Constrained Statistical Inference: A Hybrid of Statistical Theory, Projective Geometry and Applied Optimization Techniques

In many data applications, in addition to determining whether a given risk factor affects an outcome, researchers are often interested in whether the factor has an increasing or decreasing effect. For instance, a clinical trial may test which dose provides the minimum effect; a toxicology study may wish to determine the effect of increasing exposure to a harmful contaminant on human health; and an economist may wish to determine an individual's optimal preferences subject to a budget constraint. In such situations, constrained statistical inference is typically used for analysis, as estimation and hypothesis testing incorporate the parameter orderings, or restrictions, in the methodology. Such methods unite statistical theory with elements of projective geometry and optimization algorithms. In many different models, authors have demonstrated constrained techniques lead to more efficient estimates and improved power over unconstrained methods, albeit at the expense of additional computation. In this paper, we review significant advancements made in the field of constrained inference, ranging from early work on isotonic regression for several normal means to recent advances of constraints in Bayesian techniques and mixed models. To illustrate the methods, a new analysis of an environmental study on the health effects in a population of newborns is provided

Statistical inference for normal means with order restrictions and applications to dose-response studies

Scientific experiments often compare several treatment means with a control mean. In particular, such multiple comparisons arise in biopharmaceutical studies in which it is desirable to conduct the inferences in a specified order and failure to achieve the desired inference at any step renders subsequent comparisons unnecessary. In clinical trials, an important dosing quantity is the minimum effective dose (MED), defined as the minimum dose such that the mean response is clinically significantly better than the mean response of the control by a practical significant difference. In relation to MED estimation, previous authors have either failed to account for the monotonicity of the dose-response means or considered the case of a zero clinically significant difference. In this thesis, an innovative approach using Kuhn-Tucker conditions to evaluate the optimal confidence lower bound at each step in a closed step-down testing procedure is derived and simulation results are presented

Processed data for CHMS 2007–2009: Bisphenol A, phthalates and lead and learning and behavioral problems in Canadian children 6–19 years of age

This article presents processed data from an analysis of cross-sectional data from Cycle 1 of the Canadian Health Measures Survey (CHMS) to examine the potential association between urinary concentrations of BPA and phthalate metabolites and child learning and behavioral problems, considering important covariates such as gender, blood lead and environmental tobacco smoke (ETS). These processed data are related to the research on a subset of the children (Arbuckle et al., 2016) [1]. The Strengths and Difficulties Questionnaire (SDQ) outcomes of interest were emotional symptoms, hyperactivity/inattention, and a total difficulties SDQ score, with borderline and abnormal scores grouped together and compared with children with normal scores. Other outcomes studied included reported learning disability, ADD/ADHD (attention deficit disorder/attention deficit hyperactivity disorder) and use of psychotropic medications to treat behavioral disorders in the past month. Data are presented for all children 6–19 years of age combined.Weighted simple logistic regression estimates for important covariates of each of the outcomes from CHMS Cycle 1 children are reported. Odds ratios based on weighted multiple logistic regression estimates for urinary BPA and phthalate metabolites (including specific gravity as a covariate) and blood lead are presented for the reported outcomes ADD/ADHD, learning disability and psychotropic medications, as well as the SDQ outcomes emotional symptoms, hyperactivity/inattention and total difficulties. Keywords: Bisphenol A, Lead, Phthalates, Behavior, Childre

Early Experience Analyzing Dietary Intake Data from the Canadian Community Health Survey—Nutrition Using the National Cancer Institute (NCI) Method

Background: One of the underpinning elements to support evidence-based decision-making in food and nutrition is the usual dietary intake of a population. It represents the long-run average consumption of a particular dietary component (i.e., food or nutrient). Variations in individual eating habits are observed from day-to-day and between individuals. The National Cancer Institute (NCI) method uses statistical modeling to account for these variations in estimation of usual intakes. This method was originally developed for nutrition survey data in the United States. The main objective of this study was to apply the NCI method in the analysis of Canadian nutrition surveys. Methods: Data from two surveys, the 2004 and 2015 Canadian Community Health Survey—Nutrition were used to estimate usual dietary intake distributions from food sources using the NCI method. The effect of different statistical considerations such as choice of the model, covariates, stratification compared to pooling, and exclusion of outliers were assessed, along with the computational time to convergence. Results: A flowchart to aid in model selection was developed. Different covariates (e.g., age/sex groups, cycle, weekday/weekend of the recall) were used to adjust the estimates of usual intakes. Moreover, larger differences in the ratio of within to between variation for a stratified analysis or a pooled analysis resulted in noticeable differences, particularly in the tails of the distribution of usual intake estimates. Outliers were subsequently removed when the ratio was larger than 10. For an individual age/sex group, the NCI method took 1 h–5 h to obtain results depending on the dietary component. Conclusion: Early experience in using the NCI method with Canadian nutrition surveys data led to the development of a flowchart to facilitate the choice of the NCI model to use. The ability of the NCI method to include covariates permits comparisons between both 2004 and 2015. This study shows that the improper application of pooling and stratification as well as the outlier detection can lead to biased results. This early experience can provide guidance to other researchers and ensures consistency in the analysis of usual dietary intake in the Canadian context

Identification of chemical mixtures to which Canadian pregnant women are exposed: The MIREC Study

Depending on the chemical and the outcome, prenatal exposures to environmental chemicals can lead to adverse effects on the pregnancy and child development, especially if exposure occurs during early gestation. Instead of focusing on prenatal exposure to individual chemicals, more studies have taken into account that humans are exposed to multiple environmental chemicals on a daily basis. The objectives of this analysis were to identify the pattern of chemical mixtures to which women are exposed and to characterize women with elevated exposures to various mixtures. Statistical techniques were applied to 28 chemicals measured simultaneously in the first trimester and socio-demographic factors of 1744 participants from the Maternal-Infant Research on Environment Chemicals (MIREC) Study. Cluster analysis was implemented to categorize participants based on their socio-demographic characteristics, while principal component analysis (PCA) was used to extract the chemicals with similar patterns and to reduce the dimension of the da

Effects of Age, Season, Gender and Urban-Rural Status on Time-Activity: Canadian Human Activity Pattern Survey 2 (CHAPS 2)

Estimation of population exposure is a main component of human health risk assessment for environmental contaminants. Population-level exposure assessments require time-activity pattern distributions in relation to microenvironments where people spend their time. Societal trends may have influenced time-activity patterns since previous Canadian data were collected 15 years ago. The Canadian Human Activity Pattern Survey 2 (CHAPS 2) was a national survey conducted in 2010–2011 to collect time-activity information from Canadians of all ages. Five urban and two rural locations were sampled using telephone surveys. Infants and children, key groups in risk assessment activities, were over-sampled. Survey participants (n = 5,011) provided time-activity information in 24-hour recall diaries and responded to supplemental questionnaires concerning potential exposures to specific pollutants, dwelling characteristics, and socio-economic factors. Results indicated that a majority of the time was spent indoors (88.9%), most of which was indoors at home, with limited time spent outdoors (5.8%) or in a vehicle (5.3%). Season, age, gender and rurality were significant predictors of time activity patterns. Compared to earlier data, adults reported spending more time indoors at home and adolescents reported spending less time outdoors, which could be indicative of broader societal trends. These findings have potentially important implications for assessment of exposure and risk. The CHAPS 2 data also provide much larger sample sizes to allow for improved precision and are more representative of infants, children and rural residents

Additional file 1: of Concentrations of persistent organic pollutants in maternal and cord blood from the maternal-infant research on environmental chemicals (MIREC) cohort study

Results of Statistical Hypothesis Testing—MIREC Persistent Organic Pollutants Analysis-Using censoring methods. Table S1 Results for MIREC persistent organic pollutants in maternal blood by Parity (μg/L). Table S2 Results for MIREC persistent organic pollutants in maternal blood by maternal age (μg/L). Table S3 Results for MIREC persistent organic pollutants in maternal blood by smoking status (μg/L). Table S4 Results for MIREC persistent organic pollutants in maternal blood by household income (μg/L). Table S5 Results for MIREC persistent organic pollutants in maternal blood by pre-BMI (μg/L). Table S6 Results for MIREC persistent organic pollutants in maternal blood by place of birth (μg/L). Table S7 Results for MIREC persistent organic pollutants in maternal blood by fasting (μg/L). Table S8 Results for MIREC persistent organic pollutants in maternal blood by maternal education (μg/L). Table S9 Results for MIREC persistent organic pollutants in maternal blood by whether using non-stick cooking vessels. Table S10 Results for MIREC persistent organic pollutants in maternal blood by whether using non-stick cooking vessels in the microwave. Table S11 Results for MIREC persistent organic pollutants in maternal blood by year of collection. Table S12 Results for MIREC persistent organic pollutants in maternal blood by intake of bacon. Table S13 Results for MIREC persistent organic pollutants in maternal blood by intake of fish. Table S14 Results for MIREC persistent organic pollutants in maternal blood by intake of Hamburger. Table S15 Results for MIREC persistent organic pollutants in maternal blood by intake of pork. Table S16 Results for MIREC persistent organic pollutants in maternal blood by intake of poultry. Table S17 Results for MIREC persistent organic pollutants in maternal blood by intake of steak. Table S18 Comparison of demographic groups when the INTERACTION between BMI and total lipid was significant. Table S19 Comparison of demographic groups when the INTERACTION was significant between year of collection and total lipid. Table S20 Comparison of demographic groups when the INTERACTION was significant between intake of bacon and total lipid. Table S21 Results for MIREC persistent organic pollutants in cord blood by infant gender (μg/L). Table S22 Results for MIREC persistent organic pollutants in cord blood by season of collection (μg/L). Table S23 Results for MIREC persistent organic pollutants in cord blood by smoking status of mother (µg/L). (DOCX 207 kb