Jonckheere's Test Research Articles

Adaptive Jonckheere-type tests for ordered alternatives

Testing against ordered alternatives in the c -sample location problem plays an important role in statistical practice. The parametric test proposed by Barlow et al .-in the following, called the 'B-test'-is an appropriate test under the model of normality. For non-normal data, however, there are rank tests which have higher power than the B-test, such as the Jonckheere test or so-called Jonckheere-type tests introduced and studied by Buning and Kossler. However, we usually have no information about the underlying distribution. Thus, an adaptive test should be applied which takes into account the given data set. Two versions of such an adaptive test are proposed, which are based on the concept introduced by Hogg in 1974. These adaptive tests are compared with each of the single Jonckheere-type tests in the adaptive scheme and also with the B-test. It is shown via Monte Carlo simulation that the adaptive tests behave well over a broad class of symmetric distributions with short, medium and long tails, as well as for asymmetric distributions.

Theory & Methods: The Asymptotic Power Of Jonckheere‐Type Tests For Ordered Alternatives

For the c‐sample location problem with ordered alternatives, the test proposed by Barlow et al. (1972 p. 184) is an appropriate one under the model of normality. For non‐normal data, however, there are rank tests which have higher power than the test of Barlow et al., e.g. the Jonckheere test or so‐called Jonckheere‐type tests recently introduced and studied by Büning & Kössler (1996). In this paper the asymptotic power of the Jonckheere‐type tests is computed by using results of Hájek (1968) which may be considered as extensions of the theorem of Chernoff & Savage (1958). Power studies via Monte Carlo simulation show that the asymptotic power values provide a good approximation to the finite ones even for moderate sample sizes.

A modified logrank test for censored survival data under order restrictions

We previously proposed a class of ordered weighted logrank tests for analyzing censored survival data under order restrictions. However the power of these tests is asymmetrical with respect to possible alternative configurations and could be inferior to the non-ordered logrank test in extreme cases. A modified ordered logrank test is proposed to remedy this situation. The test is shown to be asymptotically locally equivalent to the generalized Jonckheere's test but computationally simpler.

Season of birth in autism: a fiction revisited.

Variations of season of birth among autistic individuals were studied. The replicability of previously reported increases in birth rates in the months of March and August were examined in groups of individuals with autism or mental retardation (the comparison group). The sample was obtained from the Yale Child Study Center Developmental Disabilities Clinic and from the DSM-IV Autism/PDD field trial. Data were analyzed by applying the Jonckheere test of ordinal trend and the chi-square test, with Yates correction factor. With respect to March and August births, and with calculations based on the beginning and middle of the month, no significant seasonal effect was observed. Samples were subcategorized into verbal and mute groups, and again results failed to support the seasonality hypothesis.

Nonparametric Tests for Trend: Jonckheere's Test, a Modification and a Maximum Test

Jonckheere's test is a frequently used nonparametric trend test for the evaluation of preclinical studies and clinical dose-finding trials. In this paper, a modification of Jonckheere's test is proposed. If the exact permutation distribution is used for inference, the modified test can fill out the level of the type I error in a much more complete way and is substantially more powerful than the common Jonckheere test. If the asymptotic normality is used for inference, the modified test is slightly more powerful. In addition, a maximum test is investigated which is more robust concerning an a priori unknown dose-response shape. The robustness is advantageous, especially in a closed testing procedure. The different tests are applied to two example data sets.

Nonparametric Tests for Trend: Jonckheere's Test, a Modification and a Maximum Test

Nonparametric Tests for Trend: Jonckheere's Test, a Modification and a Maximum Test

Seroprevalence of Toxoplasma gondii and Trichinella spiralis in North Carolina Black Bears (Ursus americanus)

Serum samples from 143 hunter-killed black bears were collected during the 1996 and 1997 black bear hunting seasons in eastern North Carolina. All samples were tested for antibodies to Toxoplasma gondii by the modified agglutination test. Antibodies to T. gondii were present in 120 of 143 (84%) bears. Females had significantly higher titers than males (Wilcoxon rank sums test, P = 0.045), and titers increased with age (Jonckheere test, P = 0.01). Samples collected during 1996 (n = 79) were tested for antibodies to Trichinella spiralis by enzyme-linked immunosorbent assay. No samples were positive for antibodies to T. spiralis.

Design and analysis for survival data under order restrictions with a modified logrank test.

We previously proposed a class of ordered weighted logrank tests for analysing censored survival data under order restrictions. However, the power of these tests is asymmetrical with respect to possible alternative configurations. While it is superior in most cases, the power can be inferior to the non-ordered logrank test in extreme cases. We propose a modified ordered logrank test which performs uniformly better than the non-ordered test. The power of the modified test is equivalent to the generalized Jonckheere's test but its computation is much simpler. We give sample size requirements for sufficient power to reject the global null hypothesis at specified hazard ratios between the control group and the best group. Following Fisher's least significant difference (LSD) strategy for multiple comparisons, power investigations indicate that the nominal power for the global test carries over to the control versus best comparison during pairwise testing. The power for detecting intermediate survival differences is inadequate but the sample sizes required to detect such differences may be impractical in most applications.

Design and analysis for survival data under order restrictions with a modified logrank test

We previously proposed a class of ordered weighted logrank tests for analysing censored survival data under order restrictions. However, the power of these tests is asymmetrical with respect to possible alternative configurations. While it is superior in most cases, the power can be inferior to the non-ordered logrank test in extreme cases. We propose a modified ordered logrank test which performs uniformly better than the non-ordered test. The power of the modified test is equivalent to the generalized Jonckheere's test but its computation is much simpler. We give sample size requirements for sufficient power to reject the global null hypothesis at specified hazard ratios between the control group and the best group. Following Fisher's least significant difference (LSD) strategy for multiple comparisons, power investigations indicate that the nominal power for the global test carries over to the control versus best comparison during pairwise testing. The power for detecting intermediate survival differences is inadequate but the sample sizes required to detect such differences may be impractical in most applications. © 1998 John Wiley & Sons, Ltd.

Detection of an Outlier and Evaluation of its Influence in Chronic Toxicity Studies

Targeting quantitative data in repeated-dose toxicity studies using rodents, a method for detecting an outlier and a selection problem between parametric and nonparametric approaches, based on actual toxicity data, was investigated. The consistency between the judgments of veteran toxicologists and several statistical methods (skewness, kurtosis, and the studentized residual) to detect an outlier was evaluated. The studentized residual had the highest consistency with the judgments of toxicologists and was the most effective method for detecting an outlier.The performance of the parametric (regression) method and the nonparametric method (Jonckheere test) for detecting dose-dependency was evaluated. Parametric and nonparametric approaches had a different result when outliers existed. Parametric methods are sensitive to the presence of outliers and they lose statistical power. In contrast, nonparametric approaches are robust to outliers. The identification of extreme individual measures is, however, a diff...

Trend Tests for Dichotomous Endpoints with Application to Carcinogenicity Studies

A trend test for dichotomous endpoints analogous to the nonparametric Jonckheere test is developed. The power of this and all other single trend tests for dichotomous endpoints strongly depends on the shape of the dose response curve. Combined tests which have a stable power over a wide range of the ordered alternative are suggested. One can combine several contrast tests to a so-called adjustive test which is more powerful than a Cochran-Armitage test with equally-spaced scores. The latter was recommended by Armitage (1) in case there is no a priori knowledge of the type of the trend.

Robustness and efficiency of some tests for ordered alternatives in the C-Sample location problem

For the c-sample location problem with ordered alternatives we compare a test proposed by Barlow et al. (1972) and its Welch modification for the case of unequal variances with some nonparametric counterparts, the Jonckheere test and modifications of the Jonckheere test. In these modifications the Mann-Whitney statistic is replaced by other two-sample linear rank statistics. The comparison is referred to the actual level and the power of the tests and it is carried out via Monte Carlo simulation assuming short-, medium- and long-tailed as well as asymmetric distributions. It turns out that in the case of unequal variances and symmetric distributions the Welch modification of the test of Barlow et al is the most α-robust test among the tests considered, but for equal variances special Jonckheere-type tests are to be preferred.

Association of vascular endothelial growth factor expression with intratumoral microvessel density and tumour cell proliferation in human epidermoid lung carcinoma

Vascular endothelial growth factor (VEGF) expression, vascularisation and tumour cell proliferation were analysed in 91 human epidermoid lung carcinomas using immunohistochemistry. A polyclonal anti-VEGF antibody was used for VEGF expression, a polyclonal antibody directed against human von Willebrand factor (factor VIII) to identify blood vessels and the proliferating cell nuclear antigen (PCNA) as a marker for proliferating cells. Positive staining for VEGF was obtained in 54 out of 91 cases (59%), the number of blood vessels varied from zero to 64 counts (mean 9.4) and the proportion of PCNA-positive cells varied from 1.3% to 72.1% (mean 25.2%). The mean PCNA labelling index and mean microvessel count in VEGF-positive tumours were significantly higher than those in VEGF-negative tumours (Wilcoxon rank sum test, P<0.0001; p<0.05). In addition, PCNA labelling index significantly increased with increasing VEGF expression (Jonckheere test, P<0.0001). In contrast, no association was found between PCNA labelling index and tumour vascularity (r=0.07, P=0.48). The close correlation of VEGF expression with tumour cell proliferation and microvessel density suggests that VEGF acts both as an autocrine growth factor and as stimulator for angiogenesis. However, tumour cell proliferation and microvessel growth and/or density may be regulated by separate mechanisms.

Association between Survival Time and Ordinal Covariates

An application of the method of rank correlation is proposed for testing independence between a censored survival time and an ordinal covariate. The test statistic counts the number of concordances minus the number of discordances at each time with event(s) and adds across times; it is expressible as a score statistic within the proportional hazards framework. The proposed test includes, as a special case, a generalization of Jonckheere's test against ordered alternatives and as applied to the analysis of categorical data, it can be seen as a generalization of the Mantel-Haenszel procedure.

Angiogenesis as a Diagnostic Factor in Primary Breast Cancer: Microvessel Quantitation by Stereological Methods and Correlation with Color Doppler Sonography

<i>Background</i>: In contrast to benign lesions without signs of inflammation, malignant tumors have a capacity for angiogenesis. Therefore it was of interest to evaluate with color Doppler ultrasound if breast carcinomas showed higher vascularization than benign lesions. To enable a correlation with the pathoanatomic situation of vascularization, stereological methods were used to quantify microvessel volume, surface and length as indicators for angiogenesis. <i>Patients and Methods</i>: Two hundred and five patients with a palpable and/or mammographically seen breast tumor were investigated before they underwent surgery with color Doppler ultrasound for the detection of blood flow in the tumor or in an area around the tumor within a distance of 2 cm. In 101 cases microvessels of the tumor were identified by immunohistochemistry using the monoclonal mouse antibody (JC70) that detects the vascular endothelium-associated antigen CD31 and quantified by stereological methods. The quantified vessel volume, surface, and length were compared to color flow results and other prognostic factors in breast cancer. <i>Results</i>: The detection of blood flow by color Doppler sonography in the tumor and in the peritumoral region was significantly higher in malignant than in benign breast lesions (p = 0.003). By stereological quantitation of microvessels it could be shown that breast carcinoma had a significantly higher volume, surface and length of vessels than fibroadenoma (p < 0.00001 and p < 0.0001). In the group of breast cancers a significant correlation was found between high length of microvessels per mm3 tumor and tumor size (p = 0.04 – Jonckheere test), a negative estrogen receptor (p < .007) and a negative progesterone receptor (p = 0.005). No correlation was found between microvessel length and nodal status, tumor grade, ploidy status, and S-phase fraction. <i>Conclusions</i>: Microvessel count in breast tumors, using the JC70 antibody to CD31, and stereology for quantitation in a three-dimensional fashion, is an effective method to look for the extent of angiogenesis and to correlate Doppler flow results with pathoanatomic vascular data. With color Doppler sonography an effective clinical method is available for distinguishing between benign and malignant lesions.

Multivariate generalizations of jonckheere's test for ordered alternatives

In many dose-response studies, each of several independent groups of animals is treated with a different dose of a substance. Many response variables are then measured on each animal. The distributions of the response variables may be nonnormal, and Jonckheere's (1954) test for ordered alternatives in the one-way layout is sometimes used to test whether the level of a single variable increases with increasing dose. In some applications, however, it is important to consider a set of response variables simultaneously. For instance, an increase in each of certain enzymes in the blood serum may suggest liver damage. To test whether these enzyme levels increase with increasing dose, it may be preferable to consider these enzymes as a group, rather than individually. I propose two multivariate generalizations of Jonckheere's univariate test. Each multivariate test statistic is a function of coordinate-wise Jonckheere statistics—one a sum, the other a quadratic form. The sum statistic can be used to test the alt...

A NONPARAMETRIC TEST AGAINST ORDERED ALTERNATIVES FOR DATA DEFINED BY INTERVALS

Abstract. The paper deals with a generalization of the Jonckheere test against ordered alternatives which allows for arbitrary censoring. It includes some previously published tests as special cases.

A Distribution-Free Rank Test for Ordered Alternatives in Randomized Complete Block Designs

Abstract A distribution-free rank test for detecting ordered alternatives in randomized complete block designs and repeated measures designs is proposed for four or fewer treatments. The null hypothesis distribution of the statistic is well-known and readily available to the user. The article establishes the asymptotic normality of an appropriately standardized form of the statistic and the consistency of the test. Asymptotic relative efficiency comparisons are made with Jonckheere's test, Page's L, Hollander's test, and a normal theory competitor. The authors illustrate the good intermediate sample size characteristics of the test via a Monte Carlo study.

The Power of Jonckheere's Test

Abstract This paper discusses the power of Jonckheere's test under the ordered alternative hypothesis. It is shown that the power of the test is bounded significantly away from one under certain shift alternatives and sample sizes.

The Power of Jonckheere's Test

The Power of Jonckheere's Test