Fast rates for estimation error and oracle inequalities for model section

We consider complexity penalization methods for model selection. These methods aim to choose a model to optimally trade off estimation and approximation errors by minimizing the sum of an empirical risk term and a complexity penalty. It is well known that if we use a bound on the maximal deviation between empirical and true risks as a complexity penalty, then the risk of our choice is no more than the approximation error plus twice the complexity penalty. There are many cases, however, where complexity penalties like this give loose upper bounds on the estimation error. In particular, if we choose a function from a suitably simple convex function class with a strictly convex loss function, then the estimation error (the difference between the risk of the empirical risk minimizer and the minimal risk in the class) approaches zero at a faster rate than the maximal deviation between empirical and true risks. In this paper, we address the question of whether it is possible to design a complexity penalized model selection method for these situations. We show that, provided the sequence of models is ordered by inclusion, in these cases we can use tight upper bounds on estimation error as a complexity penalty. Surprisingly, this is the case even in situations when the difference between the empirical risk and true risk (and indeed the error of any estimate of the approximation error) decreases much more slowly than the complexity penalty. We give an oracle inequality showing that the resulting model selection method chooses a function with risk no more than the approximation error plus a constant times the complexity penalty.

Socioeconomic inequalities in weight status among mid-aged adults : the contribution of perceptions of weight status and weight-control behaviours

Background Socioeconomically-disadvantaged adults in developed countries experience a higher prevalence of a number of chronic diseases, such as cardiovascular disease, type 2 diabetes, osteoarthritis and some forms of cancer. Overweight and obesity are major risk factors for these diseases. Lower socioeconomic groups have a greater prevalence of overweight and obesity and this may contribute to their higher morbidity and mortality. International studies suggest that socioeconomic groups may differ in their self-perceptions of weight status and their engagement in weightcontrol behaviours (WCBs). Research has shown that lower socioeconomic adults are more likely to underestimate their weight status, and are less likely to engage in WCBs. This may contribute (in part) to the marked inequalities in weight status observed at the population level. There are few, and somewhat limited, Australian studies that have examined the types of weight-control strategies people adopt, the barriers to their weight control, the determinants of their perceived weight status and WCBs. Furthermore, there are no known Australian studies that have examined socioeconomic differences in these factors to better understand the reasons for socioeconomic inequalities in weight status. Hence, the overall aim of this Thesis is to examine why socioeconomically-disadvantaged group experience a greater prevalence of overweight and obesity than their more-advantaged counterparts. Methods This Thesis used data from two sources. Men and women aged 45 to 60 years were examined from both data source. First, the longitudinal Australian Diabetes, Obesity and Lifestyle (AusDiab) Study were used to advance our knowledge and understanding of socioeconomic differences in weight change, perceived weight status and WCBs. A total of 2753 participants with measured weights at both baseline (1999-2000) and follow-up (2004-2005) were included in the analyses. Percent weight change over the five-year interval was calculated and perceived weight status, WCBs and highest attained education were collected at baseline. Second, the Candidate conducted a postal questionnaire from 1013 Brisbane residents (69.8 % response rate) to investigate the relationship between socioeconomic position, determinants of perceived weight status, WCBs, and barriers and reasons to weight control. A test-retest reliability study was conducted to determine the reliability of the new measures used in the questionnaire. Most new measures had substantial to almost perfect reliability when considering either kappa coefficient or crude agreement. Results The findings from the AusDiab Study (accepted for publication in the Australian and New Zealand Journal of Public Health) showed that low-educated men and women were more likely to be obese at baseline compared to their higheducated respondents (O.R. = 1.97, 95 % C.I. = 1.30-2.98 and O.R. = 1.52, 95 % C.I. = 1.03-2.25, respectively). Over the five year follow-up period (1999-2000 to 2004- 05) there were no socioeconomic differences in weight change among men, however socioeconomically-disadvantaged women had greater weight gains. Participants perceiving themselves as overweight gained less weight than those who saw themselves as underweight or normal weight. There was no relationship between engaging in WCBs and five-year weight change. The postal questionnaire data showed that socioeconomically-disadvantaged groups were less likely to engage in WCBs. If they did engage in weight control, they were less likely to adopt exercise strategies, including moderate and vigorous physical activities but were more likely to decrease their sitting time to control their weight. Socioeconomically-disadvantaged adults reported more barriers to weight control; such as perceiving weight loss as expensive, requiring a lot of cooking skills, not being a high priority and eating differently from other people in the household. These results have been accepted for publication in Public Health Nutrition. The third manuscript (under review in Social Science and Medicine) examined socioeconomic differences in determinants of perceived weight status and reasons for weight control. The results showed that lower socioeconomic adults were more likely to specify the following reasons for weight control: they considered themselves to be too heavy, for occupational requirements, on recommendation from their doctor, family members or friends. Conversely, high-income adults were more likely to report weight control to improve their physical condition or to look more attractive compared with those on lower-incomes. There were few socioeconomic differences in the determinants of perceived weight status. Conclusions Education inequalities in overweight/obesity among men and women may be due to mis-perceptions of weight status; overweight or obese individuals in loweducated groups may not perceive their weight as problematic and therefore may not pay attention to their energy-balance behaviours. Socioeconomic groups differ in WCBs, and their reasons and perceived barriers to weight control. Health promotion programs should encourage weight control among lower socioeconomic groups. More specifically, they should encourage the engagement of physical activity or exercise and dietary strategies among disadvantaged groups. Furthermore, such programs should address potential barriers for weight control that disadvantaged groups may encounter. For example, disadvantaged groups perceive that weight control is expensive, requires cooking skills, not a high priority and eating differently from other people in the household. Lastly, health promotion programs and policies aimed at reducing overweight and obesity should be tailored to the different reasons and motivations to weight control experienced by different socioeconomic groups. Weight-control interventions targeted at higher socioeconomic groups should use improving physical condition and attractiveness as motivational goals; while, utilising social support may be more effective for encouraging weight control among lower socioeconomic groups.

A multilevel investigation of inequalities in clinical and psychosocial outcomes for women after breast cancer

Background In Australia, breast cancer is the most common cancer affecting Australian women. Inequalities in clinical and psychosocial outcomes have existed for some time, affecting particularly women from rural areas and from areas of disadvantage. We have a limited understanding of how individual and area-level factors are related to each other, and their associations with survival and other clinical and psychosocial outcomes. Methods/Design This study will examine associations between breast cancer recurrence, survival and psychosocial outcomes (e.g. distress, unmet supportive care needs, quality of life). The study will use an innovative multilevel approach using area-level factors simultaneously with detailed individual-level factors to assess the relative importance of remoteness, socioeconomic and demographic factors, diagnostic and treatment pathways and processes, and supportive care utilization to clinical and psychosocial outcomes. The study will use telephone and self-administered questionnaires to collect individual-level data from approximately 3, 300 women ascertained from the Queensland Cancer Registry diagnosed with invasive breast cancer residing in 478 Statistical Local Areas Queensland in 2011 and 2012. Area-level data will be sourced from the Australian Bureau of Statistics census data. Geo-coding and spatial technology will be used to calculate road travel distances from patients' residence to diagnostic and treatment centres. Data analysis will include a combination of standard empirical procedures and multilevel modelling. Discussion The study will address the critical question of: what are the individual- or area-level factors associated with inequalities in outcomes from breast cancer? The findings will provide health care providers and policy makers with targeted information to improve the management of women with breast cancer, and inform the development of strategies to improve psychosocial care for women with breast cancer.

Spatial inequalities in colorectal and breast cancer survival : premature deaths and associated factors

This study examines the influence of cancer stage, distance to treatment facilities and area disadvantage on breast and colorectal cancer spatial survival inequalities. We also estimate the number of premature deaths after adjusting for cancer stage to quantify the impact of spatial survival inequalities. Population-based descriptive study of residents aged <90 years in Queensland, Australia diagnosed with primary invasive breast (25,202 females) or colorectal (14,690 males, 11,700 females) cancers during 1996-2007. Bayesian hierarchical models explored relative survival inequalities across 478 regions. Cancer stage and disadvantage explained the spatial inequalities in breast cancer survival, however spatial inequalities in colorectal cancer survival persisted after adjustment. Of the 6,019 colorectal cancer deaths within 5 years of diagnosis, 470 (8%) were associated with spatial inequalities in non-diagnostic factors, i.e. factors beyond cancer stage at diagnosis. For breast cancers, of 2,412 deaths, 170 (7%) were related to spatial inequalities in non-diagnostic factors. Quantifying premature deaths can increase incentive for action to reduce these spatial inequalities.

Does food insecurity contribute to socioeconomic inequalities in BMI?

Introduction: Food insecurity is a social determinant of health and is defined as limited ability to access sufficient amounts of nutritionally adequate or safe food for a healthy and active life. Food insecurity is associated with poor health status and the exacerbation of other health inequalities. This study examined whether an association existed between 1) socioeconomic position (SEP) and food insecurity and 2) food insecurity and weight status. Methods: Data from the 1995 National Nutrition Survey was analysed. A random sample of households (n = 13 858) were asked about dietary habits and food choices. Information about gender, age, BMI, waist circumference, household income and whether the household had run out of money to purchase food in the previous 12 months was obtained and analysed using chi-square and logistic regression. Results: Income was significantly associated with food insecurity; households with lower income were at higher risk of food insecurity. Lower income males were nine times more likely to experience food insecurity and lower income females were three times more likely to experience food insecurity than their higher income counterparts. Food insecurity was significantly associated with body mass index (BMI) among women but not men. Women experiencing food insecurity were at higher risk of overweight/obesity according to BMI and waist circumference measures. Conclusion: Evidence suggests that low income households are at higher risk of food insecurity and women who are food insecure are at higher risk of being overweight or obese. Food insecurity may mediate the association between SEP and BMI.

The influence of neighbourhood disadvantage on smoking cessation and its contribution to inequalities in smoking status

Introduction and aims: Individual smokers from disadvantaged backgrounds are less likely to quit, which contributes to widening inequalities in smoking. Residents of disadvantaged neighbourhoods are more likely to smoke, and neighbourhood inequalities in smoking may also be widening because of neighbourhood differences in rates of cessation. This study examined the association between neighbourhood disadvantage and smoking cessation and its relationship with neighbourhood inequalities in smoking. Design and methods: A multilevel longitudinal study of mid-aged (40-67 years) residents (n=6915) of Brisbane, Australia, who lived in the same neighbourhoods (n=200) in 2007 and 2009. Neighbourhood inequalities in cessation and smoking were analysed using multilevel logistic regression and Markov chain Monte Carlo simulation. Results: After adjustment for individual-level socioeconomic factors, the probability of quitting smoking between 2007 and 2009 was lower for residents of disadvantaged neighbourhoods (9.0%-12.8%) than their counterparts in more advantaged neighbourhoods (20.7%-22.5%). These inequalities in cessation manifested in widening inequalities in smoking: in 2007 the between-neighbourhood variance in rates of smoking was 0.242 (p≤0.001) and in 2009 it was 0.260 (p≤0.001). In 2007, residents of the most disadvantaged neighbourhoods were 88% (OR 1.88, 95% CrI 1.41-2.49) more likely to smoke than residents in the least disadvantaged neighbourhoods: the corresponding difference in 2009 was 98% (OR 1.98 95% CrI 1.48-2.66). Conclusion: Fundamentally, social and economic inequalities at the neighbourhood and individual-levels cause smoking and cessation inequalities. Reducing these inequalities will require comprehensive, well-funded, and targeted tobacco control efforts and equity based policies that address the social and economic determinants of smoking.

Socioeconomic inequalities in cardiovascular mortality and the role of childhood socioeconomic conditions and adulthood risk factors : a prospective cohort study with 17-years of follow up

Background The mechanisms underlying socioeconomic inequalities in mortality from cardiovascular diseases (CVD) are largely unknown. We studied the contribution of childhood socioeconomic conditions and adulthood risk factors to inequalities in CVD mortality in adulthood. Methods The prospective GLOBE study was carried out in the Netherlands, with baseline data from 1991, and linked with the cause of death register in 2007. At baseline, participants reported on adulthood socioeconomic position (SEP) (own educational level), childhood socioeconomic conditions (occupational level of respondent’s father), and a broad range of adulthood risk factors (health behaviours, material circumstances, psychosocial factors). This present study is based on 5,395 men and 6,306 women, and the data were analysed using Cox regression models and hazard ratios (HR). Results A low adulthood SEP was associated with increased CVD mortality for men (HR 1.84; 95% CI: 1.41-2.39) and women (HR 1.80; 95%CI: 1.04-3.10). Those with poorer childhood socioeconomic conditions were more likely to die from CVD in adulthood, but this reached statistical significance only among men with the poorest childhood socioeconomic circumstances. About half of the investigated adulthood risk factors showed significant associations with CVD mortality among both men and women, namely renting a house, experiencing financial problems, smoking, physical activity and marital status. Alcohol consumption and BMI showed a U-shaped relationship with CVD mortality among women, with the risk being significantly greater for both abstainers and heavy drinkers, and among women who were underweight or obese. Among men, being single or divorced and using sleep/anxiety drugs increased the risk of CVD mortality. In explanatory models, the largest contributor to adulthood CVD inequalities were material conditions for men (42%; 95% CI: −73 to −20) and behavioural factors for women (55%; 95% CI: -191 to −28). Simultaneous adjustment for adulthood risk factors and childhood socioeconomic conditions attenuated the HR for the lowest adulthood SEP to 1.34 (95% CI: 0.99-1.82) for men and 1.19 (95% CI: 0.65-2.15) for women. Conclusions Adulthood material, behavioural and psychosocial factors played a major role in the explanation of adulthood SEP inequalities in CVD mortality. Childhood socioeconomic circumstances made a modest contribution, mainly via their association with adulthood risk factors. Policies and interventions to reduce health inequalities are likely to be most effective when considering the influence of socioeconomic circumstances across the entire life course and in particular, poor material conditions and unhealthy behaviours in adulthood.

Geographic remoteness, area-level socioeconomic disadvantage and inequalities in colorectal cancer survival in Queensland : a multilevel analysis

Background To explore the impact of geographical remoteness and area-level socioeconomic disadvantage on colorectal cancer (CRC) survival. Methods Multilevel logistic regression and Markov chain Monte Carlo simulations were used to analyze geographical variations in five-year all-cause and CRC-specific survival across 478 regions in Queensland Australia for 22,727 CRC cases aged 20–84 years diagnosed from 1997–2007. Results Area-level disadvantage and geographic remoteness were independently associated with CRC survival. After full multivariate adjustment (both levels), patients from remote (odds Ratio [OR]: 1.24, 95%CrI: 1.07-1.42) and more disadvantaged quintiles (OR = 1.12, 1.15, 1.20, 1.23 for Quintiles 4, 3, 2 and 1 respectively) had lower CRC-specific survival than major cities and least disadvantaged areas. Similar associations were found for all-cause survival. Area disadvantage accounted for a substantial amount of the all-cause variation between areas. Conclusions We have demonstrated that the area-level inequalities in survival of colorectal cancer patients cannot be explained by the measured individual-level characteristics of the patients or their cancer and remain after adjusting for cancer stage. Further research is urgently needed to clarify the factors that underlie the survival differences, including the importance of geographical differences in clinical management of CRC.