuracy of results versus the probability integration model. However, due to the small number of studies typical in microarray meta-analyses, the variability between studies is challenging to estimate. The probability integration model eliminates the need to model variability between studies, and thus its implementation is more straightforward. We found in simulations of two and five studies that combining probabilities outperformed combining standardized gene expression measures for three comparison values: the percent of true discovered genes in meta-analysis versus individual studies; the percent of true genes omitted in meta-analysis versus separate studies, and the number of true discovered genes for fixed levels of Bayesian false discovery. We identified similar results when pooling two independent studies of Bacillus subtilis. We assumed that each study was produced from the same microarray platform with only two conditions: a treatment and control, and that the data sets were pre-scaled.

Conclusion

The Bayesian meta-analysis model that combines probabilities across studies does not aggregate gene expression measures, thus an inter-study variability parameter is not included in the model. This results in a simpler modeling approach than aggregating expression measures, which accounts for variability across studies. The probability integration model identified more true discovered genes and fewer true omitted genes than combining expression measures, for our data sets.     

Deconstructing language by comparative gene expression: from neurobiology to microarray

Language is a defining characteristic of our species that has emerged quite recently on an evolutionary timescale. Understanding the neurobiological substrates and genetic underpinnings of language constitutes a basic challenge for both neuroscience and genetics. The functional localization of language in the brain has been progressively refined over the last century through studies of aphasics and more recently through neuroimaging. Concurrently, structural specializations in these brain regions have been identified by virtue of their lateralization in humans and also through comparisons with homologous brain regions in non-human primate species. Comparative genomics has revealed the genome of our closest living relative, the chimpanzee, to be astonishingly similar to our own. To explore the role that changes in the regulation of gene expression have had in recent human evolution, several groups have used microarrays to compare expression levels for thousands of genes in the brain between humans and chimpanzees. By applying this approach to the increasingly refined peri-sylvian network of brain regions involved in language, it may be possible to discern functionally significant changes in gene expression that are universal among humans but unique to our species, thus casting light on the molecular basis of language in the brain.     

Deconstructing language by comparative gene expression: from neurobiology to microarray

Language is a defining characteristic of our species that has emerged quite recently on an evolutionary timescale. Understanding the neurobiological substrates and genetic underpinnings of language constitutes a basic challenge for both neuroscience and genetics. The functional localization of language in the brain has been progressively refined over the last century through studies of aphasics and more recently through neuroimaging. Concurrently, structural specializations in these brain regions have been identified by virtue of their lateralization in humans and also through comparisons with homologous brain regions in non-human primate species. Comparative genomics has revealed the genome of our closest living relative, the chimpanzee, to be astonishingly similar to our own. To explore the role that changes in the regulation of gene expression have had in recent human evolution, several groups have used microarrays to compare expression levels for thousands of genes in the brain between humans and chimpanzees. By applying this approach to the increasingly refined peri-sylvian network of brain regions involved in language, it may be possible to discern functionally significant changes in gene expression that are universal among humans but unique to our species, thus casting light on the molecular basis of language in the brain.     

Additive risk survival model with microarray data

Background  

Microarray techniques survey gene expressions on a global scale. Extensive biomedical studies have been designed to discover subsets of genes that are associated with survival risks for diseases such as lymphoma and construct predictive models using those selected genes. In this article, we investigate simultaneous estimation and gene selection with right censored survival data and high dimensional gene expression measurements.     

A comparative study of winter survival in two temperate Collembola

ABSTRACT.

• 1 We studied winter survival of two temperate collembolan species, Orchesella cincta (L.) and Tomocerus minor (Lubbock), that overwinter in adult and juvenile life stages.
• 2 A significant seasonal variation in cold hardiness, measured as lethal temperature after 24 h exposure, was found for both species. There was no difference between juveniles and adults in cold hardiness. O.cincta was more cold tolerant than T.minor.
• 3 A group of high and a group of low values for lethal temperatures could be distinguished.
• 4 Frost periods induced gut evacuation in O.cincta, but not in T.minor.
• 5 During frost periods no extra winter mortality was found in T.minor. This species moved down the soil profile as a response to a frost period without snow cover.
• 6 The winter mortality of O.cincta was difficult to estimate, since part of the population remained above ground in trees and escaped from sampling. The smallest size classes, which are restricted to the litter, had a lower winter mortality than T.minor.

     

Predicting survival time for cold exposure

The prediction of survival time (ST) for cold exposure is speculative as reliable controlled data of deep hypothermia are unavailable. At best, guidance can be obtained from case histories of accidental exposure. This study describes the development of a mathematical model for the prediction of ST under sedentary conditions in the cold. The model is based on steady-state heat conduction in a single cylinder comprised of a core and two concentric annular shells representing the fat plus skin and the clothing plus still boundary layer, respectively. The ambient condition can be either air or water; the distinction is made by assigning different values of insulation to the still boundary layer. Metabolic heat production (M) is comprised of resting and shivering components with the latter predicted by temperature signals from the core and skin. Where the cold exposure is too severe forM to balance heat loss, ST is largely determined by the rate of heat loss from the body. Where a balance occurs, ST is governed by the endurance time for shivering. End of survival is marked by the deep core temperature reaching a value of 30° C. The model was calibrated against survival data of cold water (0 to 20° C) immersion and then applied to cold air exposure. A sampling of ST predictions for the nude exposure of an average healthy male in relatively calm air (1 km/h wind speed) are the following: 1.8, 2.5, 4.1, 9.0, and >24 h for –30, –20, –10, 0, and 10° C, respectively. With two layers of loose clothing (average thickness of 1 mm each) in a 5 km/h wind, STs are 4.0, 5.6, 8.6, 15.4, and >24 h for –50, –40, –30, –20, and –10° C. The predicted STs must be weighted against the extrapolative nature of the model. At present, it would be prudent to use the predictions in a relative sense, that is, to compare or rank-order predicted STs for various combinations of ambient conditions and clothing protection.     

The dChip survival analysis module for microarray data

Background  

Genome-wide expression signatures are emerging as potential marker for overall survival and disease recurrence risk as evidenced by recent commercialization of gene expression based biomarkers in breast cancer. Similar predictions have recently been carried out using genome-wide copy number alterations and microRNAs. Existing software packages for microarray data analysis provide functions to define expression-based survival gene signatures. However, there is no software that can perform survival analysis using SNP array data or draw survival curves interactively for expression-based sample clusters.     

Assessment of survival prediction models based on microarray data

MOTIVATION: In the process of developing risk prediction models, various steps of model building and model selection are involved. If this process is not adequately controlled, overfitting may result in serious overoptimism leading to potentially erroneous conclusions. METHODS: For right censored time-to-event data, we estimate the prediction error for assessing the performance of a risk prediction model (Gerds and Schumacher, 2006; Graf et al., 1999). Furthermore, resampling methods are used to detect overfitting and resulting overoptimism and to adjust the estimates of prediction error (Gerds and Schumacher, 2007). RESULTS: We show how and to what extent the methodology can be used in situations characterized by a large number of potential predictor variables where overfitting may be expected to be overwhelming. This is illustrated by estimating the prediction error of some recently proposed techniques for fitting a multivariate Cox regression model applied to the data of a prognostic study in patients with diffuse large-B-cell lymphoma (DLBCL). AVAILABILITY: Resampling-based estimation of prediction error curves is implemented in an R package called pec available from the authors.     

AffyTrees: facilitating comparative analysis of Affymetrix plant microarray chips

Microarrays measure the expression of large numbers of genes simultaneously and can be used to delve into interaction networks involving many genes at a time. However, it is often difficult to decide to what extent knowledge about the expression of genes gleaned in one model organism can be transferred to other species. This can be examined either by measuring the expression of genes of interest under comparable experimental conditions in other species, or by gathering the necessary data from comparable microarray experiments. However, it is essential to know which genes to compare between the organisms. To facilitate comparison of expression data across different species, we have implemented a Web-based software tool that provides information about sequence orthologs across a range of Affymetrix microarray chips. AffyTrees provides a quick and easy way of assigning which probe sets on different Affymetrix chips measure the expression of orthologous genes. Even in cases where gene or genome duplications have complicated the assignment, groups of comparable probe sets can be identified. The phylogenetic trees provide a resource that can be used to improve sequence annotation and detect biases in the sequence complement of Affymetrix chips. Being able to identify sequence orthologs and recognize biases in the sequence complement of chips is necessary for reliable cross-species microarray comparison. As the amount of work required to generate a single phylogeny in a nonautomated manner is considerable, AffyTrees can greatly reduce the workload for scientists interested in large-scale cross-species comparisons.     

Predicting diet, trophic level and palaeoecology from bone stable isotope analysis: a comparative study of five red deer populations

C and N stable isotope ratios of red deer (Cervus elaphus) bone collagen (154 individuals) from five modern populations occupying geographically different habitats are reported. No significant difference was observed between deer occupying forested and non-forested environments subject to similar climatic conditions suggesting a simple “canopy effect” is not observed. Mean population δ¹³C is negatively correlated with temperature whereas mean population δ¹⁵N is positively correlated with temperature. A weak but significant positive correlation was observed between deer age and collagen δ¹³C values from the Isle of Rum population (Scotland). The amount of intra-population isotope variability is not consistent among populations; thus significant numbers of individuals from each species are required for modern food web studies, for palaeodietary baseline data, and for palaeoecological studies.     

Joint modelling of repeated transitions in follow-up data--a case study on breast cancer data

In longitudinal studies where time to a final event is the ultimate outcome often information is available about intermediate events the individuals may experience during the observation period. Even though many extensions of the Cox proportional hazards model have been proposed to model such multivariate time-to-event data these approaches are still very rarely applied to real datasets. The aim of this paper is to illustrate the application of extended Cox models for multiple time-to-event data and to show their implementation in popular statistical software packages. We demonstrate a systematic way of jointly modelling similar or repeated transitions in follow-up data by analysing an event-history dataset consisting of 270 breast cancer patients, that were followed-up for different clinical events during treatment in metastatic disease. First, we show how this methodology can also be applied to non Markovian stochastic processes by representing these processes as "conditional" Markov processes. Secondly, we compare the application of different Cox-related approaches to the breast cancer data by varying their key model components (i.e. analysis time scale, risk set and baseline hazard function). Our study showed that extended Cox models are a powerful tool for analysing complex event history datasets since the approach can address many dynamic data features such as multiple time scales, dynamic risk sets, time-varying covariates, transition by covariate interactions, autoregressive dependence or intra-subject correlation.     

Sequential interim analyses of survival data in DNA microarray experiments

Background  

Discovery of biomarkers that are correlated with therapy response and thus with survival is an important goal of medical research on severe diseases, e.g. cancer. Frequently, microarray studies are performed to identify genes of which the expression levels in pretherapeutic tissue samples are correlated to survival times of patients. Typically, such a study can take several years until the full planned sample size is available.     

Design of a seven-genome Escherichia coli microarray for comparative genomic profiling

We describe the design and evaluate the use of a high-density oligonucleotide microarray covering seven sequenced Escherichia coli genomes in addition to several sequenced E. coli plasmids, bacteriophages, pathogenicity islands, and virulence genes. Its utility is demonstrated for comparative genomic profiling of two unsequenced strains, O175:H16 D1 and O157:H7 3538 (Deltastx(2)::cat) as well as two well-known control strains, K-12 W3110 and O157:H7 EDL933. By using fluorescently labeled genomic DNA to query the microarrays and subsequently analyze common virulence genes and phage elements and perform whole-genome comparisons, we observed that O175:H16 D1 is a K-12-like strain and confirmed that its phi3538 (Deltastx(2)::cat) phage element originated from the E. coli 3538 (Deltastx(2)::cat) strain, with which it shares a substantial proportion of phage elements. Moreover, a number of genes involved in DNA transfer and recombination was identified in both new strains, providing a likely explanation for their capability to transfer phi3538 (Deltastx(2)::cat) between them. Analyses of control samples demonstrated that results using our custom-designed microarray were representative of the true biology, e.g., by confirming the presence of all known chromosomal phage elements as well as 98.8 and 97.7% of queried chromosomal genes for the two control strains. Finally, we demonstrate that use of spatial information, in terms of the physical chromosomal locations of probes, improves the analysis.     

Anaerobic survival potential of four bivalves from different habitats. A comparative survey

A comparative survey of the anaerobic survival potential of four different bivalve species and the interference of associated bacteria has been carried out. Individuals from both subtidal and intertidal environments were considered by selecting the following species: Mytilus edulis (subtidal epifaunal), Spisula subtruncata (subtidal infaunal), Macoma balthica (intertidal infaunal) and Cerastoderma edule (intertidal infaunal). Anaerobiosis was simulated in the laboratory by subjecting individuals to the following conditions: nitrogen atmosphere, air atmosphere and anoxic seawater incubation. Moreover, the effect of the antibiotic CA (chloramphenicol) was investigated, either as a pre-treatment of individuals kept under normoxic conditions for a week or directly added to the anoxic incubation media. According to survival performances of the individuals, intertidal animals that use to cope with tidal fluctuations in the coastline (emersion processes) had an extraordinary greater capacity to survive aerial exposure as compared to both nitrogen gas and anoxic seawater incubations most likely due to their capacity to perform aerobiosis at certain rate from atmospheric oxygen availability. Specifically, Macoma balthica enlarged its survival potential up to 24.8 days (LT(50)) under air exposure at 12 degrees C as compared to other specific treatments used here (4.9 days). The latter pattern was also observed, although in a much lower magnitude, for the other intertidal species Cerastoderma edule that survived 3.7 and 4.6 days (LT(50)) under nitrogen atmosphere and anoxic seawater incubation, respectively as compared to 9.5 days for emersed individuals. In contrast to the subtidal species, aerial exposure of both intertidal species led to a much higher survival performances than incubation of individuals in anoxic media with the presence of antibiotic. Survival capacity of the subtidal species Mytilus edulis and Spisula subtruncata was statistically similar under air and nitrogen atmospheres and anoxic seawater incubation. Then, subtidal species have a limited ability to air breathing as a conclusion of a similar survival in atmospheric and anoxic seawater incubations. Remarkably, M. edulis represented the only exception when considering longer-term survival capacity compared to the LT(50) values. Indeed, differences in LT(90) values for M. edulis were statistically different, values decreasing significantly from 19.7-19.9 days (under both nitrogen and air atmospheres) to 16.7 days when individuals are incubated in anoxic seawater. This may be due to the adverse effects of anaerobic bacteria that spontaneously proliferate within the static seawater incubations. As well as for S. subtruncata, possible aerobic processes under aerial exposure of mussels seemed to be not significant for the enlargement of its survival potential, since results obtained for both air and nitrogen atmospheres are similar. Pre-treatment with the antibiotic chloramphenicol caused survival capacity to increase by a factor of approx. 2 (M. edulis) and 34-44% (S. subtruncata). In contrast to intertidal species, the direct addition of the antibiotic to the incubation media caused the highest survival performances in both subtidal species. Habitat differences and species-dependent variability must be considered as significant sources of variation when studying the anaerobic performance of individuals using the most common experimental anaerobic techniques to test survival potential.     

A comparative study of tropomyosin from vertebrate ventricles

A comparative study of vertebrate ventricle tropomyosin has been carried out from the viewpoint of molecular evolution. The ventricles containing one-component tropomyosin were generally known, and in this paper those containing two components were also found in 8 species among mammals, reptiles, amphibia, and fish, but not among birds. The two components were concluded to be authentic tropomyosin and not artifacts since they showed lower electrophoretic mobilities in the presence of urea, and they were precipitated at pH 4.5 and bound to F-actin. Studies on cysteine contents and cyanogen bromide cleavage peptide patterns revealed that the characteristics of the two tropomyosin components from pig, turtle, amphibia and carp ventricles varied increasingly in that order from typical alpha- and beta-characteristics as seen in rabbit skeletal muscle tropomyosin. The single component of chicken ventricle tropomyosin showed alpha component characteristics in its electrophoretic mobility and cysteine content, and beta component characteristics in cyanogen bromide cleavage peptide pattern. The two components of carp ventricle tropomyosin seemed to be the most primitive, having two cysteine residues per molecule and a cyanogen bromide cleavage peptide pattern different from those of the two components of rabbit skeletal muscle.