Optimization of Convex Risk Functions

We consider optimization problems involving convex risk functions. By employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models, and optimality and duality theory for problems involving risk functions

Associations between loneliness and lifestyle or health-related factors of the 2012 Swiss Health Survey¹.

<p>Associations between loneliness and lifestyle or health-related factors of the 2012 Swiss Health Survey<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181442#t002fn001" target="_blank">¹</a>.</p

Multivariable adjusted associations between loneliness and lifestyle and health-related factors stratified by age group of the 2012 Swiss Health Survey¹.

<p>Multivariable adjusted associations between loneliness and lifestyle and health-related factors stratified by age group of the 2012 Swiss Health Survey<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181442#t003fn001" target="_blank">¹</a>.</p

Characteristics of the sample of the 2012 Swiss Health Survey¹.

<p>Characteristics of the sample of the 2012 Swiss Health Survey<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0181442#t001fn001" target="_blank">¹</a>.</p

Loneliness in different age groups.

<p>Prevalence of perceived frequency of loneliness by 5-year age groups.</p

Associations between lifetime agoraphobia status at baseline and inflammatory measures at baseline and follow-up.

<p>Values for inflammatory measures are given as unadjusted log10-transformed means ± standard deviation, values for interleukin-1β are given as prevalence.</p><p>CRP, C-reactive protein; TNF, tumor necrosis factor.</p><p>^a Multiple regression with log10 transformed cytokine or CRP or adiponectin.</p><p>^b Logistic regression with interleukin-1β concentration dichotomized at the median.</p><p>^c Composite score of inflammatory markers includes CRP, interleukin-6 and TNF-α. Only participants who had data available for all three of these markers were included in these analyses.</p><p>Associations between lifetime agoraphobia status at baseline and inflammatory measures at baseline and follow-up.</p

Associations between lifetime agoraphobia status at baseline and inflammatory measures (adiponectin) at follow-up, serially adjusted for covariates.

<p>Values for inflammatory measures are given as unadjusted log10-transformed means ± standard deviation, values for interleukin-1β are given as prevalence.</p><p>HDL, high-density lipoprotein; CRP, C-reactive protein; TNF, tumor necrosis factor; OR, odds ratio; 95CI, 95% confidence interval.</p><p>^a Duration between somatic evaluation at baseline and somatic evaluation at follow-up.</p><p>^b A value of “3” represents an SES of III (middle class) on the Hollingshead Scale.</p><p>^c Systolic blood pressure ≥ 140 mmHg and/or diastolic blood pressure ≥ 90 mmHg.</p><p>^d Physically active at least or more than 20 minutes twice a week.</p><p>^e Generalized anxiety disorder, panic disorder, posttraumatic stress disorder, and/or social phobia.</p><p>^f Marijuana, cocaine, solvent, hallucinogen, stimulant, sedative or/and narcotic dependence.</p><p>^g Multiple regression with log10 transformed cytokine or CRP or adiponectin.</p><p>^h Logistic regression with interleukin-1β concentration dichotomized at the median.</p><p>ⁱ Composite score of inflammatory markers includes CRP, interleukin-6 and TNF-α. Only participants who had data available for all three of these markers were included in these analyses.</p><p>Associations between lifetime agoraphobia status at baseline and inflammatory measures (adiponectin) at follow-up, serially adjusted for covariates.</p

Associations between lifetime agoraphobia status at baseline and inflammatory measures (composite score) at follow-up, serially adjusted for covariates.

<p>Values for inflammatory measures are given as unadjusted log10-transformed means ± standard deviation, values for interleukin-1β are given as prevalence.</p><p>HDL, high-density lipoprotein; CRP, C-reactive protein; TNF, tumor necrosis factor; OR, odds ratio; 95CI, 95% confidence interval.</p><p>^a Duration between somatic evaluation at baseline and somatic evaluation at follow-up.</p><p>^b A value of “3” represents an SES of III (middle class) on the Hollingshead Scale.</p><p>^c Systolic blood pressure ≥ 140 mmHg and/or diastolic blood pressure ≥ 90 mmHg.</p><p>^d Physically active at least or more than 20 minutes twice a week.</p><p>^e Generalized anxiety disorder, panic disorder, posttraumatic stress disorder, and/or social phobia.</p><p>^f Marijuana, cocaine, solvent, hallucinogen, stimulant, sedative or/and narcotic dependence.</p><p>^g Multiple regression with log10 transformed cytokine or CRP or adiponectin.</p><p>^h Logistic regression with interleukin-1β concentration dichotomized at the median.</p><p>ⁱ Composite score of inflammatory markers includes CRP, interleukin-6 and TNF-α. Only participants who had data available for all three of these markers were included in these analyses.</p><p>Associations between lifetime agoraphobia status at baseline and inflammatory measures (composite score) at follow-up, serially adjusted for covariates.</p

Associations between lifetime agoraphobia status at baseline and inflammatory measures (tumor necrosis factor-α) at follow-up, serially adjusted for covariates.

<p>Values for inflammatory measures are given as unadjusted log10-transformed means ± standard deviation, values for interleukin-1β are given as prevalence.</p><p>HDL, high-density lipoprotein; CRP, C-reactive protein; TNF, tumor necrosis factor; OR, odds ratio; 95CI, 95% confidence interval.</p><p>^a Duration between somatic evaluation at baseline and somatic evaluation at follow-up.</p><p>^b A value of “3” represents an SES of III (middle class) on the Hollingshead Scale.</p><p>^c Systolic blood pressure ≥ 140 mmHg and/or diastolic blood pressure ≥ 90 mmHg.</p><p>^d Physically active at least or more than 20 minutes twice a week.</p><p>^e Generalized anxiety disorder, panic disorder, posttraumatic stress disorder, and/or social phobia.</p><p>^f Marijuana, cocaine, solvent, hallucinogen, stimulant, sedative or/and narcotic dependence.</p><p>^g Multiple regression with log10 transformed cytokine or CRP or adiponectin.</p><p>^h Logistic regression with interleukin-1β concentration dichotomized at the median.</p><p>ⁱ Composite score of inflammatory markers includes CRP, interleukin-6 and TNF-α. Only participants who had data available for all three of these markers were included in these analyses.</p><p>Associations between lifetime agoraphobia status at baseline and inflammatory measures (tumor necrosis factor-α) at follow-up, serially adjusted for covariates.</p

Associations between lifetime agoraphobia status at baseline and inflammatory measures at baseline and follow-up.

<p>Values for inflammatory measures are given as unadjusted log10-transformed means ± standard deviation, values for interleukin-1β are given as prevalence.</p><p>CRP, C-reactive protein; TNF, tumor necrosis factor.</p><p>^a Multiple regression with log10 transformed cytokine or CRP or adiponectin.</p><p>^b Logistic regression with interleukin-1β concentration dichotomized at the median.</p><p>^c Composite score of inflammatory markers includes CRP, interleukin-6 and TNF-α. Only participants who had data available for all three of these markers were included in these analyses.</p><p>Associations between lifetime agoraphobia status at baseline and inflammatory measures at baseline and follow-up.</p