Clinical Trials

❘❙❚■ Chapter 28 | Repeated MeasurementsFigure 4. A pH profile for a subject taking part in a trial of a new drug for gastroesophageal reflux.86pH420 12 3 4Time after dose (hours)Rate or gradient of change in a response variableThe statistical approaches discussed so far mainly relate to data where the valueof the outcome variable under consideration fluctuates in the absence of a unifiedmonotonic trend for all subjects during the study period. Conversely, in situationswhere the response variable increases or decreases steadily with time, eg, in thecase of growth data, it is possible to ask more detailed questions about how theoutcome variable changes with time. This can be done by calculating the slope(or regression coefficient) of the decline/increase for each individual andcomparing these slopes using standard techniques.For the SBP data in Figure 1, most subjects show a trend towards decreasing SBP.Therefore, a linear regression line can be fitted for each of the 10 subjects – thefitted lines are displayed in Figure 5. The estimated slopes in the figure range from–3.9 for subject 7 to –0.1 for subject 3, illustrating the different rates of change inSBP for the subjects after drug administration. The change in SBP during the studyperiod was large for subject 7, dropping by 3.9 mm Hg on average at each visit,whereas the change in SBP for subject 3 was much smaller. We can assess whichdrug reduces SBP fastest by comparing the mean rates of the two treatment groups.If the data are non-linear then a non-linear model should be fitted for eachsubject’s data. For example, in a pharmacokinetic study to describe the rate ofelimination, a log-linear model is always fitted; the coefficient of the log-linearmodel is used to describe the rate of drug elimination.326