Parametric non-mixture cure models for schedule finding of therapeutic agents

We propose a phase I clinical trial design that seeks to determine the cumulative safety of a series of administrations of a fixed dose of an investigational agent. In contrast with traditional phase I trials that are designed solely to find the maximum tolerated dose of the agent, our design instead identifies a maximum tolerated schedule that includes a maximum tolerated dose as well as a vector of recommended administration times. Our model is based on a non-mixture cure model that constrains the probability of dose limiting toxicity for all patients to increase monotonically with both dose and the number of administrations received. We assume a specific parametric hazard function for each administration and compute the total hazard of dose limiting toxicity for a schedule as a sum of individual administration hazards. Throughout a variety of settings motivated by an actual study in allogeneic bone marrow transplant recipients, we demonstrate that our approach has excellent operating characteristics and performs as well as the only other currently published design for schedule finding studies. We also present arguments for the preference of our non-mixture cure model over the existing model.     

On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an unobserved set of DMUs. The model provides posterior predictive data for the unobserved DMUs to augment the frontier in the DEA that provides a posterior predictive distribution for the efficiency scores. We explore the method on a multiple-input and multiple-output DEA model. The data for the example are from a comprehensive examination of how nursing homes complete a standardized mandatory assessment of residents.     

Robust tests for the common principal components model

When dealing with several populations, the common principal components (CPC) model assumes equal principal axes but different variances along them. In this paper, a robust log-likelihood ratio statistic allowing to test the null hypothesis of a CPC model versus no restrictions on the scatter matrices is introduced. The proposal plugs into the classical log-likelihood ratio statistic robust scatter estimators. Using the same idea, a robust log-likelihood ratio and a robust Wald-type statistic for testing proportionality against a CPC model are considered. Their asymptotic distributions under the null hypothesis and their partial influence functions are derived. A small simulation study allows to compare the behavior of the classical and robust tests, under normal and contaminated data.     

R×C ecological inference: bounds, correlations, flexibility and transparency of assumptions

Summary.  Despite its potential pitfalls, ecological inference is an unavoidable part of some quantitative settings, including US voting rights litigation. In such applications, the analyst will typically encounter two-way tables with more than two rows and columns. Although several ecological inference methods are currently available for 2×2 tables, there are fewer options for analysing general R × C tables, and virtually none that model counts as opposed to fractions. We propose a count R × C method that respects the bounds deterministically, that allows for complex relationships between internal cell quantities, that is easily extensible and that results from transparent assumptions. We study the method via simulation, and then apply it to an example that is drawn from the state of Texas relevant to recent redistricting litigation there.     

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model. Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the r$r$th moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin et al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214–223]. The usefulness of these models is illustrated in a simulation study and in applications to three real data sets.     

A counterexample to Beder's conjectures about Hadamard matrices

In this note we provide a counterexample which resolves conjectures about Hadamard matrices made in this journal. Beder [1998. Conjectures about Hadamard matrices. Journal of Statistical Planning and Inference 72, 7–14] conjectured that if H$\mathit{H}$ is a maximal m×n$m\times n$ row-Hadamard matrix then m is a multiple of 4; and that if n   is a power of 2 then every row-Hadamard matrix can be extended to a Hadamard matrix. Using binary integer programming we obtain a maximal 13×32$13\times 32$ row-Hadamard matrix, which disproves both conjectures. Additionally for n being a multiple of 4 up to 64, we tabulate values of m   for which we have found a maximal row-Hadamard matrix. Based on the tabulated results we conjecture that a m×n$m\times n$ row-Hadamard matrix with m?n-7$m?n-7$ can be extended to a Hadamard matrix.     

Use of log−log survival function in modeling time-covariate interactions in Cox regression

Plotting of log−log survival functions against time for different categories or combinations of categories of covariates is perhaps the easiest and most commonly used graphical tool for checking proportional hazards (PH) assumption. One problem in the utilization of the technique is that the covariates need to be categorical or made categorical through appropriate grouping of the continuous covariates. Subjectivity in the decision making on the basis of eye-judgment of the plots and frequent inconclusiveness arising in situations where the number of categories and/or covariates gets larger are among other limitations of this technique. This paper proposes a non-graphical (numerical) test of the PH assumption that makes use of log−log survival function. The test enables checking proportionality for categorical as well as continuous covariates and overcomes the other limitations of the graphical method. Observed power and size of the test are compared to some other tests of its kind through simulation experiments. Simulations demonstrate that the proposed test is more powerful than some of the most sensitive tests in the literature in a wide range of survival situations. An example of the test is given using the widely used gastric cancer data.     

Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.     

Covariance-regularized regression and classification for high dimensional problems

Summary.  We propose covariance-regularized regression, a family of methods for prediction in high dimensional settings that uses a shrunken estimate of the inverse covariance matrix of the features to achieve superior prediction. An estimate of the inverse covariance matrix is obtained by maximizing the log-likelihood of the data, under a multivariate normal model, subject to a penalty; it is then used to estimate coefficients for the regression of the response onto the features. We show that ridge regression, the lasso and the elastic net are special cases of covariance-regularized regression, and we demonstrate that certain previously unexplored forms of covariance-regularized regression can outperform existing methods in a range of situations. The covariance-regularized regression framework is extended to generalized linear models and linear discriminant analysis, and is used to analyse gene expression data sets with multiple class and survival outcomes.