DETECTION OF GRADUAL CHANGES. STATISTICAL METHODS IN POST MARKETING SURVEILLANCE

Abstract

Surveillance can be viewed as continual observation in time where the goal is to detect a change in the underlying process as soon as possible after it has occurred. In many applications, such as post marketing surveillance, it is of special interest to detect gradual changes in the underlying process. When a drug has been marketed one needs a continuous surveillance of adverse drug reactions. This is now done by different statistical methods suggested by the Food and Drug Administration (FDA), among others. The ability to detect a linear increase by different methods of surveillance is analysed. This is compared to the case where a sudden change to a constant level occurs. Often, as in the FDA recommendations, repeated significance tests are made and this technique of surveillance is identical to the Shewhart method. Different significance tests correspond to different transformations of the observations to the variable to be used in the Shewhart test. This method is evaluated by different measures of goodness as the false alarm probability, the probability of successful detection and the predicted value, for different cases of the critical event. Evaluations of the transformations suggested by the FDA are done in the case of the critical event being a sudden shift to a constant level and for the case of a linear increase. Considerable differences are demonstrated. A method which is optimal to detect a linear increase is derived. It takes into consideration all the data up to the decision time. A linear approximation of this method is derived and the weights in this approximation are studied. A comparison with the linear approximation of the method which is optimal to detect a sudden shift, is made. For the cases studied the Shewhart method approximates the optimal method better when the critical event is a linear change than when it is a shift.