An optimized artificial neural network model for the prediction of rate of hazardous chemical and healthcare waste generation at the national level

Abstract

This paper presents a development of general regression neural network (a form of artificial neural network) models for the prediction of annual quantities of hazardous chemical and healthcare waste at the national level. Hazardous waste is being generated from many different sources and therefore it is not possible to conduct accurate predictions of the total amount of hazardous waste using traditional methodologies. Since they represent about 40% of the total hazardous waste in the European Union, chemical and healthcare waste were specifically selected for this research. Broadly available social, economic, industrial and sustainability indicators were used as input variables and the optimal sets were selected using correlation analysis and sensitivity analysis. The obtained values of coefficients of determination for the final models were 0.999 for the prediction of chemical hazardous waste and 0.975 for the prediction of healthcare and biological hazardous waste. The predicting capabilities of the models for both types of waste are high, since there were no predictions with errors greater than 25%. Also, results of this research demonstrate that the human development index can replace gross domestic product and in this context even represent a better indicator of socio-economic conditions at the national level.

Appendices

Appendix A. Details on the selected Inputs

Gross domestic product (GDP) at market prices expressed in purchasing power standard (PPS) eliminates the differences in price levels among countries, and allows the comparison of economies significantly different in absolute size. PPS is an artificial currency unit and theoretically one PPS can buy the same amount of goods and services in each country [58, 59].

Domestic material consumption (DMC) represents the sum of the annual amount of raw material extracted from the country and the difference of all physical imports and exports [60].

Human development index (HDI) is a composite index that measures the average achievement in each specific country in three fundamental dimensions of human development: long and healthy life, knowledge and decent standard of living. The indicators used to calculate HDI are: for the health component—life expectancy at birth, for the education component—mean years of schooling (for adults) and expected years of mean schooling (for children), and for the standard of living component—the log of the purchasing power parity (PPP)—adjusted Gross National Income (GNI) [61, 62].

Value added of industry (or agriculture) refers to the contribution of industry (or agriculture) to overall GDP. Value added is the net output of a sector (e.g. industry or agriculture) adding up all outputs and subtracting intermediate inputs. Value added in industry comprises value added in mining, manufacturing, construction, electricity, water and gas. Value added in agriculture comprises value added in livestock production and cultivation of crops, but also includes value added in forestry, hunting and fishing [63].

Final energy consumption includes information about annual data on quantities of crude oil, oil products, natural gas and manufactured gases, electricity and derived heat, solid fossil fuels, renewables and wastes covering the full spectrum of the energy sector from supply through transformation to final energy consumption by chemical and petrochemical industries [64, 65]. Final energy consumption in chemical and petrochemical industries for this study is normalized and expressed as kg of oil equivalent per capita.

Total intramural expenditure on research and development is in fact gross domestic expenditure on research and development in the specific country. It aggregates the total expenditure on research and development (RD) financed by a country’s institutions including research and development performed abroad but financed by national institutions—while it excludes RD performed within a country, but funded from abroad [66]. The funding sectors are: the business enterprise sector, the government sector, public general university funds, higher education sector and private non-profit sector.

Life expectancy at birth is an indicator that represents the average number of years that a new-born could expect to live if the prevailing patterns of mortality at the time of its birth were to stay the same throughout its life [67].

Data about the inability to face unexpected financial expenses were obtained through householder surveys on the capacity to cover unexpected cost from own resources. Unexpected costs refer to amounts equal to the poverty threshold for each specific country expressed as a monthly sum [68, 69].

Death rate, crude or crude death rate indicates the number of deaths occurring during the year, per 1000 inhabitants estimated at midyear [63].

Bed days indicate the number of hospitals days per capita for all causes of diseases except V00-Y98 (External causes of morbidity and mortality) and Z38 (live born infants according to place of birth) [70].

Appendix B. The model performance metrics used in this study

The coefficient of determination represents the degree of linear correlation between the predicted and observed values. This is a measure of the ability of the model to predict an outcome in the linear regression setting [71]. Although it provides limited information, R² is often used due to its simplicity.

If O _i is the observed value, P _i is the predicted value, O _m and P _m are the means of the observed and predicted data, and n is the number of observations then the coefficient of determination can be shown as:

$${R^2}=1 - \frac{{\sum\nolimits_{{i=1}}^{n} {{{({O_i} - {P_i})}^2}} }}{{\sum\nolimits_{{i=1}}^{n} {{{({O_i} - {O_m})}^2}} }}.$$

(7)

If there is an intercept in the linear model, R² is equal to the square of the correlation coefficient [71]:

$${R^2}={\left( {\frac{{\sum\nolimits_{{i=1}}^{n} {({O_i} - {O_m})({P_i} - {P_m})} }}{{\sqrt {\sum\nolimits_{{i=1}}^{n} {{{({O_i} - {O_m})}^2}\sum\nolimits_{{i=1}}^{n} {{{({P_i} - {P_m})}^2}} } } }}} \right)^2}.$$

(8)

The root mean squared error (RMSE) is the square root of the mean square error (MSE) which is the average of the squares of the difference between the actual and predicted values [72]. Due to the fact that the RMSE is expressed in the units of the variables, it is much more convenient and easier to interpret than the coefficient of determination [47],

$${\text{RMSE}}=\sqrt {\frac{1}{n}\left[ {\sum\limits_{{i=1}}^{n} {{{({P_i} - {O_{_{i}}})}^2}} } \right]} .$$

(9)

The mean absolute error (MAE) is the mean value of the absolute value of the difference between the observed and predicted values:

$${\text{MAE}}=\sum\limits_{{i=1}}^{n} {\frac{{\left| {{O_i} - {P_i}} \right|}}{n}} .$$

(10)

The mean absolute percentage error (MAPE) represents a measure of the accuracy of the predicted values in relation to the measured, expressed in percentages:

$${\text{MAPE}}=\frac{{100}}{n}\sum\limits_{{i=1}}^{n} {\frac{{\left| {{O_i} - {P_i}} \right|}}{{\left| {{O_i}} \right|}}} .$$

(11)

Generally, when MAPE is less than 10%, the forecast is highly accurate, at 10–20% the forecast is good, at 20–50% the forecast is reasonable, and for more than 50%, the forecast is inaccurate [73], but the limits used for the assessment of forecast accuracy may vary for different applications.

The percentage of predictions within a factor of the observed values (FA) demonstrates the ability of the model to give accurate prediction for each test case [47],

$${\text{FA}}1.1=0.9<\frac{{{P_i}}}{{{O_i}}}<1.1,$$

(12)

$${\text{FA}}1.2=0.83<\frac{{{P_i}}}{{{O_i}}}<1.2,$$

(13)

$${\text{FA}}1.25=0.8<\frac{{{P_i}}}{{{O_i}}}<1.25.$$

(14)

The index of agreement shows the degree of medium agreement between the actual and the predicted values, as well as the error between them. It is a relative and standardized statistical performance indicator with values between 0 (poor agreement) and 1 (excellent agreement) [74],

$${\text{IA}}=1 - \frac{{\sum\nolimits_{{i=1}}^{n} {{{({O_i} - {P_i})}^2}} }}{{\sum\nolimits_{{i=1}}^{n} {{{\left( {\left| {{P_i} - {O_m}} \right|+\left| {{O_i} - {O_m}} \right|} \right)}^2}} }}.$$

(15)