# University of Twente Student Theses

## Optimising the invitation strategy for colon cancer screening

Manders, J.
(2018)
*Optimising the invitation strategy for colon cancer screening.*

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Abstract: | This final project is in corporation with Bevolkingsonderzoek Oost. Each year 420; 000 clients in the Eastern part of the Netherlands have to be invited to participate in the colon cancer screening program. An invitation consists of a letter and a self-test. When the client decides to participate he sends the test sample to the laboratory. This test gives an indication whether cancer might be present or not. In case of a negative (desirable) result, the client will be invited again 2 years later. In case of a positive (undesirable) result the client is referred and should get an intake appointment within 3 weeks in a nearby colonoscopy centre (CC) for a follow-up examination. Average participation- and referral rates are 73% and 4:7% respectively. Goals: Currently Bevolkingsonderzoek Oost uses two separate algorithms in the screening process. The first algorithm decides which clients can be invited, based on the available intake capacity of the nearby colonoscopy centres (CCs). The second algorithm schedules the intake appointments for clients with positive results without using any information of the first linking algorithm. This method is not as generic and stable as it is desired to be. Frequently parameters in the current algorithms need to be changed in order to react to events and to adapt the invitation process. To overcome this fire-fighting and to find an optimal invitation strategy, this research is started. Method: The first step is to find an optimal matching between clients from postcode areas (PC4) to week numbers and CCs where travel time is minimized and the number of clients linked to the nearest CC is maximized. We develop a Mixed Integer Linear Program (MILP) to determine how many clients we can invite on the available capacity in a week and CC such that possible intake appointments can take place at these intake slots. We also minimize the number of clients that cannot be invited, called the rest group. Participation- and referral rate are stochastic variables, because we do not know how many clients will participate and how many will have a positive result. Under possible realizations of these uncertain parameters, within their intervals [70%; 76%] and [4:3%; 5:1%], we still want to invite all clients and make sure that intake appointments can take place in a nearby CC within 3 weeks. We use robust optimisation to find a safe solution to the matching problem. When a client is linked to a CC and a week, we want to have a high probability that his intake appointment can take place in the determined CC and week. In the first two parts of the research the time that a client needs to respond is not taken into account, this response time is uncertain. In part three we determine the optimal moment of sending the invitations to clients, such that the possible intake appointment can take place at the desired week and CC as determined previously by the MILP or the robust optimisation model. We develop a Stochastic Dynamic Program (SDP) for this, which we then decompose into smaller SDPs corresponding to a single CC each. We model the response time of clients with an exponential distribution. We find an optimal invitation strategy based on the number of outstanding invitations, the number of positive results and the number of already invited clients in each week of the year. Results and Conclusion: The results of the MILP and the robust optimisation consist of invitation strategies which tell us how many clients from which postcode areas we should link to which week and CC. The main output parameters that tell us the quality of the solutions are the size of the rest group, the adherence (which postcode areas are linked to which CCs) and the percentage of clients that cannot be linked to the nearest CC. The deterministic MILP gives a matching with other adherence numbers than currently used at Bevolkingsonderzoek Oost. The number of clients that cannot be linked to the nearest CC is decreased from 40% in the current situation to 17:3%. The adherence of the MILP model is therefore more optimal and the number of rescheduled intake appointments can be decreased. However, the available intake capacity over region East still does not align with the distribution of clients over region East. Our model gives a possible rest group of 3:3% instead of 7:8% with the current adherence. With robust optimisation we are able to find a ”safe” solution to the matching problem and we immunize against the uncertainty in participation- and referral rate. We use the budgeted uncertainty approximation type, which rules out any large deviations from the cumulative number of needed intake appointments in a CC and week. By using the best suitable safety parameter we build in buffer capacity in the intake slots, by inviting slightly less clients than possible in the deterministic case. The safe solutions give us a rest group of 9% at the end of the year. The great advantage of the safe solution is that the probability that a client cannot have his intake appointment in the determined week and CC decreases to only 8% instead of the 22% when the MILP solution is considered. In the time uncertainty model we neglect the pr´e-announcement period of 2 weeks. One of the reasons for this is that not sending the pr ´e-announcement letters can save e37,500 each year. We only have results of the single CC SDP model for small instances with few clients and higher participation and referral rates than in practice. These preliminary results suggest a structured invitation strategy where invitations are send during the year when enough clients still need to be invited. Inviting will occur under the conditions that in the current week (1) the number of outstanding invitations is small and (2) the number of positive results is not to large. However, further research is needed to develop the SDP models for the use in practical instances. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 31 mathematics |

Programme: | Applied Mathematics MSc (60348) |

Link to this item: | http://purl.utwente.nl/essays/76371 |

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