Replicate designs

Kedwards, T.J., Maund, S.J., and Chapman, PE. (1999a and 1999b). Community level analysis of ecotoxicological field studies 1 Biological Monitoring and 11 Replicated design studies. Environmental Toxicology and Chemistry 18, 149-157 and 158-166. 

This author recommends a minimum plot size of 4 rows x 200 ft for each treated plot. Foliar sampling would occur on the middle two rows with a 10-ft buffer on each end. Soil sampling would occur on each side of the middle two rows with a 10-ft buffer on each end. The 180-ft rows should be divided into 60-ft replicates designated as A, B, and C. The untreated plot should be 2 rows x 50 ft. For tree crops, 3 rows x 14 trees should be treated. The middle row should be sampled excluding the first and last trees. 

I. Mohmood and H. Mahayni, A limited sampling approach in bioequivalence studies application to long half life drugs and replicate design studies, Int. J. Clin. Ther, 37, 275 (1999). 

Generating two replicate designs provides a measure of variability within a method due to chance. 

As was mentioned above, a disadvantage of this approach is that the variation that is measured at each replicated design point will be from many sources, including sources of environmental variation, and it will be impossible to attribute the variation to a particular source. Another disadvantage of this approach is that it assumes that the variation experienced at the design points during the course of the experiment is similar to that experienced in practice in the real world. Frequently an experiment will be well-controlled and so the variation experienced will be considerably less than that normally encountered. 

When some of the possible data points are omitted in factorial designs they are known as fractionally or partially replicated designs. The choice of points to be omitted is of considerable importance. There is no single fractional replicate which is best for any given complete factorial design. Usually the experimenter will have some idea as to the expected effects. When this sort of intuition is available, a particular design may be developed to fit a particular problem. 

In two-way analysis of variance with no replications, interaction of factors was part of the experimental error or more precisely of the residual variance. To separate the interaction from the residual variance or from experimental error variance, it is necessary to replicate design point, i.e. all combinations of rows and columns k... 

If the arithmetic of Cochran s test is below the tabular value, the null hypothesis that variances are equal is accepted. Tabular values are in Table I and are determined for the associated threshold or significance level a=0.05 and degree of freedom fi=n-l number of data used in calculating the variance sf is reduced by one, or in other words the number of replicated design points (trials) is reduced by one and the f2-number of variances or number of trials. 

Fractional replicate designs Categorical/qualitative and quantitative Screening of factors... 

Variables ai (lj and x are actual effects of i rows, j columns and the k factor level. One can notice that the k index is bracketed to indicate that in the design of Latin squares there are no m results, as is the case with a three-factorial design with one design-point replication. Design of Latin squares actually has m2 observations or data. 

Note that in preliminary calculations the sum of replicated design points-trials is taken as the response, and thus the number of replicated design points n is introduced Eq. (2.70). As there exists replication of trials, it is evident that the error sum of squares is calculated in accord with analysis of variance methodology. To enable comparison of such variance determination with classical analysis of variance, it is necessary to transform Table 2.107 into Table 2.108. 

The reproducibility variance from five replicated design points has the value Sp =60.93 or Sp=7.81. 

The confidence of the response estimate by a regression model differs in different simplex points. Let the variance of response estimate be Sy, and let the variance of replicated design points be Sy2. An example of determining a variance of response estimate is demonstrated on a second-order regression model for a three-component mixture. 

Variances of replicated design points are equal, so that the reproducibility variance is ... 

Figure 3.34 The same 23 1 fractional replicate design (i+def) in the process factors d, e, and f set up at the three points of composition...

Some regulatory authorities permit the use of scaling to broaden the bioequivaience limits. In a two-period design, the limits are scaled to the residual standard deviation, or in a replicate design, to the within-subject standard deviation of the comparator formulation (16-18). 

For single-dose studies, replicate designs that reduce the total number of subjects required have been also proposed (22,24,32,41) for the assessment of BE for HV drugs. Roughly, about half as many volunteers are needed in a four-period study than in a two-period investigation to attain the same statistical power. 

However, replicate designs (as multiple-dose studies) lead to increased duration of exposure to the drug and, moreover, potential practical problems may arise, e.g., increased incidence of subject withdrawals. In addition, in certain cases, e.g., for drugs with long half-lives, replicated designs are difficult to apply. 

The scaling factor, ay/, in the case of a two-period design is the residual standard deviation, (Trcs, estimated from ANOVA, while for a replicate design the within-subject standard deviation of the R formulation, (Twr> is used. 

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