Assessment of occupational safety risks in Floridian solid waste systems using Bayesian analysis

Abstract

Safety risks embedded within solid waste management systems continue to be a significant issue and are prevalent at every step in the solid waste management process. To recognise and address these occupational hazards, it is necessary to discover the potential safety concerns that cause them, as well as their direct and/or indirect impacts on the different types of solid waste workers. In this research, our goal is to statistically assess occupational safety risks to solid waste workers in the state of Florida. Here, we first review the related standard industrial codes to major solid waste management methods including recycling, incineration, landfilling, and composting. Then, a quantitative assessment of major risks is conducted based on the data collected using a Bayesian data analysis and predictive methods. The risks estimated in this study for the period of 2005–2012 are then compared with historical statistics (1993–1997) from previous assessment studies. The results have shown that the injury rates among refuse collectors in both musculoskeletal and dermal injuries have decreased from 88 and 15 to 16 and three injuries per 1000 workers, respectively. However, a contrasting trend is observed for the injury rates among recycling workers, for whom musculoskeletal and dermal injuries have increased from 13 and four injuries to 14 and six injuries per 1000 workers, respectively. Lastly, a linear regression model has been proposed to identify major elements of the high number of musculoskeletal and dermal injuries.

Keywords

Risk assessment safety injuries municipal solid waste disposal solid waste management statistical analysis

Introduction and literature review

In 2010 alone, Americans generated about 250 million tonnes tonne (t) = 1000 kg or 2204.6 lb (instead of ton = 1016.05 kg or 2240 lb UK (907 kg or 2000 lb US)) – please confirm units or re-calculate as necessary – please check throughout the article.]of waste compared with 210 million tonnes in 1997 (United States, Environmental Protection Agency, 2010). The municipal solid waste (MSW) generated in the United States has steadily increased over the past 15 years owing to several factors, including a larger population, urbanisation, industry, and technological impacts (see Figure 1(a) from United States, Environmental Protection Agency, 2010). The increasingly complex arena of waste management stores significant potential for safety risks. Such risks are owing to heavy workloads, toxic or carcinogenic microbiological/chemical substances, and proximity to dust and fungi. The workers’ surrounding contamination can also cause health complications. The risks involved with handling waste is so great that the United States Bureau of Labor Statistics ranks sanitation workers as the 7th most dangerous job in the US (2011).

Since the state of Florida generates 8–14% of the total US waste generation (Figure 1(a)), the exposure of Floridian solid waste workers to occupational safety hazards is an area of vital concern. As shown in Figure 1(a), the collected MSW in the state of Florida has a similar trend to that of the overall US over the last 15 years. In Figure 1(b), non-fatal incidence rates from the five most populated US states are presented. The state of Florida has the third highest non-fatal incidence rate only behind New York and Illinois. Florida (population: 19 million people) has an even higher number of non-fatal than Texas (population: 26 million). Hence, this study primarily focuses on the assessment of occupational risks to workers in the MSW management industry in the state of Florida.

In the past, several studies have been conducted to assess the occupational safety risks of MSW workers. Planting the seeds of these efforts, An et al. (1999) conducted a preliminary quantitative analysis comprised of an injury distribution and analysis of variance for primary injuries among MSW workers in Florida from 1994 to 1997. Their analysis of Floridian workers’ compensation data exposed the high rates of musculoskeletal and dermal injuries suffered by MSW workers. Although possible occupational health risks of MSW labourers were considered in their study, a health hazard assessment or prediction distributions were not addressed. Moreover, their work is majorly referred to the collection stage of solid waste systems. Hence, there is need to expand this area for all solid waste management (SWM) methods. Following the earlier work of An et al. (1999), Englehardt et al. (2003) proved the validity of using a predictive Bayesian analysis for musculoskeletal and dermal injuries among MSW workers. Englehardt et al. (2003) conducted a pilot study to construct an unconditional predictive Bayesian distribution for the risks associated with Floridian refuse collectors by integrating over probabilities of parameters of the considered distribution. Although advantageous, the scope of the study was too small and it lacks assessment of the other major waste treatment methods, namely, recycling, landfilling, and composting workers. Consequently, there is a need for an up-to-date study based on new statistical approaches, as there have been many changes in the solid waste industry’s policies and operations over the last two decades.

Other investigators decided to focus their work on discovering what exact risks posed the greatest threat to sanitation workers out in the field. Lavoie and Guertin (2001) investigated specific types of exposures in SWM plants. In their study, three household waste recycling plants have been chosen to find the risk levels of microbiological and chemical substances. Statistical analyses, such as a student t-test, were utilised to demonstrate the significant differences between these plants. Although Lavoie and Guertin’s study covered the recycling stage of SWM lifecycle, it is based on basic statistical analysis and also limited data without any assessment or evaluation method. Backaglu et al. (2004) have utilised a statistical sampling method to evaluate the health impact of airborne pollutants on incinerator workers in a specific incineration facility in Turkey. To this end, places where the maximum exposure has been expected were selected to analyse the samples. Using the obtained data from sampling, values of hazardous pollutants, including volatile organic compounds (VOCs), semi-volatile organic compounds (SVOCs), and dioxins, were statistically analysed. Although interests, this study concentrates on safety hazards identification in an incineration facility without any assessment of data related to exposed facility workers. Athanasiou et al. (2010) investigated respiratory problems among MSW collectors in Greece. To this end, cross-sectional surveys have been conducted among MSW collectors, which the statistical assessment of results has revealed that exposure to bio-aerosols, dust, exhaust fumes, and bad weather conditions play an important role in the development of respiratory problems. Similar to former studies, this study is limited to a specific SWM method and small case study. Bleck and Wettberg (2012) have assessed waste collection occupation in developing countries using an occupational safety and health (OSH)-action cycle method with five steps, including identifying workplaces and procedures, identifying hazards, evaluating and prioritising risks, deciding on preventive action, and taking action. Based on obtained data form assessment, they have designed a pushcart for waste collectors in developing countries considering ergonomic concerns. The assessment area and method for selected previous studies are shown in Table 1.

Table 1.

Comparison of selected work on assessment of health and safety hazards among MSW workers.

	SWM method					Assessment type
	Coll.	Rec.	Inc.	LF	Comp.	Basic statistical	Predict. Bayesian	Statistical sampling	Qualitative approach	OSH-action cycle	Multiple regression
An et al. (1999)	✓					✓
Lavoie and Guertin (2001)		✓				✓
Englehardt et al. (2003)	✓						✓
Bakoglu et al. (2004)			✓					✓
Athanasiou et al. (2010)	✓								✓
Bleck and Wettberg (2012)	✓									✓
This study	✓	✓		✓	✓	✓	✓				✓

OSH: occupational safety and health; SWM: solid waste management; Coll: Collection; Rec.: Recycling; Inc.: Incineration; LF: Landfill; Comp.: Composting; OSH: occupational safety and health; SWM: solid waste management.

Although occupational and safety hazards among MSW workers is an important subject, remarkably, not many epidemiologic or medical research studies have been conducted to scientifically address these risks. This is mostly owing to the lack of available data unveiling the impact of exposure to solid waste on the safety of workers. Data for previous studies are majorly utilised of a very short time span and occupation thus may not represent the long-term impacts of these exposures. To address these concerns, this study seeks to develop a posterior distribution for major injury with unknown parameters, and then, propose a predictive distribution for major hazards in the fundamental MSW management process based on the resulting data. To this end, necessary data to perform a Bayesian data analysis was obtained through several reliable sources from both public and private entities using standard industrial codes (SICs). Then, major injuries for each method of SWM were investigated based on 2005–2012 data. The assessment of safety risks for SWM workers was finally found and exhibited via the lens of a predictive Bayesian analysis. Lastly, regression models are proposed to estimate the number of musculoskeletal and dermal injuries among MSW workers using a multiple regression method, which shows the effect of number of workers, waste processed per day, and traffic violations on number of injuries.

Data collection

In this study, our aim is to assess the safety risks of solid waste workers in the state of Florida for various stakeholders, such as government agencies, industrial investors, researchers, unions, solid waste workers, and nearby communities. Therefore, collection of reliable data from various sources constitutes a major task in this study. Once collected, this data will be used in our statistical analysis in further stages of our work.

Workers compensation data

The reported exposures for SWM workers are collected through workers’ compensation data provided by the Florida Department of Financial Service (http://www.myfloridacfo.com/). The collected data includes workers’ compensation claims for cases of more than seven calendar lost work days, reported under SICs 4953, 5093, 4212, and 2875. The corresponding North American Industry Classification codes (NAICs) and detailed descriptions of these SIC codes are illustrated in Table 2.

Table 2.

NAICs for SWM.

SIC code	NAIC codes	Description
4212	562111	Solid waste collection
	562112	Hazardous waste collection
	562119	Other waste collection
	484110	General freight trucking
4953	562211	Hazardous waste treatment and disposal
	562212	Solid waste landfill
	562213	Solid waste combustors and incinerators
	562219	Other non-hazardous waste treatment and disposal
	562920	Materials recovery facilities
2875	325314	Fertiliser (mixing only) manufacturing
5093	423930	Recyclable material merchant wholesalers
7359	562991	Septic tank and related services
4959	562998	All other miscellaneous waste management services

NAIC: North American Industry Classification code; SIC: Standard Industrial Code.

Italic entries represent major constituents of solid waste in the state of Florida.

NAICs, which are shown in Tables 2, address all types of specific categories in solid waste industries. Some of these categories however, may constitute an infinitesimal share of risks considered in this work. Accordingly, we focus on the NAICs that capture the major constituents of solid waste in the state of Florida (see highlighted NAICs in Table 2). The 2012 proportions of SWM methods in Florida have revealed that landfilling, recycling, and composting constitute 84% of MSW management methods (48% landfilling, 35% recycling, and 1% composting). Incineration makes up the other 16%, but we could not find reliable data on the injuries during this process. To this end, the codes most worth mentioning are: NAIC 562211 (SIC 4953), includes employees of firms primarily involved in the operation of refuse systems; NAIC 484110 (SIC 4212), includes only those workers reported as refuse collectors; and NAIC 423930 (SIC 5093), considered to represent the recycling industry. Meanwhile, compost and fertiliser industry workers are reported under NAIC 325314 (SIC 2875) and the landfill industry is considered to be represented under NAIC code 562212 (SIC 4953). Total MSW work force population data is collected in order to complete the statistical analysis and derive the estimates of the considered risks in terms of probabilities. Population information is obtained from datasets on the Census Bureau’s and US Bureau of Labor Statistics’ websites. The workforce population sizes used in this work are compiled in Table 3 by NAICs.

Table 3.

Estimated MSW work force populations among solid waste workers in the State of Florida.

NAICS (SIC) (industries represented)	2005	2006	2007	2008	2009	2010	2011	2012
484110 (4212) (refuse collectors, excluding other trucking)	5981	6882	6907	6656	6630	6312	6413	6541
325314 (2875) (compost manufacturing)	U	885	850	941	848	826	802	858
423930 (5093) (recycling industry workers)	2466	2928	3237	3675	3372	2921	3669	4118
562211 (4953) (primarily collection)	852	1075	1052	1156	1082	745	878	853
562212 (4953) (landfill industry worker)	600	592	494	575	501	485	506	536
Total MSW and recycling workers (estimated)	9899	12,362	12,540	13,003	12,433	11,289	12,268	12,906

MSW: municipal solid waste; NAICS: North American Industry Classification code; SIC: standard industrial code; U: no available data for that category.

In order to conduct statistical analyses, reported exposures between 2005 and 2012 were collected, leading to a yearly exposure percentage. In Table 4, percentages based on reported exposures and MSW workforce population for each type of SWM method are presented; using Table 4, one can discern an exposure trend from 2005 to 2012.

Table 4.

Reported exposure statistics among solid waste workers in the State of Florida (2005–2012).

Facilities		2005	2006	2007	2008	2009	2010	2011	2012
Refuse collector	Reported exposure	109	117	124	153	166	166	120	148
	Total population	6833	7957	7959	7812	7712	7057	7290	7394
	Percentage	1.60	1.47	1.56	1.96	2.15	2.35	1.65	2.00
Recycle workers	Reported exposure	46	48	59	71	58	68	78	92
	Total population	2466	2928	3237	3675	3372	2921	3669	4118
	Percentage	1.87	1.64	1.82	1.93	1.72	2.33	2.13	2.23
Compost worker	Reported exposure	10	11	5	2	3	3	3	4
	Total population	F	885	850	941	848	826	802	859
	Percentage	—	1.24	0.59	0.21	0.35	0.36	0.37	0.47
Landfill workers	Reported exposure	41	5	12	14	8	30	42	24
	Total population	600	592	494	575	501	485	506	536
	Percentage	6.83	0.84	2.43	2.42	1.60	6.19	8.30	4.48

Identification of major injuries by SWM method

Insurance organisations have specific injury description codes to store worker compensations data efficiently. These codes were used in this study to discover the nature of major injuries in each type of SWM method. Figure 2 illustrates the percentage of reported injuries in each method. A percentage scale was used to illustrate injuries and diseases for all types of SWM methods adequately in one chart. As addressed in Figure 2, major injuries in all methods commonly include sprain/strains, lacerations, fractures, and contusions. Statistical analyses are conducted on the basis of these major injuries.

Methods

Statistical inference (estimation) involves drawing conclusions about quantities that are not observed from detectable numerical data. For instance, in SWM, a new waste collection facility might be designed to compare the 5-year injury rates for solid waste workers using the new facility. The injury rate probabilities demand a large population of solid waste workers, which is not feasible. Therefore, inferences about the true and reliable probabilities must be based on samples of the full worker population. The objective of statistical analyses in this study is to assess injury rates for Floridian refuse collectors, recycling, landfill, and composting workers. In accordance with the SWM literature review, the predictive Bayesian method is applied to analyse the injury rates data. In a predictive Bayesian method, the total injury rates from available information without computation are assessed (Englehardt et al., 2003). Since the Poisson distribution has been demonstrated theoretically as a distribution of the number of events over a period, the annual injury rates were assumed to follow a Poisson distribution. Next, a Bayesian data analysis for the Poisson distribution is applied to propose a statistical inference. The following sections discuss the Bayesian data analysis.

Bayesian data analyses for Poisson distribution

The Poisson distribution is a discrete probability distribution that states the probability of a given number of events occurring in a fixed interval of time and/or space. Since this study intends to evaluate injury rates among solid waste workers, data point (y) follows the Poisson distribution with rate λ, then the probability distribution of a single observation y is (Bunn et al., 2011):

p (y | λ) = \frac{λ^{y} e^{- λ}}{y!}, for y = 0, 1, 2, \dots

(1)

For a vector y = ( $y_{1}, . . ., y_{n}$ ) of independent and identically distributed observations, the likelihood distribution is (D’Agostini, 2003):

p (y | λ) = \prod_{i = 1}^{n} \frac{1}{y_{i}!} λ^{y_{i}} e^{- λ}

\propto λ^{t (y)} e^{- n λ}

(2)

where $t (y) = \sum_{i = 1}^{n} y_{i}$ is the sufficient statistic. The likelihood can be rewritten as an exponential family of the form:

p (y | λ) \propto e^{- n λ} e^{t (y) \log λ}

(3)

Considering conjugate prior distribution, the posterior distribution is (Gelman and Hill, 2006):

λ | y ~ Gamma (α + n \bar{y}, β + n)

(4)

The negative binomial distribution with conjugate families and the known forms of the prior and posterior densities can be used to find the marginal distribution p(y), using the formula:

p (y) = \frac{p (y | λ) p (λ)}{p (λ | y)}

(5)

Thus, the prior predictive distribution for the Poisson model from one observation is:

p (y) = \frac{Poisson (y | λ) Gamma (λ | α, β)}{Gamma (λ | α + y . 1 + β)} = \frac{Γ (α + y) β^{α}}{Γ (α) y! {(1 + β)}^{α + β}}

(6)

The resulting equation is known as the negative binomial density (Box and Tiao, 2011; Gelman et al., 2013):

y ~ Neg - bin (α, β)

(7)

Predictive Bayesian assessment

As previously mentioned, the number of injuries over a planning period is assumed to follow a Poisson distribution. The expected number of injuries in this study is equal to Poisson parameter λ. Considering the Gamma prior distribution for expected injuries, a marginal predictive distribution of an incident number that accounts for uncertainty in λ is:

P (n | α, Β, I, \bar{n_{i}}) = \frac{{(Β + I)}^{(α + I \bar{n_{i}})} Γ (n + α + I \bar{n_{i}})}{Γ (n + 1) Γ (α + I \bar{n_{i}}) {(β + I + 1)}^{(n + α + I \bar{n_{i}})}}

(8)

In equation (10), n is the integer number of incidents over a planning period, α and β are parameters of the Gamma prior distribution, $p (n | α, β, I \bar{n_{i}})$ is the unconditional discrete probability distribution of the incident number, I is the number of data points, and $\bar{n_{i}}$ is the mean of the incident data. Equation (10) is a negative binomial distribution with parameters $s = α + I n_{i}$ and $p = (β + I)$ / $(β + I + 1)$ . Consequently, the mean and variance of equation (17) are (Englehardt et al., 2003):

E [n] = α + I n_{i} E [n] = \frac{α + I \bar{n_{i}}}{β + I}

(9)

Var [n] = \frac{α + I \bar{n_{i}}}{β + I} + \frac{α + I \bar{n_{i}}}{{(β + I)}^{2}}

(10)

In equation (10), the simulation method is applied when the mean injury number is large, since it requires extensive computation (Englehardt et al., 2003). Annual injury numbers are the sums of injuries over shorter time periods. Hoel et al. (1971) addressed that (1) the sum of all events over multiple time periods is Poisson-distributed and (2) for a large number of time intervals, the same sum is normally distributed by the Central Limit Theorem. Therefore, for large incident numbers, the (discrete) Poisson distribution converges to the (continuous) normal. The same result applies to the negative binomial distribution. Consequently, probability distributions for SWM methods are compared with normal distributions derived using Monte Carlo simulation.

Assessment results of Floridian solid waste systems

Following the identification of major injuries for SWM methods in the section ‘Identification of major injuries by SWM method’, a statistical analyses that largely consist of Bayesian data analysis and predictive Bayesian analysis are conducted in this section. Required data for these statistical analyses are presented in Table 5. This data was collected for major injuries associated with each SWM method.

Table 5.

Major hazards among solid waste workers in the State of Florida for SWM methods.

Facility	Factors	2005	2006	2007	2008	2009	2010	2011	2012
Refuse collector	Strain/sprain (reported per year) ( $y_{j}$ )	58	50	57	64	74	61	73	74
	Total number of refuse collectors ( $n_{j}$ )	6833	7957	7959	7812	7712	7057	7290	7394
	Rate of injuries per thousand ( $\frac{y_{j}}{n_{j}}$ *1000)	8	6	7	8	10	9	10	10
Recycling workers	Laceration, puncture and rupture (reported per year) ( $y_{j}$ )	46	48	59	71	58	68	78	92
	Total number of recycle workers ( $n_{j}$ )	2466	2928	3237	3675	3372	2921	3669	4118
	Rate of major hazards per thousand ( $\frac{y_{j}}{n_{j}}$ *1000)	19	16	18	19	17	23	21	22
Landfill workers	Sprain, strain and fracture (reported per year) ( $y_{j}$ )	12	3	9	5	4	22	30	15
	Total number of landfill workers ( $n_{j}$ )	600	592	494	575	501	485	506	536
	Rate of major hazards per thousand ( $\frac{y_{j}}{n_{j}}$ *1000)	20	5	18	9	8	45	59	28
Composting worker	Sprain, strain and contusion (reported per year) ( $y_{j}$ )	U	3	2	1	1	2	1	1
	Total number of compost workers ( $n_{j}$ )	U	885	850	941	848	826	802	859
	Rate of major hazards per thousand ( $\frac{y_{j}}{n_{j}}$ *1000)	U	3	2	1	1	2	1	1

U: no available data for that category.

Since this study uses data that was reported annually, the injury rate is assumed to follow a Poisson distribution with parameter λ (rate of injuries per year per 1000 workers). The parameters required to apply a predictive Bayesian data analysis are displayed in Table 6. Estimated values for λ were obtained by fitting a Poisson distribution on prior data (2005–2011). The latest data is from 2012, thereby acting as sample data in the Bayesian data analysis. Residual parameters involving $I, \bar{n_{i}}, α, β, \frac{α}{β}, μ^{*}, σ^{2 *}$ were produced by using equations (8), (9), and (10). The prior distribution of the Poisson parameter λ was assumed to be following a gamma distribution. It should be noted that parameters α and β of the gamma distribution were found by the method of moments.

Table 6.

Estimated parameters for predictive Bayesian data analysis of major injuries among solid waste workers in the State of Florida.

Parameter	Sprains/strains for refuse collectors	Lacerations, punctures and ruptures for recycling workers	Sprains/strains and fractures for landfill workers	Sprains/strains and contusions for composting workers
Poisson
Estimated $λ$	8	19	23	2
Sample data	10	22	28	1
I	1	1	1	1
$\bar{n_{i}}$	8.5	19.37	23.43	1.66
$α$	1	1	1	1
$β$	0.12	0.05	0.04	0.5
$\frac{α}{β}$	8	19	23	2
Normal
I	1	1	1	1
$\bar{n_{i}}$	8.5	19.37	23.43	1.6
$α$	1	1	1	1
$β$	0.12	0.05	0.04	0.5
$\frac{α}{β}$	8	19	23	2
$μ^{*}$	8.49	19.37	23.49	1.62
$σ^{2 *}$	9.53	21.77	26.11	1.81
Negative binomial
Size	69	156	187.84	13.8
Probability	0.89	0.88	0.89	0.90

The prior, likelihood, and posterior distributions for refuse collectors were plotted in Figure 3(a)–(c) using R software version 3.0.2. Meanwhile, the predictive Bayesian probability distribution is plotted using equations (8)–(10). The prior distribution of sprains/strains for refuse collectors is plotted in Figure 3(a) using workers’ compensation data from 2005 to 2011. Since the mean of the Poisson (prior) distribution is 7, $λ$ ‘s quantities around 7 have greater probabilities than other sprain/strain injury rates. In the next step, the likelihood distribution was plotted by obtaining the latest data (2012). The latest data shows a mean of 10 sprain/strain injuries per 1000 waste collectors; this is greater than the mean of the prior distribution. The posterior distribution presents the distribution of estimates of interest by utilising the prior and likelihood distributions. Since the sprain/strain injury rates increased in the likelihood distribution, the mean of the posterior distribution also increases. Comparing Figure 3(a) with Figure 3(c) reveals that the mean of sprain/strain injuries has increased by 1. Consequently, the mean of the posterior distribution became around 9. At last, Figure 3(d) was obtained through a Monte Carlo simulation of equation (8). An estimated normal distribution was fitted to find the predictive distribution of sprain/strain injury rates for waste collectors. Figure 3(c) illustrates the probabilities of sprain/strain mean injury rates; however, it lacks the distribution of the injury rates. For this aim, Figure 3(d) is a predictive distribution that shows the injury rates with their probabilities. The estimated normal distribution with defined mean and variance was plotted to find the sprain/strain injury probabilities. The estimated normal distribution mean (µ) and standard deviation (σ) were calculated to be 8.49 and 3.09 per 1000 collectors, respectively (see Table 5).

Similarly, the outcomes of a Bayesian data analysis for lacerations, ruptures, and punctures among recycling workers are depicted in Figure 4(a)–(d). Figure 4(a) shows the estimated mean (λ) probability based on prior knowledge, where the mean quantity is 19 major injuries per thousand recycling workers. Meanwhile, the latest data (2012) indicates 22 per thousand laceration, rupture, or puncture injuries per thousand recycling workers. The higher rate of injury in the likelihood distribution has led to an increase in the mean injury rate in the posterior distribution (see Figure 4(a)–(c)). This increase occurred because the posterior distribution was produced by the standardised multiplication of the prior and likelihood distributions. The mean of the major injuries in the posterior distribution is around 19. In Figure 4(d), the predictive Bayesian distribution for lacerations, ruptures, and punctures was plotted with its approximate normal distribution. A Monte Carlo simulation of equation (8) yielded the black points, and the approximate normal distribution was plotted to discern the estimated distribution. It shows that the mean of lacerations, ruptures, and punctures among recycling workers ( $μ^{*}$ ) is 19.37 and related variance ( $σ^{2 *}$ ) is 21.77.

Figure 5 establishes the prior, likelihood, and posterior distributions for sprains/strains and fractures (major injuries) among landfill workers. The mean of major injuries from prior data is 23 injuries per 1000 workers. When reviewing Table 4, it becomes apparent that the abnormally high rates of injury in the years from 2008 to 2010 brought about the high mean injury rate. The latest data (2012) has a likelihood distribution with a mean of 28. Since the prior distribution and sample data have means of 23 and 28, respectively, the mean with the highest probability for the posterior distribution is around 25. Likewise, the predictive Bayesian distribution was plotted using Monte Carlo simulation and estimated parameters in Table 5. The estimated mean and variance of the predictive distribution are, respectively, 23.49 and 26.11.

Finally, Bayesian data analyses were conducted again with respect to the occupational/environmental risks of composting workers. The reported exposures are distributed around 1 to 4 (especially around 1), which lead to greater uncertainties in the Poisson Bayesian data analysis and predictive distribution. As can be noticed from Figure 6, Bayesian analyses show that the mean of the sprain/strain and fracture rate among composting workers continues to be equal to 1. Since the rate of injuries is not high enough, the approximate normal distribution does not fit the simulation results.

In order to summarise the conducted Bayesian data analysis for major injuries among solid waste workers in the State of Florida, Table 7 illustrates the mean (µ) of prior, likelihood, posterior, and predictive distribution with the highest probability. Using Table 7, the effect of likelihood distributions (related to the most recent data) on prior distributions can be seen in posterior and predictive distributions.

Table 7.

Comparison of prior, likelihood, posterior, and predictive mean of Bayesian data analysis among solid waste workers in the State of Florida.

SWM occupation	Prior distribution µ with highest probability	Likelihood µ with highest probability	Posterior distribution µ with highest probability	Mean of predictive distribution
Refuse collectors	8	10	8–9	8.49
Recycling workers	19	22	20	19.37
Landfill workers	23	28	25–26	23.49
Composting workers	1	1	1	1.62

Finally, confidence intervals of number of injuries (per 1000 workers) based on estimated parameters of predictive distribution are provided to act as a good estimate for unknown parameters (number of injuries) for each SWM method. Confidence intervals for different confidence levels (90%, 95%, and 99%) are provided in Table 8. The confidence level of the confidence interval indicates the probability that the confidence range for injury rates captures the true number of injuries (per 1000 workers) from true population.

Table 8.

Confidence intervals for injury rates for major injuries among Floridian solid waste workers.

	$μ$	$σ^{2}$	90% CI	95% CI	99% CI
Sprains/strains for refuse collectors	8.49	9.53	(6.69,10.29)	(6.35,10.63)	(5.68,11.29)
Lacerations, punctures, and ruptures for recycling workers	19.37	21.77	(16.65,22.09)	(16.13,22.60)	(15.13,23.61)
Sprains/strains and fractures for landfill workers	23.49	26.11	(20.51,26.47)	(19.95,27.03)	(18.85,28.13)
Sprains/strains and contusion for composting workers	1.62	1.81	(0.83,2.40)	(0.69,2.55)	(0.39,2.84)

Analysis of predictive Bayesian results and linear regression model

Motivated by the high rates of fatality and injury among solid waste workers, as well as the significance of providing greater knowledge of the potential hazards in order to protect workers from them more effectively, this study has been implemented to show the posterior distribution for the mean of injuries and predictive estimation for said injuries. To discover and investigate SWM hazards, they were initially categorised based on reported exposure from 2005–2012 in the State of Florida. In the next stage, injury rates (per 1000 workers) were illustrated in the section ‘Data collection’ based on the SICs (NAICs), and major injuries were discovered in the section ‘Identification of major injuries by SWM method’. Results from this study have revealed that MSW workers in the State of Florida mostly suffer from two major injury categories: The first major category, musculoskeletal injuries, includes sprains/strains, fractures, and contusion injuries; The second major category, dermal injuries, is comprised of lacerations, ruptures, and punctures. Before considering safety measures for SWM workers, these categories can be prioritised by choosing a reference dataset for comparison. Englehardt et al. (2003), analysed potential injuries for Floridian MSW workers, with comparable categories, from 1993–1997 data. Once the hazards were categorised, data was analysed in correspondence with SIC codes 4212 and 4953. To compare the injury rates between these two datasets (1993–1997 and 2005–2012), the latter is categorised into musculoskeletal and dermal categories. The sample data and estimated parameters used to properly compare the two datasets are depicted in Table 9.

Table 9.

Comparison of estimated Bayesian data analyses parameters of musculoskeletal and dermal injuries among refuse collection and recycling workers in the State of Florida between two datasets (1994–1997 and 2005–2012).

Parameter	Musculoskeletal injuries (1993–1997)		Musculoskeletal injuries (2005–2012)		Dermal injuries (1993–1997)		Dermal injuries (2005–2012)
SICs	4212 and 4953	5093	4212 and 4953	5093	4212 and 4953	5093	4212 and 4953	5093
Poisson
Estimated $λ$	88	14	17	15	15	5	3	7
Sample data	66	17	17	17	12	4	3	5
I	5	5	8	8	5	5	8	8
$\bar{n_{i}}$	88.33	13.59	16.84	14.56	15.03	4.52	3.4	6.5
$α$	1	1	1	1	1	1	1	1
$β$	0.011	0.07	0.06	0.07	0.06	0.2	0.33	0.14
$\frac{α}{β}$	88	≈17	≈17	≈15	15	5	3	≈7
Normal
I	5	5	8	8	5	5	8	8
$\bar{n_{i}}$	88.33	13.59	16.84	14.56	15.03	4.52	3.4	6.5
$α$	1	1	1	1	1	1	1	1
$β$	0.011	0.07	0.06	0.07	0.06	0.2	0.33	0.14
$\frac{α}{β}$	88	≈17	≈17	≈15	≈15	5	3	≈7
$μ^{*}$	88.34	13.60	16.84	14.55	15.05	4.65	3.38	6.51
$σ^{2 *}$	105.97	16.28	18.93	16.36	18.02	5.57	3.80	7.29
Negative binomial
Size	442.65	68.95	135.72	117.48	76.15	23.6	28.2	53
Probability	0.83	0.83	0.89	0.89	0.83	0.84	0.89	0.89

SIC: standard industrial code.

In Figure 7(a), the predictive distribution and estimated normal distribution for musculoskeletal injuries are plotted for both datasets in parallel. This figure exhibits how the injury rates have decreased noticeably in the newer dataset. The mean of the estimated normal distribution has decreased from 88.34 musculoskeletal injuries to 16.84 over 1000 refuse collectors. Furthermore, musculoskeletal injuries for 2005–2012 have a lower standard deviation, i.e. are more concentrated around the mean of the distribution. The same comparison has been conducted for dermal injuries, as demonstrated by Figure 7(b). Dermal injury rates have drastically shrunk between the two datasets; it is even greater a difference than the decrease in musculoskeletal injuries. The mean of the estimated normal distribution has decreased from 15.05 to 3.38. Moreover, the standard deviation of the 2005–2012 dataset has a lower standard deviation (it has decreased from 4.24 to 1.94), indicating a more precise prediction. The mean in the newer dataset is 3.38 injuries per 1000 workers, which is considered a reasonable standard. Therefore, it seems rational to prioritise preventive plans for musculoskeletal injuries among refuse collectors over dermal injuries.

The section ‘Data collection’ declared that SWM injuries are mostly composed of refuse collection and recycling process. Consequently, data comparison for recycling workers has been conducted for the two datasets (1993–1997 and 2005–2012). To better illustrate this data, the sample data and estimated parameters of the injuries during these two processes are provided in Table 9.

In Figure 8(a), the predictive distributions of musculoskeletal injuries for recycling workers and their estimated normal distributions have been plotted. Unlike musculoskeletal injuries for refuse collectors, the musculoskeletal injury rates among recycling workers have actually increased. Furthermore, the standard deviations of both datasets are close (4.03 versus 4.04). Therefore, preventive initiatives for recycling workers to decrease musculoskeletal injuries should be placed as a higher priority than refuse collectors. Correspondingly, the predictive and estimated normal distributions for dermal injuries among recycling workers have been plotted in Figure 8(b). In this case, the rate of injuries for dataset 2 (2005–2012) has again increased in comparison with dataset 1 (1993–1997). The mean has increased from 5.57 to 6.51 for the estimated normal distribution. Plus, the standard deviation has increased by 0.34, although they are still considered to be close quantities.

Comparing the 2005–2012 data with the 1993–1997 data has revealed that injury rates among refuse collectors in both musculoskeletal and dermal injuries have been reduced significantly. However, at the same time, an increase in injury rates in both musculoskeletal and dermal injuries among recycling workers has also been observed. In addition, results of this assessment have indicated that Floridian recycling workers may experience a high occupational illness rate, based on reported and studied occupational diseases.

This study has revealed that musculoskeletal and dermal injuries have constituted a high number of the injuries inflicted upon on-the-job MSW workers. To this end, a linear regression model was applied to discover the major reasons that affect the total number of musculoskeletal and dermal injuries. While non-linear models can be also used, a linear regression model is preferred because of its ease of implementation and high level of accuracy. In the constructed linear regression model, the number of musculoskeletal injuries is estimated as a linear combination of workers’ workload (waste processed (in million)/thousand workers), traffic violations in million, and year parameter. Total population of workers and total of processed waste are related to workers workload, which can affect the number of injuries significantly. Furthermore, since driver/helper occupations constitute a noticeable portion of musculoskeletal injuries (44% of injuries), it has been considered as an element in the regression model. Since a drastic decrease in the number of injuries was observed in 2005, binary parameter, namely year parameter, is considered, which before 2005 was equal to one and from 2005 it was equal to zero. Similarly, number of dermal injuries is estimated as a linear combination of workload and year parameter. Based on a 13-year dataset (2000–2013), the regression model and its parameters are shown in equation (11) and Table 10:

# ofinjuries = β + x_{1} * workload (\frac{wasteprocessed (million)}{perthousandworkers} + x_{2} * trafficviolation + x_{3} * yearparameter ({\begin{matrix} 2000 - 20041 \\ 2005 - 20120 \end{matrix})

(11)

Table 10.

Result of regression analysis to discover major injuries among solid waste workers in the State of Florida.

	Parameters	Musculoskeletal injuries	Dermal injuries
Coefficients	$β$	287	16.2
	( $x_{1}$ )	69.2	10.3
	( $x_{2}$ )	13.2	0
	( $x_{3}$ )	265	65.7
	R ²	92.7%	96.9%
	F ratio	63.69	157.12

The results of the regression model have shown that increasing the workload will lead to higher numbers of both musculoskeletal and dermal injuries with different coefficients (see Table 10). Number of traffic violation (in million) also has a positive coefficient, which it means an increase in the number of traffic violations will likely increase the number of musculoskeletal injuries. As it can be seen in Table 10, $R^{2}$ for both regression models are more than 90%, which means that the data is pretty close to the fitted regression.

Conclusion and future research

In this article, by using predictive Bayesian estimation and linear regression model, we provide an occupational and health risk analysis for major SWM systems in the State of Florida, including waste collection, recycling, landfill, and composting. In addition to considering a comprehensive area of solid waste systems, in order to obtain injury distributions and the main injury factors, 13 years of datasets have been exploited to create an extremely comprehensive predictive Bayesian estimation and linear regression model. Lastly, waste collectors and recycling distributions are compared with those from a previous study that was built around 1993–1997 data. This comparison has revealed that injury rates among refuse collectors in both musculoskeletal and dermal injuries in the period 2005–2012 have been reduced significantly. However, an alarming increase in injury rates in both musculoskeletal and dermal injuries among recycling workers has also been observed. Results of this assessment have indicated that, based on reported and studied occupational disease rates, Floridian recycling workers need to establish meaningful health and safety initiatives to decrease injury rates.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been funded by the Hinkley Center for Solid and Hazardous Waste Management under the Award No. 1132021.

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