Random data, definition

In a careful meta-analysis, 29 randomized, controlled studies of the incidence of transient radicular irritation were identified (243). Lidocaine and mepivacaine were identified as the two local anesthetics that most commonly cause transient radicular irritation, while prilo-caine, bupivacaine, and ropivacaine had the lowest incidences. Owing to insufficient data, definitive statements could not be made about the effects of the baricity of the local anesthetic, the concentration, and the effect of vasoconstrictors, although all these factors seemed not to be relevant. With regard to intrathecal ropivacaine, the incidence in the formal studies was zero. However, there has been one previous report after intrathecal administration, and one report of transient radicular irritation following epidural anesthesia with ropivacaine the symptoms resolved within 24 hours (244). 

Uncertainty expresses the range of possible values that a measurement or result might reasonably be expected to have. Note that this definition of uncertainty is not the same as that for precision. The precision of an analysis, whether reported as a range or a standard deviation, is calculated from experimental data and provides an estimation of indeterminate error affecting measurements. Uncertainty accounts for all errors, both determinate and indeterminate, that might affect our result. Although we always try to correct determinate errors, the correction itself is subject to random effects or indeterminate errors. 

Which patients should be in which data set is something that should be considered before analysis data sets are created. For example, it is often decided that all analysis data sets should have a record for a subject if that subject was randomized to treatment and is considered an intent-to-treat subject. Whether this is true or not, the specifications for analysis data sets should make it clear who should be present in any analysis data set. Here is a list of common populations and their definitions ... 

By its very definition, the MaxEnt method is optimally suited to flexibly reconstruct distributions whose main features are well represented in the available data, that is either in the observations or in the prior structural knowledge. When this is the case, the missing structure can be reasonably approximated by a collection of randomly and independently distributed constituents (by missing structure here we mean all those structural details which are not completely defined by the prior knowledge). 

The guidelines provide variant descriptions of the meaning of the term linearity . One definition is, ... ability (within a given range) to obtain test results which are directly proportional to the concentration (amount) of analyte in the sample [12], This is an extremely strict definition, one which in practice would be unattainable when noise and error are taken into account. Figure 63-la schematically illustrates the problem. While there is a line that meets the criterion that test results are directly proportional to the concentration of analyte in the sample , none of the data points fall on that line, therefore in the strictest sense of the phrase, none of the data representing the test results can be said to be proportional to the analyte concentration. In the face of nonlinearity of response, there are systematic departures from the line as well as random departures, but in neither case is any data point strictly proportional to the concentration. 

The average of a number of fine observations having random scatter is definitely more accurate, precise and, hence, more cogent than coarse data that appear to agree perfectly. 

The data supporting the long-term efficacy of carbamazepine are strong and substantial in some respects, but controversial and lacking definitive confirmation in others. As outlined in Table 6-2, a group of studies present data on carbamazepine prophylaxis with some degree of control in terms of randomization or blindness. With a few exceptions [Bellaire et al. 1990 Elphick et al. 1988 Placidi et al. 1986], most studies reported carbamazepine to be of equal efficacy compared with that of lithium. The response rate in these double-blind or partially controlled studies is also similar to the rate reported in the larger open literature. 

The optimal duration of treatment with cholinesterase inhibitors has not been definitively established. Most randomized controlled trials in patients with mild to moderate Alzheimer s disease have been 26 weeks in duration or less. However, some data (mostly open-label continuation data of placebo-controlled trials) suggest continued benefits with treatment for 1 year or longer (Bullock and Dengiz 2005 Doody et al. 2001a Farlow et al. 2000 Grossberg et al. 2004 Lyketsos et al. 2004 Mohs et al. 2001 Pirttila et al. 2004 Raskind et al. 2000, 2004 Rogers et al. 2000 Small et al. 2005 Wilcock et al. 2003 Winblad et al. 2001). 

The remaining errors in the data are usually described as random, their properties ultimately attributable to the nature of our physical world. Random errors do not lend themselves easily to quantitative correction. However, certain aspects of random error exhibit a consistency of behavior in repeated trials under the same experimental conditions, which allows more probable values of the data elements to be obtained by averaging processes. The behavior of random phenomena is common to all experimental data and has given rise to the well-known branch of mathematical analysis known as statistics. Statistical quantities, unfortunately, cannot be assigned definite values. They can only be discussed in terms of probabilities. Because (random) uncertainties exist in all experimentally measured quantities, a restoration with all the possible constraints applied cannot yield an exact solution. The best that may be obtained in practice is the solution that is most probable. Actually, whether an error is classified as systematic or random depends on the extent of our knowledge of the data and the influences on them. All unaccounted errors are generally classified as part of the random component. Further knowledge determines many errors to be systematic that were previously classified as random. 

It was postulated from the comparative data in Tables I and II and other observations that angiotensin had a definite compact conformational structure even though it is a linear peptide and should be a random coil. Tritium-exchange studies (39), CD (40), and NMR evidence (41, 42) now give support to this view. NMR studies with angiotensin, oxytocin, and vasopressin thus far have not indicated conformational restriction on the benzene rings, but the thin-film dialysis data are inconsistent with any conformation in which these bulky groups are extended from the otherwise compact conformation. 

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