Using an autoregressive model to detect departures from steady states in unequally spaced tumour biomarker data

A new method, based on a continuous time autoregressive [CAR(1)] model of time series data, is provided for detecting departures of tumour markers from steady states in breast cancer patients following surgery. A Kalman filter recursive algorithm is used to calculate the likelihood function arising from the CAR(1) model and to calculate recursive residuals, which are monitored by a Shewhart-Cusum scheme. This approach can be used to monitor the serial marker data of large numbers of patients even when the series are short and the data are serially correlated and unequally spaced. Further, the methodology can be used to recommend appropriate testing intervals.