Selection effects of source of contraceptive supply in an analysis of discontinuation of contraception: multilevel modelling when random effects are correlated with an explanatory variable

Summary. Conventional multilevel models assume that the explanatory variables are uncorrelated with the random effects. In some situations, this assumption may be invalid. One such example is the evaluation of a health or social programme that is non-randomly placed and/or in which participation is voluntary. In this case, there may be unobserved factors influencing the placement of the programme and the decision to participate that are correlated with the unobserved factors that influence the outcome of interest. The paper presents an application of a multiprocess multilevel model to assess the difference in rates of discontinuation of contraception between private and Government family planning providers, while accounting for the possibility that there may be unobserved individual and community level factors that influence both a couple's choice of provider and their probability of discontinuation.     

Amplification of Sensitivity Analysis in Matched Observational Studies

A sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed. In matched observational studies of treatment effects, a key assumption in some analyses is that subjects matched for observed covariates are comparable, and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching. What properties would such an unobserved covariate need to have to materially alter the inference about treatment effects? For ease of calculation and reporting, it is convenient that the sensitivity analysis be of low dimension, perhaps indexed by a scalar sensitivity parameter, but for interpretation in specific contexts, a higher dimensional analysis may be of greater relevance. An amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points, perhaps a 'curve,' in a higher dimensional sensitivity analysis such that the possible inferences are the same for all points in the set. Possessing an amplification, an investigator may calculate and report the low dimensional analysis, yet have available the interpretations of the higher dimensional analysis.     

Criteria for surrogate end points based on causal distributions

Summary.  When a treatment has a positive average causal effect (ACE) on an intermediate variable or surrogate end point which in turn has a positive ACE on a true end point, the treatment may have a negative ACE on the true end point due to the presence of unobserved confounders, which is called the surrogate paradox. A criterion for surrogate end points based on ACEs has recently been proposed to avoid the surrogate paradox. For a continuous or ordinal discrete end point, the distributional causal effect (DCE) may be a more appropriate measure for a causal effect than the ACE. We discuss criteria for surrogate end points based on DCEs. We show that commonly used models, such as generalized linear models and Cox's proportional hazard models, can make the sign of the DCE of the treatment on the true end point determinable by the sign of the DCE of the treatment on the surrogate even if the models include unobserved confounders. Furthermore, for a general distribution without any assumption of parametric models, we give a sufficient condition for a distributionally consistent surrogate and prove that it is almost necessary.     

The determinants of price in online auctions: more evidence from unbalanced panel data

This study provides an alternative approach that takes account of the unobserved effects of each seller under a sample selection framework while using online auction data. We use data collected from Yahoo! Kimo Auction (Taiwan) to demonstrate that earlier empirical results of online auction studies may be biased due to violating the assumption of independence of the error terms between sample observations. Empirical findings show that seller reputation is no longer as the most important factor for buyers to bid on items, while the sample data confirm the unobserved heterogeneity of sellers and sample selection problem.     

Bayesian deconvolution of oil well test data using Gaussian processes

We use Bayesian methods to infer an unobserved function that is convolved with a known kernel. Our method is based on the assumption that the function of interest is a Gaussian process and, assuming a particular correlation structure, the resulting convolution is also a Gaussian process. This fact is used to obtain inferences regarding the unobserved process, effectively providing a deconvolution method. We apply the methodology to the problem of estimating the parameters of an oil reservoir from well-test pressure data. Here, the unknown process describes the structure of the well. Applications to data from Mexican oil wells show very accurate results.     

Binary discrete choice under asymmetric restrictions

A crucial assumption of discrete choice models requires that observed individual behavior is a direct function of unobserved individual utility maximization. There are situations, however, where observed behavior is ambiguous with respect to maximum utility. This is the case, when individual utility maximization is hampered by global restrictions of action. Typically, such restrictions are tied to particular decision alternatives, which causes an asymmetric influencing on individual behavior. The existence of global asymmetric restrictions upon individual behavior can be treated as a second unobserved variable. This leads to two separate models, which have to be estimated simultaneously: a decision model on the one hand and a restriction model on the other. The standard decision model arises as a special case with a zero restriction probability. McKelvey/Zavoina's PseudoR ² can be employed as a straightforward evaluation of the goodness-of-fit. Neglecting the presence of asymmetric restrictions or considering them as symmetric effects leads to biased estimators. This is discussed in a formal manner and demonstrated by means of a simulation study. The bias may occur in either direction. It is not only restricted to the model parameters themselves, but also to their standard errors. To avoid such bias, it seems advisable to use the extended model if ever possible and test for a zero restriction probability. I wish to thank Reinhard Hujer, Jo Grammig, Matthias Lob, Notburga Ott, Reinhold Schnabel and an anonymous referee for helpful comments on earlier drafts of this paper.     

Seasonal Adjustment of Time Series Using One-Sided Filters

This article presents a model-based signal extraction seasonal adjustment procedure to extract estimates of the independent unobserved seasonal and nonseasonal components from an observed time series. The decomposition yields a one-sided filter that is optimal for adjusting the most recent observation under the assumption of using only the past observed series. Some advantages of this procedure are that no forecasts are required for implementation and there are no problems of revision of estimates or questions of concurrent adjustment. Comparisons are made with existing procedures using two-sided filters.     

A Stepwise Confidence Interval Procedure Under Unknown Variances Based on an Asymmetric Loss Function for Toxicological Evaluation

One of the most important issues in toxicity studies is the identification of the equivalence of treatments with a placebo. Because it is unacceptable to declare non‐equivalent treatments to be equivalent, it is important to adopt a reliable statistical method to properly control the family‐wise error rate (FWER). In dealing with this issue, it is important to keep in mind that overestimating toxicity equivalence is a more serious error than underestimating toxicity equivalence. Consequently asymmetric loss functions are more appropriate than symmetric loss functions. Recently Tao, Tang & Shi (2010) developed a new procedure based on an asymmetric loss function. However, their procedure is somewhat unsatisfactory because it assumes that the variances of various dose levels are known. This assumption is restrictive for some applications. In this study we propose an improved approach based on asymmetric confidence intervals without the restrictive assumption of known variances. The asymmetry guarantees reliability in the sense that the FWER is well controlled. Although our procedure is developed assuming that the variances of various dose levels are unknown but equal, simulation studies show that our procedure still performs quite well when the variances are unequal.     

Welfare gains of the poor: An endogenous Bayesian approach with spatial random effects

We introduce a Bayesian instrumental variable procedure with spatial random effects that handles endogeneity, and spatial dependence with unobserved heterogeneity. We find through a limited Monte Carlo experiment that our proposal works well in terms of point estimates and prediction. We apply our method to analyze the welfare effects generated by a process of electricity tariff unification on the poorest households. In particular, we deduce an Equivalent Variation measure where there is a budget constraint for a two-tiered pricing scheme, and find that 10% of the poorest municipalities attained welfare gains above 2% of their initial income.     

An Approach of Stocks Substitution Strategy Using Fuzzy Interval Correlation Coefficient

The classical Pearson's correlation coefficient has been widely adopted in various fields of application. However, when the data are composed of fuzzy interval values, it is not feasible to use such a traditional approach to evaluate the correlation coefficient. In this study, we propose the specific calculation of fuzzy interval correlation coefficient with fuzzy interval data to measure the relationship between various stocks. As such, the study is able to offer an improving measure of investment strategy for stocks substitution via the analysis of the fuzzy interval correlation. In addition, we use empirical studies to verify the validity of our proposal on fuzzy interval correlation coefficient using data from companies in electric machinery and plastic sectors in Taiwan.     

Estimation of Main Effect When Covariates Have Non-Proportional Hazards

The Cox proportional hazards (PH) regression model has been widely used to analyze survival data in clinical trials and observational studies. In addition to estimating the main treatment or exposure group effect, it is common to adjust for additional covariates using the Cox model. It is well known that violation of the PH assumption can lead to estimates that are biased and difficult to interpret, and model checking has become a routine procedure. However, such checking might focus on the primary group comparisons, and the assumption can still be violated when adjusting for many of the potential covariates. We study the effect of violation of the PH assumption of the covariates on the estimation of the main group effect in the Cox model. The results are summarized in terms of the bias and the coverage properties of the confidence intervals. Overall in randomized clinical trials, the bias caused by misspecifying the PH assumption on the covariates is no more than 15% in absolute value regardless of sample size. In observational studies where the covariates are likely correlated with the group variable, however, the bias can be very severe. The coverage properties largely depend on sample size, as expected, as bias becomes dominating with increasing sample size. These findings should serve as cautionary notes when adjusting for potential confounders in observational studies, as the violation of PH assumption on the confounders can lead to erroneous results.     

An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data

Several survival regression models have been developed to assess the effects of covariates on failure times. In various settings, including surveys, clinical trials and epidemiological studies, missing data may often occur due to incomplete covariate data. Most existing methods for lifetime data are based on the assumption of missing at random (MAR) covariates. However, in many substantive applications, it is important to assess the sensitivity of key model inferences to the MAR assumption. The index of sensitivity to non-ignorability (ISNI) is a local sensitivity tool to measure the potential sensitivity of key model parameters to small departures from the ignorability assumption, needless of estimating a complicated non-ignorable model. We extend this sensitivity index to evaluate the impact of a covariate that is potentially missing, not at random in survival analysis, using parametric survival models. The approach will be applied to investigate the impact of missing tumor grade on post-surgical mortality outcomes in individuals with pancreas-head cancer in the Surveillance, Epidemiology, and End Results data set. For patients suffering from cancer, tumor grade is an important risk factor. Many individuals in these data with pancreas-head cancer have missing tumor grade information. Our ISNI analysis shows that the magnitude of effect for most covariates (with significant effect on the survival time distribution), specifically surgery and tumor grade as some important risk factors in cancer studies, highly depends on the missing mechanism assumption of the tumor grade. Also a simulation study is conducted to evaluate the performance of the proposed index in detecting sensitivity of key model parameters.     

盈余质量对自愿性信息披露的影响及作用机理

自愿性信息披露是管理层对外传递公司价值,缓解信息不对称的重要手段,是强制性财务报告的有益补充。财务报告的盈余信息不但通过契约制定约束了管理层行为,其盈余质量也反映了管理层可信度并影响自愿披露的估值作用,这些都会影响公司自愿披露行为。本文以上市公司自愿披露的前瞻性信息为对象,分析了盈余质量对自愿性信息披露的影响及作用机理。实证结果证实了盈余质量对自愿性信息披露有契约作用和鉴证作用;契约作用表现为盈余质量可通过降低代理成本提高自愿披露水平;而鉴证作用体现在盈余质量为自愿披露信息提供了可鉴证性保障,提高了公司价值与自愿披露水平的相关性。     

Job Durations With Worker- and Firm-Specific Effects: MCMC Estimation With Longitudinal Employer–Employee Data

We study job durations using a multivariate hazard model allowing for worker-specific and firm-specific unobserved determinants. The latter are captured by unobserved heterogeneity terms or random effects, one at the firm level and another at the worker level. This enables us to decompose the variation in job durations into the relative contribution of the worker and the firm. We also allow the unobserved terms to be correlated in a model that is primarily relevant for markets with small firms. For the empirical analysis, we use a Portuguese longitudinal matched employer–employee dataset. The model is estimated with a Bayesian Markov chain Monte Carlo (MCMC) estimation method. The results imply that unobserved firm characteristics explain almost 40% of the systematic variation in log job durations. In addition, we find a positive correlation between unobserved worker and firm characteristics.     

Copula regression spline models for binary outcomes

We introduce a framework for estimating the effect that a binary treatment has on a binary outcome in the presence of unobserved confounding. The methodology is applied to a case study which uses data from the Medical Expenditure Panel Survey and whose aim is to estimate the effect of private health insurance on health care utilization. Unobserved confounding arises when variables which are associated with both treatment and outcome are not available (in economics this issue is known as endogeneity). Also, treatment and outcome may exhibit a dependence which cannot be modeled using a linear measure of association, and observed confounders may have a non-linear impact on the treatment and outcome variables. The problem of unobserved confounding is addressed using a two-equation structural latent variable framework, where one equation essentially describes a binary outcome as a function of a binary treatment whereas the other equation determines whether the treatment is received. Non-linear dependence between treatment and outcome is dealt using copula functions, whereas covariate-response relationships are flexibly modeled using a spline approach. Related model fitting and inferential procedures are developed, and asymptotic arguments presented.     

Using quantile averages in matched observational studies

In two observational studies, one investigating the effects of minimum wage laws on employment and the other of the effects of exposures to lead, an estimated treatment effect's sensitivity to hidden bias is examined. The estimate uses the combined quantile averages that were introduced in 1981 by B. M. Brown as simple, efficient, robust estimates of location admitting both exact and approximate confidence intervals and significance tests. Closely related to Gastwirth's estimate and Tukey's trimean, the combined quantile average has asymptotic efficiency for normal data that is comparable with that of a 15% trimmed mean, and higher efficiency than the trimean, but it has resistance to extreme observations or breakdown comparable with that of the trimean and better than the 15% trimmed mean. Combined quantile averages provide consistent estimates of an additive treatment effect in a matched randomized experiment. Sensitivity analyses are discussed for combined quantile averages when used in a matched observational study in which treatments are not randomly assigned. In a sensitivity analysis in an observational study, subjects are assumed to differ with respect to an unobserved covariate that was not adequately controlled by the matching, so that treatments are assigned within pairs with probabilities that are unequal and unknown. The sensitivity analysis proposed here uses significance levels, point estimates and confidence intervals based on combined quantile averages and examines how these inferences change under a range of assumptions about biases due to an unobserved covariate. The procedures are applied in the studies of minimum wage laws and exposures to lead. The first example is also used to illustrate sensitivity analysis with an instrumental variable.     

Effects of unmeasured heterogeneity in the linear transformation model for censored data

We investigate the effect of unobserved heterogeneity in the context of the linear transformation model for censored survival data in the clinical trials setting. The unobserved heterogeneity is represented by a frailty term, with unknown distribution, in the linear transformation model. The bias of the estimate under the assumption of no unobserved heterogeneity when it truly is present is obtained. We also derive the asymptotic relative efficiency of the estimate of treatment effect under the incorrect assumption of no unobserved heterogeneity. Additionally we investigate the loss of power for clinical trials that are designed assuming the model without frailty when, in fact, the model with frailty is true. Numerical studies under a proportional odds model show that the loss of efficiency and the loss of power can be substantial when the heterogeneity, as embodied by a frailty, is ignored. An erratum to this article can be found at     

Maximum likeihood estimation of an intraclass correlation in a bivariate normal distribution with missing observations

The maximum likeihood estimate is considered for an intraclass correlation coefficent in a bivariate normal distribution when some observations on either of the varibles are missuing. The estimate is given as the soulution of a polynomial equation of degree seven. An approximate confidence interval and a test procedure for the intraclass correlation are constricted based on an asymptotic variance stabilizing transformation of the resulting estimator. The distributional results are also considered under violation of the normality assumption. A Monte Carlo study was performed to examine the finite sample properties of the maximum likelihood estimator and to evaluate the proposed procedures for hypotheses testing and interval estimation.     

The internal relocation premium: are migrants positively or negatively selected? Evidence from Italy

This paper analyzes the wage returns from internal migration for recent graduates in Italy. We employ a switching regression model that accounts for the endogeneity of the individual's choice to relocate to get a job after graduation: the omission of this selection decision can lead to biased estimates, as there is potential correlation between earnings and unobserved traits, exerting an influence on the decision to migrate. The empirical results sustain the appropriateness of the estimation technique and show that there is a significant pay gap between migrants and non-migrants; migrants seem to be positively selected and the migration premium is downward biased through OLS estimates. The endogeneity of migration shows up both as a negative intercept effect and as a positive slope effect, the second being larger than the first: bad knowledge of the local labor market and financial constraints lead migrants to accept a low basic wage but, due to relevant returns to their characteristics, they finally obtain a higher wage than the others.     

Finding the best treatment under heavy censoring and hidden bias

Summary.  We analyse male survival duration after hospitalization following an acute myocardial infarction with a large ( N =11024) Finnish data set to find the best performing hospital district (and to disseminate its treatment protocol). This is a multiple-treatment problem with 21 treatments (i.e. 21 hospital districts). The task of choosing the best treatment is difficult owing to heavy right censoring (73%), which makes the usual location measures (the mean and median) unidentified; instead, only lower quantiles are identified. There is also a sample selection issue that only those who made it to a hospital alive are observed (54%); this becomes a problem if we wish to know their potential survival duration after hospitalization, if they had survived to a hospital contrary to the fact. The data set is limited in its covariates—only age is available—but includes the distance to the hospital, which plays an interesting role. Given that only age and distance are observed, it is likely that there are unobserved confounders. To account for them, a sensitivity analysis is conducted following pair matching. All estimators employed point to a clear winner and the sensitivity analysis indicates that the finding is fairly robust.