Estimation of vaccine requirement by using time series analysis

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

Table 2: Yearwise and month wise OPV doses used

Table 3: Model Statistics

Table 4: Exponential Smoothing Model Parameters

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