Percentile parametric estimates

In case the sample distribution is not normal, the 5 percentile of the sample distribution can be estimated non-parametrically in the same way as the LoB. However, parametric estimation is more efficient and should be used when possible. 

Figure 14-10 DoD plot for comparison of two drug assays parametric analysis. A histogram shows the relative frequency of N = 65 differences with the estimated Gaussian density distribution. Parametrically estimated 2.5, and 97.5 percentiles are shown with 90% CIs.

Parametric Estimates of Percentiles and Their Confidence Intervals... 

Example The parametric estimate of the 2.5 percentile of serum triglycerides was determined previously by the logarithmic transformation. The 0.90 confidence limits of the lower percentile are then... 

When a parametric distribution is fitted, each datum contributes to the estimate of each parameter or percentile. Whether this is good or not depends on whether the distribution to be fitted is reasonable. If it is assumed that one can identify the true distribution, the data will be used in a way that is in some sense optimal. In the real world, where the best distribution is uncertain, it may happen that estimated frequencies for one tail of a distribution are sensitive to observations on the other tail, e.g., estimates of high concentration percentiles are sensitive to observed low concentrations. 

If a parametric distribution (e.g. normal, lognormal, loglogistic) is fit to empirical data, then additional uncertainty can be introduced in the parameters of the fitted distribution. If the selected parametric distribution model is an appropriate representation of the data, then the uncertainty in the parameters of the fitted distribution will be based mainly, if not solely, on random sampling error associated primarily with the sample size and variance of the empirical data. Each parameter of the fitted distribution will have its own sampling distribution. Furthermore, any other statistical parameter of the fitted distribution, such as a particular percentile, will also have a sampling distribution. However, if the selected model is an inappropriate choice for representing the data set, then substantial biases in estimates of some statistics of the distribution, such as upper percentiles, must be considered. 

Figure 16-4 Central 95% reference interval.The 2,5 and 97,5 percentiles and their 0.90 confidence intervals of the 500 serum triglyceride concentrations (Figure i 6-3), as determined by the parametric method (see text). The curves are the estimated probability distributions.

The parametric method for the determination of percentiles and their confidence intervals assumes a certain type of distribution, and it is based on estimates of population parameters, such as the mean and the standard deviation. We are, for example, using a parametric method if we believe that the true distribution is Gaussian and determine the reference limits (percentiles) as the values located 2 standard... 

Originally a simple nonparametric method for determination of percentiles was recommended by the IFCC. However, the newer bootstrap method is currently the best method available for determination of reference limits. The more complex parametric method is seldom necessary, but it will also be presented here owing to its popularity and frequent misapplication. When we compare the results obtained by these methods, we usually find that the estimates of the percentiles are very similar. Detailed descriptions of these methods are given later in this chapter. 

The parametric method is much more complicated than the simple nonparametric method and requires computer software. The method is presented here under separate headings for testing of type of distribution, transformation of data, and the estimation of percentiles and their confidence intervals. 

It is also possible to estimate the confidence limits of percentiles determined by the parametric method. The method is presented in a later section. 

Percentile estimate with respect to a positive reference serum Non-parametric methods are preferable for the estimation... 

IM is directly represented at each IM level by the empirical distribution of the EDP results extracted from the pertinent analyses. In other words, any statistical quantity of EDP given the IM (mean, 16/50/84 percentile, standard deviation, etc.) can be estimated directly from the corresponding EDP values without any need for parametric or nonparametric regression, thus considerably simplifying postprocessing. 

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