Sequentially calibrating a Bayesian microsimulation model to incorporate new information and assumptions

Background Microsimulation models are mathematical models that simulate event histories for individual members of a population. They are useful for policy decisions because they simulate a large number of individuals from an idealized population, with features that change over time, and the resulting event histories can be summarized to describe key population-level outcomes. Model calibration is the process of incorporating evidence into the model. Calibrated models can be used to make predictions about population trends in disease outcomes and effectiveness of interventions, but calibration can be challenging and computationally expensive. Methods This paper develops a technique for sequentially updating models to take full advantage of earlier calibration results, to ultimately speed up the calibration process. A Bayesian approach to calibration is used because it combines different sources of evidence and enables uncertainty quantification which is appealing for decision-making. We develop this method in order to re-calibrate a microsimulation model for the natural history of colorectal cancer to include new targets that better inform the time from initiation of preclinical cancer to presentation with clinical cancer (sojourn time), because model exploration and validation revealed that more information was needed on sojourn time, and that the predicted percentage of patients with cancers detected via colonoscopy screening was too low. Results The sequential approach to calibration was more efficient than recalibrating the model from scratch. Incorporating new information on the percentage of patients with cancers detected upon screening changed the estimated sojourn time parameters significantly, increasing the estimated mean sojourn time for cancers in the colon and rectum, providing results with more validity. Conclusions A sequential approach to recalibration can be used to efficiently recalibrate a microsimulation model when new information becomes available that requires the original targets to be supplemented with additional targets.

Classical Fuzzy Retrial Queue with Working Vacation using Hexagonal Fuzzy Numbers

Using fuzzy techniques “Classical Fuzzy Retrial Queue with Working Vacation(WV) using Hexagonal Fuzzy Numbers” is discussed in this paper. We acquire model in fuzzy environment as the average orbit length, Probability(Pr) that the server busy, and Pr(the server is in a WV period), the sojourn time of a customer in the queue. Finally numerical results are presented.

Discrete Time Hybrid Semi-Markov Models in Manpower Planning

Discrete time Markov models are used in a wide variety of social sciences. However, these models possess the memoryless property, which makes them less suitable for certain applications. Semi-Markov models allow for more flexible sojourn time distributions, which can accommodate for duration of stay effects. An overview of differences and possible obstacles regarding the use of Markov and semi-Markov models in manpower planning was first given by Valliant and Milkovich (1977). We further elaborate on their insights and introduce hybrid semi-Markov models for open systems with transition-dependent sojourn time distributions. Hybrid semi-Markov models aim to reduce model complexity in terms of the number of parameters to be estimated by only taking into account duration of stay effects for those transitions for which it is useful. Prediction equations for the stock vector are derived and discussed. Furthermore, the insights are illustrated and discussed based on a real world personnel dataset. The hybrid semi-Markov model is compared with the Markov and the semi-Markov models by diverse model selection criteria.

States Transitions Inference of Postpartum Depression Based on Multi-State Markov Model

Background: Postpartum depression (PPD) has been recognized as a severe public health problem worldwide due to its high incidence and the detrimental consequences not only for the mother but for the infant and the family. However, the pattern of natural transition trajectories of PPD has rarely been explored. Methods: In this research, a quantitative longitudinal study was conducted to explore the PPD progression process, providing information on the transition probability, hazard ratio, and the mean sojourn time in the three postnatal mental states, namely normal state, mild PPD, and severe PPD. The multi-state Markov model was built based on 912 depression status assessments in 304 Chinese primiparous women over multiple time points of six weeks postpartum, three months postpartum, and six months postpartum. Results: Among the 608 PPD status transitions from one visit to the next visit, 6.2% (38/608) showed deterioration of mental status from the level at the previous visit; while 40.0% (243/608) showed improvement at the next visit. A subject in normal state who does transition then has a probability of 49.8% of worsening to mild PPD, and 50.2% to severe PPD. A subject with mild PPD who does transition has a 20.0% chance of worsening to severe PPD. A subject with severe PPD is more likely to improve to mild PPD than developing to the normal state. On average, the sojourn time in the normal state, mild PPD, and severe PPD was 64.12, 6.29, and 9.37 weeks, respectively. Women in normal state had 6.0%, 8.5%, 8.7%, and 8.8% chances of progress to severe PPD within three months, nine months, one year, and three years, respectively. Increased all kinds of supports were associated with decreased risk of deterioration from normal state to severe PPD (hazard ratio, HR: 0.42–0.65); and increased informational supports, evaluation of support, and maternal age were associated with alleviation from severe PPD to normal state (HR: 1.46–2.27). Conclusions: The PPD state transition probabilities caused more attention and awareness about the regular PPD screening for postnatal women and the timely intervention for women with mild or severe PPD. The preventive actions on PPD should be conducted at the early stages, and three yearly; at least one yearly screening is strongly recommended. Emotional support, material support, informational support, and evaluation of support had significant positive associations with the prevention of PPD progression transitions. The derived transition probabilities and sojourn time can serve as an importance reference for health professionals to make proactive plans and target interventions for PPD.

Estimates of stage-specific preclinical sojourn time across 21 cancer types.

e18584 Background: Cancer progression rates following diagnosis are readily measured. However, the progression rate of cancer during the preclinical sojourn time is generally unobserved. Understanding the duration of preclinical stages (“dwell time”) would allow clinicians to better identify appropriate screening intervals for cancer. We therefore elicited estimates of progression rate during the preclinical sojourn time for a wide variety of malignancies from a panel of clinical experts. Methods: We used a validated consensus methodology (RAND/UCLA modified Delphi panel method) to elicit per-stage dwell time estimates for 20 solid cancers and lymphoma from experts. Eleven experienced oncologists (general and subspecialists) from community and academic centers reviewed literature on the natural history of disease and estimated in number of years (<1 to 9+ years) how long it would take each cancer to progress from the beginning of clinically detectable Stage I/II/III to the beginning of the next stage in untreated adults. Cancer histological subtypes were grouped and experts were asked to provide an overall rating. Ratings were completed before and after a discussion of areas of disagreement. Results: Expert estimates and range of dwell time for 21 cancer types are provided in Table. Prostate and thyroid cancer were estimated to be the slowest growing, taking approximately 7 and 5 years respectively to progress through Stage I (range 4-8), 5 years to progress through Stage II (range 3-7), and 3 and 4 (range 2-5) years respectively to progress through Stage III. Esophageal, lung, liver/intrahepatic bile-duct, gallbladder, and pancreatic cancers were estimated to progress quickly through all three stages (1-2 years per stage). Conclusions: These findings summarize practicing oncologists’ estimates of dwell time in preclinical disease. Experts agreed on dwell times although ranges were large and differences in cancer subtypes were not captured. Generally, estimates trend with published data on survival with treatment: cancers with higher survival (e.g., prostate, thyroid) were estimated to grow slower, while cancers with lower survival (e.g., pancreatic, liver/intrahepatic bile-duct, gallbladder) were estimated to grow faster. These estimates could be useful when determining screening intervals for these or any subset of these cancers. [Table: see text]

Pooled vs. Dedicated Queues when Customers Are Delay-Sensitive

It is generally accepted that operating with a combined (i.e., pooled) queue rather than separate (i.e., dedicated) queues is beneficial because pooling queues reduces long-run average sojourn time. In fact, this is a well-established result in the literature when jobs cannot make decisions and servers and jobs are identical. An important corollary of this finding is that pooling queues improves social welfare in the aforementioned setting. We consider an observable multiserver queueing system that can be operated with either dedicated queues or a pooled one. Customers are delay-sensitive, and they decide to join or balk based on queue length information upon arrival; they are not subject to an external admission control. In this setting, we prove that, contrary to the common understanding, pooling queues can increase the long-run average sojourn time so much that the pooled system results in strictly smaller social welfare (and strictly smaller consumer surplus) than the dedicated system under certain conditions. Specifically, pooling queues hurts performance when the arrival-rate-to-service-rate ratio is large (e.g., greater than one) and the normalized service benefit is also large. We prove that the performance loss due to pooling queues can be significant. Our numerical studies demonstrate that pooling queues can decrease the social welfare (and consumer surplus) by more than 95%. The benefit of pooling is commonly believed to increase with system size. In contrast, we show that when delay-sensitive customers make rational joining decisions, the magnitude of the performance loss due to pooling can strictly increase with the system size. This paper was accepted by Terry Taylor, operations management.