The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique

A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to the change-point, so it cannot be solved by the method of the traditional linear expectile regression model. For this model, a new estimation method is proposed by a smoothing technique, that is, using Gaussian kernel function to approximate the indicator function in the objective function. It can not only estimate the regression coefficients and change-point location simultaneously, but also have better estimation effect, which compensates for the insufficiency of the previous estimation methods. Under the given regularity conditions, the theoretical proofs of the consistency and asymptotic normality of the proposed estimators are derived. There are two parts of numerical simulations in this paper. Simulation 1 discusses various error distributions at different expectile levels under different conditions, the results show that the mean values of the biases of the estimation method in this paper, and other indicators, are very small, which indicates the robust property of the new method. Simulation 2 considers the symmetric and asymmetric bent lien expectile regression models, the results show that the estimated values of the estimation method in this paper are similar to the true values, which indicates the estimation effect and large sample performance of the proposed method are excellent. In the application research, the method in this paper is applied to the Arctic annual average temperature data and the Nile annual average flow data. The research shows that the standard errors of the estimation method in this paper are very similar to 0, indicating that the parameter estimation accuracy of the new method is very high, and the location of the change-point can be accurately estimated, which further confirms that the new method is effective and feasible.

Confidence intervals for point-of-stabilization of content uniformity

Within the framework of continuous pharmaceutical manufacturing, we are interested in statistical modeling of the initial behavior of the production line. Assuming a gradually changing sequence of a suitable product quality characteristic (e.g., the content uniformity), we estimate the so-called point-of-stabilization (PoSt) and construct corresponding confidence regions based on appropriate asymptotic distributions and bootstrap. We investigate linear, quadratic, and nonlinear gradual change models both in homoscedastic and heteroscedastic setup. We propose a new nonlinear E_max gradual change model and show that it is applicable even if the true model is linear. Asymptotic distribution of the PoSt estimator is known only in a homoscedastic linear and quadratic model and, therefore, bootstrap approximations are used to construct one-sided PoSt confidence intervals.

Effects of expanding a non-contributory health insurance scheme on out-of-pocket healthcare spending by the poor in Turkey

Introduction

Insufficient or no health insurance creates financial access barriers to healthcare services, especially for vulnerable populations. The Green Card scheme, a non-contributory government-funded health insurance scheme for the poor in Turkey, was expanded in 2003–2006 and has provided citizens with extended benefits. We study the effects of this expansion of the Green Card scheme on out-of-pocket healthcare expenditures for low-income households.

Methods

We use difference-in-differences study design to examine the causal impact of having a Green Card on financial protection in terms of out-of-pocket health expenditures and catastrophic expenditures for the poor in Turkey. In addition, we implement quantile regression analysis to examine how the benefits expansion affects the poor who have the largest out-of-pocket expenditures and are in the upper tail of the health spending distribution.

Results

We find that the expansion of benefits coverage leads to significant reductions in annualised out-of-pocket healthcare expenditures for dental care, diagnostics services, pharmaceuticals and total medical spending. We show that the decline in spending by Green Card beneficiaries corresponds to about 33% as per cent of total per-household medical spending. Quantile regression analysis shows that the scheme is even more effective at reducing expenditures for those people facing large health expenditures. The scheme reduces the incidence of catastrophic expenditures by nearly 50% among those with the largest annual out-of-pocket expenditures.

Conclusions

Increasing benefits coverage for a non-contributory insurance programme leads to financial protection for the poor by reducing out-of-pocket and catastrophic health expenditures. It is even more effective at reducing out-of-pocket health spending for those whose health expenditures that lie on the high end of healthcare spending distribution.

Detecting Multiple Change Points Using Adaptive Regression Splines With Application to Neural Recordings

Time series, as frequently the case in neuroscience, are rarely stationary, but often exhibit abrupt changes due to attractor transitions or bifurcations in the dynamical systems producing them. A plethora of methods for detecting such change points in time series statistics have been developed over the years, in addition to test criteria to evaluate their significance. Issues to consider when developing change point analysis methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many changes as contained in potentially high-dimensional time series. Here, a general method called Paired Adaptive Regressors for Cumulative Sum is developed for detecting multiple change points in the mean of multivariate time series. The method's advantages over alternative approaches are demonstrated through a series of simulation experiments. This is followed by a real data application to neural recordings from rat medial prefrontal cortex during learning. Finally, the method's flexibility to incorporate useful features from state-of-the-art change point detection techniques is discussed, along with potential drawbacks and suggestions to remedy them.

Stepwise Signal Extraction via Marginal Likelihood

This paper studies the estimation of stepwise signal. To determine the number and locations of change-points of the stepwise signal, we formulate a maximum marginal likelihood estimator, which can be computed with a quadratic cost using dynamic programming. We carry out extensive investigation on the choice of the prior distribution and study the asymptotic properties of the maximum marginal likelihood estimator. We propose to treat each possible set of change-points equally and adopt an empirical Bayes approach to specify the prior distribution of segment parameters. Detailed simulation study is performed to compare the effectiveness of this method with other existing methods. We demonstrate our method on single-molecule enzyme reaction data and on DNA array CGH data. Our study shows that this method is applicable to a wide range of models and offers appealing results in practice.

COVARIANCE ASSISTED SCREENING AND ESTIMATION

Consider a linear model Y = X β + z, where X = X_n,p and z ~ N(0, I_n ). The vector β is unknown and it is of interest to separate its nonzero coordinates from the zero ones (i.e., variable selection). Motivated by examples in long-memory time series (Fan and Yao, 2003) and the change-point problem (Bhattacharya, 1994), we are primarily interested in the case where the Gram matrix G = X'X is non-sparse but sparsifiable by a finite order linear filter. We focus on the regime where signals are both rare and weak so that successful variable selection is very challenging but is still possible. We approach this problem by a new procedure called the Covariance Assisted Screening and Estimation (CASE). CASE first uses a linear filtering to reduce the original setting to a new regression model where the corresponding Gram (covariance) matrix is sparse. The new covariance matrix induces a sparse graph, which guides us to conduct multivariate screening without visiting all the submodels. By interacting with the signal sparsity, the graph enables us to decompose the original problem into many separated small-size subproblems (if only we know where they are!). Linear filtering also induces a so-called problem of information leakage, which can be overcome by the newly introduced patching technique. Together, these give rise to CASE, which is a two-stage Screen and Clean (Fan and Song, 2010; Wasserman and Roeder, 2009) procedure, where we first identify candidates of these submodels by patching and screening, and then re-examine each candidate to remove false positives. For any procedure β̂ for variable selection, we measure the performance by the minimax Hamming distance between the sign vectors of β̂ and β. We show that in a broad class of situations where the Gram matrix is non-sparse but sparsifiable, CASE achieves the optimal rate of convergence. The results are successfully applied to long-memory time series and the change-point model.

Evolutions in both co-payment and generic market share for common medication in the Belgian reference pricing system

BACKGROUND

In Belgium, a co-insurance system is applied in which patients pay a portion of the cost for medicines, called co-payment. Co-payment is intended to make pharmaceutical consumers more responsible, increase solidarity, and avoid or reduce moral hazards.

OBJECTIVE

Our objective was to study the possible influence of co-payment on sales volume and generic market share in two commonly used medicine groups: cholesterol-lowering medication [statins (HMG-CoA reductase inhibitors) and fibrates] and acid-blocking agents (proton pump inhibitors and histamine H2 receptor antagonists).

METHODS AND DATA

The data were extracted from the Pharmanet database, which covers pharmaceutical consumption in all Belgian ambulatory pharmacies. First, the proportion of sales volume and costs of generic products were modelled over time for the two medicine groups. Second, we investigated the relation between co-payment and contribution by the national insurance agency using change-point linear mixed models.

RESULTS

The change-point analysis suggested several influential events. First, the generic market share in total sales volume was negatively influenced by the abolishment of the distinction in the maximum co-payment level for name brands and generics in 2001. Second, relaxation of the reimbursement conditions for generic omeprazole stimulated generic sales volume in 2004. Finally, an increase in co-payment for generic omeprazole was associated with a significant decrease in omeprazole sales volume in 2005. The observational analysis demonstrated several changes over time. First, the co-payment amounts for name-brand and generic drugs converged in the observed time period for both medicine groups under study. Second, the proportion of co-payment for the total cost of simvastatin and omeprazole increased over time for small packages, and more so for generic than for name-brand products. For omeprazole, both the proportion and the amount of co-payment increased over time. Third, over time the prescription of small packages shifted to an emphasis on larger packages.

CONCLUSIONS

As maximum co-payment levels decreased over time, they overruled the reference pricing system in Belgium. The changes in co-payment share over time also significantly affected sales volume, but whether physicians or patients are the decisive actors on the demand side of pharmaceutical consumption remains unclear.

Statistical models for quantitative bioassay

We discuss various statistical approaches useful in the analysis of nutritional dose-response data with a continuous response. The emphasis is on the multivariate case with several predictors. The methods which will be discussed can be classified into parametric models, including change-point models, and nonparametric models, which rely on smoothing methods such as weighted local linear fitting. The methods will be illustrated with the analysis of data generated from a folate depletion-repletion bioassay experiment conducted on rats, where the measured growth rate of the rate is the response variable. We also discuss the biological conclusions that can be drawn from applying various statistical methods to this data set.