A Proposal for Analyzing Pagoclone Trials

A typical medical trial to test the efficacy of a treatment involves two groups--the treatment group and the placebo group, the members of which are assigned randomly.  The objective is to see if a response variable, i.e., treatment outcome, is different between the two groups. Analysis of variance (ANOVA) methodologies provide statistical tests as to whether or not the means of the two groups are significantly different.

This approach regards each group as a unit of observation and requires looking at the average of the responses within the two groups. The hope, when using grouped averages, is that the random assignments of individuals to the groups will have made all of the averages (as well as the standard deviations and higher order moments) of other possibly relevant explanatory variables essentially equal across the two groups. When the populations of the groups are relatively small, this assumption may not be valid.

Furthermore, grouped data analyses may obscure relationships that can be delineated when, instead, individuals within the groups are viewed as the units of observation. In addition, ANOVA methodologies are not able to handle very well the inclusion of many other variables (particularly those that are continuous) that may also explain response outcomes.

We propose an alternative approach based on regression analysis, which is utilized extensively in fields like economics, but very little in medical research. Regression analysis can be regarded as a supplement to ANOVA techniques to extract additional information from the individual data that may be hidden by grouping the data.

The regression model discussed below explicitly teases out the placebo effect as measured by a suggestibility variable. Consider a pagoclone trial consisting of N individuals in the treatment group and M in the placebo group for a total participation of N+M individuals.

Let DFB be the value of a disfluency measure for an individual before treatment (with either pagoclone or the placebo) and DFA the value of the measure after treatment. For example, DFA and DFB might be the results from the Stuttering Severity Instrument. Further, let SUG be a measure of suggestibility for an individual at the start of the trial, which can be constructed, for example, from the MISS questionnaire discussed in the last post. Define a dummy variable T such that:

T = 1 if the individual received pagoclone
   = 0 if the individual received a placebo.

Then a regression model describing the treatment outcome might be specified as:

DFA = a + b*DFB + c*T + d*SUG + e                                                           (1)

where a, b, c, and d are parameters to be estimated and e is an error term. The error term includes all possible explanatory variables that may have been excluded from the model and errors in the measurement of DFA as well as of each of the explanatory variables.

The model parameters can be estimated on the basis of the observations from the N+M individuals using any of a number of statistical analysis packages supporting regression analysis. The error terms for each of the observations are used to calculate a measure of goodness of fit, namely R-squared, which ranges between 0 and 1 where 1 represents a perfect fit to the data and 0 represents no fit. The parameter estimates will each have associated standard errors that can be used to calculate significance levels for the parameters.

The model can be expanded by including nonlinear terms (and additional associated parameters) such as DFA-squared, SUG-squared, DFA*SUG, and T*SUG. Moreover, if the trial involves different dosages of pagoclone, we can take that into account by adding additional dummy variables. For example, if pagoclone is administered in two different dosages, then we utilize two dummy variables, T1 and T2 defined by:

T1 = 1 for pagoclone at level 1 dosage
     = 0 otherwise
T2 = 1 for pagoclone at level 2 dosage
     = 0 otherwise

So for (T1, T2), level 1 dosage is represented by (1, 0), while (0, 1) represents level 2 dosage, and (0, 0) refers to the placebo group.

An alternative model incorporating the explanatory variables in equation (1) is a log-log model expressed as:

ln(DFA) = a + b*ln(DFB) +c*T + d*ln(SUG) + e                                                    (2)

where ln is the natural logarithm. Nonlinear terms can also be introduced into this model. Once the parameters of log-log model are estimated, we can rewrite the model as:

ln(DFA/DFB) = a + (b – 1)*ln(DFB) + c*T + d*ln(SUG) + e                                   (3)

where we used the property of logarithms that ln(DFA/DFB) = ln(DFA) – ln(DFB). The percentage reduction of disfluency is given by (1 - DFA/DFB)*100.

Regression analyses of the kinds discussed above may contribute to the specification and validation of suggestibility measures that would be useful in identifying trial participants who may be strongly responsive to placebos. This information can then be used to develop treatment trials that utilize limited resources more efficiently.

(Copyright 2011)