Communications in Statistics: Theory and Methods

Phase IV clinical trials are designed to monitor long-term side effects of medical treatment. For instance, childhood cancer survivors treated with chest radiation and/or anthracycline are often at risk of developing cardiotoxicity during their adulthood. Often the primary focus of a study could be on estimating the cumulative incidence of a particular outcome of interest such as cardiotoxicity. However, it is challenging to evaluate patients continuously and usually, this information is collected through cross-sectional surveys by following patients longitudinally...

We develop a new globally convergent optimization method for solving a constrained minimization problem underlying the minimum density power divergence estimator for univariate Gaussian data in the presence of outliers. Our hybrid procedure combines classical Newton's method with a gradient descent iteration equipped with a step control mechanism based on Armijo's rule to ensure global convergence. Extensive simulations comparing the resulting estimation procedure with the more prominent robust competitor, Minimum Covariance Determinant (MCD) estimator, across a wide range of breakdown point values suggest improved efficiency of our method...

Two new nonconvex penalty functions - Laplace and arctan - were recently introduced in the literature to obtain sparse models for high-dimensional statistical problems. In this paper, we study the theoretical properties of Laplace and arctan penalized ordinary least squares linear regression models. We first illustrate the near-unbiasedness of the nonzero regression weights obtained by the new penalty functions, in the orthonormal design case. In the general design case, we present theoretical results in two asymptotic settings: (a) the number of features, <mml:math xmlns:mml="https://www...

The problem of constructing locally D -optimal designs for two-variable logistic model with no interaction has been studied in many literature. In Kabera, Haines, and Ndlovu (2015), the model is restricted to have positive slopes and negative intercept for the assumptions that the probability of response increases with doses for both drugs and that the probability of response is less than 0.5 at zero dose level of both drugs. The design space mainly discussed is the set [0, ∞) × [0, ∞), while the finite rectangular design space is presented only in scenarios where the results for the unlimited design space are still appropriate...

This article considers a way to test the hypothesis that two collections of objects are from the same uniform distribution of such objects. The exact p -value is calculated based on the distribution for the observed overlaps. In addition, an interval estimate of the number of distinct objects, when all objects are equally likely, is indicated.

In this work, we show that Spearman's correlation coefficient test about <mml:math xmlns:mml="https://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mspace/><mml:mo>:</mml:mo><mml:msub><mml:mi>ρ</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> found in most statistical software is theoretically incorrect and performs poorly when bivariate normality assumptions are not met or the sample size is small...

We propose a new measure of variable importance in high-dimensional regression based on the change in the LASSO solution path when one covariate is left out. The proposed procedure provides a novel way to calculate variable importance and conduct variable screening. In addition, our procedure allows for the construction of p -values for testing whether each coe cient is equal to zero as well as for testing hypotheses involving multiple regression coefficients simultaneously; bootstrap techniques are used to construct the null distribution...

Vascular access for hemodialysis is of paramount importance. Although studies have found that central venous catheter (CVC) is often associated with poor outcomes and switching to arteriovenous fistula (AVF) and arteriovenous grafts (AVG) is beneficial, it has not been fully elucidated how the effect of switching of access on outcomes changes over time and whether the effect depends on switching time. In this paper we propose to relate the observed survival time for patients without access change and the counterfactual time for patients with access change using an AFT model with time-varying effects...

When effect modifiers influence the decision to participate in randomized trials, generalizing causal effect estimates to an external target population requires the knowledge of two scores - the propensity score for receiving treatment and the sampling score for trial participation. While the former score is known due to randomization, the latter score is usually unknown and estimated from data. Under unconfounded trial participation, we characterize the asymptotic efficiency bounds for estimating two causal estimands - the population average treatment effect and the average treatment effect among the non-participants - and examine the role of the scores...

When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson's disease, increasing intermittent dropout over time yielded missing measurements of physical function. In this example, we assume data are missing completely at random, since the chance that a data point was missing appears to be unrelated to either outcomes or covariates...

Semi-competing risks data often arise in medical studies where the terminal event (e.g., death) censors the non-terminal event (e.g., cancer recurrence), but the non-terminal event does not prevent the subsequent occurrence of the terminal event. This article considers regression modeling of semi-competing risks data to assess the covariate effects on the respective non-terminal and terminal event times. We propose a copula-based framework for semi-competing risks regression with time-varying coefficients, where the dependence between the non-terminal and terminal event times is characterized by a copula and the time-varying covariate effects are imposed on two marginal regression models...

In prognostic/diagnostic medical research, it is often the goal to identify a biomarker that differentiates between patients with and without a condition, or patients that will have good or poor response to a given treatment. The statistical literature is abundant with methods for evaluating single biomarkers for these purposes. However, in practice, a single biomarker rarely captures all aspects of a disease process; therefore, it is often the case that using a combination of biomarkers will improve discriminatory ability...

Dependent censoring is common in many medical studies, especially when there are multiple occurrences of the event of interest. Ghosh and Lin (2003) and Hsieh, Ding and Wang (2011) proposed estimation procedures using an artificial censoring technique. However, if covariates are not bounded, then these methods can cause excessive artificial censoring. In this paper, we propose estimation procedures for the treatment effect based on a novel application of propensity scores. Simulation studies show that the proposed method provides good finite-sample properties...

We describe and compare two methods for the group sequential design of two-arm experiments with Poisson distributed data, which are based on a normal approximation and exact calculations respectively. A framework to determine near-optimal stopping boundaries is also presented. Using this framework, for a considered example, we demonstrate that a group sequential design could reduce the expected sample size under the null hypothesis by as much as 44% compared to a fixed sample approach. We conclude with a discussion of the advantages and disadvantages of the two presented procedures...

The gap time between recurrent events is often of primary interest in many fields such as medical studies (Cook and Lawless 2007; Kang, Sun, and Zhao 2015; Schaubel and Cai 2004), and in this paper, we discuss regression analysis of the gap times arising from a general class of additive transformation models. For the problem, we propose two estimation procedures, the modified within-cluster resampling (MWCR) method and the weighted risk-set (WRS) method, and the proposed estimators are shown to be consistent and asymptotically follow the normal distribution...

The log-normal distribution is widely used to model non-negative data in many areas of applied research. In this paper, we introduce and study a family of distributions with non-negative reals as support and termed the log-epsilon-skew normal (LESN) which includes the log-normal distributions as a special case. It is related to the epsilon-skew normal developed in Mudholkar and Hutson (2000) the way the log-normal is related to the normal distribution. We study its main properties, hazard function, moments, skewness and kurtosis coefficients, and discuss maximum likelihood estimation of model parameters...

In many cluster randomization studies, cluster sizes are not fixed and may be highly variable. For those studies, sample size estimation assuming a constant cluster size may lead to under-powered studies. Sample size formulas have been developed to incorporate the variability in cluster size for clinical trials with continuous and binary outcomes. Count outcomes frequently occur in cluster randomized studies. In this paper, we derive a closed-form sample size formula for count outcomes accounting for the variability in cluster size...

A robust regression methodology is proposed via M-estimation. The approach adapts to the tail behavior and skewness of the distribution of the random error terms, providing for a reliable analysis under a broad class of distributions. This is accomplished by allowing the objective function, used to determine the regression parameter estimates, to be selected in a data driven manner. The asymptotic properties of the proposed estimator are established and a numerical algorithm is provided to implement the methodology...

We propose a new class of two-stage parameter estimation methods for semiparametric ordinary differential equation (ODE) models. In the first stage, state variables are estimated using a penalized spline approach; In the second stage, form of numerical discretization algorithms for an ODE solver is used to formulate estimating equations. Estimated state variables from the first stage are used to obtain more data points for the second stage. Asymptotic properties for the proposed estimators are established. Simulation studies show that the method performs well, especially for small sample...

Continuous-time multi-state models are commonly used to study diseases with multiple stages. Potential risk factors associated with the disease are added to the transition intensities of the model as covariates, but missing covariate measurements arise frequently in practice. We propose a likelihood-based method that deals efficiently with a missing covariate in these models. Our simulation study showed that the method performs well for both 'missing completely at random' and 'missing at random' mechanisms...