Wald Test Statistics Research Articles

RNASeqDesign: A framework for RNA-Seq genome-wide power calculation and study design issues.

Massively parallel sequencing (a.k.a. next-generation sequencing, NGS) technology has emerged as a powerful tool in characterizing genomic profiles. Among many NGS applications, RNA sequencing (RNA-Seq) has gradually become a standard tool for global transcriptomic monitoring. Although the cost of NGS experiments has dropped constantly, the high sequencing cost and bioinformatic complexity are still obstacles for many biomedical projects. Unlike earlier fluorescence-based technologies such as microarray, modelling of NGS data should consider discrete count data. In addition to sample size, sequencing depth also directly relates to the experimental cost. Consequently, given total budget and pre-specified unit experimental cost, the study design issue in RNA-Seq is conceptually a more complex multi-dimensional constrained optimization problem rather than one-dimensional sample size calculation in traditional hypothesis setting. In this paper, we propose a statistical framework, namely "RNASeqDesign", to utilize pilot data for power calculation and study design of RNA-Seq experiments. The approach is based on mixture model fitting of p-value distribution from pilot data and a parametric bootstrap procedure based on approximated Wald test statistics to infer genome-wide power for optimal sample size and sequencing depth. We further illustrate five practical study design tasks for practitioners. We perform simulations and three real applications to evaluate the performance and compare to existing methods.

Risk Assessment of Acute, All-Cause 30-Day Readmission in Patients Aged 65+: a Nationwide, Register-Based Cohort Study.

Hospital readmission is considered an adverse health outcome in older people, adding additional pressure on clinical resources within health care services. Despite numerous studies on risk factors for readmissions, studies find different strengths of respective determinants and there is a need to explore and identify patterns of risk factors in larger cohorts. Exploring and identifying patterns of risk factors for acute, all-cause 30-day readmission in a Danish cohort of patients aged 65+. Register-based cohort study using individual-level linkable information on demographics, social determinants, clinical conditions, health care utilization, and provider determinants obtained from primary and secondary health care. Historic cohort of 1,267,752 admissions in 479,854 patients, aged 65+, discharged from Danish public hospitals from January 2007 to September 2010. We included patient-level variables and admission-level variables. Outcome was acute, all-cause 30-day readmission. Data was analyzed by univariable and multivariable logistic regression. Strength of associations was analyzed using Wald test statistics. Receiver operating characteristic (ROC) analysis was used for quantification of predictive ability. For validation, we used split-sample design. Acute admission and number of days since previous hospital discharge were factors strongly associated with readmission. Patients at risk of future readmission suffered from comorbidity, consumed more drugs, and were frequent users of in- and outpatient health care services in the year prior to the index admission. Factors related to index admission were only weakly associated with readmission. The predictive ability was 0.709 (0.707-0.711) for acute readmission. In a general population of older people, we found that pre-hospital factors rather than hospital factors account for increased risk of readmission and are dominant contributors to predict acute all-cause 30-day readmission. Therefore, risk for excess readmission should be shared across sectors and focus the care trajectory over time rather than distinct care episodes.

Gender perspective on life insurance demand in Ghana

Purpose Against the background that Ghanaians seldom purchase insurance policies, the purpose of this paper is to investigate the determinants of life insurance uptake among male and female household heads in Ghana. Design/methodology/approach The study employs data on 775 male and 233 female household heads from the sixth round of the Ghana Living Standards Survey. Adjusted Wald test statistics and logistic regressions are employed for the empirical estimations. Findings Results from the adjusted Wald test show that the sampled male household heads significantly differ from their female counterparts in terms of the selected socioeconomic and demographic characteristics. Though ill health status, higher wealth, being self-employed or in wage or salaried employment and residing in either of the three northern regions (upper east, upper west and northern regions) in Ghana broadly affect the demand for life insurance among both male and female heads, other factors are peculiar to either parties. Particularly, whereas female heads who are married and those with more dependants have a higher propensity of purchasing life insurance policies, their male counterparts with higher education are more likely to buy life insurance policies. Research limitations/implications The paper adds to the paucity of cross-sectional studies on life insurance demand in Africa. Practical implications Based on the explored determinants, insurers could better regulate the purchase of their products by taking into consideration the gender differences to maximize their sales and enhance economic growth and development. Originality/value This paper explores the gender dynamics in the determinants of life insurance demand in a developing country, Ghana. Besides, findings from related literature are reported to be mixed. Though the current paper is not wholly nationally representative, it utilizes data from across all the ten administrative regions of Ghana. To the best of the authors’ knowledge, no prior study has been conducted in this manner.

The Intervening Influence of Economic Growth on Fiscal Policy Stance and Public Expenditure in Kenya

This paper investigates the intervening influence of economic growth on the relationship between fiscal policy stance and public expenditure in Kenya from 1964 to 2015 using a Vector Error Correction Model. The results indicate that economic growth has an intervening influence on the relationship between fiscal policy stance and public expenditure in Kenya. The findings further show that fiscal policy, economic growth and public expenditure are cointegrated using the Johansen test and the bound test but there is no short-run causality between the variables as indicated by the Wald test statistics. The findings suggest that economic growth explains the extent to which fiscal policy stance affects the level of public expenditure in Kenya even though fiscal policy stance has a negative relationship with public expenditure.

Fiscal Policy Stance and Public Expenditure in Kenya

This paper investigates the relationship between fiscal policy stance and public expenditure in Kenya from 1964 to 2015 using a Vector Error Correction Model. The results indicate that there is a negative relationship between fiscal policy stance and public expenditure. The findings further indicate that fiscal policy and public expenditure are cointegrated using the Johansen test and the bound test but there is no short-run causality between the variables as indicated by the Wald test statistics. This means that fiscal policy stance does not have a strong direct effect on public expenditure as supported by the theory of fiscal policy that policy makers could have a lower incentive to pursue public interests as compared to their personal interests.

Power and sample size calculation incorporating misspecifications of the variance function in comparative clinical trials with over-dispersed count data.

Over-dispersed count data are frequently observed in clinical trials where the primary endpoint is occurrence of clinical events. Sample sizes of comparative clinical trials with these data are typically calculated under negative binomial models or quasi-Poisson models with specified variance functions, or under the assumption that the specified "working" variance functions are correctly specified. In this article, we propose a sample size formula anticipating misspecifications of the working variance function. We derived a method based on the asymptotic distribution of a Wald test statistic with a sandwich-type robust variance estimator under quasi-Poisson models. Under misspecifications of the working variance function, the asymptotic variance of the estimator of the treatment effect is expressed as a form involving both true and working variance functions. Our sample size formula includes several existing formulas as special cases when the working variance function is correctly specified as the true variance function. We also consider a sensitivity analysis for possible misspecifications of the "true" variance function when estimating sample sizes using our formula. A simulation study demonstrated the adequacy of our formulas in finite sample size settings. An application to a clinical trial to evaluate the treatment effect on prevention of COPD exacerbation is provided.

Muscle-strengthening and aerobic activities and mortality among 3+ year cancer survivors in the U.S.

This study examined the association between adherence to American College of Sports Medicine and American Cancer Society guidelines on aerobic and muscle-strengthening activities and mortality risks among 3+ year cancer survivors in the U.S. The observational study was based on 1999-2009 National Health Interview Survey Linked Mortality Files with follow-up through 2011. After applying exclusion criteria, there were 13,997 observations. The hazard ratios (HRs) for meeting recommendations on muscle-strengthening activities only, on aerobic activities only, and on both types of physical activity (i.e., adhering to complete guidelines) were calculated using a reference group of cancer survivors engaging in neither. Unadjusted and adjusted HRs of all-cause, cancer-specific, and cardiovascular disease-specific mortalities were estimated using Cox proportional hazards models. In all models, compared to the reference group, cancer survivors adhering to complete guidelines had significantly decreased all-cause, cancer-specific, and cardiovascular disease-specific mortalities (HRs ranged from 0.37 to 0.64, p's < 0.05). There were no statistically significant differences between hazard rates of cancer survivors engaging in recommended levels of muscle-strengthening activities only and the reference group (HRs ranged from 0.76 to 0.94, p's > 0.05). Wald test statistics suggested a significant dose-response relationship between levels of adherence to complete guidelines and cancer-specific mortality. While muscle-strengthening activities by themselves do not appear to reduce mortality risks, such activities may provide added cancer-specific survival benefits to 3+ year cancer survivors who are already aerobically active.

Composite Likelihood Methods Based on Minimum Density Power Divergence Estimator.

In this paper, a robust version of the Wald test statistic for composite likelihood is considered by using the composite minimum density power divergence estimator instead of the composite maximum likelihood estimator. This new family of test statistics will be called Wald-type test statistics. The problem of testing a simple and a composite null hypothesis is considered, and the robustness is studied on the basis of a simulation study. The composite minimum density power divergence estimator is also introduced, and its asymptotic properties are studied.

New methods of testing nonlinear hypothesis using iterative NLLS estimator

This research paper discusses the method of testing nonlinear hypothesis using iterative Nonlinear Least Squares (NLLS) estimator. Takeshi Amemiya [1] explained this method. However in the present research paper, a modified Wald test statistic due to Engle, Robert [6] is proposed to test the nonlinear hypothesis using iterative NLLS estimator. An alternative method for testing nonlinear hypothesis using iterative NLLS estimator based on nonlinear hypothesis using iterative NLLS estimator based on nonlinear studentized residuals has been proposed. In this research article an innovative method of testing nonlinear hypothesis using iterative restricted NLLS estimator is derived. Pesaran and Deaton [10] explained the methods of testing nonlinear hypothesis. This paper uses asymptotic properties of nonlinear least squares estimator proposed by Jenrich [8]. The main purpose of this paper is to provide very innovative methods of testing nonlinear hypothesis using iterative NLLS estimator, iterative NLLS estimator based on nonlinear studentized residuals and iterative restricted NLLS estimator. Eakambaram et al. [12] discussed least absolute deviation estimations versus nonlinear regression model with heteroscedastic errors and also they studied the problem of heteroscedasticity with reference to nonlinear regression models with suitable illustration. William Grene [13] examined the interaction effect in nonlinear models disused by Ai and Norton [14] and suggested ways to examine the effects that do not involve statistical testing. Peter [15] provided guidelines for identifying composite hypothesis and addressing the probability of false rejection for multiple hypotheses.

DIRECTIONALLY DIFFERENTIABLE ECONOMETRIC MODELS

The current article examines the limit distribution of the quasi-maximum likelihood estimator obtained from a directionally differentiable quasi-likelihood function and represents its limit distribution as a functional of a Gaussian stochastic process indexed by direction. In this way, the standard analysis that assumes a differentiable quasi-likelihood function is treated as a special case of our analysis. We also examine and redefine the standard quasi-likelihood ratio, Wald, and Lagrange multiplier test statistics so that their null limit behaviors are regular under our model framework.

Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component

AbstractThis paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu () and is based on a Feasible Generalized Least Squares procedure that uses a super‐efficient estimator of the sum of the autoregressive coefficients α when α = 1. The resulting Wald test statistic asymptotically follows a chi‐square distribution in both the I(0) and I(1) cases. To improve the finite sample properties of the test, we use a bias‐corrected version of the OLS estimator of α proposed by Roy and Fuller (). We show that our procedure is substantially more powerful than currently available alternatives. We illustrate the usefulness of our method via an application to modelling the trend of global and hemispheric temperatures.

Abstract P4-12-01: Independent validation of EarlyR gene signature in BIG 1-98: A randomized, double-blind, phase III trial comparing letrozole and tamoxifen as adjuvant endocrine therapy for postmenopausal women with hormone receptor-positive, early breast cancer

Abstract Background: EarlyR is a prognostic gene signature score in ER+ breast cancer (BC) computed from the expression values of ESPL1, SPAG5, MKI67, PLK1 and PGR using a novel algorithm. EarlyR has been validated in multiple cohorts profiled on Affymetrix and Illumina microarrays. This study sought to verify prognostic features of EarlyR in a cohort of BIG 1-98. Patients and Methods: Illumina DASL assay was used to measure gene expression in FFPE tissue of primary BC from a case-cohort sampling subset of postmenopausal women in BIG 1-98 treated with adjuvant endocrine therapy (letrozole or tamoxifen). Chemotherapy treatment was at the discretion of individual physicians and patients. Among the 1218 patients centrally reviewed with sufficient RNA material for the DASL assay, 1174 with ER+ status and assessed for EarlyR are included in the analytic cohort. EarlyR scores and pre-specified risk strata (≤25=low, 26-75=intermediate, &amp;gt;75=high) were computed, while blinded to clinical data. The analysis endpoints included distant recurrence free interval (DRFI) defined as time from randomization to BC recurrence at a distant site within 8 years and BC free-interval (BCFI) defined as time from randomization to first invasive BC recurrence at a local, regional or distant site or invasive contralateral BC within 8 years. Weighted proportional hazards models (univariate and multivariate, stratified by treatment assignment) were used to adjust for Kaplan-Meier, hazard ratio estimates and Wald test statistics to obtain unbiased analyses and to give consistent estimates. Results: The distribution of the EarlyR risk groups was 67% low, 19% intermediate and 14% high risk in this ER+ cohort. EarlyR was prognostic for 8-year DRFI (P-trend=0.008). Patients with high EarlyR risk score (&amp;gt;75) had significantly increased risk of distant recurrence within 8 years (univariate HR=1.73, 95%CI: 1.14-2.64) compared to low EarlyR risk group (≤25). The estimated 8-year DRFI (95%CI) is 84%(80%-88%) for high risk vs. 91%( 89%-92%) for low risk, corresponding to an absolute DRFI risk reduction of 7% (low vs high). EarlyR is also prognostic of 8-year BCFI in ER+ (P-trend=0.002) with the estimated 8-year BCFI (95%CI) 79%(75%-84%) for high risk vs. 88%( 86%-89%) for low risk. Consistent results were observed in ER+, HER2- (P-trend=0.01 for DRFI, P-trend=0.004 for BCFI), in ER+, LN- (P-trend=0.05 for DRFI, P-trend=0.03 for BCFI) and ER+, LN+ (P-trend=0.08 for DRFI, P-trend=0.03 for BCFI) subsets. Conclusions: This study confirmed the prognostic significance of EarlyR using FFPE tissue from the BIG 1-98 trial. In analyses of all ER+ patients and subsets LN-, LN+ and HER2-, EarlyR classifies 65%-70% of patients as low risk, 11-16% as high risk, and &amp;lt; 20% as intermediate risk. In these subsets, the size of the low risk group is larger and the size of the intermediate risk group is smaller than those reported for commercially available signatures. EarlyR identifies a set of high-risk patients with relatively poor prognosis who may be considered for additional treatment. The clinical utility of EarlyR requires further study. Citation Format: Buechler S, Gray KP, Gökmen-Polar Y, Willis S, Thürlimann B, Kammler R, Leyland-Jones B, Badve SS, Regan MM. Independent validation of EarlyR gene signature in BIG 1-98: A randomized, double-blind, phase III trial comparing letrozole and tamoxifen as adjuvant endocrine therapy for postmenopausal women with hormone receptor-positive, early breast cancer [abstract]. In: Proceedings of the 2016 San Antonio Breast Cancer Symposium; 2016 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2017;77(4 Suppl):Abstract nr P4-12-01.

Self-weighted LAD-based inference for heavy-tailed threshold autoregressive models

The least squares estimator of the threshold autoregressive (TAR) model may not be consistent when its tail is less than or equal to 2. Neither theory nor methodology can be applied to model fitting in this case. This paper is to develop a systematic procedure of statistical inference for the heavy-tailed TAR model. We first investigate the self-weighted least absolute deviation estimation for the model. It is shown that the estimated slope parameters are n-consistent and asymptotically normal, and the estimated thresholds are n-consistent, each of which converges weakly to the smallest minimizer of a compound Poisson process. Based on this theory, the Wald test statistic is considered for testing the linear restriction of slope parameters and a procedure is given for inference of threshold parameters. We finally construct a sign-based portmanteau test for model checking. Simulations are carried out to assess the performance of our procedure and a real example is given.

A Wald-type test statistic for testing linear hypothesis in logistic regression models based on minimum density power divergence estimator

In this paper a robust version of the classical Wald test statistics for linear hypothesis in the logistic regression model is introduced and its properties are explored. We study the problem under the assumption of random covariates although some ideas with non random covariates are also considered. The family of tests considered is based on the minimum density power divergence estimator instead of the maximum likelihood estimator and it is referred to as the Wald-type test statistic in the paper. We obtain the asymptotic distribution and also study the robustness properties of the Wald type test statistic. The robustness of the tests is investigated theoretically through the influence function analysis as well as suitable practical examples. It is theoretically established that the level as well as the power of the Wald-type tests are stable against contamination, while the classical Wald type test breaks down in this scenario. Some classical examples are presented which numerically substantiate the theory developed. Finally a simulation study is included to provide further confirmation of the validity of the theoretical results established in the paper.

Wald tests for variance-adjusted equivalence assessment with normal endpoints

ABSTRACTEquivalence tests may be tested with mean difference against a margin adjusted for variance. The justification of using variance adjusted non-inferiority or equivalence margin is for the consideration that a larger margin should be used with large measurement variability. However, under the null hypothesis, the test statistic does not follow a t-distribution or any well-known distribution even when the measurement is normally distributed. In this study, we investigate asymptotic tests for testing the equivalence hypothesis. We apply the Wald test statistic and construct three Wald tests that differ in their estimates of variances. These estimates of variances include the maximum likelihood estimate (MLE), the uniformly minimum variance unbiased estimate (UMVUE), and the constrained maximum likelihood estimate (CMLE). We evaluate the performance of these three tests in terms of type I error rate control and power using simulations under a variety of settings. Our empirical results show that the asymptotic normalized tests are conservative in most settings, while the Wald tests based on ML- and UMVU-method could produce inflated significance levels when group sizes are unequal. However, the Wald test based on CML-method provides an improvement in power over the other two Wald tests for medium and small sample size studies.

New Approaches in Monitoring Multivariate Categorical Processes based on Contingency Tables in Phase II

In some statistical process control (SPC) applications, quality of a process or product is characterized by contingency table. Contingency tables describe the relation between two or more categorical quality characteristics. In this paper, two new control charts based on the WALD and Stuart score test statistics are designed for monitoring of contingency table‐based processes in Phase‐II. The performances of the proposed control charts are compared with the generalized linear test (GLT) control chart proposed in the literature. The results show the better performance of the proposed control charts under small and moderate shifts. Moreover, new schemes are proposed to diagnose which cell corresponding to different levels of categorical variables is responsible for out‐of‐control signal. In addition, we propose EWMA–WALD and EWMA–Stuart score test control charts to improve the performance of Shewhart‐based control charts in detecting small and moderate shifts in contingency table parameters. Meanwhile, we compare the performances of two proposed EWMA‐based control charts with the ones of three existing control charts called EWMA–GLT, EWMA–GLRT and an EWMA‐type control chart for multivariate binomial/multinomial processes along with the ones of the corresponding Shewhart‐based control charts. A numerical example is given to show the efficiency of the proposed methods. Finally, the effect of parameter estimation in Phase I based on m historical contingency table on the performance of the Shewhart‐based control charts is studied. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model

In this paper we consider the capital asset pricing model under the multivariate normal distribution for modeling asset returns. We develop and implement local influence diagnostic techniques not based on likelihood displacement. The main interest is to consider the test of mean–variance efficiency of a given portfolio as objective function. Sensitivity of maximum likelihood estimators of slopes is also considered. For this purpose, first and second-order local influence measures are calculated under a case weights perturbation scheme. In particular, for our objective functions, which have nonzero first derivative at the critical point, the proposed second-order measures are scale invariant, unlike the normal curvature. The performance of the proposed measures is illustrated by using two real data sets as well as a simulation study and a simulated data set. Empirical results seem to indicate that the Wald test statistic is less sensitive to atypical returns than maximum likelihood estimators of the slopes. By the other hand, there is some evidence about the convenience of jointly using first and second-order influence measures, to detect months/days with outlying returns, principally in Wald test statistic.

A practical test for strict exogeneity in linear panel data models with fixed effects

This paper provides a practical test for strict exogeneity in linear panel data models with fixed effects when the number of individuals N goes to infinity while the number of time periods T is fixed. The test is based on the supremum of a sequence of Wald test statistics. Under suitable conditions, we establish the asymptotic distribution of the test statistic and consistency of the test. A bootstrap procedure is proposed to improve the finite sample performance and the validity of the procedure is justified. We investigate the finite sample performance of the test via a small set of Monte Carlo simulations.

Likelihood inference for Type I bivariate Pólya–Aeppli distribution

ABSTRACTThis article discusses likelihood inference for the Type I bivariate Pólya–Aeppli distribution. The Type I bivariate Pólya–Aeppli distribution was derived by Minkova and Balakrishnan by using compounding with geometric random variables and the trivariate reduction method. They also discussed the moment estimation of the parameters of the Type I bivariate Pólya–Aeppli distribution. Here, we carry out a simulation study to compare the performance of the developed Maximum Likelihood Estimation (MLE) method with the moment estimation. The obtained results show that, through the MLEs require more computational time compared to the moment estimates (MoM), the MLEs perform better, in most of the settings, than the MoM. Finally, we apply the Type I bivariate Pólya–Aeppli model to a real dataset containing the frequencies of railway accidents in two subsequent six-year periods for the purpose of illustration. We also carry out some hypothesis tests using the Wald test statistic. From these results, we conclude that the two variables belong to the same univariate Pólya–Aeppli distribution, but are correlated.

Finite-sample distributions of the Wald, likelihood ratio, and Lagrange multiplier test statistics in the classical linear model

ABSTRACTIn this note, it is shown that the finite-sample distributions of the Wald, likelihood ratio, and Lagrange multiplier statistics in the classical linear regression model are members of the generalized beta model introduced by McDonald and Xu (1995a). This is useful for examining the properties of these test statistics. For example, this characterization makes it easy to find distribution, quantile, and density functions for each test statistic, makes it clear why Wald tests may overreject the null hypothesis using asymptotic critical values, and formalizes the fact that the Lagrange multiplier statistic follows a distribution with bounded support.