**Control
and management of airborne chemical exposures in the workplace**

Occupational hygiene’s main
goal is to identify hazards, and evaluate, control and manage risks in the
workplace. A significant part of these activities relies on acquiring knowledge
about exposure levels experienced by workers through breathing air contaminated
with chemicals. Such exposure assessment can be required for several purposes.
Chemical risk assessment in the workplace often relies on comparing workers’
exposures to occupational exposure limits (OELs) or guidelines set by various
organizations or governing bodies. Exposure assessment can also be performed in
order to understand factors that determine exposure intensity in order to
target intervention. For example it is often interesting to compare exposures
before and after the implementation of a control measure, to assess differences between different situations (e.g. day vs night
shift, or task A vs task B), and evaluate changes over time to monitor gradual
improvement or worsening of exposure conditions.

While some exposure
assessment needs can be met through indirect methods such as control banding or
the use of mathematical models, in most situations direct measurement of
exposure through sampling and analysis of the air breathed by workers is
necessary.

**Implications
of environmental variability on exposure assessment: the exposure distribution**

When measuring exposures in
the workplace, the aim is generally not to acquire knowledge only about the
particular period of time sampled, but to infer from this period what is
usually happening under the same circumstances. Hence the objective is to
obtain a representative picture of exposures corresponding to a set of
conditions. For example, when evaluating a worker’s exposure level for a full workshift, one would want to use that exposure information
to gain knowledge about all other unmeasured days. Indeed, it’s the ensemble of
exposure-days experienced by the workers, the so-called exposure distribution,
which reflects risk.

It was recognized early on
that exposure levels in the workplace vary considerably across both location
and time. Even measurements integrated over a full work shift and taken
repeatedly for a similar work situation can often show 10-fold variations from
one day to another [1–4]. Therefore exposure
corresponding to a particular situation (e.g. painting metal parts in a body
shop) cannot be described by a typical single concentration value. It is rather
characterized by an ensemble of different exposure levels due to minute
variations in many determining factors (e.g. surface being painted, open/closed
doors, air movement, worker’s experience, etc.). Designing a sampling strategy
that accounts for this type of variability and allows drawing of an accurate
portrait of the exposure distribution for any situation is consequently very
challenging.

**Statistics
in occupational hygiene: the lognormal distribution**

Statistical methods
developed to address the challenge posed by environmental variability started
to appear in the mid-1990s in guidelines published by prominent organizations.
Namely, the American Occupational hygiene Association (AIHA) [5], the National Institute of
Occupational Safety and Health (NIOSH) [6], the British Occupational
Health Society (BOHS) [7] and the Institut
National de Recherche et de Sécurité
(INRS) in France [8] published guidelines for
the comparison of exposure levels to exposure limits.

These
methods are based on the assumption that environmental variability is
adequately modelled by the lognormal distribution model [1–4]. Under this model, it is assumed, for a given
exposure group (e.g. stainless steel welders in a parts manufacturing
facility), that the ensemble of exposure levels experienced by workers in this
group over a period of relatively stable work conditions (e.g. a year),
referred to as the exposure distribution, follows a lognormal model. Then, when
a set of measurements are taken, they are assumed to form a random sample from
this exposure distribution. It is therefore possible to use this sample to draw
conclusions on the exposure distribution itself, including measured and
unmeasured days. There is now a large body of evidence suggesting the lognormal
model is a reasonable default assumption for most exposure situations involving
vapors and aerosols [9].

Several parameters of the
lognormal distribution are recommended by current guidelines as risk indices
and should be estimated from a set of exposure measurements. These parameters,
presented in more detail near the end of this document in appendix A, are
briefly summarized here. Exceedance is the proportion of exposures in the
exposure distribution that are higher than the OEL. There is a general
consensus that exceedance lower than 5% corresponds to acceptable exposure
conditions (i.e. less than ~10 days in a year for fullshift
exposures) [10]. Alternatively, one could
estimate the 95^{th} percentile of the exposure distribution, i.e. the
value below which lies 95% of the exposure distribution. Hence, if the 95^{th}
percentile is lower than the OEL, one could infer that exceedance is lower than
5%. For some agents that have chronic effects, the arithmetic mean of the
exposure distribution over a long period of time provides a useful index of
risk, and can be used for epidemiologic purposes or when a long term cumulative
exposure threshold has been established [10]. Risk, as measured by
exceedance or the arithmetic mean, is often assessed at the group level (i.e.
within so-called similar exposure groups), and the group risk is applied to all
workers within that group. In some cases
workers might experience different risk within an exposure group. In these
cases, in addition to group risk (e.g. as measured by group exceedance) it is
advisable to estimate the probability that a single worker would have an
unacceptable exposure distribution (e.g. the probability that a single worker
might have a personal level exceedance greater than 5%). Individual risk is not
calculated for each individual, it is a global measure of the likelihood that a
random individual might experience much higher risk than the rest of the group.

**Numerical
and statistical analysis needs for the interpretation of occupational exposure
data**

Statistical procedures for
the above lognormal parameters and their uncertainty are not described in
standard statistical textbooks, which are mostly centered on the normal
distribution. Instead, they have been gradually developed since the 1990s
onward and are continuing to evolve [11]. While these developments
trickled down from research papers into guidelines from occupational hygiene
associations over time [12], their implementation can
be complicated, making it difficult for practitioners who may lack the
statistical knowledge and tools to perform such calculations. In Quebec, the
Sampling guide for air contaminants in the workplace [37] is referred to by the
regulation as a reference on the level of accuracy required for how to assess
exposure regulatory compliance to OELs. The guide provides detailed
instructions on how to compare one measurement to the OEL to determine whether
exposure on the measured day was compliant, which is essential for regulatory
compliance officers. However it does not include comprehensive documentation
about the lognormal distribution and the associated risk metrics.

We identified only 4 freely
available practical evaluation tools that permit estimation of at least one of
the statistical parameters useful for risk assessment of airborne chemicals in occupational
hygiene including: IHSTAT^{[1]} (Excel
worksheet), AltrexChimie^{[2]} (standalone
downloadable software), IHDA Lite^{[3]} (freeware
version of standalone downloadable software), BW_Stat^{[4]}(Excel
worksheet). IHSTAT is an excel worksheet developed by AIHA and recently
improved with the collaboration of researchers from IRSST and University of
Montréal. AltrexChimie was developed as a
collaborative effort between industry and INRS in France. IHDA Lite is the
freeware version of the IHDA software, developed by Exposure Assessment
Solutions Inc, and based on a framework described
recently in the literature. BW_Stat, like IHSTAT, is
an excel worksheet. It was developed collaboratively by Theo Scheffers, from the Dutch society of occupational hygiene,
and Tom Geens, from the Belgium society of occupational
hygiene.

**Bayesian
methods to interpret occupational exposure data**

The lognormal parameters
useful for risk assessment (e.g. exceedance) have traditionally been estimated
using so-called ‘frequentist’ methods. More recently, Bayesian statistics have
been proposed as a worthy alternative estimation approach. In Bayesian
inference, one establishes prior beliefs about a set of unknown parameters in
the form of probability distributions. Bayes theorem is then used to update
these beliefs with empirical observations, resulting in ‘posterior’ probability
distributions for the parameters of interest. While the theory was established
during the 18^{th} century, Bayesian methods have only gained
popularity relatively recently with the advent of high computing power.
Bayesian statistics have been recently proposed for use in occupational hygiene
because they permit the integration of expert judgement (in the form of prior
beliefs) into measurement data [13–16].

There are other significant advantages to using Bayesian
statistics to interpret occupational hygiene data. Bayesian inference is probabilistic in
nature, therefore instead of a hypothesis test or a confidence interval, with
interpretations that are often difficult to convey to the layman, Bayesian
analysis provides answers to questions in the direct form of “what is the
probability that” (e.g. "what is the probability that this group is
overexposed more than 5% of days"; or, "what is the probability that
this intervention reduced exposure levels by at least 50%"). This greatly
facilitates risk communication. Furthermore, two technical challenges currently
not appropriately tackled by traditional approaches, namely the handling of
non-detects and incorporating measurement error into an assessment, are easily
integrated into a Bayesian approach [17–22].

The Bayesian framework
therefore appears to be a very promising avenue to improve data analysis and
interpretation in occupational hygiene. Unfortunately, its implementation is
currently out of reach of practitioners, as running Bayesian computations
requires advanced software and technical knowledge, usually limited to academic
specialists.

**Challenges
with data interpretation and risk communication using modern approaches **

As mentioned above, the
statistical skills required to understand and interpret occupational hygiene
data as outlined in most recent guidelines are very specific. They are not part
of the basic statistics taught in many traditional educational programs in
basic sciences. More than 10 years of
teaching these concepts to occupational hygiene practitioners by the principal
investigator of this project (JL) showed that they are not well mastered.
Recent studies on expert judgement also showed that hygienists performed better
when taught specific courses about lognormal statistics [23,24]. In Québec, modern
approaches to data interpretation were reviewed and summarized in a recent
IRSST report [25]. The authors specifically
pointed out that these approaches require statistical notions and calculation
tools not widespread in the field.

In addition to the need to
facilitate the use of adequate statistics, risk communication is also a
challenge that would benefit from any improvement as these concepts often
appear obscure to decision makers and workers. For instance, it is possible to
have an exposure situation where a set of measurements are all under the OEL,
but the estimated proportion of exposures expected to be over the OEL during
unmeasured days would be much greater than the generally accepted 5%. This
particular assessment would probably seem counter-intuitive to an uninformed audience.
The difficulty and lack of tools to efficiently communicate statistical results
in a convincing way to non-specialists may also explain the slow appropriation
of modern guidelines by practitioners in the field.

**Summary
of knowledge gaps and needs**

Considerable spatial and temporal variability observed in levels of exposure has historically represented an important challenge to their interpretation. There now exists a consensus framework for their analysis based on the lognormal distribution. These developments, although permitting a better assessment of risk compared to historical approaches, have not been widely adopted by occupational hygiene practitioners. Indeed, they involve statistical notions not usually taught in traditional training programs and require calculations not usually feasible with common tools such as calculators or spreadsheet programs. The few specific tools currently available are an important step forward but do not yet represent a comprehensive answer to practitioners’ needs. Moreover, available tools are standalone, and are not easily amenable to integration within an existing data management structure. Finally, Bayesian methods represent a very promising approach to data interpretation in occupational hygiene, but are currently not accessible to practitioners. In conclusion, in order to support the adoption in the field of modern guidelines for occupational hygiene data interpretation and improve chemical risk assessment practice there is a significant need for better knowledge translation, and for accessible and comprehensive tools.

The gap between the refinement of statistical methods
available to interpret exposure data in the literature and guidelines, and
actual practice are the reason for this endeavour. This Website aims at
supporting practitioners in using state of the art approaches. The first tools implemented make use of the
Shiny application from the RStudio developers,
which permits to interface a heavy duty statistical package (R) with a
webpage. Therefore visitors can enter their data on our Webpage and have our
server perform calculations otherwise not readily accessible. In particular,
this permits the use of very the powerful Bayesian
technology directly from your armchair. The expostats
website is ever-evolving as we develop new tools, improve and validate existing
ones, and research ways to better communicate outputs from statistical
analyses.

In parallel to expostats.ca, our team recently got funded by
IRSST (2015-2018) to create an integrated IH data interpretation platform that
would use the same calculation engine (Bayesian) to treat a wide ensemble of
data interpretation questions while addressing technical challenges (e.g. non
detects). This project, provisionally called Webexpo,
will primarily yield an open access library of algorithms available in several
languages which anyone can use to create practical tools, online or standalone.
Of course we will also create a Website based on these algorithms, with a heavy
focus on user-friendliness and risk communication.

The recommended approaches
to comparing measured exposure levels to an exposure limit have significantly
evolved during the last 30 years. The initial guideline utilizing a statistical
framework for interpretation, proposed by the NIOSH in 1977, recommended that
exposures should be controlled so that less than 5% of exposure levels
experienced by a worker exceed the OEL [6] ( i.e. ‘exceedance’ should
be <5%; a concept also found in the more recent European standard [26]). At that time, NIOSH
proposed to verify this by comparing a single exposure value to an action limit
set at half the OEL. Although this proposition was based on statistical grounds
and provided a practical way to perform risk assessment, it was later
recognised that this action level was too close to the OEL to ensure adequate
protection of the workers. In other words, comparing one measurement to half
the OEL did not permit to ensure that 95% of unmeasured exposures would be
under the OEL [27–30]. Further methodological
developments in the following decades identified three risk metrics based on
the lognormal distribution (see below) which were embraced in a recent workshop
about the upcoming new set of guidelines from NIOSH [31]. In all cases, the exposure
distribution underlying the samples taken is the ensemble of exposure values
experienced by a group of workers sharing similar exposure conditions (i.e. a
homogenous, or similar, exposure group).

a.
Proportion
of exposures exceeding the OEL (exceedance)

This metric is directly
related to NIOSH’s proposal that less than 5% of exposures should exceed the
OEL. Applied to shift-long exposures, the exposure distribution of interest
would comprise of all time-weighted-averaged (TWA) exposures occurring during a
period of stable conditions, typically a year. One would then collect a random
sample from this exposure distribution and estimate the proportion of days
expected to be associated with exposure over the OEL. Because the estimate is
made from a sample of the exposure distribution, uncertainty has to be taken
into account through the calculation of confidence limits around the estimate. This
approach, recommended by INRS in France, forms the basis of the current French
regulation [8,32,33], which equates compliance
to an OEL to the demonstration that, based on 9 measurements, the 70% upper
confidence limit of the exceedance is smaller than 5%. Put in simpler terms,
one has to demonstrate with at least 70% certainty that less than 5% of
exposures are over the OEL. Comparing the exceedance fraction to 5% is
numerically equivalent to comparing the estimated 95^{th} percentile of
the underlying distribution to the OEL. The latter calculation is recommended
in the current guidelines from AIHA [10].

b.
Long
term arithmetic mean of the exposure distribution

Toxicokinetic models have
shown that the arithmetic mean of the long term distribution of exposure levels
is one of the most adequate risk metric for evaluating cumulative damage from
exposure to most chronic toxicants, rather than exceedance [34]. Within this framework, one
would make a number of measurements, estimate the arithmetic mean of the
underlying exposure distribution as well as confidence limits around the point
estimate, and compare them with the OEL. The current guidelines from the AIHA
recommend this approach in cases where the exposure limit has explicitly been
defined as a long term cumulative dose index (‘LTA-OEL, Long term average OEL’)
[10].

c.
Individual
risk: probability that a random worker within the group would have unacceptable
risk despite an acceptable exposure distribution for the group.

Following seminal work by Kromhout, Rappaport and Symanski [35,36], it was recognized in the
late 1990s that the traditional practice of grouping workers performing similar
tasks in the same environment into so-called homogenous exposure groups could
result in underestimation of risk for some members of the group. Thus, despite
an acceptable group exposure distribution, high variability of exposure between
workers could result in a distinct possibility that some workers would have an
unacceptable individual exposure distribution. This was notably reflected in
the AIHA guidelines, where ‘homogenous exposure group’ was replaced with
‘similar exposure group’ in most recent editions. The AIHA also recommends
using analysis of variance methods when enough data is available to assess
empirically whether the group is indeed ‘homogeneous’ [5,10,12]. This concept is an
integral part of the most recent guidelines by the BOHS “Testing Compliance
with Occupational Exposure Limits” [7]. The guideline is a 2-step
process. The exposure group distribution is first evaluated to assess whether
less than 5% of exposures are above the OEL (similar to the French
recommendation described above). If group risk is acceptable, then the
guideline requires testing to determine whether there is significant exposure
variability between workers within the group to estimate the probability that a
random worker’s exposure distribution would correspond to more than 5% of
overexposure. If this probability is estimated greater than 20%, the
guideline’s diagnosis is “failure to comply”.

The previous metrics can
also be used for analyses other than comparison with OELs, including evaluation
of the effect of exposures determinants (e.g. effect of an intervention).

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