Summary-measures approach

We can, of course, analyse the individual measurements, either independently at each time point (that is to say, repeating the same form of analysis using the different time points) or globally using a so-called repeated measures analysis. (Some issues to do with this will be treated in Chapter 10 and need not concern us here.) An alternative is to use the so-called summary measures approach, whereby, in an initial stage, we combine the multiple measures on individual patients into statistics which are then, in a second stage, analysed further. A very simple and obvious summary measure is the... 

Model E takes a completely different tack and uses the so-called summary-measures approach (Senn et al, 2000). Here the problem is tackled in two stages. In the first stage an estimate of (3 is produced from every one of the 16 subjects by fitting model (21.8) to the four observations for that subject. (Of course, thereby, an estimate of a is also produced from each subject, but this is not of direct interest here.) This means that the problem is reduced to one of analysing the 16 estimates from the 16 subjects. One degree of freedom is used up for the overall estimate of j8 produced from these 16 estimates and so there are 15 residual degrees of freedom. This approach has the advantage that the issue of correlation between measurements is finessed since the 16 estimates of j5 are, in fact, independent. 

The truth probably lies between these two extremes, and this is where the random-effects model F is useful. Like the summary-measures approach, with which it has conceptually much in common, this also has two levels. However, these two levels are not treated as two stages but are handled together in one model and fitting process. The individual intercept and slopes, and ft, form the first level. These are considered to be random drawings from a population with a Normal population of such values with parameters and the covariance between slope and... 

This sort of choice between models occurs all the time in PK/PD work. This is because even where, and unlike the example above, a subject or patient is given a single treatment, repeated blood samples are taken and we wish to use the observed concentration -time profiles to estimate particular parameters. We thus have a repeated-measures problem. Often a summary-measures approach is used. For example, in bioequivalence studies AUCs are compared for different formulations. These AUCs are always calculated first for each subject before proceeding to the modelling process. On the other hand, in certain applications it is not possible to cover all desired blood sampling points in all patients. Different times are used for different patients to minimize the number of samples taken. The only way in which this can be drawn together is via a random-effects approach. 

Summary measures approach. A means of analysing repeated-measures designs which proceeds in two stages. In the first, the repeated measures on each subject are reduced to a summary statistic. In the second stage, these statistics are treated as the data of the problem and analysed conventionally. The advantage is that whereas the original data will not all be independent, the summary measures are. The issue of correlation between the repeated measures is thus finessed. The problem resurfaces to some extent, however, if more than one summary measure is required per subject to capture the essence of the effect of treatment. The main disadvantage of the approach is that it can be inefficient if there are unequal amounts of information per subject. 

The family of distributions Fi(y) represents the uncertainty in the unknown y due to uncertainty in the models structure it can be probabihstically combined in a summary measure by means of a standard Bayesian approach (Apostolakis, 1993). Indicating with p Mi) the epistemic probability which expresses the analyst s confidence in the set of assumptions underpinning the /-th model (here the term epistemic... 

In summary, several approaches and measures exist for evaluating ontologies, and their selection should be derived based on the goal of the evaluation. 

In summary, measurement of interfacial rheology can take one of two approaches, either dilational or shear. The choice of approach will depend on its suitability to particular applications. The most accurate and reproducible results tend to come from methods that utilize small, reversible applied stresses and strains, thus minimizing any disruption or damage to the interfadal layer. 

Another approach to measurement of surface tension, density, and viscosity is the analysis of capillary waves or ripples whose properties are governed by surface tension rather than gravity. Space limitations prevent more than a summary presentation here readers are referred to several articles [123,124]. 

The use of nuclear techniques for the detection of buried expls (in mines) has been investigated by the US Army over the past 25 years. The basic approach is the use of a direct beam of highly penetrating radiation to irradiate the soil and the measurement of a reflected, scattered, induced or secondary signal to indicate the presence of a buried mine. A complete historical review and analysis of this work has been prepared by Coleman et al (Ref 18), A brief summary of the highlights of the overall effort is provided here... 

Direct Measurement of HO, in the Troposphere. Techniques to measure tropospheric concentrations of HO have been reviewed (O Brien Hard, submitted to Advances in Chemistry, 1991) so only a summary will be given here. The most extensively researched technique for [HO ] measurement in the troposphere is based on laser-induced fluorescence (LIF) of HO. This approach has been developed in many configurations directing the laser into the free atmosphere and collecting fluorescence back scatter (LIDAR) (105,106,107) LIF of air sampled at atmospheric pressure... 

Outcome measurement is not discussed further in this chapter, hut it should he emphasized that some distinctive contributions could be made by economics. These include the development of summary unidimensional measures (discussed in the cost-utility section earlier), and benefit valuation in monetary terms (with its attendant difficulties, even though valuation methods are breaking new ground). However, acceptable (and potentially insightful) economic evaluations can be conducted without resorting to utility or benefit measurement. Cost-effectiveness and cost-consequences approaches have a lot to offer, building on outcome measures which will be more familiar to non-economist researchers in the field. It is for this reason that cost-effectiveness and cost-consequences analyses, linked to drug trials, are the most likely to be used over the next few years. 

In summary, models can be classified in general into deterministic, which describe the system as cause/effect relationships and stochastic, which incorporate the concept of risk, probability or other measures of uncertainty. Deterministic and stochastic models may be developed from observation, semi-empirical approaches, and theoretical approaches. In developing a model, scientists attempt to reach an optimal compromise among the above approaches, given the level of detail justified by both the data availability and the study objectives. Deterministic model formulations can be further classified into simulation models which employ a well accepted empirical equation, that is forced via calibration coefficients, to describe a system and analytic models in which the derived equation describes the physics/chemistry of a system. 

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