A score test for binary data with patient non-compliance

A score test is developed for binary clinical trial data, which incorporates patient non-compliance while respecting randomization. It is assumed in this paper that compliance is all-or-nothing, in the sense that a patient either accepts all of the treatment assigned as specified in the protocol, or none of it. Direct analytic comparisons of the adjusted test statistic for both the score test and the likelihood ratio test are made with the corresponding test statistics that adhere to the intention-to-treat principle. It is shown that no gain in power is possible over the intention-to-treat analysis, by adjusting for patient non-compliance. Sample size formulae are derived and simulation studies are used to demonstrate that the sample size approximation holds. Copyright © 2003 John Wiley & Sons, Ltd.

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.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Genetic parameters for test-day yield of milk, fat and protein in buffaloes estimated by random regression models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

TEST

Der Müller und die fünf Räuber, Überfall²³

A Test of Association between Qualitative Trait and a Set of SNPs

2000 Mathematics Subject Classification: 62P10, 92D10, 92D30, 62F03

Test for Independence of the Variables with Missing Elements in One and the Same Column of the Empirical Correlation Matrix

2000 Mathematics Subject Classification: 62H15, 62H12.

TEST BINARY IMPORT

Der Müller und die fünf Räuber, Überfall²³

Testing the random walk hypothesis with variance ratio statistics

Mestrado em Finanças

Determinants of skin self-examination (SSE) in men aged 50 years or older

Background: Queensland men aged 50 years and older are at high risk for melanoma. Early detection via skin self examination (SSE) (particularly whole-body SSE) followed by presentation to a doctor with suspicious lesions, may decrease morbidity and mortality from melanoma. Prevalence of whole-body SSE (wbSSE) is lower in Queensland older men compared to other population subgroups. With the exception of the present study no previous research has investigated the determinants of wbSSE in older men, or interventions to increase the behaviour in this population. Furthermore, although past SSE intervention studies for other populations have cited health behaviour models in the development of interventions, no study has tested these models in full. The Skin Awareness Study: A recent randomised trial, called the Skin Awareness Study, tested the impact of a video-delivered intervention compared to written materials alone on wbSSE in men aged 50 years or older (n=930). Men were recruited from the general population and interviewed over the telephone at baseline and 13 months. The proportion of men who reported wbSSE rose from 10% to 31% in the control group, and from 11% to 36% in the intervention group. Current research: The current research was a secondary analysis of data collected for the Skin Awareness Study. The objectives were as follows: • To describe how men who did not take up any SSE during the study period differed from those who did take up examining their skin. • To determine whether the intervention program was successful in affecting the constructs of the Health Belief Model it was aimed at (self-efficacy, perceived threat, and outcome expectations); and whether this in turn influenced wbSSE. • To determine whether the Health Action Process Approach (HAPA) was a better predictor of wbSSE behaviour compared to the Health Belief Model (HBM). Methods: For objective 1, men who did not report any past SSE at baseline (n=308) were categorised as having ‘taken up SSE’ (reported SSE at study end) or ‘resisted SSE’ (reported no SSE at study end). Bivariate logistic regression, followed by multivariable regression, investigated the association between participant characteristics measured at baseline and resisting SSE. For objective 2 proxy measures of self-efficacy, perceived threat, and outcome expectations were selected. To determine whether these mediated the effect of the intervention on the outcome, a mediator analysis was performed with all participants who completed interviews at both time points (n=830) following the Baron and Kenny approach, modified for use with structural equation modelling (SEM). For objective 3, control group participants only were included (n=410). Proxy measures of all HBM and HAPA constructs were selected and SEM was used to build up models and test the significance of each hypothesised pathway. A likelihood ratio test compared the HAPA to the HBM. Results: Amongst men who did not report any SSE at baseline, 27% did not take up any SSE by the end of the study. In multivariable analyses, resisting SSE was associated with having more freckly skin (p=0.027); being unsure about the statement ‘if I saw something suspicious on my skin, I’d go to the doctor straight away’ (p=0.028); not intending to perform SSE (p=0.015), having lower SSE self-efficacy (p<0.001), and having no recommendation for SSE from a doctor (p=0.002). In the mediator analysis none of the tested variables mediated the relationship between the intervention and wbSSE. In regards to health behaviour models, the HBM did not predict wbSSE well overall. Only the construct of self-efficacy was a significant predictor of future wbSSE (p=0.001), while neither perceived threat (p=0.584) nor outcome expectations (p=0.220) were. By contrast, when the HAPA constructs were added, all three HBM variables predicted intention to perform SSE, which in turn predicted future behaviour (p=0.015). The HAPA construct of volitional self-efficacy was also associated with wbSSE (p=0.046). The HAPA was a significantly better model compared to the HBM (p<0.001). Limitations: Items selected to measure HBM and HAPA model constructs for objectives 2 and 3 may not have accurately reflected each construct. Conclusions: This research added to the evidence base on how best to target interventions to older men; and on the appropriateness of particular health behaviour models to guide interventions. Findings indicate that to overcome resistance those men with more negative pre-existing attitudes to SSE (not intending to do it, lower initial self-efficacy) may need to be targeted with more intensive interventions in the future. Involving general practitioners in recommending SSE to their patients in this population, alongside disseminating an intervention, may increase its success. Comparison of the HBM and HAPA showed that while two of the three HBM variables examined did not directly predict future wbSSE, all three were associated with intention to self-examine skin. This suggests that in this population, intervening on these variables may increase intention to examine skin, but not necessarily the behaviour itself. Future interventions could potentially focus on increasing both the motivational variables of perceived threat and outcome expectations as well as a combination of both action and volitional self-efficacy; with the aim of increasing intention as well as its translation to taking up and maintaining regular wbSSE.

Right-angle crash vulnerability of motorcycles at signalized intersections : mixed logit analysis

Motorcycles are particularly vulnerable in right-angle crashes at signalized intersections. The objective of this study is to explore how variations in roadway characteristics, environmental factors, traffic factors, maneuver types, human factors as well as driver demographics influence the right-angle crash vulnerability of motorcycles at intersections. The problem is modeled using a mixed logit model with a binary choice category formulation to differentiate how an at-fault vehicle collides with a not-at-fault motorcycle in comparison to other collision types. The mixed logit formulation allows randomness in the parameters and hence takes into account the underlying heterogeneities potentially inherent in driver behavior, and other unobserved variables. A likelihood ratio test reveals that the mixed logit model is indeed better than the standard logit model. Night time riding shows a positive association with the vulnerability of motorcyclists. Moreover, motorcyclists are particularly vulnerable on single lane roads, on the curb and median lanes of multi-lane roads, and on one-way and two-way road type relative to divided-highway. Drivers who deliberately run red light as well as those who are careless towards motorcyclists especially when making turns at intersections increase the vulnerability of motorcyclists. Drivers appear more restrained when there is a passenger onboard and this has decreased the crash potential with motorcyclists. The presence of red light cameras also significantly decreases right-angle crash vulnerabilities of motorcyclists. The findings of this study would be helpful in developing more targeted countermeasures for traffic enforcement, driver/rider training and/or education, safety awareness programs to reduce the vulnerability of motorcyclists.

Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests

Selection criteria and misspecification tests for the intra-cluster correlation structure (ICS) in longitudinal data analysis are considered. In particular, the asymptotical distribution of the correlation information criterion (CIC) is derived and a new method for selecting a working ICS is proposed by standardizing the selection criterion as the p-value. The CIC test is found to be powerful in detecting misspecification of the working ICS structures, while with respect to the working ICS selection, the standardized CIC test is also shown to have satisfactory performance. Some simulation studies and applications to two real longitudinal datasets are made to illustrate how these criteria and tests might be useful.

Informational efficiency of the European Union emission allowance market

This thesis studies the informational efficiency of the European Union emission allowance (EUA) market. In an efficient market, the market price is unpredictable and profits above average are impossible in the long run. The main research problem is does the EUA price follow a random walk. The method is an econometric analysis of the price series, which includes an autocorrelation coefficient test and a variance ratio test. The results reveal that the price series is autocorrelated and therefore a nonrandom walk. In order to find out the extent of predictability, the price series is modelled with an autoregressive model. The conclusion is that the EUA price is autocorrelated only to a small degree and that the predictability cannot be used to make extra profits. The EUA market is therefore considered informationally efficient, although the price series does not fulfill the requirements of a random walk. A market review supports the conclusion, but it is clear that the maturing of the market is still in process.