Estimating mixed-effects differential equation models

Ordinary differential equations (ODEs) are popular tools for modeling complicated dynamic systems in many areas. When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models. Rather than using the ODE numeric solution directly, which requires providing initial conditions, this method estimates a spline function to approximate the dynamic process using smoothing splines. A roughness penalty term is defined using the ODEs, which measures the fidelity of the spline function to the ODEs. The smoothing parameter, which controls the trade-off between fitting the data and maintaining fidelity to the ODEs, can be specified by users or selected objectively by generalized cross validation. The spline coefficients, the ODE random effects, and the ODE fixed effects are estimated in three nested levels of optimization. Two simulation studies show that the proposed method obtains good estimates for mixed-effects ODE models. The semiparametric method is demonstrated with an application of a pharmacokinetic model in a study of HIV combination therapy.     

Optimal location and capability of oil-spill response facilities for the south coast of Newfoundland

The south coast of Newfoundland (Canada) includes both open sea and semi-enclosed waterways which collectively account for over 20,000 vessel movements annually. Every such movement poses the risk of an oil spill which can endanger the fragile marine life and tourism locales in the region, and is a source of concern to the communities. In an effort to analyze the problem, we present a two-stage stochastic programming approach which tackles both the location and stockpile of equipment at the emergency response facilities. The proposed optimization program was tested on realistic data collected from publicly available reports and through personal communications with emergency response personnel. These data were then varied to solve a number of scenarios which account for the stochastic nature of the problem parameters. Although only two response facilities seem to be appropriate for almost all scenarios, the size of equipment stockpile is a function of both the societal disutility factor and the trade-off between environmental cost and facility and equipment acquisition cost.     

Evacuation Risks: A Tentative Approach for Quantification

This study tries to assess the risk of deaths and injuries from motor vehicle accidents associated with an evacuation of population groups in case of nuclear plant accidents. The risk per person–km is evaluated using: (a) data from previous evacuation: information from Soufriere evacuation (Guadeloupe Island 1976) and Mississauga (1979), added to Hans and Sell's data: no road accident occurred for a sample of 1,500,000 persons; (b) national recording system for motor vehicle accident: the rates of 2.2 10 ^-8 deaths per person–km and 32 10^-8 injuries per person–km is calculated as an average. These last rates in France overestimate the number of casualties. A reasonable hypothesis is to assume that the probability of road accident occurrence follows a Poisson distribution, as these events are independent and unfrequent, as no accident was observed in a sample of 1,500,000 persons the probability is between 0 and an upper value of 0.24 10^-8 deaths per person-km and 3.29 10^-8 injuries per person–km. The average and maximum population involved within different radii around French and U.S. Nuclear power sites are taken as a sample size in order to study the total risk of deaths and injuries in the hypothesis of an evacuation being necessary to protect the populations.     

Is Workers' Compensation a Substitute for Unemployment Insurance?

This paper examines how the Workers' Compensation (WC) and Unemployment Insurance (UI) programs interact to influence the duration of claims due to workplace accidents. We use longitudinal WC administrative micro-data on more than 30,000 workers in the Canadian construction industry for the period 1976–1986. For the estimations, we use the Meyer (1990) semi-parametric proportional hazard model. Our results show, in particular, that a reduction in the UI replacement ratio is associated with an increase in the duration of claims due to severe accidents that are difficult to diagnose. Moreover, the duration of spells on WC is much higher when an accident occurs in December, a month which corresponds to the beginning of the lay-off season in the construction sector. This result is consistent with the fact that WC benefits are more generous than UI benefits in Canada.     

PROBLEM SOLVING SELF-APPRAISAL AND COPING EFFORTS IN DISTRESSED AND NONDISTRESSED COUPLES*

The present study sought to investigate the relationship between problem solving self-appraisal (i.e., perceived confidence, personal control, approach-avoidance), specific coping efforts (negotiation, optimistic comparisons, advice seeking, emotional discharge, selective ignoring, and resignation) and marital distress. Seventy-five couples completed the Problem Solving Inventory, the Marital Coping Questionnaire, and the Dyadic Adjustment Scale. When compared to nondistressed spouses, distressed spouses showed less problem solving confidence, a tendency to avoid different problem solving activities, and poor strategies to control their behavior. In addition, three coping efforts-optimistic comparisons, negotiation, and resignation–differentiated distressed from nondistressed spouses. However, the results of multiple regression analysis suggest that specific coping efforts are more important than problem solving self–appraisal in predicting marital satisfaction. These findings are discussed in terms of the role of cognitive factors in marital dysfunction.     

Men's recognition of violence against women and spousal abuse: comparison of three groups of men

Our goal was to assess whether men in the following three groups differ in their ability to recognize and judge the severity of diverse forms of aggressive behavior: (a) men who reported being physically aggressive toward their spouses and who were entering treatment for domestic violence; (b) men who, after participating in a treatment program, were no longer physically violent; and (c) men who reported never having been physically violent towards their spouses (NPV group-non-physically violent). All 81 men in the study reported being verbally aggressive toward their spouses. Men who had been in treatment for spousal abuse and who had not been physically violent toward their spouses since finishing the program were better able than the other two groups to recognize emotionally abusive behaviors.     

"I'm still swimming"

Treatment of bipolar affective disorder is often difficult and lengthy. Enabling participation in a return to work process is equally daunting, primarily due to the dramatic and oftentimes sudden shifts in mood and thought. The following case study attempts to illustrate the complicated process of return to [and stay at] work for an individual who has mixed bipolar affective disorder. Work has always played a significant role in Ray's life and remains a valued goal and accomplishment for Ray. Work has been a means to structure and routine, and it has been from this routine that wellness has become possible for Ray. The metaphor, "I'm still swimming" helps to illustrate the continual treading of water, which both Ray and his occupational therapist [first author] have experienced over the past 6 years. This case study illustrates the strategies employed in maximizing the person-environment-occupation fit for Ray, as well as the importance of collaboration and partnership in the return-to-work process. It is also meant to stimulate thought and discussion about what is important for occupational therapists, and other health professionals to consider, when attempting the task of return-to-work for an individual with mixed bipolar affective disorder.