Analysis and Diagnostics of Categorical Variables with Multiple Outcomes

Surveys often contain qualitative variables for which respondents may select any number of the outcome categories. For instance, for the question "What type of contraceptive have you used?" with possible responses (oral, condom, lubricated condom, spermicide, and diaphragm), respondents would be instructed to select as many of the J = 5 outcomes as apply. This situation is known as multiple responses and outcomes are referred to as items. This thesis discusses several approaches to analysing such data. For stratified multiple response data, we consider three ways of defining the common odds ratio, a summarising measure for the conditional association between a row variable and the multiple response variable, given a stratification variable. For each stratum, we define the odds ratio in terms of: 1 item and 2 rows, 2 items and 2 rows, and 2 items and 1 row. Then we consider two estimation approaches for the common odds ratio and its (co)variance estimators for these types of odds ratios. The model-based approach treats the J items as a Jdimensional binary response and then uses logit models directly for the marginal distribution of each item by applying the generalised estimating equation (GEE) (Liang and Zeger 1986) method. The non-model-based approach uses Mantel-Haenszel (MH) type estimators. The model-based (or marginal model) approach is still applicable for more than two explanatory variables. Preisser and Qaqish (1996) proposed regression diagnostics for GEE. Another model fitting approach is the homogeneous linear predictor model (HLP) based on maximum likelihood (ML) introduced by Lang (2005). We investigate deletion diagnostics as the Cook distance and DBETA for multiple response data using HLPmodels (Lang 2005), which have not been considered yet, and propose a simple "delete=replace" method as an alternative approach for deletion. Methods are compared with the GEE approach. We also discuss the modelling of a repeated multiple response variable, a categorical variable for which subjects can select any number of categories on repeated occasions. Multiple responses have been considered in the literature by various authors; however, repeated multiple responses have not been considered yet. Approaches include the marginal model approach using the GEE and HLP methods, and generalised linear mixed models (GLMM). For the GEE method, we also consider possible correlation structures and propose a groupwise correlation estimation method yielding more efficient parameter estimates if the correlation structure is indeed different for different groups, which is confirmed by a simulation study. Ordered categorical variables occur in many applications and can be seen as a special case of multiple responses. The proportional odds model, which uses logits of cumulative probabilities, is currently the most popular model. We consider two approaches focusing on the mis-specification of a covariate. The binary approach considers the proportional oddsmodel as J-1 logistic regression models and applies the cumulative residual process introduced by Arbogast and Lin (2005) for logistic regression. The multivariate approach views the proportional odds model as a member of the class of multivariate generalised linear models (MGLM), where the response variable is a vector of indicator responses

Wilson confidence intervals for the two-sample log-odds-ratio in stratified 2 x 2 contingency tables

Large-sample Wilson-type con fidence intervals (CIs) are derived for a parameter of interest in many clinical trials situations: the log-odds-ratio, in a two sample experiment comparing binomial success proportions, say between cases and controls. The methods cover several scenarios: (i) results embedded in a single 2 x 2 contingency table, (ii) a series of K 2 x 2 tables with common parameter, or (iii) K tables, where the parameter may change across tables under the influence of a covariate. The calculations of the Wilson CI require only simple numerical assistance, and for example are easily carried out using Excel. The main competitor, the exact CI, has two disadvantages: It requires burdensome search algorithms for the multi-table case and results in strong over-coverage associated with long confidence intervals. All the application cases are illustrated through a well-known example. A simulation study then investigates how the Wilson CI performs among several competing methods. The Wilson interval is shortest, except for very large odds ratios, while maintaining coverage similar to Wald-type intervals. An alternative to the Wald CI is the Agresti-Coull CI, calculated from Wilson and Wald CIs, which has same length as the Wald CI but improved coverage

Capturing Multivariate Spatial Dependence: Model, Estimate and then Predict

Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction between these two dependencies that is the focus of Genton and Kleiber's paper under discussion. We see the problem of ensuring that any multivariate spatial covariance matrix is nonnegative definite as important, but we also see it as a means to an end. That "end" is solving the scientific problem of predicting a multivariate field. [arXiv:1507.08017].Comment: Published at http://dx.doi.org/10.1214/15-STS517 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

mipfp: An R Package for Multidimensional Array Fitting and Simulating Multivariate Bernoulli Distributions

This paper explains the mipfp package for R with the core functionality of updating an d-dimensional array with respect to given target marginal distributions, which in turn can be multi-dimensional. The implemented methods include the iterative proportional fitting procedure (IPFP), the maximum likelihood method, the minimum chi-square and least squares procedures. The package also provides an application of the IPFP to simulate data from a multivariate Bernoulli distribution. The functionalities of the package are illustrated through two practical examples: the update of a 3-dimensional contingency table to match the targets for a synthetic population and the estimation and simulation of the joint distribution of the binary attribute impaired pulmonary function as used by Qaqish, Zink, and Preisser (2012)

The effects of omitting components in a multilevel model with social network effects

Multilevel models are often used to account for the hierarchical structure of social data and the inherent dependencies to produce estimates of regression coefficients, variance components associated with each level, and accurate standard errors. Social network analysis is another important approach to analysing complex data that incoproate the social relationships between a number of individuals. Extended linear regression models, such as network autoregressive models, have been proposed that include the social network information to account for the dependencies between persons. In this article, we propose three types of models that account for both the multilevel structure and the social network structure together, leading to network autoregressive multilevel models. We investigate theoretically and empirically, using simulated data and a data set from the Dutch Social Behavior study, the effect of omitting the levels and the social network on the estimates of the regression coefficients, variance components, network autocorrelation parameter, and standard errors

Generalized Mantel–Haenszel estimators for simultaneous differential item functioning tests

The Mantel–Haenszel estimator is one of the most popular techniques for measuring differential item functioning (DIF). A generalization of this estimator is applied to the context of DIF to compare items by taking the covariance of odds ratio estimators between dependent items into account. Unlike the Item Response Theory, the method does not rely on the local item independence assumption which is likely to be violated when one item provides clues about the answer of another item. Furthermore, we use these (co)variance estimators to construct a hypothesis test to assess DIF for multiple items simultaneously. A simulation study is presented to assess the performance of several tests. Finally, the use of these DIF tests is illustrated via application to two real data setsPeer ReviewedPostprint (author's final draft

Global effect of COVID-19 pandemic on physical activity, sedentary behaviour and sleep among 3- to 5-year-old children: a longitudinal study of 14 countries

Background: The restrictions associated with the 2020 COVID-19 pandemic has resulted in changes to young children’s daily routines and habits. The impact on their participation in movement behaviours (physical activity, sedentary screen time and sleep) is unknown. This international longitudinal study compared young children’s movement behaviours before and during the COVID-19 pandemic. Methods: Parents of children aged 3–5 years, from 14 countries (8 low- and middle-income countries, LMICs) completed surveys to assess changes in movement behaviours and how these changes were associated with the COVID-19 pandemic. Surveys were completed in the 12 months up to March 2020 and again between May and June 2020 (at the height of restrictions). Physical activity (PA), sedentary screen time (SST) and sleep were assessed via parent survey. At Time 2, COVID-19 factors including level of restriction, environmental conditions, and parental stress were measured. Compliance with the World Health Organizations (WHO) Global guidelines for PA (180 min/ day [≥60 min moderate- vigorous PA]), SST (≤1 h/day) and sleep (10-13 h/day) for children under 5 years of age, was determined. Results: Nine hundred- forty-eight parents completed the survey at both time points. Children from LMICs were more likely to meet the PA (Adjusted Odds Ratio [AdjOR] = 2.0, 95%Confidence Interval [CI] 1.0,3.8) and SST (AdjOR = 2.2, 95%CI 1.2,3.9) guidelines than their high-income country (HIC) counterparts. Children who could go (Continued on next page (Continued from previous page) outside during COVID-19 were more likely to meet all WHO Global guidelines (AdjOR = 3.3, 95%CI 1.1,9.8) than those who were not. Children of parents with higher compared to lower stress were less likely to meet all three guidelines (AdjOR = 0.5, 95%CI 0.3,0.9). Conclusion: PA and SST levels of children from LMICs have been less impacted by COVID-19 than in HICs. Ensuring children can access an outdoor space, and supporting parents’ mental health are important prerequisites for enabling pre-schoolers to practice healthy movement behaviours and meet the Global guidelines

Physical activity, screen time and the COVID-19 school closures in Europe – an observational study in 10 countries

To date, few data on how the COVID-19 pandemic and restrictions affected children’s physical activity in Europe have been published. This study examined the prevalence and correlates of physical activity and screen time from a large sample of European children during the COVID-19 pandemic to inform strategies and provide adequate mitigation measures. An online survey was conducted using convenience sampling from 15 May to 22 June, 2020. Parents were eligible if they resided in one of the survey countries and their children aged 6–18 years. 8395 children were included (median age [IQR], 13 [10–15] years; 47% boys; 57.6% urban residents; 15.5% in self-isolation). Approximately two-thirds followed structured routines (66.4% [95%CI, 65.4–67.4]), and more than half were active during online P.E. (56.6% [95%CI, 55.5–57.6]). 19.0% (95%CI, 18.2–19.9) met the WHO Global physical activity recommendation. Total screen time in excess of 2 h/day was highly prevalent (weekdays: 69.5% [95%CI, 68.5–70.5]; weekend: 63.8% [95%CI, 62.7–64.8]). Playing outdoors more than 2 h/day, following a daily routine and being active in online P.E. increased the odds of healthy levels of physical activity and screen time, particularly in mildly affected countries. In severely affected countries, online P.E. contributed most to meet screen time recommendation, whereas outdoor play was most important for adequate physical activity. Promoting safe and responsible outdoor activities, safeguarding P.E. lessons during distance learning and setting pre-planned, consistent daily routines are important in helping children maintain healthy active lifestyle in pandemic situation. These factors should be prioritised by policymakers, schools and parents. Highlights • To our knowledge, our data provide the first multi-national estimates on physical activity and total screen time in European children roughly two months after COVID-19 was declared a global pandemic. • Only 1 in 5 children met the WHO Global physical activity recommendations. • Under pandemic conditions, parents should set pre-planned, consistent daily routines and integrate at least 2-hours outdoor activities into the daily schedule, preferable on each day. Schools should make P.E. lessons a priority. Decision makers should mandate online P.E. be delivered by schools during distance learning. Closing outdoor facilities for PA should be considered only as the last resort during lockdowns