## Research

Bipolar disorder is a mental illness which causes an individual's mood to swing from one extreme to another, resulting in periods of depression and mania. The exact cause is not understood although genetic and environmental factors are known to play a part. The aim of this project is to use mathematical models to predict mood fluctuations and help in understanding and managing the disorder. The Department of Psychiatry in Oxford runs a scheme whereby patients can fill in a mood questionnaire each week and return the answer by text message. In this way, the weekly mood changes of 150 patients have been monitored continually over the last five years and provided a valuable database for analysis. Some studies have applied dynamical systems theory to model mood in bipolar disorder [1], while others have used non-linear time series approaches to develop measures for characterising mood changes [2]. For this project we are relatively rich in data and so have started by applying standard time series forecasting methods. However the mood time series are non-uniform in time while most time series methods assume uniformly spaced data. So we are developing measures of non-uniformity in order to characterise the data set and we have adopted some methods from spatial statistics to handle non-uniformity. For example, we use the variogram rather than the correlogram to examine correlation structure and we use Gaussian process regression (kriging) instead of trying to regularise the time series or imputing missing values. Kriging leads to better results than linear smoothers that depend on uniformly sampled time series, although the difference in accuracy is marginal on our data set [3] [4]. We have found gender differences in mood dynamics, a result for which there is evidence in the psychiatric literature on bipolar disorder. There is also evidence of seasonality: some people get more depressed in the winter. There are no significant gender differences in time series uniformity, nor does the diagnostic subtype (the specific kind of bipolar disorder) affect the uniformity of response, a result that is unexpected since some subtypes can be associated with erratic behaviour. The measures of non-uniformity may also be useful in a clinical setting because they relate to the reliability of the patient's response, a quality that is potentially informative. They are applicable more generally to any non-uniform time series and may find further applications in the burgeoning field of medical telemonitoring [5] . Further work is planned on other regression methods and on optimal covariance functions and inference methods for this application. A research statement is available here and a poster showing some results is available here. REFERENCES [1] A. Gottschalk, M. S. Bauer, and P. C. Whybrow, “Evidence of chaotic mood variation in bipolar disorder,” Archives of General Psychiatry, vol. 52, no. 11, pp. 947–959, Nov 1995. [Online][2] T. Glenn, P. C. Whybrow, N. Rasgon, P. Grof, M. Alda, C. Baethge, and M. Bauer, “Approximate entropy of self-reported mood prior to episodes in bipolar disorder,” Bipolar Disorders, vol. 8, no. 5p1, pp. 424–429, Oct 2006. [Online] [3] P.J. Moore, M.A. Little, P.E. McSharry, J.R. Geddes, G.M. Goodwin (2012) Forecasting depression in bipolar disorder using cellphone telemonitoring.IEEE Transactions on Biomedical Engineering [Online] [4] Moore P.J., Little, M, McSharry P, Forecasting mood in bipolar disorder, International Symposium on Forecasting, Prague, 2011. [Online] [5] P.J. Moore., [other authors tba] Correlates of depression in bipolar disorder. (available on request) |