Sufficient reduction methods for multivariate time-dependent health surveillance data

ABSTRACT

Early detection with a low false alarm rate (FAR) is the main aim of outbreak detection as used in public health surveillance or in regard to bioterrorism. Multivariate surveillance is preferable to univariate surveillance since correlation between series (CBS) is recognized and incorporated. Sufficient reduction has proved a promising method for handling CBS, but has not previously been used when correlation within series (CWS) is present. Here we develop sufficient reduction methods for reducing a p-dimensional multivariate series to a univariate series of statistics shown to be sufficient to monitor a sudden, but persistent, shift in the multivariate series mean. Correlation both within and between series is taken into account, as public health data typically exhibit both forms of association. Simultaneous and lagged changes and different shift sizes are investigated. A one-sided exponentially weighted moving average chart is used as a tool for detection of a change. The performance of the proposed method is compared with existing sufficient reduction methods, the parallel univariate method and both VarR and Z charts. A simulation study using bivariate normal autoregressive data shows that the new method gives shorter delays and a lower FAR than other methods, which have high FARs when CWS is clearly present.     

Evaluation of multivariate surveillance

Multivariate surveillance is of interest in many areas such as industrial production, bioterrorism detection, spatial surveillance, and financial transaction strategies. Some of the suggested approaches to multivariate surveillance have been multivariate counterparts to the univariate Shewhart, EWMA, and CUSUM methods. Our emphasis is on the special challenges of evaluating multivariate surveillance methods. Some new measures are suggested and the properties of several measures are demonstrated by applications to various situations. It is demonstrated that zero-state and steady-state ARL, which are widely used in univariate surveillance, should be used with care in multivariate surveillance.     

A spatial scan statistic for survival data based on generalized life distribution

ABSTRACT

For many years, detection of clusters has been of great public health interest and widely studied. Several methods have been developed to detect clusters and their performance has been evaluated in various contexts. Spatial scan statistics are widely used for geographical cluster detection and inference. Different types of discrete or continuous data can be analyzed using spatial scan statistics for Bernoulli, Poisson, ordinal, exponential, and normal models. In this paper, we propose a scan statistic for survival data which is based on generalized life distribution model that provides three important life distributions, viz. Weibull, exponential, and Rayleigh. The proposed method is applied to the survival data of tuberculosis patients in Nainital district of Uttarakhand, India, for the year 2004–05. The Monte Carlo simulation studies reveal that the proposed method performs well for different survival distributions.     

A Comparison of Multiple Outlier Detection Methods for Regression Data

The problem of outliers in statistical data has attracted many researchers for a long time. Consequently, numerous outlier detection methods have been proposed in the statistical literature. However, no consensus has emerged as to which method is uniformly better than the others or which one is recommended for use in practical situations. In this article, we perform an extensive comparative Monte Carlo simulation study to assess the performance of the multiple outlier detection methods that are either recently proposed or frequently cited in the outlier detection literature. Our simulation experiments include a wide variety of realistic and challenging regression scenarios. We give recommendations on which method is superior to others under what conditions.     

Spatial Cluster Detection for Longitudinal Outcomes Using Administrative Regions

This article proposes a new spatial cluster detection method for longitudinal outcomes that detects neighborhoods and regions with elevated rates of disease while controlling for individual level confounders. The proposed method, CumResPerm, utilizes cumulative geographic residuals through a permutation test to detect potential clusters which are defined as sets of administrative regions, such as a town or group of administrative regions. Previous cluster detection methods are not able to incorporate individual level data including covariate adjustment, while still being able to define potential clusters using informative neighborhood or town boundaries. Often, it is of interest to detect such spatial clusters because individuals residing in a town may have similar environmental exposures or socioeconomic backgrounds due to administrative reasons, such as zoning laws. Therefore, these boundaries can be very informative and more relevant than arbitrary clusters such as the standard circle or square. Application of the CumResPerm method will be illustrated by the Home Allergens and Asthma prospective cohort study analyzing the relationship between area or neighborhood residence and repeated measured outcome, occurrence of wheeze in the last six months, while taking into account mobile locations.     

A Comparison of Spatiotemporal Surveillance Methods for Nonhomogeneous Change Size

Spatiotemporal surveillance, especially in detection of emerging outbreaks is of particular importance. When an outbreak spreads across some areas, the incidence rate at the center of the outbreak area might be expected to be much higher than the rate at its edge. However, to the best of our knowledge, all existing methods assume a uniformly increasing rate across the entire area of the outbreak. The purpose of this study is to compare the performance of the spatiotemporal surveillance methods such as multivariate cumulative sum (MCUSUM) or multivariate exponentially weighted moving average (MEWMA) when the changes in size are nonhomogeneous. Monte Carlo simulations were conducted to examine the properties of these spatiotemporal surveillance methods and compared them in terms of the detection speed and the identification rate under various scenarios. The results showed that when nonhomogeneous change sizes are involved, the MCUSUM method taking into account spatial nonhomogeneity of increase rates yields a better identification than the method ignoring such change size pattern although the detection speeds are similar. Further, a case study for the detection of male thyroid cancer data in New Mexico in the United States was performed to demonstrate the applicability of these methods.     

Detection capability of residual control chart for stationary process data

SUMMARY In recent years, methods for dealing with autocorrelated data in the statistical process control environment have been proposed. A primary method is based on modeling the process data and applying control charts to the residuals. However, the residual charts do not have the same properties as the traditional charts. In the literature, there has been no systematic study on the detection capability of the residual chart for the stationary processes. The article develops a measure of the detection capability of the residual chart for the general stationary processes. Conditions under which the residual chart reduces or increases the detection capability are given. The relationships between the detection capability and the average run length of the residual chart are also established.     

Variable-Selection-Based Epidemic Disease Diagnosis

Epidemic surveillance in a community involves monitoring infection trend, triggering alarms before outbreaks, and identifying sources and paths of disease transmission. Algorithms for outbreak detection that are derived from industrial statistical process control (SPC) and scan statistics have been reported in the literature, but there are relatively few methods reported for identifying transmission paths. In this work, we propose an expanded spatial-temporal (EST) model for identifying infection sources. Three dimensional information, subject, location, and time, are expanded into a two-dimensional space by dividing the time horizon into segments and multiplying each segment by the locations. Based on the EST model, we further propose a variable-selection algorithm to identify potential location/time combinations as sources of infection, and thus achieve diagnosis. Numerical simulations show that the proposed scheme is effective in locating infection sources.     

Statistical Classification Methods in Consumer Credit Scoring: a Review

Credit scoring is the term used to describe formal statistical methods used for classifying applicants for credit into 'good' and 'bad' risk classes. Such methods have become increasingly important with the dramatic growth in consumer credit in recent years. A wide range of statistical methods has been applied, though the literature available to the public is limited for reasons of commercial confidentiality. Particular problems arising in the credit scoring context are examined and the statistical methods which have been applied are reviewed.     

Monitoring point patterns for the development of space–time clusters

Existing statistical methods for the detection of space–time clusters of point events are retrospective, in that they are used to ascertain whether space–time clustering exists among a fixed number of past events. In contrast, prospective methods treat a series of observations sequentially, with the aim of detecting quickly any changes that occur in the series. In this paper, cumulative sum methods of monitoring are adapted for use with Knox's space–time statistic. The result is a procedure for the rapid detection of any emergent space–time interactions for a set of sequentially monitored point events. The approach relies on a 'local' Knox statistic that is useful in retrospective analyses to detect when and where space–time interaction occurs. The distribution of the local Knox statistic under the null hypothesis of no space–time interaction is derived. The retrospective local statistic and the prospective cumulative sum monitoring method are illustrated by using previously published data on Burkitt's lymphoma in Uganda.     

高维大数据基因网络中的社区发现——以NC方法为例

从大量基因中识别出致病基因是大数据下的一个十分重要的高维统计问题。基因间网络结构的存在使得对于致病基因的识别已从单个基因识别扩展到基因模块识别。从基因网络中挖掘出基因模块就是所谓的社区发现（或节点聚类）问题。绝大多数社区发现方法仅利用网络结构信息,而忽略节点本身的信息。Newman和Clauset于2016年提出了一个将二者有机结合的基于统计推断的社区发现方法（简称为NC方法）。本文以NC方法为案例,介绍统计方法在实际基因网络中的应用和取得的成果,并从统计学角度提出了改进措施。通过对NC方法的分析可以看出对于以基因网络为代表的非结构化数据,统计思想和原理在数据分析中仍然处于核心地位。而相应的统计方法则需要针对数据的特点及关心的问题进行相应的调整和优化。     

Likelihood‐based and marginal inference methods for recurrent event data with covariate measurement error

Recurrent event data arise commonly in medical and public health studies. The analysis of such data has received extensive research attention and various methods have been developed in the literature. Depending on the focus of scientific interest, the methods may be broadly classified as intensity‐based counting process methods, mean function‐based estimating equation methods, and the analysis of times to events or times between events. These methods and models cover a wide variety of practical applications. However, there is a critical assumption underlying those methods–variables need to be correctly measured. Unfortunately, this assumption is frequently violated in practice. It is quite common that some covariates are subject to measurement error. It is well known that covariate measurement error can substantially distort inference results if it is not properly taken into account. In the literature, there has been extensive research concerning measurement error problems in various settings. However, with recurrent events, there is little discussion on this topic. It is the objective of this paper to address this important issue. In this paper, we develop inferential methods which account for measurement error in covariates for models with multiplicative intensity functions or rate functions. Both likelihood‐based inference and robust inference based on estimating equations are discussed. The Canadian Journal of Statistics 40: 530–549; 2012 © 2012 Statistical Society of Canada     

Models for surveillance data under reporting delay: applications to US veteran first-time suicide attempters

Surveillance data provide a vital source of information for assessing the spread of a health problem or disease of interest and for planning for future health-care needs. However, the use of surveillance data requires proper adjustments of the reported caseload due to underreporting caused by reporting delays within a limited observation period. Although methods are available to address this classic statistical problem, they are largely focused on inference for the reporting delay distribution, with inference about caseload of disease incidence based on estimates for the delay distribution. This approach limits the complexity of models for disease incidence to provide reliable estimates and projections of incidence. Also, many of the available methods lack robustness since they require parametric distribution assumptions. We propose a new approach to overcome such limitations by allowing for separate models for the incidence and the reporting delay in a distribution-free fashion, but with joint inference for both modeling components, based on functional response models. In addition, we discuss inference about projections of future disease incidence to help identify significant shifts in temporal trends modeled based on the observed data. This latter issue on detecting ‘change points’ is not sufficiently addressed in the literature, despite the fact that such warning signs of potential outbreak are critically important for prevention purposes. We illustrate the approach with both simulated and real data, with the latter involving data for suicide attempts from the Veteran Healthcare Administration.     

<Emphasis Type="BoldItalic">MAD-STEC</Emphasis>: a method for multiple automatic detection of space-time emerging clusters

Crime or disease surveillance commonly rely in space-time clustering methods to identify emerging patterns. The goal is to detect spatial-temporal clusters as soon as possible after its occurrence and to control the rate of false alarms. With this in mind, a spatio-temporal multiple cluster detection method was developed as an extension of a previous proposal based on a spatial version of the Shiryaev–Roberts statistic. Besides the capability of multiple cluster detection, the method have less input parameter than the previous proposal making its use more intuitive to practitioners. To evaluate the new methodology a simulation study is performed in several scenarios and enlighten many advantages of the proposed method. Finally, we present a case study to a crime data-set in Belo Horizonte, Brazil.     

Evaluations of some Exponentially Weighted Moving Average methods

The need for statistical surveillance has been noted in many different areas, and examples of applications include the detection of an increased incidence of a disease, the detection of an increased radiation level and the detection of a turning point in a leading index for a business cycle. In all cases, preventive actions are possible if the alarm is made early. Several versions of the EWMA (Exponentially Weighted Moving Average) method for monitoring a process with the aim of detecting a shift in the mean are studied both for the one-sided and the two-sided case. The effects of using barriers for the one-sided alarm statistic are also studied. One important issue is the effect of different types of alarm limits. Different measures of evaluation, suitable in different types of applications, are considered such as the expected delay, the ARL¹, the probability of successful detection and the predictive value of an alarm, to give a broad picture of the features of the methods. Results from a large-scale simulation study are presented both for a fixed ARL0 and a fixed probability of a false alarm. It appears that important differences from an inferential point of view exist between the one- and two-sided versions of the methods. It is demonstrated that the method, usually considered as a convenient approximation, is to be preferred over the exact version in the overwhelming majority of applications.     

A Bayesian approach to sequential analysis in post‐licensure vaccine safety surveillance

With rapid development of computing technology, Bayesian statistics have increasingly gained more attention in various areas of public health. However, the full potential of Bayesian sequential methods applied to vaccine safety surveillance has not yet been realized, despite acknowledged practical benefits and philosophical advantages of Bayesian statistics. In this paper, we describe how sequential analysis can be performed in a Bayesian paradigm in the field of vaccine safety. We compared the performance of the frequentist sequential method, specifically, Maximized Sequential Probability Ratio Test (MaxSPRT), and a Bayesian sequential method using simulations and a real world vaccine safety example. The performance is evaluated using three metrics: false positive rate, false negative rate, and average earliest time to signal. Depending on the background rate of adverse events, the Bayesian sequential method could significantly improve the false negative rate and decrease the earliest time to signal. We consider the proposed Bayesian sequential approach to be a promising alternative for vaccine safety surveillance.     

Multiparameter evidence synthesis in epidemiology and medical decision-making: current approaches

Summary.  Alongside the development of meta-analysis as a tool for summarizing research literature, there is renewed interest in broader forms of quantitative synthesis that are aimed at combining evidence from different study designs or evidence on multiple parameters. These have been proposed under various headings: the confidence profile method, cross-design synthesis, hierarchical models and generalized evidence synthesis. Models that are used in health technology assessment are also referred to as representing a synthesis of evidence in a mathematical structure. Here we review alternative approaches to statistical evidence synthesis, and their implications for epidemiology and medical decision-making. The methods include hierarchical models, models informed by evidence on different functions of several parameters and models incorporating both of these features. The need to check for consistency of evidence when using these powerful methods is emphasized. We develop a rationale for evidence synthesis that is based on Bayesian decision modelling and expected value of information theory, which stresses not only the need for a lack of bias in estimates of treatment effects but also a lack of bias in assessments of uncertainty. The increasing reliance of governmental bodies like the UK National Institute for Clinical Excellence on complex evidence synthesis in decision modelling is discussed.     

Sequential case series analysis for pharmacovigilance

Summary.  The self-controlled case series method is used to evaluate drug safety, particularly the safety of paediatric vaccines with respect to rare adverse reactions. We propose a group sequential version of the method for prospective surveillance of drug safety. We focus on the surveillance of new vaccines. We develop methods that are based on the sequential probability ratio test applied at predetermined surveillance intervals, using both simple and composite alternative hypotheses. We investigate the properties of the methods analytically in a simple setting and by simulations in more realistic scenarios. The methods are applied to data on influenza vaccine and Bell's palsy, and to data on measles, mumps and rubella vaccine and bleeding disorders.     

On the use and evaluation of prospective scan methods for health-related surveillance

Summary.  We review some prospective scan-based methods that are used in health-related applications to detect increased rates of mortality or morbidity and to detect bioterrorism or active clusters of disease. We relate these methods to the use of the moving average chart in industrial applications. Issues that are related to the performance evaluation of spatiotemporal scan-based methods are discussed. In particular we clarify the definition of a recurrence interval and demonstrate that this measure does not reflect some important aspects of the statistical performance of scan-based, and other, surveillance methods. Some research needs in this area are given.     

Multivariate outbreak detection

Online monitoring is needed to detect outbreaks of diseases such as influenza. Surveillance is also needed for other kinds of outbreaks, in the sense of an increasing expected value after a constant period. Information on spatial location or other variables might be available and may be utilized. We adapted a robust method for outbreak detection to a multivariate case. The relation between the times of the onsets of the outbreaks at different locations (or some other variable) was used to determine the sufficient statistic for surveillance. The derived maximum-likelihood estimator of the outbreak regression was semi-parametric in the sense that the baseline and the slope were non-parametric while the distribution belonged to the one-parameter exponential family. The estimator was used in a generalized-likelihood ratio surveillance method. The method was evaluated with respect to robustness and efficiency in a simulation study and applied to spatial data for detection of influenza outbreaks in Sweden.