Mantel tests

The problem arises when attempting to statistically evaluate the degree of congruence between trees from different data sets. Among several formal methods which have been developed, we used the Mantel test (1967). This is a non parametric procedure, based on randomization, which generates statistical sign ificance levels for correlational measures of similarity between distance matrices. We selected this... 

For the allozymic data, Rogers (1972) distances were used, since Mantel test requires metric distances, and Nei s D are not. Results are summarized in Table 1. As already seen, molecular data matrices showed a statistically significant correlation with one another. On the other hand, morphometric matrices were not congruent with one another. However, while body and appendage morphometrics and epiphallus shape were not correlated to any data matrix either morphological or... 

FIG, 28-20 Assembly of a corrosion-test spool and specimens. Mantell, ed., Engineering Materials Handbook, McGraw-Hill, New York, 1958. )... 

Here you can still use the Pearson chi-square test as shown in the 2x2 table example as long as your response variable is nominal and merely descriptive. If your response variable is ordinal, meaning that it is an ordered sequence, and you can use a parametric test, then you should use the Mantel-Haenszel test statistic for parametric tests of association. For instance, if in our previous example the variable called headache was coded as a 2 when the patient experienced extreme headache, a 1 if mild headache, and a 0 if no headache, then headache would be an ordinal variable. You can get the Mantel-Haenszel /pvalue by running the following SAS code ... 

On occasion you need to perform a test for association between two categorical variables while stratifying, or controlling, for a third variable. The Cochran-Mantel-Haenszel test for association stratifies by a third variable to give proper weight to strata size. In the previous example, let s assume that you want to stratify your analysis by center to control for differences in center size. You can then run a Cochran-Mantel-Haenszel test like this ... 

The Cochran-Mantel-Haenszel (CMH) test contains three different tests for association. The following table describes each test and shows where the / -value can be found in your pvalue data set. 

For Cochran-Mantel-Haenszel tests in PROC FREQ, you usually want to structure your TABLE statement in the following way ... 

These tests are based on the generalized logistic function (Cox, 1972). Specifically one can use the Cocrhan-Armitage test (or its parallel, Mantel-Haenszel verson) for monotonic trend as heterogeneity test. 

As we shall see later the data type to a large extent determines the class of statistical tests that we undertake. Commonly for continuous data we use the t-tests and their extensions analysis of variance and analysis of covariance. For binary, categorical and ordinal data we use the class of chi-square tests (Pearson chi-square for categorical data and the Mantel-Haenszel chi-square for ordinal data) and their extension, logistic regression. 

The formula for the test statistic is somewhat complex, but again this statistic provides the combined evidence in favour of treatment differences. When Mantel and Haenszel developed this procedure they calculated that when the treatments are identical the probabilities associated with its values follow a x i distribution. This is irrespective of the number of outcome categories, and the test is sometimes referred to as the chi-square one degree of freedom test for trend. 

For binary, categorical and ordinal data there is also an approach which is a further form of the Mantel-Haenszel chi-square test. You will recall that the MH test is used for ordinal responses comparing two treatments. Well, this procedure generalises to allow ordering across the treatment groups in addition, for each of... 

The Cochran-Mantel-Haenszel (CMH) tests are a collection of procedures that extend the simple chi-squared tests introduced in Chapter 4 to incorporate the multicentre setting. Landis, Heyman and Koch (1978) provide further details. 

Mantel-Haenszel test, the combined studies indicated a highly significant difference (c - 483 df = 1 p < 10 This finding represents overwhelming statistical evidence that in schizophrenia, antipsychotics prevent relapse. 

Two studies found maprotiline to be clearly superior to placebo and two other studies found trends in the same direction ( p < 0.001, combined data) (Table 7-5) (105, 106, 107 and 108). More than 1,600 patients were randomly assigned to either maprotiline or a standard HCA 660 on maprotiline did well, and 247 showed minimal improvement, no change, or worsened. For the HCAs (usually imipramine or amitriptyline), 640 patients did well, and 255 showed minimal improvement, no change, or worsened. In summary, 73% did well with maprotiline, and 72% did well with a standard antidepressant. Combining these data with the Mantel-Haenszel test indicated no difference in efficacy (Table 7-6). Maprotiline has a dose-dependent risk of seizures. As with TCAs and amoxapine, overdoses of maprotiline can be lethal. %... 

Compared with TCAs and MAOIs, BZDs have a rapid onset of action, have fewer unpleasant adverse effects, and are considerably less toxic. Despite these advantages, however, BZDs (with the possible exception of alprazolam, discussed later) generally appear devoid of true antidepressant effects. When the results of several well-controlled studies totalling 1,275 patients were summarized, the overall response to BZDs was 51% versus 73% for standard antidepressants. This generated a highly significant difference (p < 10 ) on the Mantel-Haenzsel test in favor of the antidepressants (Table 7-15). 

We performed a Mantel-Haenszel test on three studies comparing SAMe with placebo and found that this agent was significantly better (i.e., chi square = 26.0 p < 3 X 10 ) (253). A second Mantel-Haenszel test on nine studies comparing SAMe with standard antidepressants revealed a chi square of 6.7 ( p < 0.01). In sum, 109 of 142 SAMe-treated patients and 80 of 124 TCA-treated patients were classified as responders (i.e., a 12% difference favoring SAMe) ( 253). 

Kjellstrom, T., P. Kennedy, S. Wallis, and C. Mantell. 1986. Physical and Mental Development of Children with Prenatal Exposure to Mercury from Fish. Stage 1 Preliminary Test at Age 4. Report 3080. Solna, Sweden National Swedish Environmental Protection Board. 

Relationships between the individual LOE can be examined via principal components analysis (PCA). Correlations among principal components for individual LOE indicate concordance or agreement. Relationships between different SQT LOE can also be assessed using other methods including Mantel s test (Legendre and Fortin, 1989) coupled with a measure of similarity or ordination canonical discriminant (or correspondence) analyses multidimensional scaling (MDS). 

The analytical approach to safety data is limited but growing (Dubey et al., 2006). Some suitable statistical techniques that can be employed include Fisher s exact test, the Mantel-Haenszel test, and the adapted Cochran-Mantel-Haenszel test, all of which can be used to compare adverse event rates between treatment groups (see Chow and Liu, 2004, for further details). 

Kjellstrom T, Kennedy P, Wallis S, Mantell C (1986) Physical and mental development of children with prenatal exposure to mercury from fish. Stage 1. Preliminary tests at age 4. Solna, National Swedish Environmental Board (Report No. 3080). 

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