Using semi-Markov processes to study timeliness and tests used in the diagnostic evaluation of suspected breast cancer.

Diagnostic evaluation of suspected breast cancer due to abnormal screening mammography results is common, creates anxiety for women and is costly for the healthcare system. Timely evaluation with minimal use of additional diagnostic testing is key to minimizing anxiety and cost. In this paper, we propose a Bayesian semi-Markov model that allows for flexible, semi-parametric specification of the sojourn time distributions and apply our model to an investigation of the process of diagnostic evaluation with mammography, ultrasound and biopsy following an abnormal screening mammogram. We also investigate risk factors associated with the sojourn time between diagnostic tests. By utilizing semi-Markov processes, we expand on prior work that described the timing of the first test received by providing additional information such as the mean time to resolution and proportion of women with unresolved mammograms after 90 days for women requiring different sequences of tests in order to reach a definitive diagnosis. Overall, we found that older women were more likely to have unresolved positive mammograms after 90 days. Differences in the timing of imaging evaluation and biopsy were generally on the order of days and thus did not represent clinically important differences in diagnostic delay. Copyright © 2016 John Wiley & Sons, Ltd.

Deriving benefit of early detection from biomarker-based prognostic models.

Many prognostic models for cancer use biomarkers that have utility in early detection. For example, in prostate cancer, models predicting disease-specific survival use serum prostate-specific antigen levels. These models typically show that higher marker levels are associated with poorer prognosis. Consequently, they are often interpreted as indicating that detecting disease at a lower threshold of the biomarker is likely to generate a survival benefit. However, lowering the threshold of the biomarker is tantamount to early detection. For survival benefit to not be simply an artifact of starting the survival clock earlier, we must account for the lead time of early detection. It is not known whether the existing prognostic models imply a survival benefit under early detection once lead time has been accounted for. In this article, we investigate survival benefit implied by prognostic models where the predictor(s) of disease-specific survival are age and/or biomarker level at disease detection. We show that the benefit depends on the rate of biomarker change, the lead time, and the biomarker level at the original date of diagnosis as well as on the parameters of the prognostic model. Even if the prognostic model indicates that lowering the threshold of the biomarker is associated with longer disease-specific survival, this does not necessarily imply that early detection will confer an extension of life expectancy.

Modeling nonhomogeneous Markov processes via time transformation.

Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.