Nonparametric Estimation of the Number of Drug Users in Hong Kong Using Repeated Multiple Lists

We update a previous approach to the estimation of the size of an open population when there are multiple lists at each time point. Our motivation is 35 years of longitudinal data on the detection of drug users by the Central Registry of Drug Abuse in Hong Kong. We develop a two‐stage smoothing spline approach. This gives a flexible and easily implemented alternative to the previous method which was based on kernel smoothing. The new method retains the property of reducing the variability of the individual estimates at each time point. We evaluate the new method by means of a simulation study that includes an examination of the effects of variable selection. The new method is then applied to data collected by the Central Registry of Drug Abuse. The parameter estimates obtained are compared with the well known Jolly–Seber estimates based on single capture methods.     

Population size estimation for capture-recapture models with applications to epidemiological data

The capture-recapture method is applied to estimate the population size of a target population based on ascertainment data in epidemiological applications. We generalize the three-list case of Chao & Tsay (1998) to situations where more than three lists are available. An estimation procedure is presented using the concept of sample coverage, which can be interpreted as a measure of overlap information among multiple list records. When there is enough overlap, an estimator of the total population size is proposed. The bootstrap method is used to construct a variance estimator and confidence interval. If the overlap rate is relatively low, then the population size cannot be precisely estimated and thus only a lower (upper) bound is proposed for positively (negatively) dependent lists. The proposed method is applied to two data sets, one with a high and one with a low overlap rate.     

Regression analysis of panel count data with covariate-dependent observation and censoring times

Panel count data often occur in a long-term study where the primary end point is the time to a specific event and each subject may experience multiple recurrences of this event. Furthermore, suppose that it is not feasible to keep subjects under observation continuously and the numbers of recurrences for each subject are only recorded at several distinct time points over the study period. Moreover, the set of observation times may vary from subject to subject. In this paper, regression methods, which are derived under simple semiparametric models, are proposed for the analysis of such longitudinal count data. Especially, we consider the situation when both observation and censoring times may depend on covariates. The new procedures are illustrated with data from a well-known cancer study.     

Modelling spatio-temporal air pollution data from a mobile monitoring station

ABSTRACT

Environmental data is typically indexed in space and time. This work deals with modelling spatio-temporal air quality data, when multiple measurements are available for each space-time point. Typically this situation arises when different measurements referring to several response variables are observed in each space-time point, for example, different pollutants or size resolved data on particular matter. Nonetheless, such a kind of data also arises when using a mobile monitoring station moving along a path for a certain period of time. In this case, each spatio-temporal point has a number of measurements referring to the response variable observed several times over different locations in a close neighbourhood of the space-time point. We deal with this type of data within a hierarchical Bayesian framework, in which observed measurements are modelled in the first stage of the hierarchy, while the unobserved spatio-temporal process is considered in the following stages. The final model is very flexible and includes autoregressive terms in time, different structures for the variance-covariance matrix of the errors, and can manage covariates available at different space-time resolutions. This approach is motivated by the availability of data on urban pollution dynamics: fast measures of gases and size resolved particulate matter have been collected using an Optical Particle Counter located on a cabin of a public conveyance that moves on a monorail on a line transect of a town. Urban microclimate information is also available and included in the model. Simulation studies are conducted to evaluate the performance of the proposed model over existing alternatives that do not model data over the first stage of the hierarchy.     

Adjusted variable plots for Cox's proportional hazards regression model

Adjusted variable plots are useful in linear regression for outlier detection and for qualitative evaluation of the fit of a model. In this paper, we extend adjusted variable plots to Cox's proportional hazards model for possibly censored survival data. We propose three different plots: a risk level adjusted variable (RLAV) plot in which each observation in each risk set appears, a subject level adjusted variable (SLAV) plot in which each subject is represented by one point, and an event level adjusted variable (ELAV) plot in which the entire risk set at each failure event is represented by a single point. The latter two plots are derived from the RLAV by combining multiple points. In each point, the regression coefficient and standard error from a Cox proportional hazards regression is obtained by a simple linear regression through the origin fit to the coordinates of the pictured points. The plots are illustrated with a reanalysis of a dataset of 65 patients with multiple myeloma.     

IDENTIFYING TREATMENT EFFECTS IN MULTI-CHANNEL MEASUREMENTS IN ELECTROENCEPHALOGRAPHIC STUDIES: MULTIVARIATE PERMUTATION TESTS AND MULTIPLE COMPARISONS

A versatile procedure is described comprising an application of statistical techniques to the analysis of the large, multi‐dimensional data arrays produced by electroencephalographic (EEG) measurements of human brain function. Previous analytical methods have been unable to identify objectively the precise times at which statistically significant experimental effects occur, owing to the large number of variables (electrodes) and small number of subjects, or have been restricted to two‐treatment experimental designs. Many time‐points are sampled in each experimental trial, making adjustment for multiple comparisons mandatory. Given the typically large number of comparisons and the clear dependence structure among time‐points, simple Bonferroni‐type adjustments are far too conservative. A three‐step approach is proposed: (i) summing univariate statistics across variables; (ii) using permutation tests for treatment effects at each time‐point; and (iii) adjusting for multiple comparisons using permutation distributions to control family‐wise error across the whole set of time‐points. Our approach provides an exact test of the individual hypotheses while asymptotically controlling family‐wise error in the strong sense, and can provide tests of interaction and main effects in factorial designs. An application to two experimental data sets from EEG studies is described, but the approach has application to the analysis of spatio‐temporal multivariate data gathered in many other contexts.     

Testing list effects and diagnosing individual catchabilities in the Rasch model

The Rasch model is useful in the problem of estimating the population size from multiple incomplete lists. It is of great interest to tell whether there are list effects and whether individuals differ in their catchabilities. These two important model selection problems can be easily addressed conditionally. A conditional likelihood ratio test is used to evaluate the list effects and several graphical methods are used to diagnose the individual catchabilities, while neither the unknown population size nor the unknown mixing distribution of individual catchabilities is required to be estimated. Three epidemiological applications are used for illustration.     

Identification of Multivariate Responders/Non-Responders Using Bayesian Growth Curve Latent Class Models

In this paper, we propose a multivariate growth curve mixture model that groups subjects based on multiple symptoms measured repeatedly over time. Our model synthesizes features of two models. First, we follow Roy and Lin (2000) in relating the multiple symptoms at each time point to a single latent variable. Second, we use the growth mixture model of Muthén and Shedden (1999) to group subjects based on distinctive longitudinal profiles of this latent variable. The mean growth curve for the latent variable in each class defines that class's features. For example, a class of "responders" would have a decline in the latent symptom summary variable over time. A Bayesian approach to estimation is employed where the methods of Elliott et al (2005) are extended to simultaneously estimate the posterior distributions of the parameters from the latent variable and growth curve mixture portions of the model. We apply our model to data from a randomized clinical trial evaluating the efficacy of Bacillus Calmette-Guerin (BCG) in treating symptoms of Interstitial Cystitis. In contrast to conventional approaches using a single subjective Global Response Assessment, we use the multivariate symptom data to identify a class of subjects where treatment demonstrates effectiveness. Simulations are used to confirm identifiability results and evaluate the performance of our algorithm. The definitive version of this paper is available at onlinelibrary.wiley.com.     

On discrimination and classification with multivariate repeated measures data

We study the problem of classification with multiple q-variate observations with and without time effect on each individual. We develop new classification rules for populations with certain structured and unstructured mean vectors and under certain covariance structures. The new classification rules are effective when the number of observations is not large enough to estimate the variance–covariance matrix. Computational schemes for maximum likelihood estimates of required population parameters are given. We apply our findings to two real data sets as well as to a simulated data set.     

Monitoring foreclosure rates with a spatially risk-adjusted Bernoulli CUSUM chart for concurrent observations

Frequently in process monitoring, situations arise in which the order that events occur cannot be distinguished, motivating the need to accommodate multiple observations occurring at the same time, or concurrent observations. The risk-adjusted Bernoulli cumulative sum (CUSUM) control chart can be used to monitor the rate of an adverse event by fitting a risk-adjustment model, followed by a likelihood ratio-based scoring method that produces a statistic that can be monitored. In our paper, we develop a risk-adjusted Bernoulli CUSUM control chart for concurrent observations. Furthermore, we adopt a novel approach that uses a combined mixture model and kernel density estimation approach in order to perform risk-adjustment with regard to spatial location. Our proposed method allows for monitoring binary outcomes through time with multiple observations at each time point, where the chart is spatially adjusted for each Bernoulli observation's estimated probability of the adverse event. A simulation study is presented to assess the performance of the proposed monitoring scheme. We apply our method using data from Wayne County, Michigan between 2005 and 2014 to monitor the rate of foreclosure as a percentage of all housing transactions.     

Object detection in multi-epoch data

In astronomy multiple images are frequently obtained at the same position of the sky for follow-up coaddition as it helps one go deeper and look for fainter objects. With large scale panchromatic synoptic surveys becoming more common, image co-addition has become even more necessary as new observations start to get compared with coadded fiducial sky in real time. The standard coaddition techniques have included straight averages, variance weighted averages, medians etc. A more sophisticated nonlinear response chi-square method is also used when it is known that the data are background noise limited and the point spread function is homogenized in all channels. A more robust object detection technique capable of detecting faint sources, even those not seen at all epochs which will normally be smoothed out in traditional methods, is described. The analysis at each pixel level is based on a formula similar to Mahalanobis distance.     

Nonparametric estimation of the limiting availability

The point availability of a repairable system is the probability that the system is operating at a specified time. As time increases, the point availability converges to a positive constant called the limiting availability. Baxter and Li (1994a) developed a technique for constructing nonparametric confidence intervals for the point availability. However, nonparametric estimators of the limiting availability have not previously been studied in the literature. In this paper, we consider two separate cases: (1) the data are complete and (2) the data are subject to right censorship. For each case, a nonparametric confidence interval for the limiting availability is derived. Applications and simulation studies are presented.deceased after the paper was accepted     

Occupancy numbers for dynamic heterogeneous populations: Estimate of particles lifetimes

A dynamic model of a heterogeneous population is studied. Particles belonging to a population are divided, at every time t, into a finite number of classes according to their types and the partition changes over time. The role of the occupancy numbers, namely the cardinality of each class, is highlighted. The relationship between the stochastic process of occupancy numbers and the process of particle types is analyzed. The main goal of this paper is the estimation of the lifetime of each particle at a given time t, when the observed data are the history of the process of the number of dead particles up to t. Furthermore, a discrete time approximation of the filter is given.     

Inference methods for saturated models in longitudinal clinical trials with incomplete binary data

In the longitudinal studies with binary response, it is often of interest to estimate the percentage of positive responses at each time point and the percentage of having at least one positive response by each time point. When missing data exist, the conventional method based on observed percentages could result in erroneous estimates. This study demonstrates two methods of using expectation-maximization (EM) and data augmentation (DA) algorithms in the estimation of the marginal and cumulative probabilities for incomplete longitudinal binary response data. Both methods provide unbiased estimates when the missingness mechanism is missing at random (MAR) assumption. Sensitivity analyses have been performed for cases when the MAR assumption is in question.     

Alternating event processes during lifetimes: population dynamics and statistical inference

In the literature studying recurrent event data, a large amount of work has been focused on univariate recurrent event processes where the occurrence of each event is treated as a single point in time. There are many applications, however, in which univariate recurrent events are insufficient to characterize the feature of the process because patients experience nontrivial durations associated with each event. This results in an alternating event process where the disease status of a patient alternates between exacerbations and remissions. In this paper, we consider the dynamics of a chronic disease and its associated exacerbation-remission process over two time scales: calendar time and time-since-onset. In particular, over calendar time, we explore population dynamics and the relationship between incidence, prevalence and duration for such alternating event processes. We provide nonparametric estimation techniques for characteristic quantities of the process. In some settings, exacerbation processes are observed from an onset time until death; to account for the relationship between the survival and alternating event processes, nonparametric approaches are developed for estimating exacerbation process over lifetime. By understanding the population dynamics and within-process structure, the paper provide a new and general way to study alternating event processes.     

Overview of Friedman’s Test and Post-hoc Analysis

When the null hypothesis of Friedman’s test is rejected, there is a wide variety of multiple comparisons that can be used to determine which treatments differ from each other. We will discuss the contexts where different multiple comparisons should be applied, when the population follows some discrete distributions commonly used to model count data in biological and ecological fields. Our simulation study shows that sign test is very conservative. Fisher’s LSD and Tukey’s HSD tests computed with ranks are the most liberal. Theoretical considerations are illustrated with data of the Azores Buzzard (Buteo buteo rothschildi) population from Azores, Portugal.     

Scalable spatio‐temporal Bayesian analysis of high‐dimensional electroencephalography data

We present a scalable Bayesian modelling approach for identifying brain regions that respond to a certain stimulus and use them to classify subjects. More specifically, we deal with multi‐subject electroencephalography (EEG) data with a binary response distinguishing between alcoholic and control groups. The covariates are matrix‐variate with measurements taken from each subject at different locations across multiple time points. EEG data have a complex structure with both spatial and temporal attributes. We use a divide‐and‐conquer strategy and build separate local models, that is, one model at each time point. We employ Bayesian variable selection approaches using a structured continuous spike‐and‐slab prior to identify the locations that respond to a certain stimulus. We incorporate the spatio‐temporal structure through a Kronecker product of the spatial and temporal correlation matrices. We develop a highly scalable estimation algorithm, using likelihood approximation, to deal with large number of parameters in the model. Variable selection is done via clustering of the locations based on their duration of activation. We use scoring rules to evaluate the prediction performance. Simulation studies demonstrate the efficiency of our scalable algorithm in terms of estimation and fast computation. We present results using our scalable approach on a case study of multi‐subject EEG data.     

Detecting multiple change points in piecewise constant hazard functions

The National Cancer Institute (NCI) suggests a sudden reduction in prostate cancer mortality rates, likely due to highly successful treatments and screening methods for early diagnosis. We are interested in understanding the impact of medical breakthroughs, treatments, or interventions, on the survival experience for a population. For this purpose, estimating the underlying hazard function, with possible time change points, would be of substantial interest, as it will provide a general picture of the survival trend and when this trend is disrupted. Increasing attention has been given to testing the assumption of a constant failure rate against a failure rate that changes at a single point in time. We expand the set of alternatives to allow for the consideration of multiple change-points, and propose a model selection algorithm using sequential testing for the piecewise constant hazard model. These methods are data driven and allow us to estimate not only the number of change points in the hazard function but where those changes occur. Such an analysis allows for better understanding of how changing medical practice affects the survival experience for a patient population. We test for change points in prostate cancer mortality rates using the NCI Surveillance, Epidemiology, and End Results dataset.     

Estimation from incomplete data in longitudinal surveys

In longitudinal surveys where a number of observations have to be made on the same sampling unit at specified time intervals, it is not uncommon that observations for some of the time stages for some of the sampled units are found missing. In the present investigation an estimation procedure for estimating the population total based on such incomplete data from multiple observations is suggested which makes use of all the available information and is seen to be more efficient than the one based on only completely observed units. Estimators are also proposed for two other situations; firstly when data is collected only for a sample of time stages and secondly when data is observed for only one time stage per sampled unit.