Naive data pooling

If only a few data per subject is available, they are sometimes pooled and considered as coming from one hyperanimal. If several observations are available at the same time they are averaged and means and standard deviations can be calculated. In a second step the mean values are fitted to a pharmacokinetic model. (NAD (naive averaging data method) (Steimer et al. 1985)). A different naive technique is the NPD (naive pooled data) method proposed by Sheiner (Sheiner and Beal 1980). Again all data are pooled, but fitted in one step to a pharmacokinetic model. In both cases intra and inter individual random effects are confounded. An influence of covariates cannot be determined by this approach... 

Naive Pooled Approach. The naive pooled approach, proposed by Sheiner and Beal, involves pooling all the data from all individuals as if they were from a single individual to obtain population parameter estimates.Generally, the naive pooled approach performs well in estimating population pharmacokinetic parameters from balanced pharmacokinetic data with small between-subject variations, but tends to confound individual differences and diverse sources of variability, and it generally performs poorly when dealing with imbalanced data. Additionally, caution is warranted when applying the naive pooled approach for PD data analysis because it may produce a distorted picture of the exposure-response relationship and thereby could have safety implications when applied to the treatment of individual patients. ... 

Sheiner and Beal proposed the NAIVE pooled data (NPD) approach for the method in which all data from all individuals are considered as arising from one unique individual. Unlike the NAD approach, the NPD approach is far more general. It can easily deal with experimental data, non-standard data, and routine pharmacokinetic data. After a unique fitting of all data at once, parameter estimates are obtainable. It may perform well when variations between subjects are small. This is occasionally the case in a group of homogeneous laboratory animals from a given strain, but it is rarely true for humans. The drawbacks of NPD are the same as those of NAD, as has been repeatedly pointed The NPD approach... 

NAIVE pooled data Preclinical pharmacokinetics/ toxicokientics, experimental data Simplicity Very sensitive to imbalance and confounding correlations in the dataset... 

Sheiner and Beal (19) proposed the term naive pooled data (NPD) approach for the method in which all data from all individuals are considered as arising from one unique individual. This reference subject is characterized by a set of parameters With least-squares fitting, (j) will be the parameter vector minimizing the global objective function... 

Michaelis-Menten PK model and the one- and two-compartment models (20, 21). In all instances, a comparison was made with the naive pooled data and standard two-stage approaches for the analysis of the two types of data. The FO approach outperformed the NPD and the STS approaches on both data types. Despite the approximation, the FO approach provides good parameter estimates. When the residual error increases, the STS approach quickly deteriorates, especially with respect to variance parameters. However, the STS approach still performs reasonably well but the bias and imprecision of the estimates tend to increase with increasing residual error (21). Estimates of residual random effects have been shown to deteriorate with the FO approach when residual error increases (49). 

We start by showing that, in principle, the means and the naive pooled methods behave quite similarly. We shall call a data set balanced with respect to covari-ates if the numbers of observations are the same for any given combination of the covariates. 

Data in these studies were generated from a so-called giant rat study in our laboratory. Animals were sacrificed to obtain serial blood and tissue samples. Each point represents the measurement from one individual rat and data from all these different rats were analyzed together to obtain a time prohle as though it came from one giant rat. A naive pooled data analysis approach was therefore employed for all model fittings using ADAPT II software (21). The maximum likelihood method was used with the variance model specified as V(a, 6, h) = (j Y(d, where V a, 9, ti) is the variance for the ith point, Y 6, t,) is the ith predicted value from the dynamic model, 9 represents the estimated structural parameters, and oi and 02 are the variance parameters that were estimated. 

Hing, J.P., Woolfrey, S.G., Greenslade, D. and Wright, P.M.C. Is mixed effects modeling or naive pooled data analysis preferred for the interpretation of single sample per subject toxicokinetic data. Journal of Pharmacokinetics and Pharmacodynamics 2001b 28 193-210. 

For example, the gene expression values are 12.79,12.53, and 12.46 for the naive condition and 11.12, 10.77, and 11.38 for the 48-h activated condition from the T-cell immune response data. The sample sizes are nj = 2 = 3. The sample means are 12.60 and 11.09 and the sample variances are 0.0299 and 0.0937, resulting in a pooled variance of (0.2029). The i-statistic is (12.60 - 11.09)/0.2029 = 7.44 and the degree of freedom is ni -I- 2 2 = 3 -I- 3 — 2 = 4. Then we ean find a p-value of 0.003. If using Welch s t-test, the t-statistic is still 7.42 sinee i = n, but we find the p-value of 0.0055 since the degree of freedom is 3.364 rather than 4. We claim that the probe set is differentially expressed under the two eonditions because its p-value is less than a predetermined significance level (e.g., 0.05). In this manner, p-values for the other probe sets ean be calculated and interpreted. In Section 4.4, the overall interpretation for p-values of all of the probe sets is described with adjustments for multiple testing. The Student s t-test and Weleh s t-test are used for samples drawn independently from two eonditions. When samples from the two conditions are paired, a different version ealled the paired t-test is more appropriate than independent t-tests ... 

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