High quality protocols facilitate proper conduct, reporting, and external review
 of clinical trials. However, the completeness of trial protocols is often
 inadequate. To help improve the content and quality of protocols, an
 international group of stakeholders developed the SPIRIT 2013 Statement
 (Standard Protocol Items: Recommendations for Interventional Trials). The SPIRIT
 Statement provides guidance in the form of a checklist of recommended items to
 include in a clinical trial protocol. This SPIRIT 2013 Explanation and Elaboration paper provides important
 information to promote full understanding of the checklist recommendations. For
 each checklist item, we provide a rationale and detailed description; a model
 example from an actual protocol; and relevant references supporting its
 importance. We strongly recommend that this explanatory paper be used in
 conjunction with the SPIRIT Statement. A website of resources is also available
 (www.spirit-statement.org). The SPIRIT 2013 Explanation and Elaboration paper, together with the Statement,
 should help with the drafting of trial protocols. Complete documentation of key
 trial elements can facilitate transparency and protocol review for the benefit
 of all stakeholders.

https://www.bmj.com/content/bmj/346/bmj.e7586.full.pdf

SPIRIT 2013 explanation and elaboration: guidance for protocols of clinical trials

DNA sequence copy number is the number of copies of DNA at a region of a genome. Cancer progression often involves alterations in DNA copy number. Newly developed microarray technologies enable simultaneous measurement of copy number at thousands of sites in a genome. We have developed a modification of binary segmentation, which we call circular binary segmentation, to translate noisy intensity measurements into regions of equal copy number. The method is evaluated by simulation and is demonstrated on cell line data with known copy number alterations and on a breast cancer cell line data set.

/pdf/circular-binary-segmentation-for-the-analysis-of-array-based-4j1juwtxxm.pdf

Circular binary segmentation for the analysis of array-based DNA copy number data.

In this article, we consider the problem of detecting multiple changepoints in large datasets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example, in genetics as we analyze larger regions of the genome, or in finance as we observe time series over longer periods. We consider the common approach of detecting changepoints through minimizing a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalized likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost, which, under mild conditions, is linear in the number of observations. This compares favorably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies, we show that our new method can...

Optimal Detection of Changepoints With a Linear Computational Cost

Bridge regression, a special family of penalized regressions of a penalty function Σ|βj|γ with γ ≤ 1, considered. A general approach to solve for the bridge estimator is developed. A new algorithm for the lasso (γ = 1) is obtained by studying the structure of the bridge estimators. The shrinkage parameter γ and the tuning parameter λ are selected via generalized cross-validation (GCV). Comparison between the bridge model (γ ≤ 1) and several other shrinkage models, namely the ordinary least squares regression (λ = 0), the lasso (γ = 1) and ridge regression (γ = 2), is made through a simulation study. It is shown that the bridge regression performs well compared to the lasso and ridge regression. These methods are demonstrated through an analysis of a prostate cancer data. Some computational advantages and limitations are discussed.

http://gautampendse.com/software/lasso/webpage/Fu1998.pdf

Penalized Regressions: The Bridge versus the Lasso

One of the key challenges in changepoint analysis is the ability to detect multiple changes within a given time series or sequence. The changepoint package has been developed to provide users with a choice of multiple changepoint search methods to use in conjunction with a given changepoint method and in particular provides an implementation of the recently proposed PELT algorithm. This article describes the search methods which are implemented in the package as well as some of the available test statistics whilst highlighting their application with simulated and practical examples. Particular emphasis is placed on the PELT algorithm and how results differ from the binary segmentation approach.

/pdf/changepoint-an-r-package-for-changepoint-analysis-4f9vs6okd3.pdf

changepoint: An R Package for Changepoint Analysis

An up-to-date, rigorous, and lucid treatment of the theory, methods, and applications of regression analysis, and thus ideally suited for those interested in the theory as well as those whose interests lie primarily with applications. It is further enhanced through real-life examples drawn from many disciplines, showing the difficulties typically encountered in the practice of regression analysis. Consequently, this book provides a sound foundation in the theory of this important subject.

Regression Analysis: Theory, Methods, and Applications

I Theoretical Development.- 1 Spatial Interaction Processes: An Overview.- 1.1 Introduction.- 1.2 Theoretical Perspectives.- 1.2.1 Macro versus Micro Theories.- 1.2.2 Static versus Dynamic Theories.- 1.2.3 Probabilistic versus Deterministic Theories.- 1.3 Analytical Framework.- 1.3.1 Measures of Spatial Separation.- 1.3.2 Spatial Aggregation Assumptions.- 1.3.3 Structural Independence Assumptions.- 1.4 Spatial Interaction Processes.- 1.4.1 Interaction Patterns.- 1.4.2 General Interaction Processes.- 1.4.3 Independent Interaction Processes.- 1.5 Relaxations of Independence.- 1.5.1 Relaxations of Frequency Independence.- 1.5.2 Relaxations of Locational Independence.- 1.5.3 More Complex Types of Interdependencies.- 2 Gravity Models: An Overview.- 2.1 Introduction.- 2.2 General Gravity Models.- 2.2.1 Model Specifications.- 2.2.2 Illustrative Examples.- 2.2.3 Behavioral Characterizations.- 2.3 Functional Specifications.- 2.3.1 Origin and Destination Functions.- 2.3.2 Deterrence Functions.- 2.4 Exponential Gravity Models.- 2.4.1 Model Specifications.- 2.4.2 Illustrative Examples.- 2.4.3 Behavioral Characterizations.- 2.5 Generalizations of the Gravity Models.- 2.5.1 Generalized Search Processes.- 2.5.2 Interaction Processes with Hierarchical Destinations.- 2.5.3 Interaction Processes with Random Destination Sets.- 3 Spatial Interaction Processes: Formal Development.- 3.1 Introduction.- 3.2 Analytical Preliminaries.- 3.2.1 Measurable Spaces.- 3.2.2 Measurable Functions.- 3.2.3 Probability Spaces.- 3.3 Interaction Probability Spaces.- 3.3.1 Interaction Patterns.- 3.3.2 Locational Attributes of Interactions.- 3.3.3 Interaction Events.- 3.3.4 Frequency Attributes of Interactions.- 3.4 Interaction Processes.- 3.4.1 Separation Configurations.- 3.4.2 General Interaction Processes.- 3.4.3 Independent Interaction Processes.- 3.5 Frequency Processes.- 3.6 Generated Frequency Processes.- 3.6.1 Poisson Frequency Processes.- 3.6.2 Poisson Characterization Theorem.- 3.7 Threshold Interaction Processes.- 3.7.1 Potential Interactions.- 3.7.2 Independent Threshold Interaction Processes.- 3.7.3 Threshold Frequency Processes.- 3.8 Search Processes.- 3.8.1 Search Events.- 3.8.2 Realized-Interaction Frequencies.- 3.8.3 Independent Search Processes.- 3.9 Relaxations of Independence.- 3.9.1 Relaxations of Frequency Independence.- 3.9.2 Relaxation of Locational Independence.- 3.9.3 More Complex Types of Interdependencies.- 3.10 Notes and References.- 4 Gravity Models: Formal Development.- 4.1 Introduction.- 4.2 Definition of Gravity Model Classes.- 4.2.1 General Gravity Models.- 4.2.2 Exponential Gravity Models.- 4.2.3 Relationships Among Model Types.- 4.3 Examples of Gravity Model Classes.- 4.3.1 Carroll-Bevis Processes.- 4.3.2 Threshold Interaction Processes.- 4.3.3 Kullback-Leibler Processes.- 4.3.4 Simple Search Processes.- 4.4 Axioms for Interaction Processes.- 4.4.1 Positive Interaction Processes.- 4.4.2 Behavioral Axioms.- 4.4.3 Relations among Axioms.- 4.5 Characterizations of Gravity Models.- 4.5.1 Analytical Preliminaries.- 4.5.2 Characterizations of General Gravity Models.- 4.5.3 Characterizations of Exponential Gravity Models.- 4.6 Generalizations of Gravity Models.- 4.6.1 Interaction Processes with Hierarchical Destinations.- 4.6.2 Interaction Processes with Random Destination Sets.- 4.6.3 Interaction Processes with Prominence Effects.- 4.7 Notes and References.- II Methods.- 5 Maximum Likelihood.- 5.1 Introduction.- 5.1.1 Preliminaries.- 5.1.2 Maximum Likelihood Estimation.- 5.1.3 A Preview of this Chapter.- 5.2 Existence and Uniqueness of ML Estimates.- 5.2.1 Condition ML1.- 5.2.2 Condition ML2.- 5.2.3 Proof of Theorem 5.1.- 5.2.4 ML Estimation for Multinomial Gravity Models.- 5.3 ML Estimation Algorithms: Special Cases.- 5.3.1 The DSF Procedure.- 5.3.2 The Evans-Kirby Procedure.- 5.3.3 The Hyman Procedure.- 5.4 The LDSF Procedure.- 5.4.1 The Procedure.- 5.4.2 An Approximation Useful for ML Estimation Algorithms.- 5.4.3 Application to Short-term Forecasting.- 5.5 General Algorithms for ML Estimates.- 5.5.1 Scoring Methods.- 5.5.2 The Modified Scoring Procedure.- 5.5.3 Gradient Search Procedures.- 5.5.4 Modified Gradient Search Procedures.- 5.5.5 GLIM.- 5.6 Performance of General Algorithms.- 5.6.1 The Data.- 5.6.2 Convergence.- 5.6.3 Speeds of Procedures.- 5.7 Covariance of Estimates.- 5.7.1 Covariance of $${\hat \theta _k}$$'s.- 5.7.2 Covariance of $$ {\hat{T}_{{ij}}} $$.- 5.7.3 Other Forecasts.- 5.8 Goodness of Fit.- 5.8.1 Global Measures.- 5.8.2 Residuals.- 5.9 Other Properties of ML Estimates.- 5.9.1 Asymptotic Properties.- 5.9.2 Small Sample Properties.- 5.9.3 ML Estimates from Factored Data.- 5.10 Notes and Concluding Remarks.- 5.10.1 Conclusion.- 6 Least Squares.- 6.1 Introduction.- 6.1.1 A Preview of this Chapter.- 6.2 LS Procedures.- 6.2.1 Reduction of Parameters.- 6.2.2 Gauss-Markov Conditions.- 6.2.3 Bias.- 6.2.4 Weighting.- 6.2.5 Procedures.- 6.3 Large Sample Theory.- 6.3.1 Preliminaries.- 6.3.2 The Main Theorem.- 6.3.3 A Projection Matrix.- 6.3.4 Proof of Theorem 6.1.- 6.3.5 Some Practical Details.- 6.4 Alternative Methods.- 6.4.1 Use of Iterative Reweighting in Procedure 1.- 6.4.2 Not Reducing Parameters.- 6.4.3 Use of OLS.- 6.4.4 Use of Generalized Inverses.- 6.5 Small Sample Properties.- 6.5.1 The Procedures.- 6.5.2 The Simulations.- 6.5.3 Results from Simulations.- 6.5.4 Conclusions.- 6.6 Non-linear Least Squares.- 6.7 Notes and Concluding Remarks.- 6.7.1 Conclusions.- Appendix: Skokie Data.- References.- List of Principal Definitions and Results.- Author Index.

Gravity Models of Spatial Interaction Behavior

Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.

/pdf/on-tests-for-detecting-change-in-mean-3dzueuvjl0.pdf

On Tests for Detecting Change in Mean

An important design issue relating to probe-based Advanced Traveler Information Systems (ATISs) and Advanced Traffic Management systems is the sample size of probes (or the number of link traversals by probe vehicles) per unit time used in order to obtain reliable network information in terms of link travel time estimates. The variance of the mean of travel times obtained from n probes for the same link over a fixed time period may be shown to be of the form a+b/n where a and b are link-specific parameters. Using probe travel time data from a set of signalized arterials, it is shown that a is positive for well-traveled signalized links. This implies that the variance does not go to zero with increasing n. Consequences of this fact for probe-based systems are explored. While the results presented are for a specific set of links, the authors argue that because of the nature of the underlying travel time process, the broad conclusions would not hold for most well-traveled links with signal control.

Frequency of probe reports and variance of travel time estimates

We consider tests based on one observation on each of N ≥ 2 random variables X l, …, XN to decide if the means μ of the xi 's are all equal against the one-sided alternative that a shift has occurred at some unknown point γ, (i.e. μ1, = μ2 = … = μ r < μ r+1 = … = μ N ). The x i 's are considered to be normally distributed with a common unknown variance. Bayesian tests as well as a test based on the maximum likelihood estimate of γ are considered and their powers are compared by Monte Carlo methods. The exact distribution of a Bayesian test statistic is derived. A simple application using traffic accident data is presented.

Ashish Sen

Papers

Regression Analysis: Theory, Methods, and Applications

Gravity Models of Spatial Interaction Behavior

On Tests for Detecting Change in Mean

Frequency of probe reports and variance of travel time estimates

Some One-Sided Tests for Change in Level