UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

A semi Markov model for mammographic detection of breast cancer Chan, Keith James


Mammography is used as a screening tool to detect breast cancer at an early stage. The process of breast cancer detection using mammography is modelled with a semi-Markov process composed of three states: cancer-free (0), preclinical cancer (1) and clinical cancer (2). It is assumed that screening provides the ability to detect disease while it is still in the preclinical state before it enters the clinical state, however screening measurement is subject to error. The sojourn time in the preclinical detectable phase is thus of particular interest and it plays an important role in the design and assessment of screening programmes. In previous work, the transition rate into the preclinical detectable phase has been modelled by an age-specific step function based on age at first screen. This does not lead to an increasing incidence of breast cancer with age but observations in several populations indicate that incidence increases at approximately the third power of age. This relationship is induced in the model by introducing a smooth age dependent transition rate into the preclinical detectable phase. The model is applied to data provided by The Screening Mammography Programme of British Columbia (SMPBC). A Quasi-Newton algorithm is used to minimize the negative log likelihood function to obtain maximum likelihood estimates of the model parameters. Comparisons will be made with other published results and the effect of various assumptions examined.

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.