Counting Decision Limits

In general, we assume that the statistics of counting can be adequately described by the Poisson distribution. When we calculated the various decision limits, we effectively assumed, for simplicity, the Normal distribution for the counts. We know, however, that Poisson statistics are only applicable when the probability of detection of the decay of any particular radioactive atom within the count period is small and when the statistical sample size is large. There are a number of circumstances when these conditions may not be met and we should consider whether the statistical treatment above is still valid. 

If the number of counts accumulated is small, then, even though the count distribution will be Poisson, the approximation to a Normal distribution will not be valid. This means that the relationships to calculate the decision limits given above will not be valid. For number of counts of less than 25, we must resort to the Poisson distribution itself. 

Table 5.4 Decision limits in low count situations (for 95 % confidence in each case)...

Optimum sharing of counting time between samples and background is achieved when the ratio of count times equals the ratio of sample to background activity. Decision limits are calculated according to the following equations ... 

If the number of counts is small (< 25) then the decision limits cannot be calculated from the Normal distribution but must be taken from statistical tables of the Poisson distribution. 

How does the decision limit relate to the limit of detection (LOD) Usually both terms are used synonymously, which is incorrect The LOD of a method is never given in counts or parts of a scale but Is given a dimension, such as pg/pL, ng/L or ppb, in any case the LOD is expressed in the substance domain The transfer from the signal domain of the decision limit into the substance domain of the LOD is accomplished by a valid calibration function (see Figure 3.159). 

Column manufacturers normally provide basic information about their columns, such as plate count, particle size, exclusion limit, and calibration curve. This information is necessary and fundamental, however, it is not sufficient to allow users to make an intelligent decision about a column for a specific application. For example, separation efficiency, the dependence of separation efficiency on the mobile phase, the ability to separate the system peaks from the polymer peak, the symmetry of the polymer peak, and the possible interaction with polymers are seldom provided. 

Tossing a mental coin, the decision was to analyze the case of noise proportional to the square root of the signal. This, as you will recall, is Poisson-distributed noise, characteristic of the noise encountered when the limiting noise source is the shot noise that occurs when individual photons are detected and represent the ultimate sensitivity of the measurement. This is a situation that is fairly commonly encountered, since it occurs, as mentioned previously, in UV-Vis instrumentation as well as in X-ray and gamma-ray measurements. This noise source may also enter into readings made in mass spectrometers, if the detection method includes counting individual ions. We have, in... 

The decision to use radioimmunotherapy requires consideration of the complexity, risks, and cost. The ideal candidate has limited bone marrow involvement and adequate blood cell counts. 

Microbial limits. Acceptance criteria should be set for the total count of aerobic microorganisms, the total count of yeasts and molds, and the absence of specific objectionable bacteria. A decision tree is provided in the guideline to aid in deciding which would be appropriate microbial tests. 

The geometric mean and the upper and the lower control limits are calculated from the results of examination of the first 20 RMs. Each RM is examined once. The 20 measurements are preferably done on different days and by different technicians to cover within-laboratory variations. The counts of these RMs should be plotted on a separate graph, in order to check whether these counts meet the criteria stated below (i.e. that the analytical process is under control). If the result of one or more of these 20 counts does not meet the criteria, the cause(s) for this should be identified and a decision made about the validity of the count(s). If the cause can be identified (assignable cause) then this count should be disregarded and the geometric mean and control limits recalculated from the remaining counts. If the cause cannot be found then the... 

The decision to use radioimmunotherapy must be made carefully because of the complexity, risks, and costs of the treatment regimen. Although oncologists usually select patients for therapy, the radioimmunotherapy regimen must be administered at a radiation oncology or nuclear medicine facility. Because of safety concerns related to delivery of radiation to bone marrow, candidates for radioimmunotherapy usually have limited bone marrow involvement and adequate absolute neutrophil aud platelet counts. 

Most of the effluent and environmental radioactivity measurements are made using gamma-ray spectrometry. This is a far more cost effective approach than radiochemical analysis the Instrumental measurement can be readily automated, and detection decisions can be made more or less simultaneously for many radionuclides. The validity of those decisions, and of the corresponding detection limits, however, requires either that the peaks be Isolated and lie on a linear baseline, or that a detection limit model be employed which Is more complex than that used for "simple" counting. Baseline or interference model uncertainties should be Included, and an iterative solution is required to estimate the detection limit when spectrum deconvolution is involved. Details are beyond the scope of this chapter, but a relatively simple limiting estimate can be derived by treating the estimated standard error for a low level radionuclide peak of interest as though it were the null standard error, [12, p. 81]. 

Critical limit (Lq) — a decision level Is the net count significant ... 

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