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Table of Content Volume 9 Issue 3 - March 2019


 

Estimation of vaccine requirement by using time series analysis

 

Kendre V V1*, Mumbare S S2, Dixit J V3, Wadagale A V4

 

1Associate Professor, Department of Community Medicine, BJGMC, Pune, Maharashtra, INDIA.

2Professor and Head, Department of Community Medicine, Ashwini Rural Medical College, Hospital& research center, Kumbhari, Solapur, Maharashtra, INDIA.

3Professor and Head, 2Statistician cum Lecturer, Department of Community Medicine, Government Medical College, Latur, Maharashtra.

Email: mundevarsharani@yahoo.com

 

Abstract               Background: Routine Immunization is one of the most cost effective public health interventions. This important activity is carried out at all levels of health care services. At PHCs and subcentres, vaccine requirement is calculated by fixed formula. It is difficult to estimate vaccine requirement where denominator is not known as in the case of the Government Medical College. Objective: To estimate vaccine requirement using time series analysis, at Government Medical College, Latur. Material and methods: The present study was record based; undertaken at Government Medical College, Latur. The data regarding BCG and OPV vaccines used during 2009-10 to 2014-15 was taken from immunization book. This month wise data was fed in MS-excel and analyzed using software SPSS version 21.0. Method used for time series analysis was Expert Modeler for best model fit. Time series analysis and forecasting was done using best-fit models viz. – Winter’s additive for BCG and simple seasonal model for OPV. Results: A total of 38361 doses of BCG vaccine and 67348 doses of OPV vaccine were given during the years 2009-10 to 2014-15 at Government Medical College, Latur. Ljung-Box Q statistics was significant for BCG and was not significant for OPV. Forecasting was done for BCG and OPV up to 2018-19. The vaccine requirement calculated for August 2018 and February 2019 for BCG and OPV are 681 and 950 respectively. Conclusion: Time series analysis can be used to estimate vaccine requirement at Medical Colleges.

Key Word: Vaccine estimation, time series analysis, exponential smoothing

 

 

 

INTRODUCTION

Routine Immunization is one of the most cost effective public health interventions and was first introduced in India in 19781. This important activity is carried out through Primary Health Centers, Subcenters, Rural Hospitals, and Tertiary Care Hospitals etc. Traditionally vaccine requirement is estimated with the following steps especially, where denominator is known. Conduct the head count through the Community Needs Assessment Approach or the biannual/annual survey method. For pregnant women, the headcount would provide a point estimate for only 6 months (as pregnancies in the first trimester may be undetected). Hence, multiply the headcount by 2 to arrive at an estimate for 12 months. For infants the headcount would provide a point estimate for the year. From that, monthly estimate is calculated. A wastage rate of 25% or a wastage multiplication factor (WMF) of 1.332 is allowed for all vaccines. The wastage multiplication factor for OPV is 1.18 and for BCG, it is 2.03. However this method cannot be used in situation where denominator is not known. Time series analysis is a specialized area of statistics to which many marketing researchers have had limited exposure, despite it having many important applications in marketing research (MR). Two popular univariate time series methods are exponential smoothing (e.g.- Holt-Winters) and ARIMA (autoregressive integrated moving average)4. Forecasting techniques are important tools in operational management for creating realistic expectations5. So this study was conducted to estimate vaccine requirement where head count cannot be done; for ex. Medical colleges, where people come from various districts and their number is not fix i.e. denominator is not known.

 

OBJECTIVE

To estimate vaccine requirement using time series analysis, at Government Medical College, Latur

MATERIAL AND METHODS

Study Design: The present study is cross sectional; record based study.

Study Setting: Government Medical College, Latur. A Tertiary Care Hospital is attached to Government Medical College.

Data Collection: The data regarding vaccines used viz.BCG and OPV during previous six years i.e. from 2009-10 to 2014-15 was collected from Immunization Report Book maintained at Immunization Clinic of Government Medical College. The month wise data of above six years was fed in MS-excel. This pre-processed data was then imported in Statistical Package for Social Sciences (SPSS) version 21.0 and statistical analysis was done. Then following steps were followed as analyze- forecasting- create models. Method used was Expert Modeler. While there was another method called ARIMA. But we used Expert Modeler for best model fit. In statistics, we display fit of measures. Ljung-Box statistics and number of outliers by given model. For comparing models, we used stationary R2 as model fit statistics and for individual models, we used autocorrelation function (ACF) and partial autocorrelation functions (PACF) plot. In autocorrelation and partial autocorrelations we used natural log transform with difference of 1. The lags used for study were 16. Time series analysis and forecasting was done using best-fit models

 

RESULTS

A total of 38361 doses of BCG vaccine were given during the years 2009-10 to 2014-15 at Government Medical College, Latur. Maximum number of doses were given during the year 2014 and minimum number of doses were given during 2009.Average number of doses and standard deviation is shown in Table 1. For OPV vaccine, total 67348 doses were given during the years 2009-10 to 2014-15 at Government Medical College, Latur. Maximum number of doses were given during the year 2014 and minimum number of doses were given during 2010.Average number of doses and standard deviation is shown in Table 2. For BCG vaccine, the autocorrelation function (ACF) and partial autocorrelation functions (PACF) were significant for first lag 1 and PACF decays exponentially indicating moving averages(MA) model(fig.1 and 2). The ACF and PACF were not significant at any lag for the series of OPV vaccine ( fig.3 and 4) indicating stationarity of the series. Expert modeler of SPSS ver. 21 suggested simple seasonal model as the best fit statistical model for OPV and winter’s additive model for BCG time series data. Table 3 shows model statistics. R squared value for BCG model was 0.655 and it was 0.780 for polio model. Here stationary 𝑅-squared value was used since it provides an estimate of the proportion of the total variation in the series that is explained by the model. Larger values of stationary 𝑅-squared (up to a maximum value of 1) indicate better fit. A value of 0.78 meant that the model could explain 78% of the observed variation in the series. This table also shows the Ljung-Box Q statistics and its P-value. It was not significant for polio model (p= 0.337) and it was significant for BCG model (p= 0.031). Both models detected no outlier in the data. Table 4 shows exponential smoothing model parameters. It shows values of alpha (level), gamma (trend) and delta (season) for BCG model. Here gamma value is more indicating prominence of trend component in the model. In case of polio model values of alpha (level) and delta (season) are shown. Alpha value is more in OPV model indicating prominent level component. Forecasting was done using the best model i.e. simple seasonal model for OPV and winter’s additive model for BCG till 2018-19. It is shown in table 5 and table 6 also shown by figures 5 and 6. The vaccine requirement calculated for August 2018 for BCG was 681 with 867 and 496 as upper and lower confidence intervals. For OPV vaccine, for February 2019, it was 950 with 1378 and 522 as upper and lower confidence intervals.

Table 1: Yearwise and month wise BCG doses used

Month/Year

2009

2010

2011

2012

2013

2014

April

460

507

437

458

640

570

May

474

527

456

542

560

536

June

498

530

559

570

570

530

July

340

450

475

528

196

720

August

274

485

534

593

317

678

September

128

490

659

633

560

670

October

640

596

567

594

560

660

November

600

501

493

616

620

720

December

429

544

527

456

618

680

January

509

447

473

496

470

700

February

387

382

472

580

510

652

March

506

511

621

870

580

620

Total

5245

5970

6273

6936

6201

7736

Mean

437.08

497.5

522.75

578

516.75

644.66

S.D.

140.57

54.30

68.53

108.74

132.65

66.63

 

Table 2: Yearwise and month wise OPV doses used

Month/Year

2009

2010

2011

2012

2013

2014

April

1124

911

804

745

1060

1020

May

1169

846

848

1009

1056

960

June

1137

974

947

955

986

920

July

899

844

817

870

543

1196

August

803

813

908

998

852

1440

September

818

772

933

1440

1074

1060

October

1107

872

824

121

1040

420

November

1179

834

1150

1080

1040

1160

December

802

1026

893

960

990

1300

January

845

785

777

920

820

1132

February

730

717

854

960

894

1000

March

706

870

979

1050

940

1020

Total

11319

10264

10734

11108

11295

12628

Mean

943.25

855.3333

894.5

925.6667

941.25

1052.333

S.D.

183.9586

85.43507

101.6317

301.8836

151.441

248.8107


Table 3: Model Statistics

Model

No. of Predictors

Model Fit statistics

 

Ljung-Box Q(18)

Number of Outliers

Stationary R-squared

Statistics

DF

Sig.

BCG- Model_2

0

.655

26.789

15

.031

0

Polio-Model_1

0

.780

17.787

16

.337

0

 

Table 4: Exponential Smoothing Model Parameters

Model

Estimate

SE

t

Sig.

BCG-model_2

No Transformation

Alpha (Level)

.001

.024

.042

.967

Gamma (Trend)

.500

13.342

.037

.970

Delta (Season)

.001

.123

.005

.996

Polio- Model_1

No Transformation

Alpha (Level)

.100

.059

1.700

.094

Delta (Season)

9.573E-006

.109

8.822E-005

1.000


Table 5: Yearwise forecasts for BCG vaccine requirement provided by Winter’s additive model

Model

BCG-Model_1

 

Forecast

UCL

LCL

 

Apr 2015

615

800

430

 

May 2015

619

804

434

Jun 2015

646

831

461

Jul 2015

555

740

370

Aug 2015

583

768

398

Sep 2015

626

811

441

Oct 2015

706

891

521

Nov 2015

695

880

510

Dec 2015

645

830

460

Jan 2016

619

804

434

Feb 2016

600

785

415

Mar 2016

721

906

536

Apr 2016

648

833

463

May 2016

652

837

467

Jun 2016

679

864

494

Jul 2016

587

772

402

Aug 2016

616

801

431

Sep 2016

659

844

474

Oct 2016

739

924

553

Nov 2016

727

913

542

Dec 2016

678

863

493

Jan 2017

652

837

466

Feb 2017

633

818

448

Mar 2017

754

939

569

Apr 2017

681

866

495

May 2017

684

870

499

Jun 2017

711

897

526

Jul 2017

620

805

435

Aug 2017

649

834

463

Sep 2017

692

877

507

Oct 2017

771

957

586

Nov 2017

760

945

575

Dec 2017

711

896

525

Jan 2018

684

870

499

Feb 2018

666

851

480

Mar 2018

786

972

601

Apr 2018

713

899

528

May 2018

717

903

532

Jun 2018

744

930

559

Jul 2018

653

838

467

Aug 2018

681

867

496

Sep 2018

725

910

539

Oct 2018

804

990

618

Nov 2018

793

979

607

Dec 2018

744

929

558

Jan 2019

717

903

531

Feb 2019

698

884

512

Mar 2019

819

1005

633

 

Table 6: Yearwise forecasts for OPV vaccine requirement provided by simple seasonal model

Model

Polio-Model_2

 

Forecast

UCL

LCL

Apr 2015

1035

1390

681

May 2015

1072

1429

716

Jun 2015

1078

1436

720

Jul 2015

953

1312

593

Aug 2015

1060

1422

699

Sep 2015

1107

1470

744

Oct 2015

822

1187

457

Nov 2015

1165

1532

798

Dec 2015

1086

1455

718

Jan 2016

971

1341

601

Feb 2016

950

1322

579

Mar 2016

1019

1392

645

Apr 2016

1035

1410

660

May 2016

1072

1449

696

Jun 2016

1078

1456

699

Jul 2016

953

1333

572

Aug 2016

1060

1442

678

Sep 2016

1107

1491

724

Oct 2016

822

1207

437

Nov 2016

1165

1552

778

Dec 2016

1086

1475

698

Jan 2017

971

1361

581

Feb 2017

950

1342

559

Mar 2017

1019

1412

626

Apr 2017

1035

1430

640

May 2017

1072

1469

676

Jun 2017

1078

1475

680

Jul 2017

953

1352

553

Aug 2017

1060

1461

659

Sep 2017

1107

1510

705

Oct 2017

822

1226

418

Nov 2017

1165

1571

759

Dec 2017

1086

1493

679

Jan 2018

971

1380

562

Feb 2018

950

1361

540

Mar 2018

1019

1430

607

Apr 2018

1035

1448

622

May 2018

1072

1487

658

Jun 2018

1078

1494

661

Jul 2018

953

1370

535

Aug 2018

1060

1479

641

Sep 2018

1107

1528

686

Oct 2018

822

1244

399

Nov 2018

1165

1589

741

Dec 2018

1086

1512

661

Jan 2019

971

1398

544

Feb 2019

950

1378

522

Mar 2019

1019

1448

589

DISCUSSION

In the present study of time series analysis, expert modeler of SPSS version 21 showed Winter’s additive model for BCG and simple seasonal model for OPV which are the types of exponential smoothing. The name “exponential smoothing” is attributed to the use of the exponential window function during convolution. For a given age(i.e. amount of lag),the simple exponential smoothing(SES) forecast is somewhat superior to the simple moving average(SMA) forecast because it places relatively more weight on the most recent observation i.e.,it is slightly more “responsive” to changes occurring in the recent past6. Whereas it showed ARIMA model in studies conducted by Varun Kumar,7-8, Sachin S Mumbare9. Emrah Onder5 used exponential smoothing model in his study. Sachin S Mumbare9 in his study used Box-Jenkins ARIMA (p, d, q); autoregressive integrated moving averages; nonseasonal models for the analysis and forecast the average number of children at the time of terminal contraception in each group, till 2020. He found the time series to be nonstationary, as interpreted by augmented Dickey-Fuller test, so the series was analyzed with d ≥ 1. He compared Results of the different models using fit measures like R-square, stationary R-square, mean absolute percentage error, maximum absolute percentage error, and normalized Bayesian Information Criteria. Using these parameters, he identified best-fit model for each group. Also confirmed the best-fit model using expert modeler in SPSS and tested adequacy of the best-fit model by examining autocorrelation function of the residuals. Ljung-Box test statistics was used for the same; similar to the present study. The model was ignored, if the Ljung-Box Q statistics gave significant P-value. Varun Kumar 7 in his study on forecasting Malaria Cases Using Climatic Factors in Delhi checked stationarity of the data by autocorrelation function (ACF) and partial autocorrelation function (PACF) which showed a significant peak at a lag of 12 which confirmed the presence of seasonal component in the time series data. These findings were different from the present study where ACF and PACF do not showed significant peak at lag 12. Ljung-Box (modified Box-Pierce) test was used in his study to determine if the model was correctly specified, similar to the study9 and present study. He used ARIMA (0,1,1) (0,1,0) as suggested by Expert modeler of SPSS ver. 21 as the best fit statistical model for the same. In the present study, Stationary𝑅-squared value was used as model statistics as it is preferable to ordinary 𝑅-squared when there is a trend or seasonal pattern. Larger values of stationary 𝑅-squared (up to a maximum value of 1) indicate better fit7. Varun Kumar8 in his study on Seasonality of Tuberculosis in Delhi used ARIMA model for seasonality which showed both declining trend and periodic seasonal fluctuations. In this study the expert modeler of SPSS ver. 21 suggested Winter's multiplicative model as the best fitted mathematical model. A value of stationary R- squared value of 0.698 meant that the model could explain 69.8% of the observed variation in the series. This value is more than that of stationarity R squared of BCG model and less than that of polio model in the present study; indicating better fit of polio model. A seasonal pattern exists when a series is influenced by seasonal factor (e.g.-the quarter of the year, the month, or day of week). Seasonality is always fixed and of known period10. Win wah 11 used the seasonal autoregressive moving average (SARIMA), ARIMA models with periodic components, to predict the temporal trends of the more volatile monthly TB risk among residents and non-residents in Singapore and detect seasonality. The model with the lowest value of the AIC (Akaike’s Information Criterion) was selected to analyze yearly TB cases. Using a time series analysis, an exponential model was fitted to the annual incidence rates of suicide (by any method) between 1995 and 2009. Model adequacy was tested using the mean absolute percentage error (MAPE), a measure of how much a dependent series varies from its model-predicted level12.

 

CONCLUSIONS

Expert Modeler was used in this study of time series analysis, it showed simple seasonal model as best fit model in case of OPV. It can be used to estimate vaccine requirement of OPV, as Ljung Box Q statistics is not significant. Expert modeler showed Winter’s additive model for BCG, which can be used for estimating BCG vaccine requirement with caution as the Ljung Box Q statistics is significant. Time series analysis and forecasting is objective method for calculating vaccine requirement as it gives the values with upper and lower confidence interval. It assures optimum supply of vaccine. So it can be used at Medical colleges.

 

REFERENCES

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