Queue, Hurdle, and Coxian Phase-type Model for Time Distributions Related to Early Detection and Hospitalization of Colorectal Cancer
Date Issued
2015
Date
2015
Author(s)
Jen, Hsiao-Hsuan
Abstract
Background As the incidence rate of colorectal cancer (CRC) has been increasing in Taiwan, early detection of CRC through fecal immunochemical test (FIT) screening first and then colonoscopy examination and hospitalization of CRCs cannot be overemphasized. However, the arrival rate of screenees, the non-compliers of undergoing colonoscopy, the waiting time (WT) for undergoing colonoscopy, and the length of stay (LOS) for CRCs has rendered the conventional queue model infeasible. Aims The objective was to integrate the queue process, hurdle model, and Coxian phase-type model into a unifying framework that was applied to two empirical datasets, one relating to the WT of undergoing colonoscopy from Taiwanese nationwide screening program, and the other pertaining to the LOS on hospitalized CRCs enrolled from one medical centre. Methods The hurdle model was developed in combination with a mixture of the logistic regression model that dealt with the non-compliance part and the truncated Poisson regression model pertaining to the WT distribution. The Coxian phase-type was further developed to identify the optimal hidden phase of WT. To further consider the arrival rate of screenees, we developed the queue hurdle Coxian phase-type model which is the combination of the Poisson process, hurdle model and Coxian phase-type model. Data on the LOS of 178 CRCs were modelled by the Coxian phase-type model to identify the optimal number of hidden phases. Results Part I : From 2004 to 2009, the results of the hurdle model indicate the factors associated with non-compliance for colonoscopy included female, older age group, eastern Taiwan or offshore islands area, rural area, hospital screening unit and prevalent screening rounds, and the factors associated with shorter WT for colonoscopy included middle Taiwan area, main urban area, public health centers screening unit and subsequent screening rounds. Part II : The queue hurdle 2-phase Coxian phase-type model was classified as short- and long waiting phase. The arrival rate was 0.00021 per person-days and the probability of non-compliance with colonoscopy was 0.26. Annually, around 15% subjects were so hesitant to be referred to undergo colonoscopy that they were trapped in long waiting phase. The mean WT of short waiting phase and long waiting phase were 32 days and 169 days, respectively. Further to consider the effect of risk score on the model, the queue hurdle 2-phase Coxian phase-type model indicates the mean WT in short waiting phase were 36 days and 30 days for the low score group and the high score group, separately and 167 days in longer waiting phase among these two groups. Part III : For hospitalization, the LOS with 178 CRCs was modelled by the 3-phase Coxian phase-type model classified as short-stay, medium-stay and longer-stay phase. In the short-stay phase, the expected LOS was 10 days whereas both the medium- and longer-stay phases were 49 days. When gender was taken into account, the LOS was modelled as a 2-phase Coxian phase-type model, short- and long-stay care. It shows that male would discharge or die earlier than female. Regarding age, it shows the elderly would discharge or die earlier than the young. Conclusions A new queue hurdle Coxian phase-type model was developed to solve the queue process, the hurdle issue in relation to the problem of non-compliance with the referral of positive results of screenees to have confirmatory diagnosis, and to identify hidden phases during the WT for undergoing colonoscopy among the referrals and LOS in hospitalization for the treated CRCs.
Subjects
Coxian phase-type
the hurdle model
waiting time
colorectal cancer
colorectal cancer screening
SDGs
Type
thesis
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