Liming Xiang

Statistical monitoring of multi-stage processes based on engineering models

Most manufacturing processes consist of a large number of stages. The modeling of multi-stage processes by considering physical and mechanical laws in a linear state space form is extensively reported in the literature. This type of modeling describes the quality linkage among stages. However, recent research on statistical monitoring of multi-stage processes usually makes no use of this type of approach. A Statistical Process Control (SPC) method is proposed for multi-stage processes described by an engineering state space model. As a part of Phase I SPC analysis, a maximum likelihood estimation procedure based on an EM algorithm is developed. The complex multi-stage monitoring problem is converted to a simple multi-stream monitoring problem by applying group exponential weighted moving average charts to the one-step ahead forecast errors of the model. Reported run length results show the efficiency of the proposed charting method. The effectiveness of the proposed monitoring method is illustrated by its application to data from automobile hood manufacturing and workpiece assembly.

Physical activity and nutrition behavioural outcomes of a home-based intervention program for seniors: a randomized controlled trial

BackgroundThis intervention aimed to ascertain whether a low-cost, accessible, physical activity and nutrition program could improve physical activity and nutrition behaviours of insufficiently active 60–70 year olds residing in Perth, Australia.MethodsA 6-month home-based randomised controlled trial was conducted on 478 older adults (intervention, n = 248; control, n = 230) of low to medium socioeconomic status. Both intervention and control groups completed postal questionnaires at baseline and post-program, but only the intervention participants received project materials. A modified fat and fibre questionnaire measured nutritional behaviours, whereas physical activity was measured using the International Physical Activity Questionnaire. Generalised estimating equation models were used to assess the repeated outcomes over both time points.ResultsThe final sample consisted of 176 intervention participants and 199 controls (response rate 78.5%) with complete data. After controlling for demographic and other confounding factors, the intervention group demonstrated increased participation in strength exercise (p < 0.001), walking (p = 0.029) and vigorous activity (p = 0.015), together with significant reduction in mean sitting time (p < 0.001) relative to controls. Improvements in nutritional behaviours for the intervention group were also evident in terms of fat avoidance (p < 0.001), fat intake (p = 0.021) and prevalence of frequent fruit intake (p = 0.008).ConclusionsA minimal contact, low-cost and home-based physical activity program can positively influence seniors’ physical activity and nutrition behaviours.Trial registrationanzctr.org.au Identifier: ACTRN12609000735257

Mixture cure model with random effects for clustered interval‐censored survival data

The mixture cure model is an effective tool for analysis of survival data with a cure fraction. This approach integrates the logistic regression model for the proportion of cured subjects and the survival model (either the Cox proportional hazards or accelerated failure time model) for uncured subjects. Methods based on the mixture cure model have been extensively investigated in the literature for data with exact failure/censoring times. In this paper, we propose a mixture cure modeling procedure for analyzing clustered and interval-censored survival time data by incorporating random effects in both the logistic regression and PH regression components. Under the generalized linear mixed model framework, we develop the REML estimation for the parameters, as well as an iterative algorithm for estimation of the survival function for interval-censored data. The estimation procedure is implemented via an EM algorithm. A simulation study is conducted to evaluate the performance of the proposed method in various practical situations. To demonstrate its usefulness, we apply the proposed method to analyze the interval-censored relapse time data from a smoking cessation study whose subjects were recruited from 51 zip code regions in the southeastern corner of Minnesota.

Influence diagnostics for generalized linear mixed models: applications to clustered data

The Cooks distance for generalized linear mixed models is investigated, with applications to clustered data. In particular, first-order approximations are derived for the best linear unbiased predictor of the parameters due to cluster deletion. A small-scale simulation study shows that the method provides an efficient way to identify influential clusters. The notion of joint and conditional influence is also considered to address the masking effects of cluster-wise deletion. A data set on maternity length of hospital stay illustrates the usefullness of the proposed diagnostics.

Maximum likelihood estimation in survival studies under progressive interval censoring with random removals.

ABSTRACT Censoring occurs commonly in clinical trials. This article investigates a new censoring scheme, namely, Type II progressive interval censoring with random removals to cope with the setting that patients are examined at fixed regular intervals and dropouts may occur during the study period. We discuss the maximum likelihood estimation of the model parameters and derive the corresponding asymptotic variances when survival times are assumed to be Weibull distributed. An example is discussed to illustrate the application of the results under this censoring scheme.

Improved design of proportional integral derivative charts

Jiang et al. (2002) introduced proportional integral derivative (PID) control charts for monitoring autocorrelated processes based on PID predictors and corresponding residuals. The major contribution of the PID chart is to bridge between engineering process control (EPC) techniques and statistical process control (SPC) schemes. Although the performance of PID charts has been reported in the literature, we focus on several design issues of this control scheme. In this paper, we consider the PID charting parameter design, the mean-shift pattern analysis, and the relationship between the average run-length (ARL) performance and PID parameter selection. Improved design schemes are suggested for different scenarios of autocorrelated processes and verified with Monte Carlo simulation.

How to analyze longitudinal multilevel physical activity data with many zeros

BACKGROUND Physical activity (PA) is a modifiable lifestyle factor for many chronic diseases with established health benefits. PA outcomes are measured and assessed in many longitudinal studies, but their analyses often pose difficulties due to the presence of many zeros, extreme skewness, and lack of independence, which render standard regression methods inappropriate. METHODS A two-part multilevel modeling approach is used to analyze the heterogeneous and correlated PA data. In the first part, a logistic mixed regression model is fitted to estimate the prevalence of PA and factors associated with PA participation over time. For subjects engaging in PA, a gamma mixed regression model is adopted in the second part to assess the effects of predictor variables on the repeated PA outcomes nested within clusters. Extra variations are accommodated within the modeling process by random effects assigned to each cluster and each subject in the cohort. RESULTS The findings in a longitudinal multilevel study of a community-based PA intervention for older adults demonstrate the effectiveness of the intervention program and enable the identification of pertinent factors affecting participation and PA levels over time. CONCLUSIONS The two-part mixed regression approach provides a practical and statistically valid method to analyze the skewed and correlated PA data with many zeros. The methodology can be extended to handle complex hierarchical or multilevel settings by suitable specification of the covariance structure in the random components, model fitting of which can be performed in STATA using GLLAMM with various user-specified options.

Efficient estimation for semiparametric cure models with interval-censored data

This paper is concerned with the analysis of interval-censored survival data in the presence of a non-negligible cure fraction using semiparametric non-mixture cure models. We propose a spline-based sieve estimation method which overcomes numerical difficulties encountered in the existing semiparametric maximum likelihood estimation for the unknown nonparametric component in models. This method is easy to implement using the sequential quadratic programming technique. Under certain regularity conditions, we show the consistency, asymptotic normality and semiparametric efficiency of the proposed estimators for parameters. For the nonparametric component, our estimator has an explicit convergence rate, higher than that conjectured by Liu and Shen (2009) [16]. We conduct extensive simulation studies to evaluate the finite-sample performance of the method proposed. The results suggest that our method produces generally more efficient estimators than the existing method. The application of the method is illustrated with data from a study of smoking cessation.

Interval Estimation for Weibull-Distributed Life Data Under Type II Progressive Censoring with Random Removals

This paper explores the problem of interval estimation for parameters of Weibull-distributed data, which are Type II progressively censored with random removals. Seven different confidence interval-estimation procedures are considered. Four of them are based on a parametric bootstrapping approach. Others are based on the asymptotic normality method and the likelihood ratio statistic. We conduct a Monte Carlo simulation to evaluate the performance of these procedures based on their lengths and their coverage probabilities. Furthermore, an example is presented to illustrate the application of these procedures.

Influence diagnostics for random effect survival models: Application to a recurrent infection study for kidney patients on portable dialysis

In modeling multivariate failure time data, a class of survival model with random effects is applicable. It incorporates the random effect terms in the linear predictor and includes various random effect survival models as special cases, such as the random effect model assuming Coxs proportional hazards, with Weibull baseline hazards and with power family of transformation in the relative risk function. Residual maximum likelihood (REML) estimation of parameters is achieved by adopting the generalised linear mixed models (GLMM) approach. Accordingly, influence diagnostics are developed as sensitivity measures for the REML estimation of model parameters. A data set of recurrent infections of kidney patients on portable dialysis illustrates the usefulness of the influence diagnostics. A simulation study is carried out to examine the performance of the proposed influence diagnostics.