Power and sample size for dose-finding studies with survival endpoints under model uncertainty.

Multiple comparison procedures combined with modeling techniques (MCP-Mod) (Bretz et al., 2005) is an efficient and robust statistical methodology for the model-based design and analysis of dose-finding studies with an unknown dose-response model. With this approach, multiple comparison methods are used to identify statistically significant contrasts corresponding to a set of candidate dose-response models, and the best model is then used to estimate the target dose. Power and sample size calculations for this methodology require knowledge of the covariance matrix for the estimators of the (placebo-adjusted) mean responses among the dose groups. In this article, we consider survival endpoints and derive an analytic form of the covariance matrix for the estimators of the log hazard ratios as a function of the total number of events in the study. We then use this closed-form expression of the covariance matrix to derive the power and sample size formulas. We discuss practical considerations in the application of these formulas. In addition, we provide an illustration with a motivating example on chronic obstructive pulmonary disease. Finally, we demonstrate through simulation studies that the proposed formulas are accurate enough for practical use.

A new semiparametric transformation approach to disease diagnosis with multiple biomarkers.

When multiple biomarkers are available for disease diagnosis, it is desirable to efficiently combine them to form a single index. Making use of the Neyman-Pearson paradigm, we propose a new combination/transformation approach to disease diagnosis that efficiently combines multiple biomarkers. The proposed method does not require that the biomarkers be jointly normally distributed or the covariance matrices for the diseased and the nondiseased are nondifferential. An R package is developed to implement the proposed method. Simulations and two real data examples demonstrate advantages of the new method over existing ones.

Chernoff Index for Cox Test of Separate Parametric Families.

The asymptotic efficiency of a generalized likelihood ratio test proposed by Cox is studied under the large deviations framework for error probabilities developed by Chernoff. In particular, two separate parametric families of hypotheses are considered (Cox, 1961, 1962). The significance level is set such that the maximal type I and type II error probabilities for the generalized likelihood ratio test decay exponentially fast with the same rate. We derive the analytic form of such a rate that is also known as the Chernoff index (Chernoff, 1952), a relative efficiency measure when there is no preference between the null and the alternative hypotheses. We further extend the analysis to approximate error probabilities when the two families are not completely separated. Discussions are provided concerning the implications of the present result on model selection.

Recommendation System for Adaptive Learning.

An adaptive learning system aims at providing instruction tailored to the current status of a learner, differing from the traditional classroom experience. The latest advances in technology make adaptive learning possible, which has the potential to provide students with high-quality learning benefit at a low cost. A key component of an adaptive learning system is a recommendation system, which recommends the next material (video lectures, practices, and so on, on different skills) to the learner, based on the psychometric assessment results and possibly other individual characteristics. An important question then follows: How should recommendations be made? To answer this question, a mathematical framework is proposed that characterizes the recommendation process as a Markov decision problem, for which decisions are made based on the current knowledge of the learner and that of the learning materials. In particular, two plain vanilla systems are introduced, for which the optimal recommendation at each stage can be obtained analytically.

Accelerated failure time model under general biased sampling scheme.

Right-censored time-to-event data are sometimes observed from a (sub)cohort of patients whose survival times can be subject to outcome-dependent sampling schemes. In this paper, we propose a unified estimation method for semiparametric accelerated failure time models under general biased estimating schemes. The proposed estimator of the regression covariates is developed upon a bias-offsetting weighting scheme and is proved to be consistent and asymptotically normally distributed. Large sample properties for the estimator are also derived. Using rank-based monotone estimating functions for the regression parameters, we find that the estimating equations can be easily solved via convex optimization. The methods are confirmed through simulations and illustrated by application to real datasets on various sampling schemes including length-bias sampling, the case-cohort design and its variants.

Exploratory Item Classification Via Spectral Graph Clustering.

Large-scale assessments are supported by a large item pool. An important task in test development is to assign items into scales that measure different characteristics of individuals, and a popular approach is cluster analysis of items. Classical methods in cluster analysis, such as the hierarchical clustering, K-means method, and latent-class analysis, often induce a high computational overhead and have difficulty handling missing data, especially in the presence of high-dimensional responses. In this article, the authors propose a spectral clustering algorithm for exploratory item cluster analysis. The method is computationally efficient, effective for data with missing or incomplete responses, easy to implement, and often outperforms traditional clustering algorithms in the context of high dimensionality. The spectral clustering algorithm is based on graph theory, a branch of mathematics that studies the properties of graphs. The algorithm first constructs a graph of items, characterizing the similarity structure among items. It then extracts item clusters based on the graphical structure, grouping similar items together. The proposed method is evaluated through simulations and an application to the revised Eysenck Personality Questionnaire.

A Monte Carlo method for variance estimation for estimators based on induced smoothing.

An important issue in statistical inference for semiparametric models is how to provide reliable and consistent variance estimation. Brown and Wang (2005. Standard errors and covariance matrices for smoothed rank estimators. Biometrika 92: , 732-746) proposed a variance estimation procedure based on an induced smoothing for non-smooth estimating functions. Herein a Monte Carlo version is developed that does not require any explicit form for the estimating function itself, as long as numerical evaluation can be carried out. A general convergence theory is established, showing that any one-step iteration leads to a consistent variance estimator and continuation of the iterations converges at an exponential rate. The method is demonstrated through the Buckley-James estimator and the weighted log-rank estimators for censored linear regression, and rank estimation for multiple event times data.

Design and analysis of clinical trials in the presence of delayed treatment effect.

In clinical trials with survival endpoint, it is common to observe an overlap between two Kaplan-Meier curves of treatment and control groups during the early stage of the trials, indicating a potential delayed treatment effect. Formulas have been derived for the asymptotic power of the log-rank test in the presence of delayed treatment effect and its accompanying sample size calculation. In this paper, we first reformulate the alternative hypothesis with the delayed treatment effect in a rescaled time domain, which can yield a simplified sample size formula for the log-rank test in this context. We further propose an intersection-union test to examine the efficacy of treatment with delayed effect and show it to be more powerful than the log-rank test. Simulation studies are conducted to demonstrate the proposed methods.

Diagnostic Classification Models for Testlets: Methods and Theory.

Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings.

ORACLE INEQUALITIES FOR THE LASSO IN THE COX MODEL.

We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequalities based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved by our method. However, the presented oracle inequalities are sharper since the compatibility and cone invertibility factors are always greater than the corresponding restricted eigenvalue. In the Cox regression model, the Hessian matrix is based on time-dependent covariates in censored risk sets, so that the compatibility and cone invertibility factors, and the restricted eigenvalue as well, are random variables even when they are evaluated for the Hessian at the true regression coefficients. Under mild conditions, we prove that these quantities are bounded from below by positive constants for time-dependent covariates, including cases where the number of covariates is of greater order than the sample size. Consequently, the compatibility and cone invertibility factors can be treated as positive constants in our oracle inequalities.

A composite likelihood approach for spatially correlated survival data.

The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory.

Sequential Analysis of the Cox Model under Response Dependent Allocation.

Sellke and Siegmund (1983) developed the Brownian approximation to the Cox partial likelihood score as a process of calendar time, laying the foundation for group sequential analysis of survival studies. We extend their results to cover situations in which treatment allocations may depend on observed outcomes. The new development makes use of the entry time and calendar time along with the corresponding σ-filtrations to handle the natural information accumulation. Large sample properties are established under suitable regularity conditions.

Theory of the Self-learning Q-Matrix.

Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. We establish sufficient conditions to ensure that the attributes required by each item are learnable from the data.

Subtask analysis of process data through a predictive model.

Response process data collected from human-computer interactive items contain detailed information about respondents' behavioural patterns and cognitive processes. Such data are valuable sources for analysing respondents' problem-solving strategies. However, the irregular data format and the complex structure make standard statistical tools difficult to apply. This article develops a computationally efficient method for exploratory analysis of such process data. The new approach segments a lengthy individual process into a sequence of short subprocesses to achieve complexity reduction, easy clustering and meaningful interpretation. Each subprocess is considered a subtask. The segmentation is based on sequential action predictability using a parsimonious predictive model combined with the Shannon entropy. Simulation studies are conducted to assess the performance of the new method. We use a case study of PIAAC 2012 to demonstrate how exploratory analysis for process data can be carried out with the new approach.

Accurate Assessment via Process Data.

Accurate assessment of a student's ability is the key task of a test. Assessments based on final responses are the standard. As the infrastructure advances, substantially more information is observed. One of such instances is the process data that is collected by computer-based interactive items and contain a student's detailed interactive processes. In this paper, we show both theoretically and with simulated and empirical data that appropriately including such information in the assessment will substantially improve relevant assessment precision.

New insights into scaling of fat-free mass to height across children and adults.

OBJECTIVE: Forbes expressed fat-free mass (FFM, in kg) as the cube of height (H, in m): FFM = 10.3 × H(3). Our objective is to examine the potential influence of gender and population ancestry on the association between FFM and height. METHODS: This is a cross-sectional analysis involving an existing dataset of 279 healthy subjects (155 males and 124 females) with age 5-59 years and body mass index (BMI) 14-28 kg/m(2). FFM was measured by a four-component model as the criterion. RESULTS: Nonlinear regression models were fitted: FFM = 10.8 × H(2.95) for the males and FFM = 10.1 × H(2.90) for the females. The 95% confidence intervals for the exponential coefficients were (2.83, 3.07) for the males and (2.72, 3.08) for the females, both containing hypothesized value 3.0. Population ancestry adjustment was considered in the H-FFM model. The coefficient of the H-FFM model for male Asians is smaller than that for male Caucasians (P = 0.006), while there is no statistically significant difference among African-Americans, Caucasians and Hispanics: 10.6 for the males (10.1 for Asians, 10.8 for African-Americans, 10.7 for Caucasians and 10.4 for Hispanics) and 9.6 for the females (9.3 for Asians, 9.8 for African-Americans, 9.6 for Caucasians and 9.5 for Hispanics). Age adjustment was unnecessary for the coefficient of the H-FFM model. CONCLUSION: Height is the most important factor contributing to the magnitude of FFM across most of the lifespan, though both gender and ancestry effects are significant in the H-FFM model. The proposed H-FFM model can be further used to develop a mechanistic model to explain why population ancestry, gender and age influence the associations between BMI and %Fat.

Data-Driven Learning of Q-Matrix.

The recent surge of interests in cognitive assessment has led to developments of novel statistical models for diagnostic classification. Central to many such models is the well-known Q-matrix, which specifies the item-attribute relationships. This article proposes a data-driven approach to identification of the Q-matrix and estimation of related model parameters. A key ingredient is a flexible T-matrix that relates the Q-matrix to response patterns. The flexibility of the T-matrix allows the construction of a natural criterion function as well as a computationally amenable algorithm. Simulations results are presented to demonstrate usefulness and applicability of the proposed method. Extension to handling of the Q-matrix with partial information is presented. The proposed method also provides a platform on which important statistical issues, such as hypothesis testing and model selection, may be formally addressed.

Modeling Not-Reached Items in Timed Tests: A Response Time Censoring Approach.

Time limits are imposed on many computer-based assessments, and it is common to observe examinees who run out of time, resulting in missingness due to not-reached items. The present study proposes an approach to account for the missing mechanisms of not-reached items via response time censoring. The censoring mechanism is directly incorporated into the observed likelihood of item responses and response times. A marginal maximum likelihood estimator is proposed, and its asymptotic properties are established. The proposed method was evaluated and compared to several alternative approaches that ignore the censoring through simulation studies. An empirical study based on the PISA 2018 Science Test was further conducted.

Evaluation of specific metabolic rates of major organs and tissues: comparison between men and women.

OBJECTIVES: The specific resting metabolic rates (K(i) , in kcal/kg per day) of major organs and tissues in the Reference Man were suggested in 1992 by Elia: 200 for liver, 240 for brain, 440 for heart and kidneys, 13 for skeletal muscle, 4.5 for adipose tissue and 12 for the residual mass. However, it is unknown whether gender influences the K(i) values. The aim of the present study was to compare the K(i) values observed in nonelderly nonobese men to the corresponding values in women. METHODS: Elia's K(i) values were evaluated based on a mechanistic model: REE = Σ(K(i) × T(i) ), where REE is whole-body resting energy expenditure measured by indirect calorimetry and T(i) is the mass of major organs and tissues measured by magnetic resonance imaging. Marginal 95% confidence intervals (CIs) for the model-estimated K(i) values were calculated by stepwise univariate regression analysis. Subjects were nonelderly (age 20-49 years) nonobese (BMI 18.5-29.9 kg/m(2) ) men (n = 49) and women (n = 57). RESULTS: The measured REE (REEm) and the mass of major organs and skeletal muscle were all greater in the men than in women. The predicted REE by Elia's K(i) values were correlated with REEm in men (r = 0.87) and women (r = 0.86, both P < 0.001). Elia's K(i) values were within the range of 95% CIs for both men and women groups, revealing that gender adjustment is not necessary. CONCLUSIONS: Elia's proposed adult K(i) values are valid in both nonelderly nonobese men and women. Further studies are needed to explore the potential influences of age and obesity on K(i) values in humans.

An exploratory analysis of the latent structure of process data via action sequence autoencoders.

Computer simulations have become a popular tool for assessing complex skills such as problem-solving. Log files of computer-based items record the human-computer interactive processes for each respondent in full. The response processes are very diverse, noisy, and of non-standard formats. Few generic methods have been developed to exploit the information contained in process data. In this paper we propose a method to extract latent variables from process data. The method utilizes a sequence-to-sequence autoencoder to compress response processes into standard numerical vectors. It does not require prior knowledge of the specific items and human-computer interaction patterns. The proposed method is applied to both simulated and real process data to demonstrate that the resulting latent variables extract useful information from the response processes.