Confounding errors

Figure 3 Mean predicted mental development index scores at four ages for infants in the three umbilical cord blood lead categories. Scores are least-squares means, derived from a regression equation that included only the l a priori confounders. These are the scores that infants in the three exposure groups would be expected to achieve based solely on the confounders. Error bars represent one standard error...

For a problem for which we cannot obtain an analytical solution, you need to determine sensitivities numerically. You compute (1) the cost for the base case, that is, for a specified value of a parameter (2) change each parameter separately (one at a time) by some arbitrarily small value, such as plus 1 percent or 10 percent, and then calculate the new cost. You might repeat the procedure for minus 1 percent or 10 percent. The variation of the parameter, of course, can be made arbitrarily small to approximate a differential however, when the change approaches an infinitesimal value, the numerical error engendered may confound the calculations. 

Correlations are inherent in chemical processes even where it can be assumed that there is no correlation among the data. Principal component analysis (PCA) transforms a set of correlated variables into a new set of uncorrelated ones, known as principal components, and is an effective tool in multivariate data analysis. In the last section we describe a method that combines PCA and the steady-state data reconciliation model to provide sharper, and less confounding, statistical tests for gross errors. 

The key idea of this section is to combine PCA and the steady-state data reconciliation model to provide sharper and less confounding statistical tests for gross errors, through exploiting the correlation. 

Limitations include difficulties in performing a correct exposure assessment, in some cases even a lack of information on exposure, insufficient sample size (i.e., small number of subjects in the study), selected group of subjects (e.g., the workforce), short length of follow-up, exposure to more than one substance, and potential errors (bias, confounding). 

Dose Strategy. The most insidious potentiai methodoiogical error in plasma level/clinical response studies is the possible confound due to increasing the dose too soon when a patient fails to respond. This error frequently results in missing the therapeutic threshold level because patients are not kept on the lower dose for a sufficient time to document ineffectiveness. Additionally, because patients may be responding at a slower rate than the rate of dose increases, responders at a higher dose may have actually improved at a lower dose had it been maintained for a longer period of time. 

Insofar as the scale-up of pharmaceutical liquids (especially disperse systems) and semisolids is concerned, virtually no guidelines or models for scale-up have generally been available that have stood the test of time. Uhl and Von Essen [54], referring to the variety of rules of thumb, calculation methods, and extrapolation procedures in the literature, state, Unfortunately, the prodigious literature and attributions to the subject [of scale-up] seemed to have served more to confound. Some allusions are specious, most rules are extremely limited in application, examples give too little data and limited analysis. Not surprisingly, then, the trial-and-error method is the one most often employed by formulators. As a result, serendipity and practical experience continue to play large roles in the successful pursuit of the scalable process. 

Solomon confounds the errors of the materialists of his time, and teaches us at the same time that they reasoned as foolishly as those of our day -... 

Thus one cannot, without error, confound this Humid Radical with Innate Fire. The latter is the inhabitant, the former the habitation, the dwelling. It is, in all the Mixts, the laboratory of Vulcan the hearth on which is preserved that immortal Fire, the prime-motor created from all the faculties of individuals the universal Balm, the most precious Elixir of Nature, the perfectly sublimated Mercury of Life, which Nature distributes by weight and measure to all the Mixts. He who will know how to extract this treasure from the heart, and from the hidden center of the productions of this lower world, to despoil it of its thick elementary shell, which conceals it from our eyes and to draw it from the dark prison in which it is enclosed and inactive, may boast of knowing how to make the most precious MEDICINE to relieve the human body. 

Equation (7.17) introduces a number of new parameters, although physical properties such as AHR should be available. If all the parameters are all known with good accuracy, then the introduction of a heat balance merely requires that the two parameters k0 and E/Rg — Tact be used in place of each rate constant. Unfortunately, parameters such as UAext have 20% error when calculated from standard correlations, and such errors are large enough to confound the kinetics experiments. As a practical matter, Tout should be measured as an experimental response that is used to help determine UAext. Even so, fitting the data can be extremely difficult. The sum-of-squares may have such a shallow minimum that essentially identical fits can be achieved over a broad range of parameter values. 

Because case-control and cohort studies are the most commonly used studies in epidemiology, the remaining subsections will focus on these designs. Once an association between exposure and disease has been calculated, the next step is to evaluate the study to determine whether the calculated relative risk could result from error. The error could be random (due to chance), systematic (resulting from the study design) (discussed in Section 26.2.4), or due to confounding (discussed in Section 26.2.5). 

---