High-throughput sequencing assays such as RNA-Seq, ChIP-Seq or barcode counting provide quantitative readouts in the form of count data. To infer differential signal in such data correctly and with good statistical power, estimation of data variability throughout the dynamic range and a suitable error model are required. We propose a method based on the negative binomial distribution, with variance and mean linked by local regression and present an implementation, DESeq, as an R/Bioconductor package.

/pdf/differential-expression-analysis-for-sequence-count-data-1txizymire.pdf

Differential expression analysis for sequence count data.

Multivariable regression models are powerful tools that are used frequently in studies of clinical outcomes. These models can use a mixture of categorical and continuous variables and can handle partially observed (censored) responses. However, uncritical application of modelling techniques can result in models that poorly fit the dataset at hand, or, even more likely, inaccurately predict outcomes on new subjects. One must know how to measure qualities of a model's fit in order to avoid poorly fitted or overfitted models. Measurement of predictive accuracy can be difficult for survival time data in the presence of censoring. We discuss an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities. Both types of predictive accuracy should be unbiasedly validated using bootstrapping or cross-validation, before using predictions in a new data series. We discuss some of the hazards of poorly fitted and overfitted regression models and present one modelling strategy that avoids many of the problems discussed. The methods described are applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes. Methods are illustrated with a survival analysis in prostate cancer using Cox regression.

/pdf/multivariable-prognostic-models-issues-in-developing-models-49wjg4tzp4.pdf

Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

SUMMARY Multivariable regression models are powerful tools that are used frequently in studies of clinical outcomes. These models can use a mixture of categorical and continuous variables and can handle partially observed (censored) responses. However, uncritical application of modelling techniques can result in models that poorly fit the dataset at hand, or, even more likely, inaccurately predict outcomes on new subjects. One must know how to measure qualities of a model's fit in order to avoid poorly fitted or overfitted models. Measurement of predictive accuracy can be difficult for survival time data in the presence of censoring. We discuss an easily interpretable index of predictive discrimination as well as methods for assessing calibration of predicted survival probabilities. Both types of predictive accuracy should be unbiasedly validated using bootstrapping or cross-validation, before using predictions in a new data series. We discuss some of the hazards of poorly fitted and overfitted regression models and present one modelling strategy that avoids many of the problems discussed. The methods described are applicable to all regression models, but are particularly needed for binary, ordinal, and time-to-event outcomes. Methods are illustrated with a survival analysis in prostate cancer using Cox regression. Accurate estimation of patient prognosis is important for many reasons. First, prognostic estimates can be used to inform the patient about likely outcomes of her disease. Second, the physician can use estimates of prognosis as a guide for ordering additional tests and selecting appropriate therapies. Third, prognostic assessments are useful in the evaluation of technologies; prognostic estimates derived both with and without using the results of a given test can be compared to measure the incremental prognostic information provided by that test over what is provided by prior information.' Fourth, a researcher may want to estimate the effect of a single factor (for example, treatment given) on prognosis in an observational study in which many uncontrolled confounding factors are also measured. Here the simultaneous effects of the uncontrolled variables must be controlled (held constant mathematically if using a regression model) so that the effect of the factor of interest can be more purely estimated. An analysis of how variables (especially continuous ones) affect the patient outcomes of interest is necessary to

/pdf/tutorial-in-biostatistics-multivariable-prognostic-models-4auy6032o6.pdf

Tutorial in biostatistics multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors

(2003). The Statistical Analysis of Failure Time Data. Technometrics: Vol. 45, No. 3, pp. 265-266.

The Statistical Analysis of Failure Time Data

Basic Concepts and Models. Observation Schemes, Censoring and Likelihood. Some Nonparametric and Graphical Procedures. Inference Procedures for Parametric Models. Inference procedures for Log-Location-Scale Distributions. Parametric Regression Models. Semiparametric Multiplicative Hazards Regression Models. Rank-Type and Other Semiparametric Procedures for Log-Location-Scale Models. Multiple Modes of Failure. Goodness of Fit Tests. Beyond Univariate Survival Analysis. Appendix A. Glossary of Notation and Abbreviations. Appendix B. Asymptotic Variance Formulas, Gamma Functions and Order Statistics. Appendix C. Large Sample Theory for Likelihood and Estimating Function Methods. Appendix D. Computational Methods and Simulation. Appendix E. Inference in Location-Scale Parameter Models. Appendix F. Martingales and Counting Processes. Appendix G. Data Sets. References.

Statistical Models and Methods for Lifetime Data

Statistical Models and Methods for Lifetime Data.

A number of methods have been proposed for dealing with extra-Poisson variation when doing regression analysis of count data. This paper studies negative-binomial regression models and examines efficiency and robustness properties of inference procedures based on them. The methods are compared with quasilikelihood methods.



Plusieurs methodes ont ete proposees en vue de traiter le probleme de la variation extra-poissonnienne dans une analyse de regression pour donnees de denombrement. Cet article a pour objet l'etude de modeles de regression binomiale negative et se penche sur les proprietes d'efficacite et de robustesse des methodes inferentielles decoulant des modeles. Ces dernieres sont comparees aux methodes de quasi-vraisemblancce.

/pdf/negative-binomial-and-mixed-poisson-regression-3p76ncbc6y.pdf

Negative binomial and mixed Poisson regression

Models and Frameworks for Analysis of Recurrent Events.- Methods Based on Counts and Rate Functions.- Analysis of Gap Times.- General Intensity-Based Models.- Multitype Recurrent Events.- Observation Schemes Giving Incomplete or Selective Data.- OtherTopics.

The Statistical Analysis of Recurrent Events

Methods for the analysis of panel data under a continuous-time Markov model are proposed. We present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models, and for other process characteristics such as mean sojourn times and equilibrium distributions. Generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented, and an example based on a longitudinal study of the smoking habits of school children is discussed. Questions of embeddability and estimation are examined.

Jerald F. Lawless

Papers

Statistical Models and Methods for Lifetime Data

Statistical Models and Methods for Lifetime Data.

Negative binomial and mixed Poisson regression

The Statistical Analysis of Recurrent Events

The Analysis of Panel Data under a Markov Assumption