A conditional likelihood ratio test for structural models

This paper develops a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reducedform covariance matrix. The test based on the likelihood ratio statistic is particularly simple and has good power properties. When identification is strong, the power curve of this conditional likelihood ratio test is essentially equal to the power envelope for similar tests. Monte Carlo simulations also suggest that this test dominates the Anderson- Rubin test and the score test. Dropping the restrictive assumption of disturbances normally distributed with known covariance matrix, approximate conditional tests are found that behave well in small samples even when identification is weak.

A note on the local power of the LR, Wald, score and gradient tests

This paper examines the local power of the likelihood ratio, Wald, score and gradient tests under the presence of a scalar parameter, phi say, that is orthogonal to the remaining parameters. We show that some of the coefficients that define the local powers remain unchanged regardless of whether phi is known or needs to be estimated, where as the others can be written as the sum of two terms, the first of which being the corresponding term obtained as if phi were known, and the second, an additional term yielded by the fact that phi is unknown. The contribution of each set of parameters on the local powers of the tests can then be examined. Various implications of our main result are stated and discussed. Several examples are presented for illustrative purposes

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.

Influence analysis of robust Wald-type tests

We consider a robust version of the classical Wald test statistics for testing simple and composite null hypotheses for general parametric models. These test statistics are based on the minimum density power divergence estimators instead of the maximum likelihood estimators. An extensive study of their robustness properties is given though the influence functions as well as the chi-square inflation factors. It is theoretically established that the level and power of these robust tests are stable against outliers, whereas the classical Wald test breaks down. Some numerical examples confirm the validity of the theoretical results.

An investigation of the interrelationship between manipulative therapy-induced hypoalgesia and sympathoexcitation

Objective: To investigate a proposed model in which manipulative therapy produces a treatment-specific initial hypoalgesic and sympathoexcitatory effect by activating a descending pain inhibitory system. The a priori hypothesis tested was that manipulative therapy produces mechanical hypoalgesia and sympatho-excitation beyond that produced by placebo or control. Furthermore, these effects would be correlated, thus supporting the proposed model. Design: A randomized, double-blind, placebo-controlled, repeated-measures study of the initial effect of treatment. Setting: Clinical neurophysiology laboratory. Subjects: Twenty-four subjects (13 women and 11 men; mean age, 49 yr) with chronic lateral epicondylalgia (average duration, 6.2 months). Intervention: Cervical spine lateral glide oscillatory manipulation, placebo and control. Outcome Measures: Pressure pain threshold, thermal pain threshold, pain-free grip strength test, upper limb tension test 2b, skin conductance, pileous and glabrous skin temperature and blood flux. Results: Treatment produced hypoalgesic and sympathoexcitatory changes significantly grater than those of placebo and control (p < .03). Confirmatory factor-analysis modeling, which was performed on the pain-related measures and the indicators of sympathetic nervous system function, demonstrated a significant correlation (r = .82) between the latencies of manipulation-induced hypoalgesia and sympathoexcitation. The Lagrange Multiplier test and Wald test indicated that the two latent factors parsimoniously and appropriately represented their observed variables. Conclusions: Manual therapy produces a treatment-specific initial hypoalgesic and sympathoexcitatory effect beyond that of placebo or control. The strong correlation between hypoalgesic and sympathoexcitatory effects suggests that a central control mechanism might be activated by manipulative therapy.

Monte Carlo evidence on cointegration and causation

The small sample performance of Granger causality tests under different model dimensions, degree of cointegration, direction of causality, and system stability are presented. Two tests based on maximum likelihood estimation of error-correction models (LR and WALD) are compared to a Wald test based on multivariate least squares estimation of a modified VAR (MWALD). In large samples all test statistics perform well in terms of size and power. For smaller samples, the LR and WALD tests perform better than the MWALD test. Overall, the LR test outperforms the other two in terms of size and power in small samples.

Indicadores de prognóstico em utentes com disfunção do ombro submetidos a uma intervenção terapêutica direcionada para a estabilidade dinâmica da escápulo-torácica

RESUMO: Introdução/ Objetivo: Segundo a revisão sistemática de Chester e colaboradores (2013b)apenas dois fatores de prognóstico demonstraram uma associação consistente com o resultado que foram a duração dos sintomas e a funcionalidade na avaliação inicial. O objetivo do estudo é identificar indicadores de bom e mau prognóstico em utentes com disfunção do complexo articular do ombro (DCAO), tendo por base, aspetos da avaliação inicial do utente e critérios de alta de abolição da dor, aumento da funcionalidade e da estabilidade dinâmica considerando uma intervenção terapêutica direcionada para o aumento da estabilidade dinâmica da escápulo-torácica. Metodologia: Efetuou-se um estudo de coorte clínico retrospetivo. Para tal, aplicou-se um protocolo de intervenção terapêutica e analisou-se os resultados. A amostra foi constituída por 82 indivíduos com DCAO [53 com síndrome do conflito subacromial (SCSA) e 29 com instabilidade da glenoumeral (IGU)], residentes nos distritos de Lisboa, Setúbal e Santarém com o intuito de iniciar tratamento de fisioterapia. A análise dos dados foi efetuada tendo em consideração dois procedimentos: análise univariada (através do método de Kaplan-Meier para cada CVP) e análise multifatorial (pela análise de regressão de Cox e regressão logística nos grupos de utentes com SCSA, IGU e DCAO). Resultados: O tempo mediano de continuação no tratamento em fisioterapia foi de 7 semanas para os utentes com SCSA e 6 semanas para utentes com IGU. Segundo o teste de Logrank, na análise univariada, existem sete e oito covariáveis preditoras (CVP) com associação estatisticamente significativa (p<0,05) para o subgrupo SCSA e IGU, respectivamente. De acordo com estes resultados, a primeira parte da DASH e a SPADI são as únicas CVP com associação comuns às duas disfunções. Pela análise multifatorial e, em congruência com o teste de Wald, nenhuma das CVP contribui estatisticamente para o modelo preditivo de continuidade do tratamento de fisioterapia em qualquer um dos três modelos estudados: subgrupo SCSA, subgrupo IGU e utentes com DCAO. Conclusão: Por uma análise univariada verificou-se que existem CVP associadas à alta dos tratamentos em fisioterapia e estas não são as mesmas em ambas as DCAO. Contudo, a magnitude do efeito de cada CVP nos modelos multifatoriais definidos para os grupos de utentes com SCSA, IGU e DCAO não demonstraram valor estatisticamente significativo pelo que não foi possível determinar modelos de prognóstico em utentes com DCAO.-------------ABSTRACT: Background/ Purpose: According with the systematic review from Chester and collaborators (2013b) just two prognostic factors demonstrated a consistent association with the outcome: the duration of symptoms and functionality in the initial assessment. The purpose of the study is to identify indicators of good and poor prognosis in patients with shoulder’s dysfunctions, based on aspects of the initial assessment and discharge criteria of absence of pain, increased functionality and dynamic stability considering a therapeutic intervention used to increase the dynamic stability of scapulo-thoracic. Methodology: It was conducted a retrospective study of clinical cohort. For this purpose it was applied a protocol with therapeutic intervention and the results were analyzed. The sample consisted of 82 individuals with shoulder’s dysfunction (53 with subacromial impingement (SIMP) and 29 with shoulder instability (SINS) residing in the districts of Lisbon, Setúbal and Santarém in order to start physiotherapy. Data analysis was performed taking into account two procedures: univariate analysis [using the Kaplan-Meier method for each co-variant predictor variable (CVP)] and multifactorial analysis [analysis by Cox regression and logistic regression on groups of patients with SIMP, SINS and shoulder’s dysfunction (SD)]. Results: The median time of follow-up treatment at physical therapy was 7 weeks for patients with SIMP and 6 weeks for patients with SINS. According to the Logrank test in the univariate analysis, there are seven and eight CVP with a statistically significant association (p<0.05) for the patients with SIMP and SINS, respectively. According to these results, the first part of the DASH and SPADI are the only CVP common to both disorders association. By multifatorial analyses, and in agreement with the Wald test, none of the CVP contributes statistically to the predictive model of continuity of physiotherapy treatment in any of the three studied models: patients with SIMP, patients with SINS and patients with SD. Conclusion: In an univariate analysis, it was verified that there are CVP associated with discharge from treatments of physical therapy and these are not the same in both SD. However, the magnitude of effect of each CVP in multifactorial models for defined patients groups with SIMP, SINS and SD showed no statistically significant. Therefore, it was not possible to determine prognostic models for patients with SD.

Context-dependent interpretation of the prognostic value of BRAF and KRAS mutations in colorectal cancer.

BACKGROUND: The mutation status of the BRAF and KRAS genes has been proposed as prognostic biomarker in colorectal cancer. Of them, only the BRAF V600E mutation has been validated independently as prognostic for overall survival and survival after relapse, while the prognostic value of KRAS mutation is still unclear. We investigated the prognostic value of BRAF and KRAS mutations in various contexts defined by stratifications of the patient population. METHODS: We retrospectively analyzed a cohort of patients with stage II and III colorectal cancer from the PETACC-3 clinical trial (N = 1,423), by assessing the prognostic value of the BRAF and KRAS mutations in subpopulations defined by all possible combinations of the following clinico-pathological variables: T stage, N stage, tumor site, tumor grade and microsatellite instability status. In each such subpopulation, the prognostic value was assessed by log rank test for three endpoints: overall survival, relapse-free survival, and survival after relapse. The significance level was set to 0.01 for Bonferroni-adjusted p-values, and a second threshold for a trend towards statistical significance was set at 0.05 for unadjusted p-values. The significance of the interactions was tested by Wald test, with significance level of 0.05. RESULTS: In stage II-III colorectal cancer, BRAF mutation was confirmed a marker of poor survival only in subpopulations involving microsatellite stable and left-sided tumors, with higher effects than in the whole population. There was no evidence for prognostic value in microsatellite instable or right-sided tumor groups. We found that BRAF was also prognostic for relapse-free survival in some subpopulations. We found no evidence that KRAS mutations had prognostic value, although a trend was observed in some stratifications. We also show evidence of heterogeneity in survival of patients with BRAF V600E mutation. CONCLUSIONS: The BRAF mutation represents an additional risk factor only in some subpopulations of colorectal cancers, in others having limited prognostic value. However, in the subpopulations where it is prognostic, it represents a marker of much higher risk than previously considered. KRAS mutation status does not seem to represent a strong prognostic variable.

The algebraic equality of two asymptotic tests for the hypothesis that a normal distribution has a specified correlation matrix

It is proved the algebraic equality between Jennrich's (1970) asymptotic$X^2$ test for equality of correlation matrices, and a Wald test statisticderived from Neudecker and Wesselman's (1990) expression of theasymptoticvariance matrix of the sample correlation matrix.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

Testing symmetry and homogeneity in the almost ideal demand system with co-integrated data using fully modified estimation and the bootstrap

Conventional seemingly unrelated estimation of the almost ideal demand system is shown to lead to small sample bias and distortions in the size of a Wald test for symmetry and homogeneity when the data are co-integrated. A fully modified estimator is developed in an attempt to remedy these problems. It is shown that this estimator reduces the small sample bias but fails to eliminate the size distortion.. Bootstrapping is shown to be ineffective as a method of removing small sample bias in both the conventional and fully modified estimators. Bootstrapping is effective, however, as a method of removing. size distortion and performs equally well in this respect with both estimators.

Sample size considerations in active-control non-inferiority trials with binary data based on the odds ratio

This paper presents an approximate closed form sample size formula for determining non-inferiority in active-control trials with binary data. We use the odds-ratio as the measure of the relative treatment effect, derive the sample size formula based on the score test and compare it with a second, well-known formula based on the Wald test. Both closed form formulae are compared with simulations based on the likelihood ratio test. Within the range of parameter values investigated, the score test closed form formula is reasonably accurate when non-inferiority margins are based on odds-ratios of about 0.5 or above and when the magnitude of the odds ratio under the alternative hypothesis lies between about 1 and 2.5. The accuracy generally decreases as the odds ratio under the alternative hypothesis moves upwards from 1. As the non-inferiority margin odds ratio decreases from 0.5, the score test closed form formula increasingly overestimates the sample size irrespective of the magnitude of the odds ratio under the alternative hypothesis. The Wald test closed form formula is also reasonably accurate in the cases where the score test closed form formula works well. Outside these scenarios, the Wald test closed form formula can either underestimate or overestimate the sample size, depending on the magnitude of the non-inferiority margin odds ratio and the odds ratio under the alternative hypothesis. Although neither approximation is accurate for all cases, both approaches lead to satisfactory sample size calculation for non-inferiority trials with binary data where the odds ratio is the parameter of interest.

Use of a predictive model for food insecurity estimates in Brazil

In 2004 the National Household Survey (Pesquisa Nacional par Amostras de Domicilios - PNAD) estimated the prevalence of food and nutrition insecurity in Brazil. However, PNAD data cannot be disaggregated at the municipal level. The objective of this study was to build a statistical model to predict severe food insecurity for Brazilian municipalities based on the PNAD dataset. Exclusion criteria were: incomplete food security data (19.30%); informants younger than 18 years old (0.07%); collective households (0.05%); households headed by indigenous persons (0.19%). The modeling was carried out in three stages, beginning with the selection of variables related to food insecurity using univariate logistic regression. The variables chosen to construct the municipal estimates were selected from those included in PNAD as well as the 2000 Census. Multivariate logistic regression was then initiated, removing the non-significant variables with odds ratios adjusted by multiple logistic regression. The Wald Test was applied to check the significance of the coefficients in the logistic equation. The final model included the variables: per capita income; years of schooling; race and gender of the household head; urban or rural residence; access to public water supply; presence of children; total number of household inhabitants and state of residence. The adequacy of the model was tested using the Hosmer-Lemeshow test (p=0.561) and ROC curve (area=0.823). Tests indicated that the model has strong predictive power and can be used to determine household food insecurity in Brazilian municipalities, suggesting that similar predictive models may be useful tools in other Latin American countries.

Comparing time-varying autoregressive structures of locally stationary processes

In this paper, a novel statistical test is introduced to compare two locally stationary time series. The proposed approach is a Wald test considering time-varying autoregressive modeling and function projections in adequate spaces. The covariance structure of the innovations may be also time- varying. In order to obtain function estimators for the time- varying autoregressive parameters, we consider function expansions in splines and wavelet bases. Simulation studies provide evidence that the proposed test has a good performance. We also assess its usefulness when applied to a financial time series.