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25Научная статья Original article УДК 004
EFFICIENT TIME-SERIES CLUSTERING OF DRUGS DEMAND TO INVENTORY OPTIMIZATION IN HEALTH CENTERS ЭФФЕКТИВНАЯ КЛАСТЕРИЗАЦИЯ ВРЕМЕННЫХ РЯДОВ СПРОСА НА ЛЕКАРСТВА ДЛЯ ОПТИМИЗАЦИИ ЗАПАСОВ В МЕДИЦИНСКИХ
ЦЕНТРАХ
ЁЯ
Wedyan Habeeb Hameed, Institute of Information Technology And Intelligent Systems (ITIS) Kazan Federal University, Kazan, Russia, wedy.hameed@gmail.com.
Enas Mahmoud Jassim, University of Diyala, Diyala, Iraq, enasmahmoud@uodiyala.edu.iq.
Abstract: To eliminate distribution flaws and boost pharmacy productivity, it is critical to understand the appropriate amount of drugs to keep on hand. For this purpose, it is important to forecast the demand for pharmaceutical products with high accuracy. However, even if demand can be predicted, it is not realistic to build a single demand-forecasting model for all pharmacies and for all drugs because the number of drugs handled by pharmacies is diverse, the number of stores is large, and the location of the pharmacy affects the amount of drug consumption. Therefore, in this paper, we apply the aggregation method of time series data to drug demand, and describe the results of using TSclust as a method for integrating multiple cohorts for each consumption pattern. By using this combination, it is expected that the demand
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forecasting model for pharmaceutical products will be simplified and made more efficient, thus reducing the waste of public money.
Аннотация: Чтобы устранить недостатки в распределении и повысить производительность аптек, крайне важно понимать, какое количество лекарств нужно иметь под рукой. Для этой цели важно с высокой точностью прогнозировать спрос на фармацевтическую продукцию. Однако, даже если спрос можно спрогнозировать, нереально построить единую модель прогнозирования спроса для всех аптек и для всех лекарств, поскольку количество лекарств, обрабатываемых аптеками, разнообразно, количество магазинов велико, а местоположение аптеки влияет на объем потребления лекарств. Поэтому в этой статье мы применяем метод агрегирования данных временных рядов к спросу на наркотики и описываем результаты использования TSclust в качестве метода интеграции нескольких когорт для каждой модели потребления. Ожидается, что при использовании этой комбинации модель прогнозирования спроса на фармацевтическую продукцию будет упрощена и станет более эффективной, что сократит трату государственных средств.
Key words: Forecasting, Demand, Pharmaceuticals, Model, Medicine, Tsclust.
Ключевые слова: Прогнозирование, Спрос, Фармпродукция, Модель, Медицина, Tsclust.
1. Introduction
In the context of promoting comprehensive community care by the government, pharmacies are required to bring about a change in operations that are drug-centric or patient-centered [8]. Due to the lack of human resources in the health field, it is necessary to improve work efficiency in order to respond to this change. On the other hand, in recent years, remarkable progress has been made in computer science technologies such as artificial intelligence, techniques for collecting data
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accumulated from multiple websites, and methods for processing and analyzing that data. Therefore, it can said that it is indispensable for the medical field to introduce data processing and data analysis techniques to solve the shortage of human resources. Among the websites, the site of (Pharma Cloud Inc.), which it offers many of its services for the purpose of improving the efficiency of the work of medical websites and developing the work of pharmacies. In particular, big data has collected in pharmacies daily from ClinCalc, a drug stock-sharing service. At first glance, it seems easy to build a supply and demand forecasting model for pharmaceutical products by taking advantage of this data, but the number of commodity products that pharmacies deal with is diverse, and the number of pharmacies is also large. Moreover, the drug consumption trend has greatly influenced by site conditions such as urban areas, rural areas, train stations, and office areas. Therefore, based on these characteristics, each pharmacy has a separate demand forecast model for drugs, and it differs on the others models. Therefore, in this paper, we would like to look at how to apply the forecasting method to time-series data on drugs demand and summarize multi-drug demand trends in a single cluster unit rather than a prediction model for each drug separately [5]. The drug consumption data used in this paper had collected from ClinCalc (2019) on a daily basis. 2. Existing methods of forecasting demand
There are many such services related to machine learning and artificial intelligence that have being promoted every day, but these services face many challenges when dealing with the expectations of demand for medicines. For example, among those challenges is the number of predictive models required. There are currently about 70,000 types of pharmaceutical products on the market, and more than 500 stores had added to Pharma-Cloud at the end of March 2019. When creating a forecast model for each store regarding the demand for 70,000 types of pharmaceutical products, it is necessary to create a model with more than 35 million patterns. It may not be realistic to adopt a similar approach when increasing the number of stores offering services in the future. In fact, Pharma-Cloud uses Google
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services like GCP and Big Query, but BQML has a limit on the number of forms that can created per day. 2.1 Method Suggestion
This article describes how TSclust can used to distribute the data for each drug to avoid the explosive growth in the number of models. Additionally, because of searching for similarities between time series for each drug, common characteristics of drugs with similar demand trends within the same group are included. We will also discuss the characteristics of divided groups [1]. 3. Time-series clustering.
3.1 TSclust
Time series clustering is an active research field that is applied in a wide range of fields. In fact, it occurs naturally in economics, finance, medicine, ecology, environmental studies, engineering, and many other fields, with active improvements every day. TSclust is published in CRAN1 [2] as a library that implements time series clustering. In addition, the implementation method has described in detail in [3].
3.2. Utilization of TSclust for drug demand
TSclust has used for dispensing data that represents the demand for this drug. Clustering has performed by measuring dissimilarity, distance scale, or by conventional clustering techniques. There are more than 20 classification methods implemented as methods. Here, ACF (Autocorrelation-based Dissimilarity), DTW (Dynamic Time Warping Distance), EUCL are among them. The execution results for the three methods of (Euclidean Distance) have described. Table 1 shows the top 100 drugs with the total number of prescriptions at ClinCalc store in (2019).
Table 1. The Top 100 Drugs from ClinCalc (2019)
Ran Drug Name Total Ran Drug Name Total
k Prescriptio k Prescriptio
ns (2019) ns (2019)
1 Atorvastatin 112,104,35 51 Methylphenidate 14,233,405
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2 Levothyroxin 102,595,10 3 52 Apixaban 14,042,889
3 Lisinopril 91,862,708 53 Ranitidine 13,586,751
4 Metformin 85,739,443 54 Glipizide 13,424,610
5 Metoprolol 74,578,817 55 Ergocalciferol 13,273,652
6 Amlodipine 73,542,114 56 Quetiapine 13,114,560
7 Albuterol 60,679,987 57 Budesonide; 12,473,902
8 Omeprazole 52,546,641 58 Estradiol 12,393,425
9 Losartan 51,773,869 59 Acetaminophen; 11,962,650
10 Gabapentin 47,149,505 60 Ondansetron 11,856,066
11 Hydrochlorothiazi de 38,609,803 61 Naproxen 11,762,233
12 Sertraline 37,157,933 62 Glimepiride 11,504,531
13 Simvastatin 36,812,966 63 Spironolactone 11,432,027
14 Montelukast 32,154,358 64 Clonidine 11,418,367
15 Acetaminophen; 30,355,778 65 Insulin Lispro 11,389,229
16 Pantoprazole 28,880,217 66 Loratadine 11,374,226
17 Furosemide 28,352,226 67 Cetirizine 11,110,560
18 Fluticasone 27,893,102 68 Topiramate 10,927,224
19 Escitalopram 27,510,958 69 Lorazepam 10,875,212
20 Fluoxetine 27,110,302 70 Ethinyl Estradiol; 10,860,083
21 Rosuvastatin 27,041,319 71 Lamotrigine 10,690,317
22 Bupropion 25,722,873 72 Diltiazem 10,604,813
23 Amoxicillin 25,702,634 73 Hydrochlorothiazi de; 10,268,139
24 Dextroamphetamin e; 24,600,698 74 Diclofenac 10,115,975
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25 Trazodone 23,934,213 75 Hydroxyzine 9,898,263
26 Duloxetine 23,821,965 76 Buspirone 9,881,603
27 Prednisone 22,889,929 77 Latanoprost 9,800,569
28 Tamsulosin 21,934,065 78 Paroxetine 9,783,755
29 Ibuprofen 21,746,702 79 Lisdexamfetamine 9,775,262
30 Citalopram 21,546,700 80 Fluticasone; 9,762,036
31 Meloxicam 21,459,849 81 Pregabalin 9,625,189
32 Pravastatin 20,683,277 82 Propranolol 9,277,061
33 Carvedilol 20,602,256 83 Cephalexin 9,246,463
34 Potassium 20,001,670 84 Cholecalciferol 9,068,152
35 Tramadol 19,838,715 85 Insulin Aspart 9,067,406
36 Clopidogrel 19,447,746 86 Finasteride 8,986,897
37 Insulin Glargine 19,211,653 87 Fenofibrate 8,970,219
38 Aspirin 18,143,138 88 Sitagliptin 8,866,811
39 Atenolol 18,091,488 89 Folic Acid 8,860,645
40 Venlafaxine 17,713,653 90 Doxycycline 8,809,374
41 Alprazolam 17,533,262 91 Rivaroxaban 8,799,404
42 Ethinyl Estradiol; 16,505,642 92 Tizanidine 8,729,694
43 Allopurinol 15,900,788 93 Amoxicillin; 8,372,244
44 Hydrochlorothiazi de; 15,709,833 94 Amitriptyline 8,178,156
45 Cyclobenzaprine 15,597,385 95 Lovastatin 8,091,735
46 Clonazepam 15,578,495 96 Alendronate 7,811,899
47 Zolpidem 15,419,648 97 Levetiracetam 7,560,850
48 Azithromycin 15,300,433 98 Sumatriptan 7,050,329
49 Oxycodone 14,669,103 99 Hydralazine 6,655,156
50 Warfarin 14,632,370 100 Sulfamethoxazole; 6,630,866
Source: The Top 200 Drugs of 2019. (2021, September 12). Retrieved from
ClinCalc : https ://clincalc. com/DrugStats/Top200Drugs. aspx
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3.3 Distance scale for clustering
3.3.1 The autocorrelation function (ACF)
Calculate the weighted Euclidean distance of a simple autocorrelation ACF or PACF (Partial Auto-Correlation). If neither the autocorrelation coefficient p nor Q has specified, uniform weighting is used. If p has specified, it has calculated by the following formula [2].
D (x,y) = {CPX - ^Py)tH( (Tx - Ty)1/2
The consumption tendency of medicines has its own characteristics. For example, in the case of medicines prescribed for acute diseases such as pollinosis and colds, which have strongly related to the season, the demand for medicines increases rapidly at the same time every year. For drugs that have often taken regularly, such as prescription drugs for hypertension and diabetes, the drugs have prescribed on a weekly or monthly basis, so the day the patient visits the doctor. Moreover, the required number is determined to some extent. As a result, autocorrelation has often repeated for the consumption of each drug.
3.3.2 Dynamic Time Warping (DTW)
Demand for medicines has greatly influenced by conditions such as the location and scale of pharmacies, and the number of patients visiting the pharmacy per day has affected by them. In addition, data tends to be sparse because so-called top-selling products are concentrated on specific drugs with respect to the number of products. As a result, different drugs often have different data lengths. According to the literature [4, 5], it is known that DTW is used to collect time series of similar shapes. Cluster centroids are computed with respect to DTW. A barycenter is the average sequence from a group of time series in DTW space. It is also effective for such time series data with unequal lengths. In addition, according to [2], DTW has implemented as a function based on DTW. Therefore, due to the nature of the demand data for these drugs, he expects DTW to work effectively. 3.3.3 EUCL
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The EUCL scale is the most commonly used distance scale because of its simple calculation method and small amount of calculation. If x and y are time-series data to be compared, and the ith data of x is xi, it is calculated by the following formula.
On the other hand, the problem is that it is not possible to correctly compare time-series data with different lengths and calculate the distance between time-series data with deviations in the time axis direction [6]. In this case, the purpose is to cluster the consumption tendency of pharmaceutical products and simplify the prediction model rather than correctly classify pharmaceutical products from the viewpoint of medical or pharmaceutical efficacy classification and administration route. Therefore, it has expected that it will work effectively if the point that the amount of calculation is small has emphasized [4]. 4. Application of TSclust to pharmaceutical demand
Figure 1 shows the execution of the three methods described in Section 3.3 to classify the demand for medicines into four clusters so that the results can easily and visually understood. The purpose of Pharma-Cloud is to support decision-making in the inventory management of dispensing pharmacies or pharmacists. In this paper, we will discuss the classification using his ACF, which has more than a certain number of elements for each cluster. The classification hierarchy and the number of clusters can changed accordingly.
4.1 Results of the classification of drug demand using TSclust
The existing classification system for pharmaceutical products also has various classification rules. For example, like the YJ code, it has classified according to the drug efficacy classification number, administration route and component, dosage form [7]. On the other hand, the classification using TSclust introduced in this paper is a classification derived from the consumption pattern of medicines and
N
N
i=1
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has no direct relationship with the drug efficacy classification number, administration route, or ingredients so far. However, the clustering results showed that each of the above four clusters had unique characteristics. 4.2 Characteristics of medicines in each cluster
When the above-mentioned drugs had classified into four clusters using TSclust's ACF, they have classified as follows: (1) Medicines that have often prescribed for the elderly, long-term care facilities, and elderly homes. (2) Drugs related to gastrointestinal and intestinal regulation that have expected to be neurological. (3) Drugs often prescribed for acute illness. (4) Medicines often prescribed for middle-aged lifestyle-related diseases, figure 1 shows Cluster analysis of observations by using TSclust (AFC), and figure 2 shows the number of observations in each cluster.
The medicines classified here and not all medicines on the market do not completely fall into this classification. However, this general tendency resulted in the fact that the drugs subordinate to the cluster number 1 contained many commonly used drugs. In addition, since the drugs subordinate to No. 3 have prescribed for acute diseases, they are often not the same patient, and many of them have a strong seasonal influence on demand. From these results, it can said that it had classified according to the characteristics specific to the demand for medicines.
Figure 1. Cluster analysis of observations using TSclust (AFC)
Dendrogram
Complete Linkage; Euclidean Distance
o.oo
S3.33
rr £
Observations
Source: Prepared by the researchers based on the information in table 1.
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Figure 2. The number of observations in each cluster
Number of observations
50 40 30 20 10 0
I
Number of observations
Cluster! Cluster2 Cluster3 Cluster4
Source: prepared by the researchers based on the results of TSclust (AFC). Conclusion
In this paper, we presented a method for clustering from time-series consumption patterns for drug demand forecasting. Of the three classification methods discussed in this article, the most well classified and "relatively close to the pharmacist's intuition" is the ACF classification. In addition, classification-using ACF results in clusters containing characteristics for each drug, and unlike the existing classification system, they have classified into clusters that are close to each other according to the purpose of the actual prescription and the number of prescription days. In the future, it is desired to improve the algorithm and develop a new algorithm that can reduce the amount of calculation without lowering the accuracy. Theoretical research on algorithms related to drug demand forecasting, social implementation is also an issue. By placing and receiving orders for medicines based on the prediction model of research results, it has expected to reduce sudden large-scale orders and the disposal of excess medicines. As a result, it will contribute to the optimization of the amount of medicine in stock at each pharmacy. ACKNOWLEDGEMENTS. The work has performed according to the Russian Government Program of Competitive Growth of Kazan Federal University and Diyala University.
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Literature
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4. А. М. Брандмайер, 2019. «Кластеризация распределения перестановок», https://cran.r-project.org/web/packages/pdc/pdc.pdf.
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© Wedyan Habeeb Hameed, Enas Mahmoud Jassim, 2022 Научно -образовательный журнал для студентов и преподавателей «StudNet» №6/2022.
Для цитирования: Wedyan Habeeb Hameed, Enas Mahmoud Jassim EFFICIENT TIME-SERIES CLUSTERING OF DRUGS DEMAND TO INVENTORY OPTIMIZATION IN HEALTH CENTERS// Научно-образовательный журнал для студентов и преподавателей «StudNet» №6/2022.
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