Limits of equivalence

Manure Limit of equivalent of 170 kgN/ha can be applied per year, though co-operation with other holdings is allowed. Annex VII sets maximum stocking rates Sufficient storage capacity required... 

In a prospective double-blind study of more than 600 patients, 0.6 mg/kg of DAMB was compared with 3.0 mg/kg of L-Amb, a dose relation at the lower limit of equivalent doses determined in an animal model (117). At these dosages, in a large prospective double-blind study, there was a doubling of serum creatinine concentration in 19% of neutropenic patients receiving empirical therapy with L-AmB and 34% receiving conventional amphotericin (47). 

Even if we accept the limitations to which equivalence trials are subject, if our purpose is to prove that two treatments are exactly equal it does not matter how weak our standards of proof are, we shall not be able to do so. Consider case D in Figure 15.1. The confidence limits for the true treatment difference lie well within the limits of equivalence but it is clear that we could establish much narrower limits of equivalence which the confidence limits would exceed. One way to deal with narrower limits of equivalence would be to demand lower standards of proof. For example, instead of using 90% confidence intervals we could use less stringent 50% limits in an attempt to match narrower limits of equivalence. Alternatively, we could increase the sample size. However, whatever we do we shall never succeed in shrinking the confidence intervals to a point. Hence a proof of exact equality is impossible. 

In a trial of equivalence, however, we must take the issue more seriously. The null hypotheses considered under Section 15.2.1 make explicit reference to a difference, S. Of course, we can still calculate the confidence intervals and leave it up to the reader to determine whether they fall within whatever limits of equivalence are considered appropriate (see section 15.2.9 below), but one would hardly embark on such a trial without having at least some idea as to what constitutes a success. In general, one should not assume that the clinically relevant difference used for planning conventional... 

One way to deal with this is to carry out a parallel assay comparing at least two doses of the test with two doses of the reference formulation. Ideally one should show that the two formulations exhibit equivalent dose-response. An example of such a study (Senn, 2002b Senn et ah, 1997) was mentioned in the introduction, where two forms of dry-powder inhaler were compared. The idea, essentially, is to show that the test formulation is equivalent at the same nominal dose as the standard but also not equivalent to higher or lower doses of the standard. This is not at all a foregone conclusion and one of the problems has to do with limits of equivalence, which will vary from pharmacodynamic parameter to parameter. 

In practice, neither Lindley s approach nor any of the other Bayesian suggestions is used. However, some standard frequentist approaches can be given a fiducial interpretation, which is very similar to a Bayesian one involving uninformative priors (O Quigley and Baudoin, 1988). For example, if one requires that the probability that the true unknown bioavailability ratio lies within the limits of equivalence should be at least 95%, then this is approximately equivalent to Westlake s symmetrical confidence limit approach. Alternatively, if one requires that the probability of inferior bioavailability should be less than 5% and also that the probability of superior bioavailability should be less than 5%, then this is approximately equivalent to requiring that conventional 90% limits should lie within the ranges of equivalence. 

A problem obviously exists in trying to characterise anomalies in concrete due to the limitations of the individual techniques. Even a simple problem such as measurement of concrete thickness can result in misleading data if complementary measurements are not made In Fig. 7 and 8 the results of Impact Echo and SASW on concrete slabs are shown. The lE-result indicates a reflecting boundary at a depth corresponding to a frequency of transient stress wave reflection of 5.2 KHz. This is equivalent to a depth of 530 mm for a compression wave speed (Cp) of 3000 m/s, or 706 mm if Cp = 4000 m/s. Does the reflection come from a crack, void or back-side of a wall, and what is the true Cp ... 

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

The theoretical limit of light capacity has been estimated for an ideal reaction that provides yellow light with a photopic factor of 0.85 in a quantum yield of one at 5 Af concentration as 173,000 (Im-h)/L, equivalent to the light output of a 40-W bulb burning continuously for two weeks (237). The most efficient formulation available, based on oxaUc ester chemiluminescence, produces about 0.5% of that limit, with a light capacity of 880 (Im-h)/L (237). 

The nature of potential exposure ha2ards of low level microwave energy continues to be investigated (116—118). In the United States, leakage emission from microwave ovens is regulated to the stringent limit of 5 mW/cm at 5 cm (119). There is no federal limit on emission from industrial systems but the IMPI has set a voluntary standard which specifies 10 mW/cm at 5 cm (120). Emission values are equivalent to personnel exposures at several meters, well below limits that had previously prevailed in eastern Europe. This conclusion, derived for microwave ovens, should be vaUd for all microwave systems (121). 

NO Abatement. Source performance standards for nitric acid plants in the United States were introduced by the U.S. EPA in 1971 (55). These imposed a discharge limit of 1.5 kg of NO as equivalent nitrogen dioxide per 1000 kg of contained nitric acid, which corresponds to about 200—230... 

Spunbonded fabrics are effective filters in that they are layered stmctures of relatively fine fibers, the three-dimensional stmcture of which creates a torturous path. Even relatively thin spunbonded fabrics (eg, 0.2—0.25 mm) present a significant challenge to the passage of soil fines and are suitable for use in some filtration appHcations. The porosity of geotextile fabrics is classified by means of several procedures such as flux (volume flow/area per time) and equivalent opening size (EOS), which is a measure of the apparent pore size of the openings in the fabric. The flux measures the porosity to Hquid water, and the EOS measures the porosity to soHd particles of a known diameter. Literature is available on limitations of particular styles of fabrics within an apphcation (63). 

Method Transfer. Method transfer involves the implementation of a method developed at another laboratory. Typically the method is prepared in an analytical R D department and then transferred to quahty control at the plant. Method transfer demonstrates that the test method, as mn at the plant, provides results equivalent to that reported in R D. A vaUdated method containing documentation eases the transfer process by providing the recipient lab with detailed method instmctions, accuracy and precision, limits of detection, quantitation, and linearity. 

Sihcate solutions of equivalent composition may exhibit different physical properties and chemical reactivities because of differences in the distributions of polymer sihcate species. This effect is keenly observed in commercial alkah sihcate solutions with compositions that he in the metastable region near the solubihty limit of amorphous sihca. Experimental studies have shown that the precipitation boundaries of sodium sihcate solutions expand as a function of time, depending on the concentration of metal salts (29,58). Apparently, the high viscosity of concentrated alkah sihcate solutions contributes to the slow approach to equihbrium. 

Determination of accuracy and precision should be made by analysis of repHcate sets of analyte samples of known concentration from equivalent matrix. At least three concentrations representing the entire range of the caUbration should be studied one near the minimum (MAQ), one near the middle, and one near the upper limit of the standard curve. 

A primary concern in coal-fired power generation is the release of air pollutants. Limits on SO2 output, 0.52 g/MJ equivalent of coal input to a new plant, have been estabflshed. Eor a bituminous coal of 27.9 MJ/kg there is thus an upper limit of 0.72% sulfur content. Relatively few coals can meet this requirement. The U.S. Department of Energy indicated recoverable reserves of 420 x 10 t in 1987 (2) that were categorized by sulfur content 33.5% had 0.6% S or less, 15.4% had between 0.61% and 0.83% S, 16.1% had between 0.84 and 1.67% S, 12.4% had between 1.68 and 2.50% S, and 22.6% had more than 2.5% S. The lowest sulfur coal, 86%, is found west of the Mississippi River, mainly in Montana and Wyoming, quite distant from the electric power demand centers in the East. A trend to utilization of the western coals has developed. 

The main limitation of the pilot-operated regulator is stability. When the gain in the pilot amplifier is raised too much, the loop can become unstable and oscillate or hunt. The two-path pilot regulator (see b) is also available. This regulator combines the effects of self-operated and the pilot-operated styles and mathematically produces the equivalent of proportional plus reset control of the process pressure. 

Suction Limitations of a Pump Whenever the pressure in a liquid drops below the vapor pressure corresponding to its temperature, the liquid will vaporize. When this happens within an operating pump, the vapor bubbles will be carried along to a point of higher pressure, where they suddenly collapse. This phenomenon is known as cavitation. Cavitation in a pump should be avoided, as it is accompanied by metal removal, vibration, reduced flow, loss in efficiency, and noise. When the absolute suction pressure is low, cavitation may occur in the pump inlet and damage result in the pump suction and on the impeller vanes near the inlet edges. To avoid this phenomenon, it is necessary to maintain a required net positive suction head (NPSH)r, which is the equivalent total head of liquid at the pump centerline less the vapor pressure p. Each pump manufacturer publishes curves relating (NPSH)r to capacity and speed for each pump. 

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