This chapter discusses forecasting and control. It provides analysis of observations or measurements that are being recorded sequentially in time. Time series problems arise in a wide variety of contexts. Different series entail different objectives. A series of measurements on the concentration of a tumor marker in the blood of a given test subject may be used to monitor the progression of a tumor or its response to treatment. An element of subjective assessment is almost always called for in the interpretation of the results delivered by standard forecasting methods, in the sense that a given series of measurements rarely if ever tells the whole story about the probable course of the future events.

Forecasting and control

A method for trend detection, Trigg's technique [ Oper. Res. Q. 15, 271 (1964)], has been investigated for use in monitoring trends in control data produced by multitest continuous-flow analyzers. Simulated trend data were used to optimize the method. Actual control data were analyzed retrospectively to determine the frequency of trends and the accuracy of several parameters obtained from Trigg's method. The prospective use of the technique has successfully uncovered important trends. Criteria for the interpretation of the Trigg's trend data are suggested and an algorithm for the computer implementation of Trigg’s calculations is included.

Trend Detection in Control Data: Optimization and Interpretation of Trigg's Technique for Trend Analysis

Problems in measuring heart rate variability of patients with congestive heart failure.

https://link.springer.com/content/pdf/10.1057%2Fjors.1968.30.pdf

Monitoring a Forecasting System

We wished to assess the accuracy of a modified form of Trigg's Tracking Variable (TTV) at detecting the onset of changes in systolic blood pressure. A computer model generated systolic blood pressures which changed to a new value after period of stability. A separate algorithm based on TTV indicated when a ‘significant’ change had been detected. This signal occurred when TTV had exceeded a set limit (0.8–0.99) a predetermined number of times (1–10). Five anaesthetists were shown 40 sets of data generated by same the computer model and asked to indicate the onset of changes. The greatest number of changes (94.1%) were correctly identified when TTV exceeded 0.92 on 4 consecutive determinations. The onset of the trend was detected after an average delay of 140s. The anaesthetists correctly detected 85% of the changes after an average delay of 162s. There was no statistically significant difference between the anaesthetists and the algorithm, although only one anaesthetist performed better than the modified TTV. The modified TTV detected changes in simulated invasive systolic blood pressures faster and more accurately than four of a group of five anaesthetists. Such simple trend detection systems may be useful as ‘advisory’ alarms.

A modified Trigg's Tracking Variable as an ‘advisory’ alarm during anaesthesia

The medical profession's increasing interest in monitoring, suggests that it would be appropriate to describe some of the statistical techniques used for monitoring in Operational Research and related fields. This article discusses what ‘monitoring’ means in statistical terms and describes the two most widely used statistical monitoring techniques currently available, namely the Cusum and Trigg (or smoothed error) methods. The article also discusses the possible off-line and on-line monitoring possibilities of these two methods in the medical field.

C. D. Lewis

Papers

Statistical monitoring techniques.