key: cord-0024428-g18n35bq
authors: Rashid, Muhammad; Ismail, Hammad
title: HCV extinction analysis in district Gujrat, Pakistan by using SARIMA and linear regression models
date: 2021-12-10
journal: Medicine (Baltimore)
DOI: 10.1097/md.0000000000028193
sha: 61f4c6116ea6c1e8df851860b2108ce86eff328c
doc_id: 24428
cord_uid: g18n35bq

BACKGROUND: To investigate the track of Gujrat, a District of Pakistan is very essential, either it follow-up World Health Organization (WHO) Hepatitis C Virus (HCV) elimination plan or not. This study aimed to find out HCV extinction analysis by time series forecast from District Gujrat, Pakistan. METHODS: From January 1, 2016 to December 31, 2020 total n-5,111 numbers of HCV real-time polymerase chain reaction (RT-PCR) tests were performed in Gujrat. For extinction analysis we used 2 different models, the first model was seasonal auto-regressive integrated moving average (SARIMA) and the second linear regression (LR) model. First, we fitted both models then these fitted and valid models were used to predict future HCV percentage in District Gujrat. RESULTS: In District Gujrat, the men HCV infected ratio is high with a higher viral load as compared with women, from year 2016 to 2020 male to female ratio was (53.75:53.19), (45.67:43.84), (39.67:39.36), (41.94:35.88), (37.70:31.38) respectively. HCV percentage is decreasing from 2016 to 2020 with an average of 4.98%. Our both fitted models SARIMAX (0,1,1)(0,1,1,6) at 95% confidence intervals and LR model Y = –0.379 X + 53.378 at 99% confidence intervals (P-value = .00) revealed that in June 2029 and in August 2027 respectively HCV percentage will be 0 from district Gujrat, Pakistan. CONCLUSIONS: This study concluded that both SARIMA and LR models showed an effective modeling process for forecasting yearly HCV incidence. District Gujrat, Punjab, Pakistan is on track to achieve the WHO HCV elimination plan, before 2030 HCV will be extinct from this region.

Hepatitis C virus (HCV) is a blood-borne pathogen, it affects hepatic cells and causes liver cirrhosis or hepatocellular carcinoma after untreated chronic hepatitis. HCV viral structural proteins are (C, E1, E2, and P7) whereas nonstructural core proteins are (NS2, NS3, NS4A, NS4B, NS5A, and NS5B). [1] Almost 200 million people are infected (∼5% of the population) with HCV worldwide and about 3.5 Â 10 5 deaths occur globally due to liver cancer caused by HCV. [1] In Pakistan 1 out of 20 people is infected with HCV, about 10 million people are infected with HCV by unscreened blood donation, contaminated injections practices in health care systems and utilization of unsterilized equipment that make Pakistan the second-highest HCV infected country after Egypt. [2] From 2016 to 2030 due to the increasing population of Pakistan up to 250 million, HCV prevalence will also increase from 3.9% to 5.1%. On account of this HCV chronic infection will also increase from 7.5 to 12.6 million, HCV incident infections will increase from 7.0 Â 10 5 to 1.1 million annually and 1.4 (1.0-2.0) million HCV-related deaths will occur. [3] To save these people life's from HCV-related deaths until there is no successful vaccination for HCV due to its huge genotyping variation. HCV has 7 genotypes based on its sequence and phylogenetic analysis, these 7 genotypes have 67 well-recognized subtypes and 20 provisional subtypes. [4] To combat this HCV that has vast genetic variability, World Health Organization (WHO) set a global health sector strategy to eliminate HCV infection by 2030. In this strategy, a major focus is on reducing hepatitis incidence (90%) and hepatitis mortality (65%) by 2030. [5] Unfortunately, to meet the WHO target, 76% of high-income countries are not on track and 60% are off-track by at least the next 20 years. There are just 11 countries that are on the track of the WHO plan (Australia, Canada, France, Germany, Iceland, Italy, Japan, Spain, Sweden, Switzerland, and United Kingdom). [6] To meet WHO targets Government of Pakistan established a National Hepatitis Strategic Framework (2017) (2018) (2019) (2020) (2021) in October 2017 with the participation of Federal and Provincial partners together with private sectors and NGOs that plans HCV testing and access to direct-acting antivirals treatment at a low cost in Pakistan. [7] To control hepatitis at the provincial level "The Punjab Hepatitis Act 2018" has been launched. [8] In Pakistan at the Provincial and District level allots of efforts are going to be performed but unfortunately until there is no recent comprehensive study and extinction analysis of HCV has been done at any level in Pakistan. Based on emigration and overseas Pakistani out of 154 Districts of Pakistan, District Gujrat is on 11th number therefore the major aim of this study was to find out either District Gujrat is on track with WHO plan to eliminate HCV by 2030 or not.

Gujrat is a District of Punjab that covers 1232 (sq. mi area), it consists of 3 tehsils (Gujrat, Kharian, Sarai-Alamgir) and has a 2.7 Â 10 6 population. This research work was conducted from January 1, 2016 to December 31, 2020 with the collaboration of the Department of Biochemistry and Biotechnology, University of Gujrat and Dr Mujahid Lab between concerned persons. Blood samples n-5,111 (sample size margin error 2%, confidence level [CI] 99%) [9] of positive anti-HCV screened patients were collected in Dr Mujahid Lab (DML) Gujrat and from its allcollection points (Hospital Labs) that located within district, to perform HCV RT-PCR. Research work was performed in the Biochemistry Laboratory of the University of Gujrat and Dr Mujahid Lab, Gujrat. This research work is done with the consent of patients and study design approved by the Institutional Review Board (IRB) letter reference no. UOG/ORIC/2020/292 dated November 24, 2020 of the University of Gujrat (UOG), Gujrat.

Blood sample (4 cm 3 ) from patients was collected in a Serum Gel Vacuum tube after performed the venipuncture and then incubated at 37°C for 20 to 30 minutes. After the incubation period sample was centrifuged at 4000 rpm for 2 minutes at room temperature then the upper layer of serum was separated in a sterilized (labeled) Eppendorf tube and stored at -20°C. Blood samples from all other collection points were delivered to DML in iceboxes, after received these samples were stored at -20°C till further HCV RNA extraction and amplification.

By using a commercially available kit (FavorPrep Viral Nucleic Acid Extraction Kit by Taiwan) RNA was extracted from collected serum as per manufacturer guidelines. This extracted RNA was stored at -20°C till further amplification. The amplification of HCV extracted RNA was done by RT-PCR (Cepheid Smart cycler II by America). The master mixture was prepared from a commercially available kit (HCV Real-TM Quant by Italy) by adding 300 mL of RT-PCR-mix-1, 200 mL of RT-PCR-mix-2, 20 mL of Hot Start Taq Polymerase, and 10 mL of M-MLV revertase into dithiothreitol tube according to manufacturer protocol. For amplification, 12.5 mL prepared master mixture and 12.5 mL extracted RNA were transferred into PCR reaction tube then mixed it at vortex mixer for 10 seconds then centrifuged this mixture at 8000 rpm for 40 to 60 seconds. Amplification was done under fluorescence detections (FAM & Cy3) by using kit protocol. The results were interpreted by using FAM (Green) to detect internal control and Cy3 (Yellow) to detect HCV amplified product. Viral load was calculated by using the following formula in which HCV and Internal Control (IC) cDNA copies were attained by a standard curve that was run according to manufacturer kit protocol. HCV [10] The general form of SARIMA model is (p,d,q)(P,D,Q)S. Here p, d, and q are the orders of autoregressive (AR), differences (I), and moving average (MA) whereas P, D, and Q are the seasonal orders of the autoregressive, difference and moving average. S represents the length of the seasonal periods. We adopted the following steps to process the SARIMA model. [11, 12] 2.3.1.1. Import library. To start our analysis we created the following library dataset coding in Jupyter Notebook. import warnings import pmdarima as pm import itertools import numpy as np import matplotlib import matplotlib.pyplot as plt import pandas as pd from statsmodels.tsa.arima.model import ARIMA import statsmodels.api as sm from statsmodels.tsa.stattools import adfuller from statsmodels.tools.eval_measures import rmse, aic 2.3.1.2. Data pre-analysis. To build and apply SARIMA model first preconditions like linearity, seasonality, and stationarity of the dataset were checked linearity patterns and seasonality of the dataset were checked from the Additive Decomposition model by using the following coding. To check out the stationarity of data To find the best parameters for our model we used the Pyramid auto-ARIMA model also called "auto-arima" or "pmdarima" which automatically generated the best and suitable model for forecasting based on grid search. To functionalize and install it we generated the "pmdarima" library by using the following command. From Pyramid auto-ARIMA best model was selected based on minimum Akaike Information Criterion value this selected model was then fitted for prediction analysis.

"pip install pmdarima" 

In district Gujrat, the annual percentage of HCV-infected men patients is high with a higher viral load as compared to women. (Table S1 , Supplemental Digital Content, http://links.lww.com/ MD2/A740). The results showed that overall annually percentage of HCV in 2016 was (53.38%), 2017 (44.45%), 2018 (39.47%), 2019 (38.04%), and in 2020 (33.45%). This percentage is continuously decreasing from 2016 to 2020 with an average of 4.98%. As in 2016 HCV percentage was 53.38% and in 2020 it was 33.45% in these years total of 19.93% HCV infection decrease from District Gujrat. To find out at which month and year this percentage will be zero SARIMA and linear regression models used in this study.

In the first time-series data analysis strategy we used the SARIMA model.

After importing, install and running our library we generally visualized the dataset by plotting a graph (Fig. 1) . It showed that our time series data has a linear pattern because the set of data cluster less round a straight line due to this the trend is linear. Therefore, our time series data has a linear pattern.

To identify the hidden pattern in our time series data an additive decomposition model was selected to decompose the data because data have a linear pattern. It consisted of 3 systematic components including trend, seasonality, and 1 non-systematic component called noise www.md-journal.com (Fig. 2) . This gives us more insight into our data that it has a downward linear trend and also has seasonality where the percentage value maximum twice every year. Therefore SARIMA model was selected as compared with ARIMA model.

Before modeling it was necessary to check our data are stationary or not because most time series models only work on the assumption if the time series data are stationary. Time-series data are said to be stationary if its statistical properties like mean and variance remain constant over time. We used 2 methods to determine data stationarity, in the first method rolling statistics was used to visualize our data for this we plotted the data with the rolling mean and rolling standard deviation for any case of trends (Fig. 3) . It showed that it is constant with time there is no sharp increasing or decreasing trend in our data and rolling mean and rolling standard deviation lines are approximately parallel to the x-axis or horizontal and this data was stationary. In the second method ADF test was imposed on data to check the stationarity. After performing the ADF test at 95% CI, the P-value is <.05 so we rejected null hypothesis H o so the data were stationary. Also, the test statistics are less than the critical values as shown in Table 1 . So, the dataset was stationary. 

To find the best parameters for our model we used the Pyramid auto-ARIMA model also called "auto-arima" or "pmdarima." This package automatically or itself generated the best and optimal parameters SARIMAX (0,1,1)(0,1,1,6) by Grid search. This model was selected based on the minimum values of Akaike Information Criterion metrics which was 386.473 ( Figure S1 , Supplemental Digital Content, http://links.lww.com/MD2/A739). This fitted SARIMAX (0,1,1)(0,1,1,6) model summary as elaborated in Table 2 have significant ma.L1, ma.S.L6, sigma2 (moving average Lag 1, seasonal moving average Lag 6 and variance respectively).

A diagnostic test was performed to check out acceptability and white noise to fit our model (Fig. 4) . The white noise process is defined as a sequence of residues that should be uncorrelated and normally distributed around a zero mean. From the diagnostic test, we observed that our fitted model residuals satisfied the requirements of the white noise process and have all properties like, mean close to zero, constant variance, normally distributed and no correlation. In standardized residues, residuals have a mean around zero and constant variance. In the histogram plot, we have seen that red Kernal density estimate (KDE) line followed closely with the standard notation N(0,1) line (here 0 is mean and 1 is standard deviation), and residuals stay much the same across the historical data which indicated that residuals are normally distributed. Q-Q plot showed that the ordered distribution of the residues (blue dots) followed the linear trend of samples taken from a standard normal distribution with N(0,1). This Q-Q plot also indicated that residuals are normally distributed. Correlogram shows that there is no significant correlation in the residual series. From all these, it was suggested that the fitted model was valid and acceptable. We selected this model SARIMAX(0,1,1)(0,1,1,6) to forecast future percentages of HCV.

3.2.6. Validating forecast. We applied the accepted fitted model to predict the value of the test data set at 60% from tail to check its accuracy. It showed (Fig. 5 ) that our predicted values are so 3.2.7. Forecast analysis. We used our fitted and validate model SARIMAX (0,1,1)(0,1,1,6) to predict future HCV percentage values. Blue lines (Fig. 6) show our original percentage values and the red line show forecasted percentage values for the next 10 years. This forecast has captured the seasonal pattern seen in the historical data and replicated it for the next 10 years. The greyedout area consisted of 95% CI that means the predictions will not cross that area. From this forecasting, the HCV percentage will be zero in June 2029. It means that District Gujrat is on track and following the WHO plan (HCV elimination) and HCV will extinct from District Gujrat before 2030 if the same efforts continue for its elimination.

Our dataset adopted all assumptions of the linear regression model as the goodness of fit.

Simple scattered was plotted that showed the linear relationship present between HCV percentage and months and there is no specific outlier (Fig. 7A ).

In our dataset, the sum of residual errors was zero that not violated this assumption.

In Durbin Watson (DW) test, if the tested result value of DW fall 1.5 to 2.5 then there is no autocorrelation present in data and if the tested result value is below 1.5 then autocorrelation is present. In our analysis, the Durbin Watson value was 2.054 it means that there was no autocorrelation present in our time series dataset.

To check out the homoscedasticity "Scatterplot" (Fig. 7B ) was plotted, it was shown in the figure that our data meet the assumption of homoscedasticity because observed values were not dispersed and these were along the line of best fit. In Breusch-Pagan (analog) test our ANOVA P > .05 (P = .461) so we were failed to reject the null hypothesis and our data have homoscedasticity instead of heteroscedasticity.

3.3.5. Normality. The normality of the residual was visualized by the P-P plot (Fig. 7C) . In this data are almost fall and fit the line and residues were normally distributed. Statically to check out the normality we used Kolmogorov Smirnov (KS) and Shapiro Wilk (SW) tests. In our analysis, KS test P = .200 and SW test P = .357 in these both tests our residues are not significant due to this we accepted the null hypothesis (H o ) which mean data were normality distributed.

In the second approach, we used statistical data analysis by linear regression model. First, we fit our model and then used it for prediction analysis. In this model based on 2 variables (months and HCV monthly percentage), we applied linear regression with 99% CIs level. We obtained highly significant model (P-vale = .00) that was Y = -0.379X + 53.378, in this model "Y" was dependent variable (HCV percentage), "X" was independent variable (months), "-0.379" was slope (P-value = .00) and "53.378" was intercept (P-value = .00). In our model R = 0.666 showed that there was a good relationship between dependent and independent variables. By using this model we analyzed that in August 2027 HCV percentage will be zero in District Gujrat, it is on track to WHO plan of HCV elimination before 2030.

This study revealed that in District Gujrat concerning the male and female ratio, the male's ratio is always high as compared with females. Figure 6 . Forecasting: forecast analysis indicated that HCV percentage will become zero in June 2029 (95% confidence interval).

Rashid and Ismail Medicine (2021) 100:49 www.md-journal.com men is high with a higher viral load as compared with women from the last 5 years. In Pakistan, higher HCV prevalence has been recorded in 40 to 50 years of age people and the anti HCV antibodies ratio in men (15.09%) is higher than in women (12.3%). [14] In Punjab, a province of Pakistan prevalence of anti-HCV is 8.9%. [8] In this province HCV infected female to male ratio was 18.7:17.5 respectively in which maximum patients were at the age of 41 to 61 years (33%), HCV seroprevalence in District Gujrat was 7.4% and in Northern Area (25.7%), Rawalpindi (2.45%), Multan (4.06%), Karachi (4-6%), NWFP (5%), Islamabad (5.31%), Faisalabad (20.89%), and Mardan (9%). [15, 16] In this study, it was found that in District Gujrat annual percentage of HCV in 2016 was (53.38%), 2017 (44.45%), 2018 (39.47%), 2019 (38.04%), and in 2020 (33.45%). This percentage is continuously decreasing from 2016 to 2020 with an average of 4.98%.

To eliminate this infection before 2030 WHO settled a target but 76% of countries are unable to meet this target due to low literacy rates, little awareness, and ignorable HCV screening. Pakistan cannot be achieved the WHO target until 4.9 Â 10 5 infected patients are treated per year for a decade. [17] We can meet this target if we annually diagnose 9.0 Â 10 5 HCV-infected persons and treat 7.0 Â 10 5 patients. [18] Pakistan just can meet it if we expend 9.0% of health expenditures for HCV screening and treatment per year. [19] Until now there is no study to find out either Pakistan is on track to achieve the WHO target are not due to the unavailability of comprehensively proper and authenticated data from all over regions of Pakistan. But HCV elimination is possible because the virus can be easily detected by Polymerase Chain Reaction (PCR), Unlike SARS CoV-2, HCV is a blood born disease therefore it lacks a non-human reservoir, by interrupting all modes of transmission and successful HCV The "simple scattered plot" showed that our data were not violating the assumption of linearity. (B) Scattered plot showed a graphical representation of our homoscedasticity data that were adopted most important assumption of our linear regression model. (C) P-P plot illustrated that residues were around about fitted the line and these were normally distributed.

Rashid and Ismail Medicine (2021) 100:49 Medicine treatment that revolutionized after the development of directacting antivirals with short duration, very high SVR, and minimum side effect. [20] Most important, easy availability of DDA for Hepatitis C treatment in Pakistan. Therefore by considering all these parameters if such analyses perform in the future at the Districts and Provinces level a clearer image will be seen that either country is on track to achieve HCV elimination before 2030 or not. Different machine learning techniques can be used to find out the HCV extinction analysis. In this study, the SARIMA and linear regression models used to predict the HCV percentage and extinction analysis in District Gujrat these models showed their effective modeling process. SARIMA model deals with seasonality and trends and has more long-term accuracy than the ARIMA model. One another major advantage of the SARIMA model is that it can scrutinize the high accuracy for both long-term and short-term forecasts in time series, this model demanded a large amount of historical data with continuity to fit it. [21] SARIMA model has a good panorama and has been used in the forecast analysis of several diseases. When a fitted and acceptable model is obtained, it can be used to forecast any given number of future time intervals. [22] The combination of the SARIMA-NARNN model for prediction analysis did not always provide better estimates than the single model. [23] The seasonal ARIMA (SARIMA) model was used to predict dengue cases in the population of São Paulo State, Brazil. It was suggested that it is a very effective and reliable predictive tool for disease control and prevention. [24] The Artificial Neural Networks have the best accuracy performance, it is used for modeling the non-linear problems, Artificial Neural Networks specific non-linear functions within the time series data may not be explained well in practice. [25] SARIMA model has purposed a useful tool to monitor epidemics. [11] This study has possible limitations, it is a single District level study with an average number of patient's data. We recommend that such study should be conducted in all districts and provinces level of all countries along with the vast number of consistent historical data of patients to monitor HCV elimination track. Secondly, short term historical data does not give good prediction although different approaches are being used to interpret data according to the nature of datasets there should be some latest single or hybrid model approaches that can easily apply and give accuracy and validity also for short terms time-series data to predicts, monitor, and manage the epidemics. SARIMA and linear regression models can be used to predict HCV elimination if a large number of the historical dataset is available and it does not violate any assumption. In this study, we used SARIMA and Linear Regression models to find out HCV track of District Gujrat we did not do the comparison of these models.

Based on both significantly fitted SARIM and Linear Regression models it was concluded that HCV percentage will be zero before 2030 and District Gujrat is on Track to achieve the WHO plan of HCV elimination before 2030.

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Editor: Abrar Hussain Khan.The authors have no conflicts of interest to disclose. Supplemental Digital Content is available for this article.The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.