The asymptotic power of rank tests under scale-al ternatives including contaminated distributions

1986 ◽  
Vol 38 (3) ◽  
pp. 513-522 ◽  
Author(s):  
Taka-Aki Shiraishi
Keyword(s):  
1986 ◽  
Vol 35 (3-4) ◽  
pp. 169-188 ◽  
Author(s):  
Shoutir Kishore Chatterjee ◽  
Tathagata Banerjee

In this paper we consider the problem of testing absence of regression under the nonparametric multiple regression set up with m predictors. Usual rank tests for this problem are based on particular systems of scores, the test criteria being quadratic forms in m linear rank statistics. Different standard tests correspond to different choices of the system of scores. In this paper we have proposed a test statistic which is based on the simultaneous choice of more than one system of scores. Asymptotic null distribution of the test criterion is a chisquare with m df as in the case of the usual tests. However, the use of several systems of scores results in the improvement of the asymptotic power over the test based on any one of the systems. Ofcourse the use of the test criterion in practice involves the estimation of indices involving the parent density f( . ). Certain standard estimates of these indices are noted in the last section.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 169.1-169
Author(s):  
R. Punekar ◽  
P. Lafontaine ◽  
J. H. Stone

Background:Polymyalgia rheumatica (PMR) is a chronic inflammatory condition characterized by aching and morning stiffness in the neck, shoulders and pelvic girdle. It is a common inflammatory rheumatic disease in patients age >50 years, particularly women. While giant cell arteritis (GCA) is present in 9–21% of PMR cases, many PMR patients have symptoms independent of GCA. Current treatment options are limited to long-term glucocorticoid (GC), however, with risks of GC-related complications, including cardiovascular disease, osteoporosis, and diabetes mellitus.Objectives:To compare GC use and subsequent GC-related complications in patients with PMR vs a general population (GnP) cohort.Methods:This retrospective, observational cohort study was based on Optum’s de-identified Clinformatics®Data Mart Database (study period 01Jan2006-30June2018). The PMR cohort included patients with ≥1 inpatient or ≥2 outpatient claims ≥30 days apart with PMR related diagnosis codes (ICD-9: 725.xx or ICD-10: M35.3x) between 01Jan2006–30June2017 (patient identification period) during which first occurrence of a PMR-related medical claim was set as the index date (ID). Patients with ≥1 medical claim related to rheumatoid arthritis (RA) or GCA during the study period were excluded. The GnP cohort included patients without any RA, GCA or PMR diagnosis codes during the study period, with their ID set as 12 months from the start of continuous health plan enrollment. Patients in both cohorts were required to be age ≥50 years (on ID) with continuous health plan enrollment ≥12 months pre- and post-ID. Cohorts were 1:1 propensity score matched. GC use and incidence of GC-related complications were assessed from GC initiation, starting from the baseline period (12-months pre-ID) through to the end of GC use during the post-index period (i.e. the end of data availability, end of the study period or death [whichever occurred first]). Mean, standard deviation (SD) and median values for continuous variables, and frequency (n and %) for categorical variables were compared between the matched cohorts. Wilcoxon sum rank tests andt-tests on continuous variables and Chi-square tests or Fisher’s exact tests on categorical variables between matched cohorts were conducted. Duration of GC use was analyzed using the Kaplan-Meier method and compared between matched cohorts using log-rank tests.Results:In each of the PMR and GnP cohorts, 16,865 patients were included. In both matched cohorts, median age was 76 years, median Elixhauser comorbidity index score was 2.0, and the majority (~65%) were women. The median follow-up duration was 45 months and 51 months in the PMR and GnP cohorts, respectively. A higher proportion of patients in the PMR cohort than the matched GnP cohort (90.4% vs 62.8%;p<0.001) used GC. The mean (SD) duration of GC therapy was significantly longer in the PMR cohort than in the matched GnP cohort (242.1 [±317.2] days vs 35.5 [±124.6] days;p<0.001). Although patients in the PMR cohort had a lower average daily dose of GC (prednisone equivalent) vs the GnP cohort (mean [SD] mg 16.3 [± 21.9] vs 27.8 [±24.5], respectively [p<0.0001)], the cumulative GC dose was significantly higher in the PMR cohort than the GnP cohort (2125.4 [±3689.5] mg vs 476.6 [±1450.9] mg;p<0.001). This indicates PMR patients used chronic low dose GC while the GnP patients utilized higher dose GC burst therapy less frequently. The number of incident complications associated with GC use were significantly greater in the PMR cohort, and included hypertension, diabetes, skin toxicity, infections, neuropsychiatric effects, endocrine abnormalities, renal dysfunction/ failure, ocular effects, and cardiovascular disease (p<0.05).Conclusion:The overall GC burden in patients with PMR is high. With a higher incidence of GC-related comorbidities among PMR patients, early onset of these complications may be a significant contributor to long-term healthcare costs in these patients.Acknowledgments:This study was funded by Sanofi, Inc. Medical writing, under the direction of authors, was provided by Gauri Saal, MA Economics, Prime, Knutsford, UK, and funded by Sanofi.Disclosure of Interests:Rajeshwari Punekar Shareholder of: Sanofi, Employee of: Sanofi, Patrick LaFontaine Shareholder of: Sanofi, Employee of: Sanofi, John H. Stone Grant/research support from: Roche, Consultant of: Roche


2014 ◽  
Vol 31 (3) ◽  
pp. 539-559 ◽  
Author(s):  
I. Gaia Becheri ◽  
Feike C. Drost ◽  
Ramon van den Akker

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.


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