Symptoms of schizophrenia and regularity in treatment: a stochastic analysis

Background: The alarming rise of mental disorders worldwide stimulates the need to study them from a statistical viewpoint. Schizophrenia is one of the most prevalent mental illness which is characterised by various symptoms, the presence of a cluster of which leads to its diagnosis. Regular treatment leads to a remission of the illness which might relapse on discontinuity of medicines. There have been numerous epidemiological studies and clinical trials on the illness. However, schizophrenia also poses a challenge to statisticians in theorising and statistically modeling its different aspects. Aim: This is an attempt to study, by developing suitable stochastic models, the behaviour of the symptoms of schizophrenia manifested in a patient in relation to the successive visits to the doctor. Methods: The concepts of probability theory, structure functions, binomial distribution, Markov chain, and transition probabilities are the statistical tools used to model the medical facts regarding schizophrenia. Results: By developing probabilistic and stochastic models, a relationship between the number of symptoms at the time of diagnosis and the number of revisits to the doctor has been developed and thereby an important result regarding the expected number of symptoms present at a particular visit to the doctor has been established. A Markovian model studying the pattern of the symptoms in the course to recovery has been presented and its application in the behaviour of the symptoms of schizophrenia has been verified. Conclusions: It is expected that the above results might help doctors in planning out the treatment schedule in advance. It can also lead to a further study on cost benefit analysis of the treatment process.