Modelling a response as a function of high frequency count data: the association between physical activity and fat mass

We present a new statistical modelling approach where the response is a function of high frequency count data. Our application is about investigating the relationship between the health outcome fat mass and physical activity (PA) measured by accelerometer. The accelerometer quantifies the intensity of physical activity as counts per epoch over a given period of time. We use data from the Avon longitudinal study of parents and children (ALSPAC) where accelerometer data is available as a time series of accelerometer counts per minute over seven days for a subset of children. In order to compare accelerometer profiles between individuals and to reduce the high dimension a functional summary of the profiles is used. We use the histogram as a functional summary due to its simplicity, suitability and ease of interpretation. Our model is an extension of generalised regression of scalars on functions or signal regression. It allows also multi-dimensional functional predictors and additive non-linear predictors for metric covariates. The additive multidimensional functional predictors allow investigating specific questions about whether the effect of PA varies over its intensity, by gender, by time of day or by day of the week. The key feature of the model is that it utilises the full profile of measured PA without requiring cut-points defining intensity levels for light, moderate and vigorous activity. We show that the (not necessarily causal) effect of PA is not linear and not constant over the activity intensity. Also, there is little evidence to suggest that the effect of PA intensity varies by gender or whether it happens on weekdays or on weekends

Interaction effects of region-level GDP per capita and age on labour market transition rates in Italy

Abstract The aim of this paper is to measure the effect of the interaction between age for the population of males and females aged 18 to 74 and region-level GDP per capita on labour market transition probabilities in Italy. We compare different occupational states in a sample of males and females who remained in their region of residence at two points in time (12 months apart). We estimate the transition probabilities using a flexible hierarchical logit model with interaction effects between worker age and region-level GDP per capita. We apply this model using longitudinal data from the Italian Labour Force Survey that cover the 2004–2013 period. We find empirical support for the assumption that people in the same age cohort have different labour market opportunities based on the level of GDP per capita in their region of residence. These differences are particularly relevant among younger workers

Variable selection under multiple imputation using the bootstrap in a prognostic study

Background: Missing data is a challenging problem in many prognostic studies. Multiple imputation (MI) accounts for imputation uncertainty that allows for adequate statistical testing. We developed and tested a methodology combining MI with bootstrapping techniques for studying prognostic variable selection. Method: In our prospective cohort study we merged data from three different randomized controlled trials (RCTs) to assess prognostic variables for chronicity of low back pain. Among the outcome and prognostic variables data were missing in the range of 0 and 48.1%. We used four methods to investigate the influence of respectively sampling and imputation variation: MI only, bootstrap only, and two methods that combine MI and bootstrapping. Variables were selected based on the inclusion frequency of each prognostic variable, i.e. the proportion of times that the variable appeared in the model. The discriminative and calibrative abilities of prognostic models developed by the four methods were assessed at different inclusion levels. Results: We found that the effect of imputation variation on the inclusion frequency was larger than the effect of sampling variation. When MI and bootstrapping were combined at the range of 0% (full model) to 90% of variable selection, bootstrap corrected c-index values of 0.70 to 0.71 and slope values of 0.64 to 0.86 were found. Conclusion: We recommend to account for both imputation and sampling variation in sets of missing data. The new procedure of combining MI with bootstrapping for variable selection, results in multivariable prognostic models with good performance and is therefore attractive to apply on data sets with missing values

The search for stable prognostic models in multiple imputed data sets

<p>Abstract</p> <p>Background</p> <p>In prognostic studies model instability and missing data can be troubling factors. Proposed methods for handling these situations are bootstrapping (B) and Multiple imputation (MI). The authors examined the influence of these methods on model composition.</p> <p>Methods</p> <p>Models were constructed using a cohort of 587 patients consulting between January 2001 and January 2003 with a shoulder problem in general practice in the Netherlands (the Dutch Shoulder Study). Outcome measures were persistent shoulder disability and persistent shoulder pain. Potential predictors included socio-demographic variables, characteristics of the pain problem, physical activity and psychosocial factors. Model composition and performance (calibration and discrimination) were assessed for models using a complete case analysis, MI, bootstrapping or both MI and bootstrapping.</p> <p>Results</p> <p>Results showed that model composition varied between models as a result of how missing data was handled and that bootstrapping provided additional information on the stability of the selected prognostic model.</p> <p>Conclusion</p> <p>In prognostic modeling missing data needs to be handled by MI and bootstrap model selection is advised in order to provide information on model stability.</p

Nutrition and cancer: A review of the evidence for an anti-cancer diet

It has been estimated that 30–40 percent of all cancers can be prevented by lifestyle and dietary measures alone. Obesity, nutrient sparse foods such as concentrated sugars and refined flour products that contribute to impaired glucose metabolism (which leads to diabetes), low fiber intake, consumption of red meat, and imbalance of omega 3 and omega 6 fats all contribute to excess cancer risk. Intake of flax seed, especially its lignan fraction, and abundant portions of fruits and vegetables will lower cancer risk. Allium and cruciferous vegetables are especially beneficial, with broccoli sprouts being the densest source of sulforophane. Protective elements in a cancer prevention diet include selenium, folic acid, vitamin B-12, vitamin D, chlorophyll, and antioxidants such as the carotenoids (α-carotene, β-carotene, lycopene, lutein, cryptoxanthin). Ascorbic acid has limited benefits orally, but could be very beneficial intravenously. Supplementary use of oral digestive enzymes and probiotics also has merit as anticancer dietary measures. When a diet is compiled according to the guidelines here it is likely that there would be at least a 60–70 percent decrease in breast, colorectal, and prostate cancers, and even a 40–50 percent decrease in lung cancer, along with similar reductions in cancers at other sites. Such a diet would be conducive to preventing cancer and would favor recovery from cancer as well