Population methods nonparametric

Fattinger, K. E. and Verotta, D., A nonparametric subject-specific population method for deconvolution II. External validation, J. Pharmacokinet. Biopharm., 23 611-634, 1995. 

In addition to the STS and the NLME approach, other population approaches are available, including the Bayesian and the nonparametric modeling methods. These techniques are less frequently applied in drug development. Thus, the following section will refer to the NLME approach. 

Jerling M, Merle Y, Mentre F, Mallet A. Population pharmacokinetics of clozapine evaluated with the nonparametric maximum likelihood method. Br J Clin Pharmacol 1997 44(5) 447-53. 

In Chapter 10 we saw that there are various methods for the analysis of categorical (and mostly binary) efficacy data. The same is true here. There are different methods that are appropriate for continuous data in certain circumstances, and not every method that we discuss is appropriate for every situation. A careful assessment of the data type, the shape of the distribution (which can be examined through a relative frequency histogram or a stem-and-leaf plot), and the sample size can help justify the most appropriate analysis approach. For example, if the shape of the distribution of the random variable is symmetric or the sample size is large (> 30) the sample mean would be considered a "reasonable" estimate of the population mean. Parametric analysis approaches such as the two-sample t test or an analysis of variance (ANOVA) would then be appropriate. However, when the distribution is severely asymmetric, or skewed, the sample mean is a poor estimate of the population mean. In such cases a nonparametric approach would be more appropriate. 

The sample mean is a poor measure of central tendency when the distribution is heavily skewed. Despite our best efforts at designing well-controlled clinical trials, the data that are generated do not always compare with the (deliberately chosen) tidy examples featured in this book. When we wish to make an inference about the difference in typical values among two or more independent populations, but the distributions of the random variables or outcomes are not reasonably symmetric, nonparametric methods are more appropriate. Unlike parametric methods such as the two-sample t test, nonparametric methods do not require any assumption about the shape of a distribution for them to be used in a valid manner. As the next analysis method illustrates, nonparametric methods do not rely directly on the value of the random variable. Rather, they make use of the rank order of the value of the random variable. 

In our opinion, therefore, nonparametric methods should be chosen when assumptions (such as normality for the t test) are clearly not met and the sample sizes are so small that there is very little confidence about the properties of the underlying distribution. The nonparametric method discussed in this section is a test of a shift in the distribution between two populations with a common variance represented by two samples, and it will always be valid when comparing two independent groups. 

The population analysis methods use all the available data to estimate the population. The best estimates for the parameters of an individual study are only obtained after the population distribution has been estimated by Bayesian estimation. Essentially, the various methods estimate the population parameters d in h(fi,6 ). The methods differ primarily in the form that h(fi,6jc) is assumed to have. Despite the fact that all arrive at a quantitative description of h(fi,Ooc), the different forms have been divided into parametric, semiparametric, and nonparametric. Each of these will be described. 

The statistical methods based on assumption that the lifetime were drawn from known distributed populations such as normal etc., and below there are techniques that do not make such assumptions. The methods are recognized as distribution-free statistics or nonparametric statistics. In situations where the known assumption holds, the nonparametric tests are less efficient than parametric methods. 

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