Upper confidence limit

Upper confidence limit (UCL) A statistical procedure used to estimate whether the true value is higher than the measured value. 

The upper confidence limit CL (Xmean = 90) is less than 100. 

A horizontal is drawn through the upper confidence limit marked with a circle or a square, as appropriate, in Figure 2.14... 

Figure 4.34. The confidence limits of the mean of 2 to 10 repeat determinations are given for three forms of risk management. In panel A the difference between the true mean (103.8, circle ) and the limit L is such that for n = 4 the upper confidence limit (CLu, thick line) is exactly on the upper specification limit (105) the compound risk that at least one of the repeat measurements yi >105 rises from 23 n = 2) to 72% (n = 10). In panel B the mean is far enough from the SLj/ so that the CLu (circle) coincides with it over the whole range of n. In panel C the mean is chosen so that the risk of at least one repeat measurement being above the SLu is never higher than 0.05 (circle, corresponds to the dashed lines in panels A and B).

If the risk of OOS results is disregarded, a refined strategy would be to use a flexible limit, namely < L for L = 100.56. .. 104.42, which would make the upper confidence limit CL (Xmean) coincide with the 105% specification limit (circled bold line in panel B). The OOS risk in panel B is larger than that in A for n > 4. 

The reference value is outside the (upper) confidence limit and therefore the result is classified to be incorrect. This can also be proved by the f-test... 

Likewise for this example, the Z statistic of 1.5606 corresponding to the upper correlation coefficient confidence limit is shown in the graphic below (Graphic 60) as having a p value of 0.91551 this represents the upper confidence limit for the 0.80 correlation example problem. Finally then, for the example problem the correlation confidence limits are from 0.562575 to 0.91551 (i.e., 0.56 to 0.92). 

Table 1. Percutaneous toxicity of tested agents LD50 p.c. mg/kg [2] + standard deviation or (lower - upper confidence limit).

Multistage model (equivalent to linear with use of upper confidence limit)... 

The 95% confidence limits of the estimate of the linear component of the LMS model, /, can also be calculated. The 95% upper confidence limit is termed qi and is central to the US-EPA s use of the LMS model in quantitative risk assessment, as qi represents an upper bound or worst-case estimate of the dose-response relationship at low doses. It is considered a plausible upper bound, because it is unlikely that the tme dose-response relationship will have a slope higher than qi, and it is probably considerably lower and may even be zero (as would be the case if there was a threshold). Lfse of the qj as the default, therefore, may have considerable conservatism incorporated into it. The values of qi have been considered as estimates of carcinogenic potency and have been called the unit carcinogenic risk or the Carcinogen Potency Factor (CPF). 

That the 95% upper confidence limit estimate, qi, was insensitive with only small changes in values being obtained for large changes in the data... 

Studies in rats reported renal tubular adenomas and adenocarcinomas in male and female animals at doses of 20 mg/kg/day (Kociba et al. 1977a). Metastasis to the lungs was observed. Combined incidences of renal tubular neoplasms in males (9/39, 23%) and in females (6/40, 15%) increased (p <0.05) over controls (males-1/90, females-0/90, 0%). The tumor incidence was not increased in the 0.2 and 2 mg/kg/day dose groups but there were some indications of hyperplasia in animals exposed to 2 m /kg/day. The EPA (1990f) evaluated these data and calculated a human potency factor of 7.8x10 (mg/kg/day) (qi ), representing 95% upper confidence limit of extra lifetime human risk. Based on this value, cancer risk levels of 10, 10, and 10 correspond to exposures of 0.001, 0.0001, 0.00001 mg/kg/day. 

The upper end of the confidence interval, the upper confidence limit, is given by ... 

The quantity c is very closely related to the odds ratio in fact c is the log of the OR, adjusted for the covariates. The anti-log of c (given by e"") gives the adjusted OR. Confidence intervals in relation to this OR can be constructed initially by obtaining a confidence interval for c itself and then taking the anti-log of the lower and upper confidence limits for c. 

While thep-value allows us the ability to judge statistical significance, the clinical relevance of the finding is difficult to evaluate from the calculated confidence interval because this is now on the log scale. It is usual to back-transform the lower and upper confidence limits, together with the difference in the means on the log scale, to give us something on the original data scale which is more readily interpretable. The back-transform for the log transformation is the anti-log. 

If this confidence interval is on the log scale, for example with both the odds ratio and the hazard ratio, then both the lower and upper confidence limits should be converted by using the anti-log to give a confidence interval on the original odds ratio or hazard ratio scale. 

Max., maximum level found L UCL, lower and upper confidence limits... 

The critical value of CVp has to be lower than the maximum permissible true value (e.g. lower than CVp 0.128 when there is no bias). The maximum permissible value of the true CVp will be referred to as its "target level". In order to have a confidence level of 95% that a subject method meets this required target level, on the basis of CVp estimated from laboratory tests, an upper confidence limit for CVp is calculated which must satisfy the following criterion reject the method (i.e. decide it does not meet the accuracy standard) if the 95% upper confidence limit for CVp exceeds the target level of CVp. Otherwise, accept the method. This decision criterion was implemented in the form of the Decision Rule given below which is based on assumptions that errors are normally distributed and the method is unbiased. Biased methods are discussed further below. 

For our validations, a CVp is a pooled estimate calculated from the particular type of statistical data set (36 samples) described earlier in the Statistical Experimental Design section of this report. A statistical procedure is given in Hald JL for determining an upper confidence limit for the coefficient of variation. This general theory had o be adapted appropriately for application to a pooled CVp estimate. For this design, and under the stated assumptions, there is a one-to-one correspondence between values of CVp and upper confidence limits for CVp. Therefore, the confidence limit criterion given above is equivalent to another criterion based on the relationship of CVp and its critical value. The... 

In cases where confidence limits can be calculated for the bias, the critical CV-p should be read from the dotted curve at a position corresponding to the 95% upper confidence limit for the bias. This is a conservative procedure. 

As would be expected, in order to be able to have at least 95% confidence that the true CV p does not exceed its target level, we must suffer the penalty of sometimes falsely accepting a "bad" method (i.e. one whose true CV p is unsatisfactory). Such decision errors, referred to as "type-1 errors", occur randomly but have a controlled long-term frequency of less than 5% of the cases. (The 5% probability of type-1 error is by definition the complement of the confidence level.) The upper confidence limit on CV p is below the target level when the method is judged acceptable... 

The clean room or clean zone is deemed to have met the specified air cleanliness classification if the averages of the particle concentrations measured at each of the locations and, when applicable, the 95% upper confidence limit, do not exceed the concentration limits required [13,15,19],... 

The use of MLEs of probability coefficients, rather than upper confidence limits (UCLs), to classify waste can be justified, in part, on the grounds that the assumed exposure scenarios for hypothetical inadvertent intruders at waste disposal sites are expected to be conservative compared with likely on-site exposures at future times. However, uncertainties in probability coefficients should still be considered in classifying waste. When risk is calculated using MLEs of... 

For the most frequently used low-dose models, the multi-stage and one-hit, there is an inherent mathematical uncertainty in the extrapolation from high to low doses that arises from the limited number of data points and the limited number of animals tested at each dose (Crump et al., 1976). The statistical term confidence limits is used to describe the degree of confidence that the estimated response from a particular dose is not likely to differ by more than a specified amount from the response that would be predicted by the model if much more data were available. EPA and other agencies generally use the 95 percent upper confidence limit (UCL) of the dose-response data to estimate stochastic responses at low doses. 

RI TSCA UCL UF WIPP WIPPLWA risk index Toxic Substances Control Act upper confidence limit uncertainty factor Waste Isolation Pilot Plant Waste Isolation Pilot Plant Land Withdrawal Act... 

This approach uses the upper confidence limit of the calibration intercept a0 derived from nc measurements of calibration samples [DIN 32 645] ... 

An empirical, but often practical way of sampling has been presented by EXNER et al. [1985]. They divided an area into suitable clean-up units of practical size to solve a problem of hazardous waste. Inside these strips, samples were taken along transects and some composite samples were formed from different combinations of the individual samples. After homogenization of the composite samples randomly selected aliquots of soil were taken and analyzed. The estimated arithmetic mean and its standard deviation enabled computation of an upper confidence limit for the mean concentration of the clean-up units. 

Student s t-test is frequently used in statistical evaluations of environmental chemical data. It establishes a relationship between the mean (x) of normally distributed sample measurements, their sample standard deviation (,v), and the population mean (p). Confidence intervals may be calculated based on Student s t-test (Equation 10). The upper limit of the confidence interval is compared to the action level to determine whether the sampled medium contains a hazardous concentration of a pollutant. If the upper confidence limit is below the action level, the medium is not hazardous otherwise the opposite conclusion is reached. 

If the extrapolation factor (ratio of the mouse dose to the expected human exposure adjusted for stage sensitivity, dose rate, and other relevant factors) is taken to be 1,000, the 95% upper confidence limit on the mutation rate for the lower human exposure is 0.000003. 

An estimated two-sided interval from the lower to upper confidence limit of an estimate of a statistical parameter. This interval is expected to enclose the true value of the parameter with a specified confidence. For example, 95% confidence intervals are expected to enclose the true values of estimated parameters with a frequency of 95%. 

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