Individual-level modeling of the spread of influenza within households

A class of individual-level models (ILMs) outlined by R. Deardon et al., [Inference for individual level models of infectious diseases in large populations, Statist. Sin. 20 (2010), pp. 239–261] can be used to model the spread of infectious diseases in discrete time. The key feature of these ILMs is that they take into account covariate information on susceptible and infectious individuals as well as shared covariate information such as geography or contact measures. Here, such ILMs are fitted in a Bayesian framework using Markov chain Monte Carlo techniques to data sets from two studies on influenza transmission within households in Hong Kong during 2008 to 2009 and 2009 to 2010. The focus of this paper is to estimate the effect of vaccination on infection risk and choose a model that best fits the infection data.     

The effects of missing serial effects and/or heteroscedastic errors on mixed models using repeated growth data

When a two-level multilevel model (MLM) is used for repeated growth data, the individuals constitute level 2 and the successive measurements constitute level 1, which is nested within the individuals that make up level 2. The heterogeneity among individuals is represented by either the random-intercept or random-coefficient (slope) model. The variance components at level 1 involve serial effects and measurement errors under constant variance or heteroscedasticity. This study hypothesizes that missing serial effects or/and heteroscedasticity may bias the results obtained from two-level models. To illustrate this effect, we conducted two simulation studies, where the simulated data were based on the characteristics of an empirical mouse tumour data set. The results suggest that for repeated growth data with constant variance (measurement error) and misspecified serial effects (ρ > 0.3), the proportion of level-2 variation (intra-class correlation coefficient) increases with ρ and the two-level random-coefficient model is the minimum AIC (or AIC_c) model when compared with the fixed model, heteroscedasticity model, and random-intercept model. In addition, the serial effect (ρ > 0.1) and heteroscedasticity are both misspecified, implying that the two-level random-coefficient model is the minimum AIC (or AIC_c) model when compared with the fixed model and random-intercept model. This study demonstrates that missing serial effects and/or heteroscedasticity may indicate heterogeneity among individuals in repeated growth data (mixed or two-level MLM). This issue is critical in biomedical research.     

Non parametric space-time modeling of SO2 in presence of many missing data

Given pollution measurement from a network of monitoring sites in the area of a city and over an extended period of time, an important problem is to identify the spatial and temporal structure of the data. In this paper we focus on the identification and estimate of a statistical non parametric model to analyse the SO₂ in the city of Padua, where data are collected by some fixed stations and some mobile stations moving without any specific rule in different new locations. The impact of the use of mobile stations is that for each location there are times when data was not collected. Assuming temporal stationarity and spatial isotropy for the residuals of an additive model for the logarithm of SO₂ concentration, we estimate the semivariogram using a kernel-type estimator. Attempts are made to avoid the assumption of spatial isotropy. Bootstrap confidence bands are obtained for the spatial component of the additive model that is a deterministic function which defines the spatial structure. Finally, an example is proposed to design an optimal network for the mobiles monitoring stations in a fixed future time, given all the information available.     

Perfect simulation for Reed-Frost epidemic models

The Reed-Frost epidemic model is a simple stochastic process with parameter q that describes the spread of an infectious disease among a closed population. Given data on the final outcome of an epidemic, it is possible to perform Bayesian inference for q using a simple Gibbs sampler algorithm. In this paper it is illustrated that by choosing latent variables appropriately, certain monotonicity properties hold which facilitate the use of a perfect simulation algorithm. The methods are applied to real data.     

Bayesian inference for stochastic multitype epidemics in structured populations via random graphs

Summary.  The paper is concerned with new methodology for statistical inference for final outcome infectious disease data using certain structured population stochastic epidemic models. A major obstacle to inference for such models is that the likelihood is both analytically and numerically intractable. The approach that is taken here is to impute missing information in the form of a random graph that describes the potential infectious contacts between individuals. This level of imputation overcomes various constraints of existing methodologies and yields more detailed information about the spread of disease. The methods are illustrated with both real and test data.     

Functional measurement error in functional regression

Measurement error is an important problem that has not been studied very well in the context of functional data analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors in generalized functional linear models. In this article, a novel approach is proposed to estimate the slope function in the presence of measurement error in the generalized functional linear model with a scalar response. This work significantly advances the existing conditional score method to accommodate the case where both the measurement error and independent variables lie in infinite dimensional spaces. Asymptotic results are established for the proposed estimate, and its behaviour is studied via simulations, where the response is continuous or binary. Analysis of Canadian Weather data highlights the practical utility of our method. The Canadian Journal of Statistics 48: 238–258; 2020 © 2020 Statistical Society of Canada     

Relative risk analysis of dengue cases using convolution extended into spatio-temporal model

Dengue Hemmorage Fever (DHF) cases have become a serious problem every year in tropical countries such as Indonesia. Understanding the dynamic spread of the disease is essential in order to find an effective strategy in controlling its spread. In this study, a convolution (Poisson-lognormal) model that integrates both uncorrelated and correlated random effects was developed. A spatial–temporal convolution model to accomodate both spatial and temporal variations of the disease spread dynamics was considered. The model was applied to the DHF cases in the city of Kendari, Indonesia. DHF data for 10 districts during the period 2007–2010 were collected from the health services. The data of rainfall and population density were obtained from the local offices in Kendari. The numerical experiments indicated that both the rainfall and the population density played an important role in the increasing DHF cases in the city of Kendari. The result suggested that DHF cases mostly occured in January, the wet session with high rainfall, and in Kadia, the densest district in the city. As people in the city have high mobility while dengue mosquitoes tend to stay localized in their area, the best intervention is in January and in the district of Kadia.     

Measuring Measurement Error in Economic Time Series

A spectral decomposition method is described for obtaining an upper bound on the amount of measurement error in a time series. The method is applied to generated data and to M1b, real GNP, and the CPI. The bounds provide insight into both the amount of measurement error in these series and the stochastic specification of the errors.     

The effects of measurement error on the MAX EWMAMS control chart

Recently, some researchers suggested using a single chart to monitor both location and scale parameters for a process simultaneously, in order to resolve some difficulties in control chart interpretation arising from the traditional approach. This study focuses on the Maximum Exponentially Weighted Moving Average and Mean Squared deviation (MAX EWMAMS) control chart in the presence of measurement error. An important issue in using this chart is that measurement error adversely affects the performance of the chart. In this study, we investigate the effects of measurement error on the performance of the MAX EWMAMS chart by calculating and comparing the average time to signal (ATS) associated with both the in-control and out-of-control states.     

A Partial Likelihood Estimator of Vaccine Efficacy

A partial likelihood method is proposed for estimating vaccine efficacy for a general epidemic model. In contrast to the maximum likelihood estimator (MLE) which requires complete observation of the epidemic, the suggested method only requires information on the sequence in which individuals are infected and not the exact infection times. A simulation study shows that the method performs almost as well as the MLE. The method is applied to data on the infectious disease mumps.     

A Discrete-Time Multilevel Mixture Model for Event History Data with Long-Term Survivors,with an Application to an Analysis of Contraceptive Sterilization in Bangladesh

Event history models typically assume that the entire population is at risk of experiencing the event of interest throughout the observation period. However, there will often be individuals, referred to as long-term survivors, who may be considered a priori to have a zero hazard throughout the study period. In this paper, a discrete-time mixture model is proposed in which the probability of long-term survivorship and the timing of event occurrence are modelled jointly. Another feature of event history data that often needs to be considered is that they may come from a population with a hierarchical structure. For example, individuals may be nested within geographical regions and individuals in the same region may have similar risks of experiencing the event of interest due to unobserved regional characteristics. Thus, the discrete-time mixture model is extended to allow for clustering in the likelihood and timing of an event within regions. The model is further extended to allow for unobserved individual heterogeneity in the hazard of event occurrence. The proposed model is applied in an analysis of contraceptive sterilization in Bangladesh. The results show that a woman's religion and education level affect her probability of choosing sterilization, but not when she gets sterilized. There is also evidence of community-level variation in sterilization timing, but not in the probability of sterilization.     

Correcting data for measurement error in generalized linear models

This paper discusses a general strategy for reducing measurement-error-induced bias in statistical models. It is assumed that the measurement error is unbiased with a known variance although no other distributional assumptions on the measurement-error are employed,

Using a preliminary fit of the model to the observed data, a transformation of the variable measured with error is estimated. The transformation is constructed so that the estimates obtained by refitting the model to the ‘corrected’ data have smaller bias,

Whereas the general strategy can be applied in a number of settings, this paper focuses on the problem of covariate measurement error in generalized linear models, Two estimators are derived and their effectiveness at reducing bias is demonstrated in a Monte Carlo study.     

Predicting infectious disease outbreak risk via migratory waterfowl vectors

The spread of an emerging infectious disease is a major public health threat. Given the uncertainties associated with vector-borne diseases, in terms of vector dynamics and disease transmission, it is critical to develop statistical models that address how and when such an infectious disease could spread throughout a region such as the USA. This paper considers a spatio-temporal statistical model for how an infectious disease could be carried into the USA by migratory waterfowl vectors during their seasonal migration and, ultimately, the risk of transmission of such a disease to domestic fowl. Modeling spatio-temporal data of this type is inherently difficult given the uncertainty associated with observations, complexity of the dynamics, high dimensionality of the underlying process, and the presence of excessive zeros. In particular, the spatio-temporal dynamics of the waterfowl migration are developed by way of a two-tiered functional temporal and spatial dimension reduction procedure that captures spatial and seasonal trends, as well as regional dynamics. Furthermore, the model relates the migration to a population of poultry farms that are known to be susceptible to such diseases, and is one of the possible avenues toward transmission to domestic poultry and humans. The result is a predictive distribution of those counties containing poultry farms that are at the greatest risk of having the infectious disease infiltrate their flocks assuming that the migratory population was infected. The model naturally fits into the hierarchical Bayesian framework.     

Models with Errors due to Misreported Measurements

Measurement error and misclassification models feature prominently in the literature. This paper describes misreporting error, which can be considered to fall somewhere between these two broad types of model. Misreporting is concerned with situations where a continuous random variable X is measured with error and only reported as the discrete random variable Z. Data grouping or rounding are the simplest examples of this, but more generally X may be reported as a value z of Z which refers to a different interval from the one in which X lies. The paper discusses a method for handling misreported data and draws links with measurement error and misclassification models. A motivating example is considered from a prenatal Down's syndrome screening, where the gestational age at which mothers present for screening is a true continuous variable but is misreported because it is only ever observed as a discrete whole number of weeks which may in fact be in error. The implications this misreporting might have for the screening are investigated.     

A martingale residual diagnostic for longitudinal and recurrent event data

One method of assessing the fit of an event history model is to plot the empirical standard deviation of standardised martingale residuals. We develop an alternative procedure which is valid also in the presence of measurement error and applicable to both longitudinal and recurrent event data. Since the covariance between martingale residuals at times t ₀ and t > t ₀ is independent of t, a plot of these covariances should, for fixed t ₀, have no time trend. A test statistic is developed from the increments in the estimated covariances, and we investigate its properties under various types of model misspecification. Applications of the approach are presented using two Brazilian studies measuring daily prevalence and incidence of infant diarrhoea and a longitudinal study into treatment of schizophrenia.     

Multicovariate-adjusted regression models

We introduce multicovariate-adjusted regression (MCAR), an adjustment method for regression analysis, where both the response (Y) and predictors (X ₁, …, X _p ) are not directly observed. The available data have been contaminated by unknown functions of a set of observable distorting covariates, Z ₁, …, Z _s , in a multiplicative fashion. The proposed method substantially extends the current contaminated regression modelling capability, by allowing for multiple distorting covariate effects. MCAR is a flexible generalisation of the recently proposed covariate-adjusted regression method, an effective adjustment method in the presence of a single covariate, Z. For MCAR estimation, we establish a connection between the MCAR models and adaptive varying coefficient models. This connection leads to an adaptation of a hybrid backfitting estimation algorithm. Extensive simulations are used to study the performance and limitations of the proposed iterative estimation algorithm. In particular, the bias and mean square error of the proposed MCAR estimators are examined, relative to a baseline and a consistent benchmark estimator. The method is also illustrated with a Pima Indian diabetes data set, where the response and predictors are potentially contaminated by body mass index and triceps skin fold thickness. Both distorting covariates measure aspects of obesity, an important risk factor in type 2 diabetes.     

Nonparametric estimation of survival functions for incomplete observations when the life time distribution is proportionally related ot the censoring time distribution

Let X₁, X₂…,X_n be a random sample from [ILM0001] and let Y₁, …,Y_n be a random sample from [ILM0002]. Then instead of observing a complete sample X₁,…X_n, we can only observe the pairs Z_i. = min(X_i.,Y_i) and [ILM0003] In this paper, we consider estimation of survival function [ILM0004] when [ILM0005], where β is an unknown positive real number.

     

Bayesian incorporation of repeated measurements in logistic discrimination

A common problem in medical statistics is the discrimination between two groups on the basis of diagnostic information. Information on patient characteristics is used to classify individuals into one of two groups: diseased or disease-free. This classification is often with respect to a particular disease. This discrimination has two probabilistic components: (1) the discrimination is not without error, and (2) in many cases the a priori chance of disease can be estimated. Logistic models (Cox 1970; Anderson 1972) provide methods for incorporating both of these components. The a posteriori probability of disease may be estimated for a patient on the basis of both current measurement of patient characteristics and prior information. The parameters of the logistic model may be estimated on the basis of a calibration trial. In practice, not one but several sets of measurements of one characteristic of the patient may be made on a questionable case. These measurements typically are correlated; they are far from independent. How should these correlated measurements be used? This paper presents a method for incorporating several sets of measurements in the classification of a case.     

Spatio-temporal modeling of infectious disease dynamics

A stochastic model, which is well suited to capture space–time dependence of an infectious disease, was employed in this study to describe the underlying spatial and temporal pattern of measles in Barisal Division, Bangladesh. The model has two components: an endemic component and an epidemic component; weights are used in the epidemic component for better accounting of the disease spread into different geographical regions. We illustrate our findings using a data set of monthly measles counts in the six districts of Barisal, from January 2000 to August 2009, collected from the Expanded Program on Immunization, Bangladesh. The negative binomial model with both the seasonal and autoregressive components was found to be suitable for capturing space–time dependence of measles in Barisal. Analyses were done using general optimization routines, which provided the maximum likelihood estimates with the corresponding standard errors.     

Evaluation of different statistical methods using SAS software: an in silico approach for analysis of real-time PCR data

Real-time polymerase chain reaction (PCR) is reliable quantitative technique in gene expression studies. The statistical analysis of real-time PCR data is quite crucial for results analysis and explanation. The statistical procedures of analyzing real-time PCR data try to determine the slope of regression line and calculate the reaction efficiency. Applications of mathematical functions have been used to calculate the target gene relative to the reference gene(s). Moreover, these statistical techniques compare C_t (threshold cycle) numbers between control and treatments group. There are many different procedures in SAS for real-time PCR data evaluation. In this study, the efficiency of calibrated model and delta delta C_t model have been statistically tested and explained. Several methods were tested to compare control with treatment means of C_t. The methods tested included t-test (parametric test), Wilcoxon test (non-parametric test) and multiple regression. Results showed that applied methods led to similar results and no significant difference was observed between results of gene expression measurement by the relative method.