Finite mixture distributions, sequential likelihood and the EM algorithm

A popular way to account for unobserved heterogeneity is to assume that the data are drawn from a finite mixture distribution. A barrier to using finite mixture models is that parameters that could previously be estimated in stages must now be estimated jointly: using mixture distributions destroys any additive separability of the log-likelihood function. We show, however, that an extension of the EM algorithm reintroduces additive separability, thus allowing one to estimate parameters sequentially during each maximization step. In establishing this result, we develop a broad class of estimators for mixture models. Returning to the likelihood problem, we show that, relative to full information maximum likelihood, our sequential estimator can generate large computational savings with little loss of efficiency.

Analysis of soil carbon transit times and age distributions using network theories

The long-term soil carbon dynamics may be approximated by networks of linear compartments, permitting theoretical analysis of transit time (i.e., the total time spent by a molecule in the system) and age (the time elapsed since the molecule entered the system) distributions. We compute and compare these distributions for different network. configurations, ranging from the simple individual compartment, to series and parallel linear compartments, feedback systems, and models assuming a continuous distribution of decay constants. We also derive the transit time and age distributions of some complex, widely used soil carbon models (the compartmental models CENTURY and Rothamsted, and the continuous-quality Q-Model), and discuss them in the context of long-term carbon sequestration in soils. We show how complex models including feedback loops and slow compartments have distributions with heavier tails than simpler models. Power law tails emerge when using continuous-quality models, indicating long retention times for an important fraction of soil carbon. The responsiveness of the soil system to changes in decay constants due to altered climatic conditions or plant species composition is found to be stronger when all compartments respond equally to the environmental change, and when the slower compartments are more sensitive than the faster ones or lose more carbon through microbial respiration. Copyright 2009 by the American Geophysical Union.

Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Comparison of a reduced carbohydrate and reduced fat diet for LDL, HDL, and VLDL subclasses during 9-months of weight maintenance subsequent to weight loss.

OBJECTIVES: This study compared LDL, HDL, and VLDL subclasses in overweight or obese adults consuming either a reduced carbohydrate (RC) or reduced fat (RF) weight maintenance diet for 9 months following significant weight loss. METHODS: Thirty-five (21 RC; 14 RF) overweight or obese middle-aged adults completed a 1-year weight management clinic. Participants met weekly for the first six months and bi-weekly thereafter. Meetings included instruction for diet, physical activity, and behavior change related to weight management. Additionally, participants followed a liquid very low-energy diet of approximately 2092 kJ per day for the first three months of the study. Subsequently, participants followed a dietary plan for nine months that targeted a reduced percentage of carbohydrate (approximately 20%) or fat (approximately 30%) intake and an energy intake level calculated to maintain weight loss. Lipid subclasses using NMR spectroscopy were analyzed prior to weight loss and at multiple intervals during weight maintenance. RESULTS: Body weight change was not significantly different within or between groups during weight maintenance (p>0.05). The RC group showed significant increases in mean LDL size, large LDL, total HDL, large and small HDL, mean VLDL size, and large VLDL during weight maintenance while the RF group showed increases in total HDL, large and small HDL, total VLDL, and large, medium, and small VLDL (p<0.05). Group*time interactions were significant for large and medium VLDL (p>0.05). CONCLUSION: Some individual lipid subclasses improved in both dietary groups. Large and medium VLDL subclasses increased to a greater extent across weight maintenance in the RF group.

Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Adolescent weight status and self-reported school performance in South Korea.

Using a nationally representative sample of 142 783 middle school (13-15 years old) and high school (16-18 years old) students in South Korea, this study examined whether (1) overweight and obesity are more likely to be associated with lower self-reported school performance; (2) overweight and obese students are more likely to enrol in a vocational high school as opposed to a general high school; (3) the association between obesity and poorer self-reported school performance is mediated through body image stress and health status. We found that excess weight was negatively associated with self-reported school performance among middle and general high school students, and that obese students had a higher probability of being enrolled in a vocational over a general high school. We did not find strong evidence on the mediating role of body image stress and health status.

Ambient aerosol size distributions and number concentrations measured during the Pittsburgh Air Quality Study (PAQS)

Twelve months of aerosol size distributions from 3 to 560nm, measured using scanning mobility particle sizers are presented with an emphasis on average number, surface, and volume distributions, and seasonal and diurnal variation. The measurements were made at the main sampling site of the Pittsburgh Air Quality Study from July 2001 to June 2002. These are supplemented with 5 months of size distribution data from 0.5 to 2.5μm measured with a TSI aerosol particle sizer and 2 months of size distributions measured at an upwind rural sampling site. Measurements at the main site were made continuously under both low and ambient relative humidity. The average Pittsburgh number concentration (3-500nm) is 22,000cm-3 with an average mode size of 40nm. Strong diurnal patterns in number concentrations are evident as a direct effect of the sources of particles (atmospheric nucleation, traffic, and other combustion sources). New particle formation from homogeneous nucleation is significant on 30-50% of study days and over a wide area (at least a hundred kilometers). Rural number concentrations are a factor of 2-3 lower (on average) than the urban values. Average measured distributions are different from model literature urban and rural size distributions. © 2004 Elsevier Ltd. All rights reserved.

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s).

Low Molecular Weight Opioid Peptide Esters Could be Developed as a New Class of Analgesics.

Low molecular weight opioid peptide esters (OPE) could become a class of analgesics with different side effect profiles than current opiates. OPE may have sufficient plasma stability to cross the blood brain barrier (BBB), undergo ester hydrolysis and produce analgesia. OPE of dipeptides, tyr-pro and tyr-gly conjugated to ethanol have a structure similar to the anesthestic agent, etomidate. Based upon the analgesic activity of dipeptide opioids, Lipinski's criteria, and permeability of select GABA esters to cross the BBB, opioid peptides (OP) conjugated to ethanol, cholesterol or 3-glucose are lead recommendations. Preliminary animal data suggests that tyr-pro-ethyl ester crosses the BBB and unexpectedly produces hyperalgesia. Currently, there are no approved OP analgesics available for clinical use. Clinical trials of good manufacturing practice OP administered to patients suffering from chronic pain with indwelling intrathecal pumps could resolve the issue that OP may be superior to opiates and may redirect research.

Weight loss intervention for young adults using mobile technology: design and rationale of a randomized controlled trial - Cell Phone Intervention for You (CITY).

BACKGROUND: The obesity epidemic has spread to young adults, leading to significant public health implications later in adulthood. Intervention in early adulthood may be an effective public health strategy for reducing the long-term health impact of the epidemic. Few weight loss trials have been conducted in young adults. It is unclear what weight loss strategies are beneficial in this population. PURPOSE: To describe the design and rationale of the NHLBI-sponsored Cell Phone Intervention for You (CITY) study, which is a single center, randomized three-arm trial that compares the impact on weight loss of 1) a behavioral intervention that is delivered almost entirely via cell phone technology (Cell Phone group); and 2) a behavioral intervention delivered mainly through monthly personal coaching calls enhanced by self-monitoring via cell phone (Personal Coaching group), each compared to 3) a usual care, advice-only control condition. METHODS: A total of 365 community-dwelling overweight/obese adults aged 18-35 years were randomized to receive one of these three interventions for 24 months in parallel group design. Study personnel assessing outcomes were blinded to group assignment. The primary outcome is weight change at 24 [corrected] months. We hypothesize that each active intervention will cause more weight loss than the usual care condition. Study completion is anticipated in 2014. CONCLUSIONS: If effective, implementation of the CITY interventions could mitigate the alarming rates of obesity in young adults through promotion of weight loss. ClinicalTrial.gov: NCT01092364.

Recruiting young adults into a weight loss trial: report of protocol development and recruitment results.

Obesity has spread to all segments of the U.S. population. Young adults, aged 18-35 years, are rarely represented in clinical weight loss trials. We conducted a qualitative study to identify factors that may facilitate recruitment of young adults into a weight loss intervention trial. Participants were 33 adults aged 18-35 years with BMI ≥25 kg/m(2). Six group discussions were conducted using the nominal group technique. Health, social image, and "self" factors such as emotions, self-esteem, and confidence were reported as reasons to pursue weight loss. Physical activity, dietary intake, social support, medical intervention, and taking control (e.g. being motivated) were perceived as the best weight loss strategies. Incentives, positive outcomes, education, convenience, and social support were endorsed as reasons young adults would consider participating in a weight loss study. Incentives, advertisement, emphasizing benefits, and convenience were endorsed as ways to recruit young adults. These results informed the Cellphone Intervention for You (CITY) marketing and advertising, including message framing and advertising avenues. Implications for recruitment methods are discussed.