Established equivalence

At the gel point, (3 —l) = l/p, which with the foregoing expression gives Eq. (14), thus establishing equivalence of the two procedures. The primary molecules in a condensation polymer must almost invariably conform to a most probable distribution (see Chap. VIII). The random cross-linking of primary molecules otherwise distributed in size has no counterpart in polyfunctional condensation, therefore. 

When using these concepts one has to keep in mind that homochirality by chemical similarity is not always a transitive relation and is thus not suitable for establishing equivalence. 

In two of the three plant examples, LVE s were run simultaneously with CAM or PCAM equipment for purposes of establishing equivalency according to the OSHA criterion and according to more detailed procedures given in the "Protocol Paper" C2.). CAM/LVE equivalency was demonstrated in both these cases. It was not possible to use LVE s in the third test. 

As seen in Figure 12.1, this confidence interval is completely contained between the equivalence margins —151/min to 151/min and all of the values for the treatment difference supported by the confidence interval are compatible with the definition of clinical equivalence we have established equivalence as defined. 

In contrast, suppose that the 95 per cent confidence interval had turned out to be (—171/min, 121/min). This interval is not entirely within the equivalence margins and the data are supporting potential treatment differences below the lower equivalence margin. In this case we have not established equivalence. 

Note that there are no conventional p-values here. Such p-values have no role in the evaluation of equivalence establishing equivalence is based entirely on the use of confidence intervals. 

In this case, the alternative hypothesis states that the two treatments are clinically equivalent the null hypothesis is saying that the two treatments are not equivalent. Note that the alternative encapsulates the objective we are trying to disprove the null in order to establish equivalence. 

With the p-value methodology we are rejecting the null hypothesis Hg in favour of the alternative hypothesis Hj, providing the two (one-sided) p-values are < 2.5 per cent. We have then established equivalence and we can talk in terms of the treatments being significantly equivalent. The terminology sounds almost contradictory, but is a correct statement. If either of the two p-values is above 2.5 per cent then the treatments are not significantly equivalent. 

Also, in a 1998 trace element study involving much lower concentrations (1/1000) 9 out of 10 metrology laboratories established equivalence to within 2.6%. This performance level can be compared with other laboratories (routine) where the range of results exceeded 50%. 

Obtaining a nonsignificant p-value in a superiority trial does not demonstrate that the two treatments are the same. This is an extremely important concept and one that is widely misunderstood. Again, then, obtaining a nonsignificant p-value in a superiority trial does not demonstrate that the two treatments are the same. Conventional p-values have no role in establishing equivalence. 

Before - identify the primary question, primary end-point and primary statistical analysis establish equivalence limits where necessary perform power and sample size calculations. 

In the case of non-significance, the interpretation depends upon background events. If we went into the experiment simply looking for a difference and have not given the matter further thought, then we are at a dead-end. No effect has been shown, but sadly neither can we can claim to have shown the absence of an effect. Ifwe had had the foresight to establish equivalence limits before performing the experiment, a demonstration that there is no effect of practical consequence may be possible. 

In establishing equivalence between Qualified invariants in different objects, such as lE) in caterpillars, and iV) in line graphs it is arbitrary to choose which set is the domain aixl which is the range, because of the existence of one-to-one correspondence If fv) is taken to be the image of B, then a function fg y is defined for... 

The tendency to establish equivalency relationships between functional groups, previously treated as unrelated, is one of the major motivations in the... 

The SITP is a quantity derived from the Annual Limit on Intake (ALI), an internationally accepted concept that has been acknowledged by the Government s Radioactive Waste Management Committee (RWMAC) as a valid method of establishing equivalent hazards of different waste types. The ALI is a derived limit for the permissible amount of radioactive material taken into the body of an adult radiation worker by inhalation or ingestion in a year. The ALI is the smaller value of intake of a given radionuclide in a year by the reference man that would result in either a committed effective dose equivalent of 0.05 Sv or 0.5 Sv to any individual organ or tissue. 

To account for scale-up effects, especially using dissimilar equipment, formulators have employed a variety of approaches. Typically, trial and error adjustments, empirical correlations between known machines, and several geometric rules of thumb have been devised. Usually, trial and error approaches will alter the amount of granulation liquid used, the post-liquid addition mixing time kneading, or the liquid addition rate to arrive at an acceptable formulation upon scale-up. Although particle size distribution and bulk/tap density measurements may be used to establish equivalence in these methods, often visual judgments are made by experienced operators on the floor with a feel for proper appearance and manual consistency. 

Establishing equivalence between original and transformed problem... 

In some instances (see example (e) in section 5.1, In vivo studies ) plasma concentration time-profile data are not suitable for assessing equivalence between two formulations. Although in some cases pharmacodynamic bioequivaience studies can be an appropriate tool for establishing equivalence, in others, this type of study cannot be performed because of a lack of meaningful pharmacodynamic parameters which can be measured a comparative clinical trial then has to be performed to demonstrate equivalence between... 

The methodology for establishing equivalence between pharmaceutical products by means of a clinical trial in patients with a therapeutic end-point has not yet evolved as extensively as for pharmacokinetic bioequivalence trials. However, some important items which need to be defined in the protocol can be identified. 

Collision-free is the most established equivalent term, but it sometimes gives the wrong impression that collisions do not exist at all. Collision-resistant has also been used, and computationally collision-free would seem appropriate, too. 

Zeroth Law If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other. This law simply establishes equivalence in thermodynamic systems. 

As can be seen from the table, the excipients all have pharmacopoeial monographs, but it is important to understand that compliance with a monograph does not indicate equivalence between different grades or suppliers. The monographs confirm the chemical identity and purity of the excipients but do not measure the performance of the materials as diluents. To establish the equivalency of excipients obtained from different sources, it is necessary to perform some kind of functionality testing. The Handbook of Pharmaceutical Excipients, a joint publication between the Pharmaceutical Press and the American Pharmaceutical Association, contains some details of functional tests carried out on a wide range of excipients, but the onus on establishing equivalency of excipients still remains with the user. 

It is not clear whether equivalence can be established on the basis of similar design, comparable results, or either. Alberta adopted an intensity design similar to the proposed national scheme, in part, to facilitate establishing equivalence. British Columbia, Ontario and Quebec are committed to absolute caps, and would need to demonstrate comparable results, if that test of equivalence is allowed. 

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