A Bayesian Approach for Manova Growth Model Analysis

Bayesian approaches have been demonstrated as effective methods for reliability analysis of complex systems with small-amount data, which integrate prior information and sample data using Bayes’ theorem. However, there is an assumption that precise prior probability distributions are available for unknown parameters, yet these prior distributions are sometimes unavailable in practical engineering. A possible way to avoiding this assumption is to generalize Bayesian reliability analysis approach by using imprecise probability theory. In this paper, we adopt a set of imprecise Dirichlet distributions as priors to quantify uncertainty of unknown parameters and extend traditional Bayesian reliability analysis approach by introducing an imprecise Dirichlet model (IDM). When the prior information is rare, the result of imprecise Bayesian analysis method is too rough to support engineering decision-making, so we proposed an optimization model to reduce the imprecision of the new method. Spindles are crucial for machine tools and reliability data related to spindles of new-developed machine tools are often rare. We can then use the imprecise Bayesian reliability analysis method to assess its reliability. In this paper, we mainly investigate the reliability assessment of a motorized spindle to illustrate the effectiveness of the proposed method.

This article compares the advantages and disadvantages of two multivariate methods for the analysis of small grolup communication data, log-linear contingency table analysis and multivariate analysis of variance, in the context of ani experimental design. The independent conditions were discussion procedure, task solution multiplicity, and discussion topic. Participant communication behaviors, the dependent variables, were coded into a mix of 15 task social, and procedural categories. The analyses of communication indicated that log-linzear analyasis produced thle most complex models for various behaviors, including both single-factor and multifactor termns. Multivariate analysis of variance (MANOVA) findings at tlte grolup level provided the most parsimonious explanations, with a main effect of discussion procedure. Some MANOVA results at the individual level were similar to loglitnear mnodels in their complexity, whereas others duplicated the results of the group-level MANOVA. The differing outcomes from these methods point to several design considerations that should be taken account when choosing a statistical test for group communication data.

In this paper, we exploit multivariate and functional data techniques to capture important features concerning the time dynamics of hourly one-day ahead electricity prices at Nordpool. The methods are also used to obtain pragmatic prediction schemes for these prices. Following Huisman et al. (Energy Economics 29, 2007), we first consider the 24-hourly one-day ahead prices as a 24-dimensional variable observed on a daily basis. These are analyzed by means of a multivariate analysis of variance (MANOVA) and the results are presented by some enlightening graphs. We then account for the smoothness of the curve that these 24 values form when they are seen as a function of time of the day. This smoothness is exploited by a functional analysis of variance (FANOVA). Multivariate prediction is then addressed, first by a simple univariate ARIMA scheme combined with hourly corrections obtained from the MANOVA and then by a true multivariate state space scheme.

Multivariate repeated measures data naturally arise in clinical trials and other fields such as biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normality and homogeneity. This paper proposes a finite-sample test by modifying the sums of squares matrices to make them insensitive to the heterogeneity in MANOVA. The proposed test is invariant to affine transformation and robust against nonnormality. The proposed method can be used in various experimental designs, for example, factorial design and crossover design. Under various simulation settings, the proposed method outperforms the classical Doubly Multivariate Model and Multivariate Mixed Model proposed elsewhere, especially for unbalanced sample sizes with heteroscedasticity. The applications of the proposed method are illustrated with ophthalmology data in factorial and crossover designs. The proposed method successfully identified and validated a significant main effect and demonstrated that univariate analysis could be oversensitive to small but clinically unimportant interactions.

The Growth Curve Model (GCM) is a Generalized Multivariate Analysis of Variance (GMANOVA) model especially useful in the analysis of longitudinal data, growth curves as well as other response curves. The model is a natural extension of the classical Multivariate Analysis of Variance (MANOVA) model and among other assumptions, relies on the assumption that the mean for each group can be represented as a polynomial of degree q. The assumption that the mean over time for all groups follows a polynomial of the same degree is not always satisfied, since individuals across the different groups may respond differently. An excellent scenario is when we have clustered longitudinal data, where the response over time can be represented by polynomials of different degrees. In such situations, the natural extension is to use the Extended Growth Curve Model (EGCM), where one can assume different shapes to represent different groups or clusters. In this paper, we formulate hypotheses motivated by real life scenarios involving clustered longitudinal data, and propose tests that are motivated by residuals in the EGCM. We then mathematically derive the tests and evaluate performances using simulations. We provide real data examples as illustrations.

As an important reliability metric in disc drive industries, the annual failure rate (AFR), estimated from reliability demonstration tests (RDTs), is often used to make business decisions. Due to limited test sample size and short test duration, estimating the AFR from direct test data using Weibull distribution fit may result in a wide confidence interval, raising concerns regarding the uncertainty of the AFR estimate. To improve the confidence of the estimate, this article presents a Bayesian posterior analysis approach to estimate the AFR. Prior distributions of the Weibull distribution's shape and scale parameters are presented based on historic test data. An analysis of real RDT data demonstrates that the Bayesian posterior estimate of the AFR can produce a significantly narrower confidence interval than direct Weibull fitting, promoting higher confidence to accept the AFR estimate. To evaluate the significance of the prior distribution parameters on the AFR estimate, a sensitivity analysis is presented with respect to each individual parameter. The results indicate that the standard deviation value of either β or η has a more significant impact on the AFR estimate than the mean value.

Symptom Severity Cut Points for the MD Anderson Symptom Inventory for CML (MDASI-CML)

Current analytic methods applied to multidimensional health-related quality of life (HRQOL) data do not borrow strength across analyses and do not produce summary estimates of effect. To compare a random effects modelling approach for the analysis of multidimensional HRQOL data to the following: (1) separate analyses for each dimension; (2) O'Brien's global test procedure; and (3) multivariate analysis of variance (MANOVA). Randomized clinical trial comparing 3 treatments (Trimethoprim-Sulfamethoxazole [TS], Dapsone-Trimethoprim [DT], and Clindamycin-Primaquine [CP] for Pneumocystis carinii pneumonia [PCP]). Patients with PCP enrolled in AIDS Clinical Trials Group Protocol 108. A 33-item battery assessing 7 dimensions of HRQOL: physical functioning, pain, energy, general health perceptions, disability, pulmonary symptoms, and constitutional symptoms. Analyses focused on changes in score from baseline to Day 7 (n = 145). Separate analyses for each dimension suggested a trend favoring CP versus TS, but using a Bonferroni correction no differences were statistically significant. O'Brien's global procedure for a test of no-treatment effect versus superiority of one treatment yielded P = 0.07. MANOVA did not reveal significant differences among treatment groups. A random effects model using fixed treatment and dimension effects and separate random effects for each person showed a significant overall treatment effect (P = 0.02); changes in scores for CP averaged 10 points greater than for TS. Random-effects models provide a flexible class of models for analyzing multidimensional quality of life data and estimating treatment effects because they borrow strength across dimensions.

One of the applications of Fisher's linear discriminant function (FDF) is its use in transforming multivariate data into a new univariate variable. This then makes possible a new option for the variance analysis of multivariate data, in addition to the multivariate analysis of variance (MANOVA). The aim of this work was to select groups of seven characteristics of quality in coffee seedlings using six criteria for selection, to use the FDF to transform such groupings of characteristics into a new variable, and then to compare interpretation of the results obtained from the univariate and multivariate analyses of variance of the characteristics and this new variable, with a view to its use in evaluating coffee seedlings. A randomised block design was used to assess the effect of organic fertiliser on the formation of seedlings in coffee cv. Catuai Vermelho IAC-44, evaluating the following characteristics: seedling height, diameter, root length, dry weight of shoots and roots, leaf area, number of leaves and total dry weight. According to the selection criteria used, different subsets of the selected characteristics are possible. The use of the FDF is shown to be viable in discriminating between treatments. Univariate analysis of the new variable obtained with the FDF and multivariate analysis (MANOVA) was able to detect differences between the treatments, however, it is simpler to apply FDF methodology.

Comparison of Bayesian survival analysis and Cox regression analysis in simulated and breast cancer data sets

Multivariate analysis refers to statistical techniques that simultaneously look at three or more variables in relation to the subjects under investigation with the aim of identifying or clarifying the relationships between them. These techniques have been broadly classified as dependence techniques, which explore the relationship between one or more dependent variables and their independent predictors, and interdependence techniques, that make no such distinction but treat all variables equally in a search for underlying relationships. Multiple linear regression models a situation where a single numerical dependent variable is to be predicted from multiple numerical independent variables. Logistic regression is used when the outcome variable is dichotomous in nature. The log-linear technique models count type of data and can be used to analyze cross-tabulations where more than two variables are included. Analysis of covariance is an extension of analysis of variance (ANOVA), in which an additional independent variable of interest, the covariate, is brought into the analysis. It tries to examine whether a difference persists after “controlling” for the effect of the covariate that can impact the numerical dependent variable of interest. Multivariate analysis of variance (MANOVA) is a multivariate extension of ANOVA used when multiple numerical dependent variables have to be incorporated in the analysis. Interdependence techniques are more commonly applied to psychometrics, social sciences and market research. Exploratory factor analysis and principal component analysis are related techniques that seek to extract from a larger number of metric variables, a smaller number of composite factors or components, which are linearly related to the original variables. Cluster analysis aims to identify, in a large number of cases, relatively homogeneous groups called clusters, without prior information about the groups. The calculation intensive nature of multivariate analysis has so far precluded most researchers from using these techniques routinely. The situation is now changing with wider availability, and increasing sophistication of statistical software and researchers should no longer shy away from exploring the applications of multivariate methods to real-life data sets.

Bayesian methods have been proposed as a way of synthesizing all available evidence to inform decision making. However, few practical applications of the use of Bayesian methods for combining patient-level data (i.e., trial) with additional evidence (e.g., literature) exist in the cost-effectiveness literature. The objective of this study was to compare a Bayesian cost-effectiveness analysis using informative priors to a standard non-Bayesian nonparametric method to assess the impact of incorporating additional information into a cost-effectiveness analysis. Patient-level data from a previously published nonrandomized study were analyzed using traditional nonparametric bootstrap techniques and bivariate normal Bayesian models with vague and informative priors. Two different types of informative priors were considered to reflect different valuations of the additional evidence relative to the patient-level data (i.e., "face value" and "skeptical"). The impact of using different distributions and valuations was assessed in a sensitivity analysis. Models were compared in terms of incremental net monetary benefit (INMB) and cost-effectiveness acceptability frontiers (CEAFs). The bootstrapping and Bayesian analyses using vague priors provided similar results. The most pronounced impact of incorporating the informative priors was the increase in estimated life years in the control arm relative to what was observed in the patient-level data alone. Consequently, the incremental difference in life years originally observed in the patient-level data was reduced, and the INMB and CEAF changed accordingly. The results of this study demonstrate the potential impact and importance of incorporating additional information into an analysis of patient-level data, suggesting this could alter decisions as to whether a treatment should be adopted and whether more information should be acquired.

Modern epidemiologic studies permit investigation of the complex pathways that mediate effects of social, behavioral, and molecular factors on health outcomes. Conventional analytical approaches struggle with high-dimensional data, leading to high likelihoods of both false-positive and false-negative inferences. Herein, we describe a novel Bayesian pathway analysis approach, the algorithm for learning pathway structure (ALPS), which addresses key limitations in existing approaches to complex data analysis. ALPS uses prior information about pathways in concert with empirical data to identify and quantify complex interactions within networks of factors that mediate an association between an exposure and an outcome. We illustrate ALPS through application to a complex gene-drug interaction analysis in the Predictors of Breast Cancer Recurrence (ProBe CaRe) Study, a Danish cohort study of premenopausal breast cancer patients (2002-2011), for which conventional analyses severely limit the quality of inference.

Experiments involving repeated observations of multivariate outcomes are common in biomedical and public health researches which lead to multivariate longitudinal data. These kinds of data have a unique property in the sense that they allow the researcher to study the joint evolution of the multiple outcomes over the time. Recently, there has been a considerable amount of interest on using Bayesian modelling of longitudinal data, data which commonly suffer from incomplete observations. Those Bayesian models for longitudinal data that rely on the ignorability assumption of the dropout mechanism might give misleading inferences. Hence, there is a need to further study the impact of departures from the ignorability assumption on the Bayesian estimates of the model parameters. Current methodology for Bayesian sensitivity analysis mostly involves single response variable in both cross-sectional and longitudinal studies. In this paper, we propose a multivariate extension of the Bayesian index of sensitivity to non-ignorability for the general case of multivariate longitudinal studies with the possibility of having mixed correlated outcomes and a vector of multiple non-ignorability parameters in the missing mechanism. To simultaneously model the mixed responses over the time, we use a random effect latent variable approach. We illustrate the method conducting some simulation studies and analyzing a real data set from a longitudinal study for the comparison of two oral treatments for toenail dermatophyte onychomycosis.

Objectives The purposes of this study were to investigate the attitudes toward physical education and physical activity levels of middle school students in Jiangxi Province, China, and explore the relationship between these two factors. Methods The subjects consisted of 722 middle school students (male: 371 and female: 351) from 7th to 9th grade at four public middle schools in Jiangxi Province, China. The measurement tools were used the Chinese version of Students' Attitude Toward Physical Education (Hu et al., 2014) and the Chinese version of Physical Activity Questionnaire for Adolescents (Li, 2015). For data analysis, confirmatory factor analysis (CFA), descriptive statistics, univariate analysis of variance (ANOVA), multivariate analysis of variance (MANOVA) were performed, using SPSS 26 and AMOS 27 statistical program. Results The results showed that first, participants' attitudes toward physical education were generally positive across all grades and genders, with average scores above 3.0 for all sub-factors. According to the result of MANOVA, gender had a significant impact on all dependent variables [CE: F(1, 716)=21.795, p<.05; CU: F(1, 716)=14.818, p<.05; TE: F(1, 716)=18.150, p<.05; TU: F(1, 716)=8.130, p<.05]; however, grade did not significantly affect attitudes. Second, physical activity levels varied by gender and grade, with males generally exhibiting higher (2.34) scores than females (1.88). According to a multivariate analysis of variance (MANOVA), both gender [F(1, 716)=80.342, p＜.05] and grade [F(2, 716)=24.351, p＜.05) had significant effects on physical activity scores, while the interaction effect between grade and gender was not significant [F(2, 716)=1.659, p＞.05]. Third, correlation analysis revealed slightly positive relationships between physical activity and the four sub-scales of attitude [CE (r=.290, p<.05); CU (r=.299, p<.05); TE (r=.326, p<.05); TU (r=.283, p<.05)]. Conclusions The results of this study are expected to enhance the understanding of middle school students by schools and physical education teachers for the development of physical education in China, and to contribute to the development of future physical education programs by providing theoretical evidence.