Markov model and markers of small cell lung cancer: assessing the influence of reversible serum NSE, CYFRA 21-1 and TPS levels on prognosis

High serum NSE and advanced tumour stage are well-known negative prognostic determinants of small cell lung cancer (SCLC) when observed at presentation. However, such variables are reversible disease indicators as they can change during the course of therapy. The relationship between risk of death and marker level and disease state during treatment of SCLC chemotherapy is not known. A total of 52 patients with SCLC were followed during cisplatin-based chemotherapy (the median number of tumour status and marker level assessments was 4). The time-homogeneous Markov model was used in order to analyse separately the prognostic significance of change in the state of the serum marker level (NSE, CYFRA 21-1, TPS) or the change in tumour status. In this model, transition rate intensities were analysed according to three different states: alive with low marker level (state 0), alive with high marker level (state 1) and dead (absorbing state). The model analysing NSE levels showed that the mean time to move out of state ‘high marker level’ was short (123 days). There was a 44% probability of the opposite reversible state ‘low marker level’ being reached, which demonstrated the reversible property of the state ‘high marker level’. The relative risk of death from this state ‘high marker level’ was about 2.24 times greater in comparison with that of state 0 ‘low marker level’ (Wald's test; P < 0.01). For patients in state ‘high marker level’ at time of sampling, the probability of death increased dramatically, a transition explaining the rapid decrease in the probability of remaining stationary at this state. However, a non-nil probability to change from state 1 ‘high marker level’ to the opposite transient level, state 0 ‘low marker level’, was observed suggesting that, however infrequently, patients in state 1 ‘high marker level’ might still return to state 0 ‘low marker level’. Almost similar conclusions can be drawn regarding the three-state model constructed using the tumour response status. For the two cytokeratin markers, the Markov model suggests the lack of a true reversible property of these variables as there was only a very weak probability of a patient returning to state ‘low marker level’ once having entered state ‘high marker level’. In conclusion, The Markov model suggests that the observation of an increase in serum NSE level or a lack of response of the disease at any time during follow-up (according to the homogeneous assumption) was strongly associated with a worse prognosis but that the reversion to a low mortality risk state remains possible. © 1999 Cancer Research Campaig

Assessment of possible impact of a health promotion program in Korea from health risk trends in a longitudinally observed cohort

BACKGROUND: Longitudinally observed cohort data can be utilized to assess the potential for health promotion and healthcare planning by comparing the estimated risk factor trends of non-intervened with that of intervened. The paper seeks (1) to estimate a natural transition (patterns of movement between states) of health risk state from a Korean cohort data using a Markov model, (2) to derive an effective and necessary health promotion strategy for the population, and (3) to project a possible impact of an intervention program on health status. METHODS: The observed transition of health risk states in a Korean employee cohort was utilized to estimate the natural flow of aggregated health risk states from eight health risk measures using Markov chain models. In addition, a reinforced transition was simulated, given that a health promotion program was implemented for the cohort, to project a possible impact on improvement of health status. An intervened risk transition was obtained based on age, gender, and baseline risk state, adjusted to match with the Korean cohort, from a simulated random sample of a US employee population, where a health intervention was in place. RESULTS: The estimated natural flow (non-intervened), following Markov chain order 2, showed a decrease in low risk state by 3.1 percentage points in the Korean population while the simulated reinforced transition (intervened) projected an increase in low risk state by 7.5 percentage points. Estimated transitions of risk states demonstrated the necessity of not only the risk reduction but also low risk maintenance. CONCLUSIONS: The frame work of Markov chain efficiently estimated the trend, and captured the tendency in the natural flow. Given only a minimally intense health promotion program, potential risk reduction and low risk maintenance was projected