Wednesday, February 9, 2011

More on Proposed Pagaclone Trial Analysis

In this post we look at enhancements to the models for pagoclone trial analyses discussed in the previous post.

For the logarithmic models in equations (2) and (3), the possibility exists that some trial participants will have become perfectly fluent, so that the after trial disfluency measure, DFA, will equal zero for these individuals. In this case the logarithm of DFA (or DFA/DFB) is undefined (going to minus infinity). One way to handle this problem is to replace DFA on the left hand side of equation (2) by (1+DFA) and then proceeding with the regression analysis.

Another approach to this problem would be to consider a logistics functional form,namely:

DFA/DFB = g * (exp(Z)/(1+exp(Z)) + e                                                           (4)

where g is another parameter to be estimated and, for example,

Z = a + b*DFB + c*T + d*SUG                                                                       (5)

An alternative form for Z could instead involve the natural logarithms of DFB and SUG. The parameters a, b, c, d, and g in equation (4) can be estimated by means of a non-linear regression analysis.

If DFA were always less than or equal to DFB then we could set g=1 on a priori grounds. However, we must consider the possibility that for some participants the level of disfluency at the end of the trial might be greater than before the trial. This situation could occur if the treatment actually had a negative effect on fluency for some individuals or perhaps, in some cases, the positive effects of the treatment are overwhelmed by naturally occurring fluctuations in disfluency.

We indicated in the previous post that nonlinear terms might be introduced into the analysis. One such term that might be of interest would be an interaction between the treatment term, T, and the level of disfluency before treatment, DFB. Then equation (2) in the previous post would become:

ln(DFA) = a + b*ln(DFB) + (c + h*ln(DFB))*T + d*ln(SUG) + e                        (6)

where h is another parameter to be estimated, and the coefficient associated with T, namely, c+h*ln(DFB), is no longer constant but depends on the level of disfluency measured before the trial.

The addition of this nonlinear term (assuming that h is shown to be significantly different from zero in the regression analysis) implies that the percentage reduction of disfluency, namely (1 - DFA/DFB)*100, due to pagoclone depends on the initial level of disfluency. For example, an individual with a greater level of disfluency at the start of the trial may show a lower reduction of disfluency at the end of the trial, or vice versa, depending on the value of the parameter, h.

Other hypotheses regarding the introduction of nonlinear terms could also be considered as well as the addition of other explanatory variables. Regression analyses of the kind suggested in the last two posts may materially contribute to a better understanding of the efficacy of drug treatments for stuttering and the impact of these treatments as a function of the individual's characteristics.

(Copyright 2011)

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