Confounding parameter estimations

An experimental design was developed which uncoupled the overall problem into a number of smaller parameter estimation problems. This approach reduced confounding between parameters, for both start-of-cycle and deactivation kinetics. 

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. ... 

NAIVE average data Standard preclinical pharmacokinetics / toxicokinetics data Simplicity Misidentification of the structural model, poor parameter estimation, confounded variability... 

Unlike the NAD approach, the NPD approach is far more general. It can easily deal with experimental data, nonstandard data, and routine PK 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 out (20-22). The NPD approach tends to confound individual differences and diverse sources of variability in a manner different from the NAD... 

Confounding of parameter estimations for different factors occurs if the factor combinations are highly correlated and, therefore, no difference between the factor effects can be detected. Confounding depends highly on the concrete experimental design. If, for example, the levels of two factors are changed in a constant ratio, it would not be possible to distinguish between the effects ofthose two factors. 

Full-factorial three-level designs are sometimes used for investigating few factors (two or three) although their statistical properties with respect to symmetry or confounding of parameter estimates are less favorable than those known for the two-level designs. In the case of many factors, the same problem as with... 

How can one avoid factors and their parameter estimates being confounded ... 

If this model is selected, one must then decide what variables to use for the ordinate and the abscissa. The parameters must be dose-sensitive, free of confounding variables, easily determined and preferably linear. We have evaluated this approach for estimating the bioavailability of calcium in mechanically deboned meat products (11). Typically, correlations between various bone parameters and dietary calcium are very high (r = 0.943 to 0.999). This is consistent with what others have found for similar parameters (46,47). These correlations are also similar to the those (r = 0.947 to 0.982) between the amount of calcium consumed and calcium retained (11) a good index procedure. 

Disadvantages arise mainly from the complexity of the statistical algorithms and the fact that fitting models to data is time consuming. The first-order (EO) method used in NONMEM also results in biased estimates of parameters, especially when the distribution of inter individual variability is specified incorrectly. The first-order conditional estimation (EOCE) procedure is more accurate but is even more time consuming. The objective function and adequacy of the model are based in part on the residuals, which for NONMEM are determined based on the predicted concentrations for the mean pharmacokinetic parameters rather than on the predicted concentrations for each individual. Therefore, the residuals are confounded by intraindividual, inter individual, and linearization errors. 

The parameter is an estimator of the "true" parameter Bj, but this estimate is contaminated by a contribution from the "true" two-variable interaction B23. It is said that 6j is confounded with 623, and that hj is an alias oi the confounded effects. 

A 2 " fractional factorial design (I = 12345) was used to estimate the model parameters. The design has a Resolution V and the desired parameters can be estimated free from confoundings with each other. The design matrix and the yields (%), y, obtained are given in Table 6.7. 

If this model is correct, a least squares fit of tbe model will give an unbiassed estimate, b, of tbe vector of the "true" model parameters b. However, if tbe model should contain also interaction terms, the estimated model parameters would be biassed by confounding with interaction effects. This bias occurs since the Taylor expansion is truncated after the linear terms. To analyze which second order interaction effects contaminate the true linear effects, we shall write down tbe augmented model with the second order Interaction terms included. 

The choice of design will depend on how detailed the desired infonnation is to be. If it is strongly suspected that certain variables will interact, it is recommended that terms for these interaction should be included in the model, and a design be selected which can estimate these parameters. Use a Resolution V design by which each two-variable interaction can be estimated, or use a Resolution TV design which will confound the interaction effect. These can then be isolated by complementary runs. 

The number of samples per subject used for this approach is typically small, ranging from one to six. The difficulties associated with this type of data preclude the use of the STS approach because there are not enough data to estimate the PK parameters for each subject separately. There are too few measurements to estimate the parameters accurately or the model may be unidentifiable in a specific individual. As does the pooled analysis technique, nonlinear mixed effects modeling approaches analyze the data of all individuals at once but take the interindividual random effects structure into account. This ensures that confounding correlations and imbalance that may occur in observational data are properly accounted for. 

In patients with hypothyroidism caused by hypothalamic or pituitary failure, alleviation of the chnical syndrome and restoration of serum T4 to the normal range are the only criteria available for estimating the appropriate replacement dose of levothyroxine. Concurrent use of dopamine, dopaminergic agents (bromocriptine), somatostatin or somatostatin analogs (octreotide), and corticosteroids suppresses TSH concentrations and may confound the interpretation of this monitoring parameter. ... 

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