Ranking test

Note that the term censor is introduced in the preceding table. The log-rank test (invoked in SAS with PROC LIFETEST) and the Cox proportional hazards model (invoked in SAS with PROC PHREG) allow for censoring observations in a time-to-event analysis. These tests adjust for the fact that at some point a patient may no longer be able to experience an event. The censor date is the last known time that the patient did not experience a given event and the point at which the patient is no longer considered able to experience the event. Often the censor date is the last known date of patient follow-up, but a patient could be censored for other reasons, such as having taken a protocol-prohibited medication. 

Because age is not normally distributed here, the Wilcoxon signed rank test is used to calculate the p-value and is placed into a data set called pvalue. (Inferential statistics are discussed further in Chapter 7.)... 

The p-value for the sign test or Wilcoxon signed rank test can be found in the pValue variable in the pvalue data set. If the variable is from a symmetric distribution, you can get the p-value from the Wilcoxon signed rank test, where the Test variable in the pvalue data set is Signed Rank. If the variable is from a skewed distribution, you can get the p-value from the sign test, where the Test variable in the pvalue data set is Sign. ... 

Time-to-event analysis in clinical trials is concerned with comparing the distributions of time to some event for various treatment regimens. The two nonparametric tests used to compare distributions are the log-rank test and the Cox proportional hazards model. The Cox proportional hazards model is more useful when you need to adjust your model for covariates. 

Here we assume that the daystodeath variable is the number of days to death or last known date alive for the patient. The deathcensor variable value is 1 if the patient died and 0 if the patient did not die. The p-value variable for the log-rank test is called ProbChiSq in the pvalue data set where the Test variable equals Log-Rank. ... 

Part 4 Performing a ranking test to determine if either analytical method or location affects the results as a systematic error (bias) and Part 5 Computing the efficient comparison of two methods as described by Youden and Steiner in reference [7],... 

Collaborative Laboratory Studies Part 4 - Ranking Test... 

RANKING TEST FOR LABORATORIES AND METHODS (MANUAL COMPUTATIONS)... 

This set of articles presents the computational details and actual values for each of the statistical methods shown for collaborative tests. These methods include the use of precision and estimated accuracy comparisons, ANOVA tests, Student s t-testing, The Rank Test for Method Comparison, and the Efficient Comparison of Methods tests. From using these statistical tests the following conclusions can be derived ... 

The laboratory ranking test did not show any laboratory or method outside of confidence limits, therefore neither method nor laboratory is consistently high or low in reported results. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Statistical analyses were performed with SPSS 8.0. We used a Wilcoxon signed ranks test to test for seasonality. To test for individuality we used a general linear model (GLM) with either individual or colony as a fixed factor. All tests were... 

Fig. 17.3 Proportion of spotted hyena pastings that were overmarks by age and sex. Males increased their overmarking activity with age (Wilcoxon signed-rank test, S = 32.5, P = 0.04), however, females did not (cub vs. subadult S = — 15.5, P = 0.24 across subadult periods N = 6, Friedman ANOVA x2 = 3.5, P = 0.17). Although male and female cubs did not differ in their frequency of overmarking (Mann-Whitney U test, U = 75, P = 0.67), a sex difference was apparent among subadults (U = 37, P = 0.02)...

To compare between days and locations I standardised visitation rates for each species by calculating visits to each odour type as a proportion of mean visits to the blank stations by that species, on that night, and at that location. By making the data proportional I removed effects of differing population size and density, as well as variation between nights, for example in moon phase. These data were checked for normality and symmetry, and subsequently analysed with a two-tailed Wilcoxon signed ranks test (Zar 1999) to determine whether visitation rate differed from a value of one (indicating no difference between visitation rate to an odour source... 

These methods are essential when there is any significant degree of mortality in a bioassay. They seek to adjust for the differences in periods of risk individual animals undergo. Life table techniques can be used for those data where there are observable or palpable tumors. Specifically, one should use Kaplan-Meier product limit estimates from censored data graphically, Cox-Tarone binary regression (log-rank test), and Gehan-Breslow modification of Kruskal-Wallis tests (Thomas et al., 1977 Portier and Bailer, 1989) on censored data. 

Two-sample Student s t test, Wilcoxian-Mann-Whitney Rank Test, and so on. 

The Log-Rank Test is a statistical methodology for comparing the distribution of time until the occurrence of the event in independent groups. In toxicology, the most common event of interest is death or occurrence of a tumor, but it could just as well be liver failure, neurotoxicity, or any other event which occurs only once in an individual. The elapsed time from initial treatment or observation until the event is the event time, often referred to as survival time , even when the event is not death . 

The Log-Rank Test provides a method for comparing risk-adjusted event rates, useful when test subjects in a study are subject to varying degrees of opportunity to experience the event. Such situations arise frequently in toxicology studies due to the finite duration of the study, early termination of the animal or interruption of treatment before the event occurs. 

Examples where use of the Log-Rank Test might be appropriate include comparing survival times in carcinogenity bioassay animals which are given a new treatment with those in the control group or comparing times to liver failure for several dose levels of a new NSAID where the animals are treated for 10 weeks or until cured, whichever comes first. 

The idea behind the Log-Rank Test for comparison of two life tables is simple if there were no difference between the groups, the total deaths occurring at any time should split between the two groups at that time. So if the numbers at risk in the first and second groups in (say) the sixth month were 70 and 30, respectively, and 10 deaths occurred in that month we would expect... 

The Log-Rank Test as presented by Peto et al. (1977) uses the product-limit life-table calculations rather than the actuarial estimators shown above. The distinction is unlikely to be of practical importance unless the grouping intervals are very coarse. 

Many variations of the Log-Rank Test for comparing survival distributions exist. The most common variant has the form ... 

Survival and failure times often follow the exponential distribution. If such a model can be assumed, a more powerful alternative to the Log-Rank Test is the Likelihood Ratio Test. 

Ordinal or numerical Mann-Whitney U test Wilcoxon signed rank test Kruskal-Wallis Friedman... 

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