Simulation-based Optimization Approach to Clinical Trial Supply Chain Management

Transcription

1 20 th European Symposium on Computer Aided Process Engineering ESCAPE20 S. Pierucci and G. Buzzi Ferraris (Editors) 2010 Elsevier B.V. All rights reserved. Simulation-based Optimization Approach to Clinical Trial Supply Chain Management Ye Chen*, Linas Mockus, Seza Orcun, Gintaras V. Reklaitis Purdue University, West Lafayette, IN 47907, USA, Abstract The development activities required to bring a new drug to market involve considerable expense ($1+ Billion) and can take in excess of ten years. Clinical trials constitute a critically important and very expensive part of this development process as it encompasses producing, distributing and administering the candidate therapy to volunteer patients located in different geographic zones. A number of different approaches are being pursued to reduce clinical trial costs, including innovations in trial organization and patient pool selection. In this work, we focus our attention on improved management of the supply chain which provides the dosage required by the clinical sites. A simulation-based optimization approach is presented, which includes patient demand forecasting, mathematical programming based planning, and discrete event simulation. The objective is to enhance the robustness of the supply chain under different sources of uncertainties. A case study is reported which demonstrates the application of the proposed approach. Keywords: Clinical Trial, Supply Chain, Optimization, MILP, Simulation 1. Introduction New drug development follows an extended sequence of steps (discovery, animal trials, FDA application, product and process development, three phases of clinical trials, FDA filing and approval, and launch). As a result it takes many years and considerable expense ($1+ Billion) to bring a new drug to market. The clinical trials themselves constitute a very expensive part of this process. Normally, clinical trials with different test objectives (e.g. safety, efficacy, side effects) are conducted at the same time to expedite the new drug development process, which further complicates the clinical trial supply chain. While clinical trials are in progress, the development team also continues work towards improving the manufacturing processes. The clinical trial material supply chain management problem is composed of the planning and scheduling of all transactions, operations and organizations during a trial, beginning with active ingredient manufacturing, followed by drug manufacturing and distribution to the clinical sites, and ending with dispensing the drugs to patients at each clinical site. A substantial amount of work has been reported on process industry supply chain optimization, but only a limited literature has addressed the issues faced in the pharmaceutical industry. Shah (2004) presented a review paper, categorizing previous work and analyzing the key issues for pharmaceutical supply chain optimization. There have been research activities on management of the product development pipeline, capacity planning, risk management, process development and plant design, as well as production planning and scheduling, but the issue of materials management for clinical trials has not been studied. Monkhouse et al (2006) discussed the design and development of clinical trials in some detail, but they provided little information about the actual management of the clinical trials material supply chain.

2 Ye Chen, Linas Mockus, Seza Orcun, Gintaras V. Reklaitis Traditionally, the pharmaceutical industry uses batch processes in the manufacture of pharmaceutical products both at the pilot and the commercial scale. Since these batch facilities are usually shared across various products, especially for the quantities needed for clinical trials, it is necessary to decide on the order and timing of the products to be produced. These decisions can have a large economic impact on the company at the clinical trials stage, because missing the delivery of trial dosage to patients can significantly delay completion of the trial and hence delay the time to market which in turn can mean significant loss of revenue. Deterministic mixed integer linear programs (MILP) and mixed integer nonlinear programming (MINLP) optimization methods have been proposed and used to solve resource constrained project planning and scheduling problem. Floudas and Lin (2004) presented a comprehensive review of these approaches. Most of the work reported is confined to a deterministic context. While some approaches have addressed uncertainties to generate robust schedules and plans, none of them are equipped to deal with the uncertainties faced in clinical trial supply chains. The key technical challenges in managing a clinical trial materials supply chain are to meet the needs from clinical sites, so that patients are fully supplied once they are enrolled while minimizing oversupply since unused materials cannot be re-routed to other sites due to regulatory restrictions. Not only is patient enrollment highly variable, but uncertainties also arise in manufacturing and shipment lead times, in process failures and in production yields. Furthermore, the life of a clinical trial materials supply chain, which is around 1-2 years, is significantly shorter than that of a commercial supply chain, which usually exceeds 10 years. Therefore, the strategies utilized to buffer the uncertainties in commercial supply chains become ineffective as expected values cannot be effectively used as targets. Subramanian, Pekny & Reklaitis (2001) propose a computational architecture called Sim-Opt, which combines mathematical programming and discrete event system simulation to assess the uncertainty and control the risk present in the new product development pipeline problem. Simulation-based optimization methods were found to be efficient and effective alternatives to solving a large stochastic decision problem. In this work, we propose a simulation-based optimization approach combining mathematical programming-based planning, and discrete event simulation to deal with our clinical trial materials supply chain management problem where uncertainties cannot be modeled analytically in a computationally tractable way. 2. Problem definition and assumptions 2.1 Multi-echelon production-distribution supply chain The production of drug begins with active ingredient manufacturing (API), which normally involves either a series of chemical synthesis and separation processes, or fermentation and purification processes. The API is next converted to a new drug product (NDP) by adding excipients and conducting a series of additional processing steps, followed by packaging and labelling (PL) to obtain the final drug product form. In addition to the new drug product, a placebo (the product without the API) and a comparator (a form containing a commercial drug targeting the same disease) are also produced and used. To avoid psychological biases, the placebo and comparator undergo the same manufacturing, packaging and labelling stages as the target drug to make sure the appearance of these three types are the same to insure effectiveness in double blinded clinical trials. The finished drug product forms are shipped to various clinical sites worldwide. Therefore, a clinical trial materials supply chain can be treated as a

3 Simulation-based Optimization Approach to Clinical Trial Supply Chain Management multi-echelon production/distribution supply chain including the API-NDP-PL manufacturing stages and the product distribution network. For purposes of this study we assume there are no feed material constraints. The API, NDP and PL stages are conducted in the same facility and share the same inventory location in the US. Furthermore, shipment times between these three production stages are neglected. Since, compared to commercial drug manufacturing, the volume of drugs used in a clinical trial is small, we assume there is no inventory capacity limit. All finished drugs (target drug, placebo, and comparator) will be kept in the same distribution center with a certain shelf life, and must be disposed of after their expiration date. The distribution network starts at the US distribution center and covers various clinical sites used in the clinical trial located around the world. 2.2 Batch operation of manufacture process Traditionally, the pharmaceutical industry uses the batch-campaign mode. In our models, the batch manufacturing process is described by campaign start time, number of batches in each campaign, batch size, batch processing time, drug type (target drug, placebo and comparator), and yield. Uncertainties exist in processing time and yield. Within each stage, there are multiple production lines of processing units working in parallel, and each production line could be utilized for different products. API stage only produces the active ingredient for the target drug of the trial, but there will be multiple product types at the NDP stage: target drugs at different dosage levels, placebo and comparator. Since the clinical trials will be conducted all over the world, drugs sent to a certain country should satisfy its country specific packaging and labelling requirements. Therefore, the number of stock keeping units (SKU) can grow significantly, depending on the design and topology of the clinical trial. 3. Simulation-based optimization approach 3.1 Computational framework The framework proposed for this study consists of a simulation of demands (by forecasting methods), planning method, and a discrete event simulation for assessing the robustness of the supply chain under different sources of uncertainties as depicted in Fig. 1. The forecasting function uses a simulation model to determine the demand profile for each drug product. Given demand forecasts, a planning model is used to determine the manufacturing campaign details and shipping plans. The model is implemented as a Mixed-Integer-Linear-Programs (MILP) and solved using CPLEX. A simulation model of the entire supply chain, which is developed using the discrete event simulation software, ExtendSim, captures all activities, operations and processes involved in the clinical trial. The operational plans developed via the MILP planning models serve as drivers for the execution of supply chain simulation. The quality and robustness of the plans are assessed by replicated simulation runs. Upon convergence to appropriate statistical criteria, the supply chain performance is improved by adjusting the key system parameters and repeating the Simulation-Optimization cycle. Fig. 1 Clinical trial supply chain management computational framework

4 Ye Chen, Linas Mockus, Seza Orcun, Gintaras V. Reklaitis 3.2 Demand forecasting The demand of each product, which is non-stationary, is obtained from detailed clinical site simulations. The arrival of patients can be treated as a Poisson process, and every patient is randomly assigned to different clinical trial dosages: target drug, placebo or comparator. During the treatment period, patients are required to follow preset visit profiles, which also determine the drug dispensation schedules. However, some patients may drop out during the course of the treatment for various reasons, such as loss of interest, dissatisfaction due to no observed improvement, or changes in personal life. The mean and variance of demand for each drug SKU are obtained from these simulations and are in turn used in the other supply chain decision models. 3.3 Planning As noted above, the entire clinical trial materials supply chain is divided into the API, NDP, PL, and Distribution network components. Under typical industry practice, a global coordinator works within a decentralized control supply chain, which coordinates each stage towards to a common objective. The global objective of a clinical trial materials supply chain is to satisfy the patient demand with minimum cost. The downstream demands along with campaigning/shipping plans create the demands for the upstream stages in terms of material requirement. Eqn. 1 and Eqn. 2 represent objective functions of the production and distribution sub-models, respectively. Each sub-problem seeks to minimize an objective function representing the total expected cost, consisting of several sub-problem specific cost factors. Demand data obtained from detailed patient enrollment forecasts and their simulations are aggregated into three discrete demand profile scenarios, each with certain probability. With distribution objective and constraints, an optimal shipment plan is obtained by formulating the distribution process as an MILP model solved by CPLEX. The shipment plans generate the demands for the manufacturing stages. Due to the space limitation the complete model equations are not presented herein. Min Cost = expected (Waste cost + Production cost + Holding cost) (Eqn. 1) Min Cost = expected (Waste cost + Penalty cost + Fixed cost + Variable Cost) = (cost of destruction of material + cost of product + cost of packaging component)+ (Inventory opportunity cost) + (cost of direct labor for entering shipment + cost of direct labor for processing shipment + cold chain container cost) + (cost of direct labor of selecting and picking + shipment cost + container cost) (Eqn. 2) 3.4 Discrete event simulation To investigate the quality of the plans generated, we represent each batch as a single transaction with specific properties such as start time, duration, batch type and size. Five simulation sub-models: API, NDP, PL, Distribution and clinical sites have been implemented. These models can be assembled to define any clinical trials supply chain. Within each sub-model, the batch is the flowing entity, moving through the network model. A batch waits for a specified period (could be sampled from a distribution or predefined as a property) of simulation time before proceeding to the next block. Also, this model dynamically communicates with decisions models through Excel files storing the manufacturing and distribution plans. To capture the effects of uncertainties in this supply chain, the complete supply chain simulation is repeated many times for different sampled values of the uncertain parameters to generate the distribution data with which to verify and assess the efficiency and quality of the plans generated by the decision models. The simulation model records the number of missed patients, the number of patients who successfully

5 Simulation-based Optimization Approach to Clinical Trial Supply Chain Management finished the treatment, the number of patients who drop out, and the average inventory at each clinical site and distribution center. The simulation results are used to restart the planning model to produce revised production and distribution plans. The planning and simulation loop is continued until the performance of the entire supply chain improves and converges to a satisfactory level. 4. Case study The proposed approach is demonstrated by a case study outlined in this section. The topology of the case study is shown in Fig. 2. There is only one active ingredient produced in the API stage, but four SKU s need to be produced in the NDP stage: placebo, comparator, high dosage and low dosage target drug. Since this clinical trial will be conducted in two continents (US and European), two different types of packaging and labeling are used: one for the Americas (countries A and B) and the other for the European (countries C and D). Thus, there will be eight SKUs in the final distribution center to be shipped to various clinical sites. The shelf life of these drugs is 8 months, treatment lasts for 6 weeks, and the enrollment period of this clinical trial is 24 months. There are 75 clinical sites in total: 36% of them are in country A, 24% in country B, 21% in country C, and 19% in country D. Patients arriving at each clinical site will be assigned to take either placebo or high-dose target drug or low-dose target drug or comparator randomly following 1:2:2:2 enrolment ratio. Fig. 2 Network of clinical trial supply chain case study Fig. 3 is the demand profile obtained from the demand simulation (see section 2.3). The increasing nature of the demand is due to the fact that enrollment is low at the beginning since it takes time to generate patient awareness of this clinical trial. With advertisement more and more patients enroll to the clinical trial. However, the enrollment rate drops as the trial nears the end. The valley in the figure is as a result of a combination of factors such as promotional incentives offered and variability of the enrollment start in clinical sites. The dropout rate of patients is 45% in this scenario. A patient is missed if there are not enough drugs available in that clinical site at the time of the visit. The results of the approach described in section 3 are shown in Fig. 4 and Table 1. As Fig. 4 demonstrates the inventory profiles vary significantly over time. 5. Conclusion and future work The clinical trial materials supply chain management problem is discussed and a simulation-based optimization approach, which combines stochastic mathematical planning with discrete event simulation, has been proposed. The quality and robustness of the plans generated by the planning model are assessed by replicated simulation runs.

6 Ye Chen, Linas Mockus, Seza Orcun, Gintaras V. Reklaitis We demonstrated our approach with a case study: a worldwide operated clinical trial materials supply chain management problem. The proposed approach yielded a production and distribution plan with 90% service level (Table 1). Also from the simulation, we can generate the inventory information at each clinical site. This information will be used in continuing research utilizing risk pooling strategies (e.g. Vidyarthi et al (2007)) to further mitigate the risks in clinical trials materials supply chain operation Demand Mean value Mean+std mean-std Month Fig. 3 Drug demand profile from simulation Table 1 Simulation Result Fig. 4 Drug inventories of various countries Patient Number country A country B country C country D missed Placebo dropped successful missed Dose1 dropped successful missed Dose2 dropped successful missed Comparator dropped successful Acknowledgements The authors would like to thank Eli Lilly and Company for introducing us to this problem and for their encouragement and support to pursue its solution. References 1. N. Shah, 2004, Pharmaceutical supply chains: key issues and strategies for optimization, Computers and Chemical Engineering, 28, D. C. Monkhouse, C. F. Carney, J. L. Clark, 2006, Drug Products for Clinical Trials, Informa Health Care. 3. C. A. Floudas, X. Lin, 2004, Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review, Computers and Chemical Engineering, 28, N. Vindyarthi, E. Celebi, S. Elhedhili, E. Jewkes, 2007, Integrated Production-Inventory- Distribution System Design with Risk Pooling: Model Formulation and Heuristic Solution, Transportation Science, 41, 3, D. Subramanian, J. F. Pekny, G. V. Reklaitis, 2001, A Simulation-optimization Framework for Research and Development Pipeline Management, AIChE Journal, 47(10),