A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator.

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role.

Performance evaluation in Bayesian adaptive randomization

Bayesian adaptive randomization (BAR) is an attractive approach to allocate more patients to the putatively superior arm based on the interim data while maintains good statistical properties attributed to randomization. Under this approach, patients are adaptively assigned to a treatment group based on the probability that the treatment is better. The basic randomization scheme can be modified by introducing a tuning parameter, replacing the posterior estimated response probability, setting a boundary to randomization probabilities. Under randomization settings comprised of the above modifications, operating characteristics, including type I error, power, sample size, imbalance of sample size, interim success rate, and overall success rate, were evaluated through simulation. All randomization settings have low and comparable type I errors. Increasing tuning parameter decreases power, but increases imbalance of sample size and interim success rate. Compared with settings using the posterior probability, settings using the estimated response rates have higher power and overall success rate, but less imbalance of sample size and lower interim success rate. Bounded settings have higher power but less imbalance of sample size than unbounded settings. All settings have better performance in the Bayesian design than in the frequentist design. This simulation study provided practical guidance on the choice of how to implement the adaptive design. ^

Effect of primary care availability and health insurance coverage on risk and cost of Preventable Hospitalizations in Harris County

Preventable Hospitalizations (PHs) are hospitalizations that can be avoided with appropriate and timely care in the ambulatory setting and hence are closely associated with primary care access in a community. Increased primary care availability and health insurance coverage may increase primary care access, and consequently may be significantly associated with risks and costs of PHs. Objective. To estimate the risk and cost of preventable hospitalizations (PHs); to determine the association of primary care availability and health insurance coverage with the risk and costs of PHs, first alone and then simultaneously; and finally, to estimate the impact of expansions in primary care availability and health insurance coverage on the burden of PHs among non-elderly adult residents of Harris County. Methods. The study population was residents of Harris County, age 18 to 64, who had at least one hospital discharge in a Texas hospital in 2008. The primary independent variables were availability of primary care physicians, availability of primary care safety net clinics and health insurance coverage. The primary dependent variables were PHs and associated hospitalization costs. The Texas Health Care Information Collection (THCIC) Inpatient Discharge data was used to obtain information on the number and costs of PHs in the study population. Risk of PHs in the study population, as well as average and total costs of PHs were calculated. Multivariable logistic regression models and two-step Heckman regression models with log-transformed costs were used to determine the association of primary care availability and health insurance coverage with the risk and costs of PHs respectively, while controlling for individual predisposing, enabling and need characteristics. Predicted PH risk and cost were used to calculate the predicted burden of PHs in the study population and the impact of expansions in primary care availability and health insurance coverage on the predicted burden. Results. In 2008, hospitalized non-elderly adults in Harris County had 11,313 PHs and a corresponding PH risk of 8.02%. Congestive heart failure was the most common PH. PHs imposed a total economic burden of $84 billion at an average of $7,449 per PH. Higher primary care safety net availability was significantly associated with the lower risk of PHs in the final risk model, but only in the uninsured. A unit increase in safety net availability led to a 23% decline in PH odds in the uninsured, compared to only a 4% decline in the insured. Higher primary care physician availability was associated with increased PH costs in the final cost model (β=0.0020; p<0.05). Lack of health insurance coverage increased the risk of PH, with the uninsured having 30% higher odds of PHs (OR=1.299; p<0.05), but reduced the cost of a PH by 7% (β=-0.0668; p<0.05). Expansions in primary care availability and health insurance coverage were associated with a reduction of about $1.6 million in PH burden at the highest level of expansion. Conclusions. Availability of primary care resources and health insurance coverage in hospitalized non-elderly adults in Harris County are significantly associated with the risk and costs of PHs. Expansions in these primary care access factors can be expected to produce significant reductions in the burden of PHs in Harris County.^

A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^