Trend tests

A2 Test statistic (estimate) for von Neumann s trend test (4.34)... 

The AO AC (cited in Ref. [11]) described the precision acceptance criteria at different concentrations within or between days, the details of which are provided in Table 2. Other parameters that should be tested in the precision study are the David-, Dixon- or Grubbs-, and Neumann-tests. The David-test is performed when determining whether the precision data are normally distributed. Outlier testing of the data is performed by the Dixon-test (if n < 6-8) or by the Grubbs-test (if n > 6-8), while trend testing of the data is performed by Neumann-test. Detailed methods have been described in the book written by Kromidas [29]. 

Soper, K.A. and Clark, R.L. (1990). Exact permutation trend tests for fetal survival data. Proc. 

As a general approach, most pharmaceutical statisticians begin by testing for the presence of a dose-related trend in tumor proportions. If the trend test is significant, that is, the p value is less than or equal to 0.05, pairwise comparisons are performed... 

Although in most cases the use of trend tests is appropriate since most biological responses are dose related, there are exceptions to this rule. Certain drugs, especially those with hormonal activity, may not produce classical dose responses and may even induce inverse dose-response phenomena. In these cases, a pairwise comparison may be appropriate in the absence of a significant positive trend. 

Basic forms of the trend tests (such as that of Tarone) have previously been presented in this text. These are a natural development from earlier methods of regression testing (Dinse and Lagakes, 1983), but are much more powerful. (Gaylor and Kodell, 2001). 

Group comparison tests for proportions notoriously lack power. Trend tests, because of their use of prior information (dose levels) are much more powerful. Also, it is generally believed that the nature of true carcinogenicity (or toxicity for that matter), manifests itself as dose-response. Because of the above facts, evaluation of trend takes precedence over group comparisons. In order to achieve optimal test statistics, many people use ordinal dose levels (0,1,2..., etc.) instead of the true arithmetic dose levels to test for trend. However, such a decision should be made a priori. The following example demonstrates the weakness of homogeneity tests. 

Tarone s trend test is most powerful at detecting dose-related trends when tumor onset hazard functions are proportional to each other. For more power against other dose related group differences, weighted versions of the statistic are also available see Breslow (1984) or Crowley and Breslow (1984) for details. 

Gaylor, D.W. and Kodell, R.L. (2001). Dose-response trend tests for tumorogenesis adjusted for differences in survival and body weight across doses. Toxicol. Set, 59 219-225. 

While comparisons of individual treated groups with the control group are important, a more powerful test of a possible effect of treatment will be to carry out a test for a dose-related trend. This is because most true effects of treatment tend to result in a response which increases (or decreases) with increasing dose, and because trend tests take into account all the data in a single analysis. In interpreting the results of trend tests, it should be noted that a significant trend does not necessarily imply an increased risk at lower doses. Nor, conversely, does a lack of increase at lower doses necessarily indicate evidence of a threshold (i.e., a dose below which no increase occurs). 

Trend tests are generally described as -sample tests of the null hypothesis of identical distribution against an alternative of linear order, i.e., if sample I has distribution function F i = 1 then the null hypothesis... 

Trend tests seek to evaluate whether there is a monotonic tendency in response to a change in treatment. That is, the dose response direction is absolute as dose goes up, the incidence of tumors increases. Thus the test loses power rapidly in response to the occurrences of reversals , for example, a low-dose group with a decreased tumor incidence. There are methods (Dykstra and Robertson, 1983) which smooth the bumps of reversals in long data series. In toxicology, however, most data series are short (that is, there are only a few dose levels). 

In 1985, the United States Federal Register recommended that the analysis of tumor incidence data be carried out with a Cochran-Armitage (Armitage, 1955 Cochran, 1954) trend test. The test statistic of the Cochran-Armitage test is defined as this term ... 

Antonello, J.M., Clark, R.L. and Heyse, J.F. (1993). Application of Tahey Trend Test procedures to assess developmental and reproductive toxicity. I. Measurement data. Fundam. Appl. Toxicol. 21 52-58. 

Portier, C. and Hoel, D. (1984). Type I error of trend tests in proportions and the design of cancer screens. Comm. Stat. Theory Meth. A13 1-14. 

Regression techniques are most frequently used for detection of trends in a series. For evaluating nonparametric trend tests see BERRYMAN et al. [1988]. This example series concerning the nitrate concentrations in the storage reservoir will be tested for any trends over the Ml time of observation. 

Loftis, J.C., Taylor, C.H., Newell, A.D. and Chapman, P.L. (1991) Multivariate trend testing of lake water quality. Water Resources Bulletin, 27, 461-473. 

Sanden, P., Rahm, L., Wulff, E, 1991. Non-parametric trend test of Baltic Sea data. Environmetrics, 2, 263-278. 

TABLE 15.3 Probability of Error (p) of the Chi a Trends, Tested by the Mann-Kendall Test. 

A study is considered valid if the results obtained with positive and negative controls are consistent with the laboratory s historical data and with the literature. Statistical analysis is usually applied to compare treated and negative control groups. Both pairwise and linear trend tests can be used. Because of the low background and Poisson distribution, data transformation (e.g., log transformation) is sometimes needed before using tests applicable to normally distributed data. Otherwise, nonparametric analyses should be preferred. 

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