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\begin{document}

\title{Lecture Notes on Epidemiology}



\author[1]{Arindam Basu}%
\affil[1]{University of Canterbury}%


\vspace{-1em}



  
  \date{June 10, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Epidemiology is defined as the study of the distribution and
determinants of health related states and the use of that knowledge to
prevent diseases and promote wellness. Environmental epidemiology is a
branch of Epidemiology where we study the Environment as a determinant
of human health. ~Environment is a cause of our health and wellness. By
``cause'' we mean that environmental factors as events or phenomenon
precede our health states and are associated with it. Our health states
and illnesses are caused by a number of factors and there is no one on
one association with a specific environmental correlate and health
state. Because of this, we should think of health related states and
causes of health related states where causes are components of a larger
model and the model with its component causes is the sufficient unit to
cause disease. How do determine that an exposure E is a cause of a
health outcome O? In order to decide if E is a cause of O, we need to
first establish that E has a valid association with O. By valid
association, we mean that we should explain that the association we
observe between E and O cannot be explained by chance alone, we have to
rule out that possibility. We also have to eliminate any possibility of
biased observation or reporting that can result in an apparent
association between E and O but in reality that association is spurious.
We will need to ~control for any potential or actual confounding
variable, that is, a variable that is associated both with E and O, but
does not come in any causal pathway connecting the two. After we have
established a valid association, we will then evaluate that the nature
of this association is one of cause and effect. A way to test that
association is to use Hill's considerations (often referred to as
``Hill's criteria'').~

Cause and effect or non-causal effects for that matter, need to be
studied using measurements of diseases or health related states and
measures of associations. Measures of health related states include
incidence rates and prevalence. Incidence and prevalences must be
standardised for age or other variables when more than one population or
the same population is studied over time. Measures of association
include rate ratios or relative risk estimates, odds ratios, and in case
of Environmental health, we also use impact fractions or attributable
risks to indicate the role of an environmental factor on a health
outcome in the population. ~

We obtain these measures by conducting one or more epidemiological
studies. Environmental epidemiological study designs are observational
study designs and fall in the categories of ecological studies,
cross-sectional surveys, case control studies and cohort studies. A
range of analytical strategies are used to analyse data from
epidemiological studies. These include simple linear models and linear
regression, logistic regression for case control and cross-sectional
surveys, survival analysis and Cox Proportional Hazards model for Cohort
Studies.~

Epidemiological studies form the basis of understanding Environmental
health and therefore forms a good groundwork for understanding the
processes of environmental health impact assessment. Environmental
investigations are also based on epidemiological principles. For
thinking about all environmental health related issues, it is a good
idea to start with the facts, develop an explanatory theory and identify
hyotheses based on these theories and collect facts to validate the
theories by testing hypotheses.~%
\end{abstract}%



\sloppy


Lecture Notes on Epidemiology

\subsection*{Definition and concept}\label{definition-and-concept}

Last defined epidemiology as the study of the distribution and
determinants of diseases in populations and use of that knowledge to
prevent illnesses and promote well being \cite{last2001dictionary}. This
suggests that Epidemiology is a population based study and it not only
associates with diseases but any health related state. In Epidemiology,
we study:

\begin{itemize}
\tightlist
\item
  Cause of diseases
\item
  Measure health related states
\item
  Set up study designs to solve problems
\item
  Analyse data
\end{itemize}

Cause and causal inference are based on considering that causes of
diseases or health related states is not one, but many. These are
represented in the form of causal diagrams that are pie shaped figures
where each slice of hte pie is formed by one cause that is hypothesised
(see Figure 1):\selectlanguage{english}
\begin{figure}
\centering
\includegraphics{https://www.cdc.gov/ophss/csels/dsepd/ss1978/lesson1/images/figure1.17.jpg}
\caption{{Rothman's Causal Pie}}
\end{figure}

As can be seen in the pie shaped figure, each causal model consists of
several possible causes which interact with each other. At the time of
causation of the outcome, these factors are all present and are
sufficient to cause the outcome. Hence this circle or pie is referred to
as a ``sufficient'' causal diagram. This was first proposed by Ken
Rothman \cite{rothman2005causation}.

\subsection*{Causal Inference}\label{causal-inference}

In the causal pie models, each slice of the pie is referred to as a
component cause; if several sufficient causal models are developed for
the same phenomenon, then the most common component cause or the
component cause that were to be found in all sufficient causal models
would be referred to as a necessary cause. A cause does not have to be
sufficient or necessary for cause to occur. As an example, imagine an
old woman slipping on a road of ice and breaks her hip. What was the
cause of her hip fracture? Was it her frailty? Was it the icy pavement
alone? Or can we ascribe it to an older injury that she may have
sustained that made her feel wobbly and led to slippage and fracture of
the hip? All these causes could conspire and lead to the development of
the outcome. The causes interact biologically. These causes can make up
either less than 100\% or more than 100\% if some of them overlap in the
same individual.



The notion of causal thinking is ingrained in human mind, as Rothman
argues that these ideas are formed at birth. A child cries in order to
attract the attention of his mother so that it can be fed. This sets up
a notion of one on one cause and effect as crying is the trigger that
feeds the baby \cite{rothman2005causation}. Over time, this notion of causality
becomes ingrained in our mind and forms our intuitive notions of cause
and effect. However, in Environmental Epidemiology, often multiple
events and conditions are causal factors. Often, association between two
variables can be non-causal. How do we differentiate whether an
explanatory variable is causal as opposed to non-causal? The history of
the development of causal inference is relatively recent. About 2500
years ago, the world could be explained by the words of experts and
seers and these were referred to as
\href{https://www.britannica.com/topic/Scholasticism}{scholasticism}. In
about the middle of the eighteenth century, a new form of explanatory
models arose, referred to as an
\href{http://methods.sagepub.com/reference/encyc-of-case-study-research/n171.xml}{inductivism}.
The inductivist would first observe a particular phenomenon and then
from that particular phenomenon, the inductivist would arrive at a
theory. Take the case of the old woman who fell and broke her hip. The
inductivist would observe that an old woman had slipped and broke her
hip and from here, the inductivist would argue that old age combined
with slippery surface would lead to hip fracture.
John\href{https://en.wikipedia.org/wiki/John_Stuart_Mill}{Stuart Mill}
was a proponent of inductive logic. Inductive logic was a dominant logic
that aimed to explain the world phenomena for over a hundred years; it
was later challenged by other logicians who argued the main assumption
of the induction: the observation of single events that were held as if
they would always remain the same. For example, people who would counter
argue the inductivist's logic that icy pavement and old age would lead
to fall and hip fracture would say that the conditions of the original
observation might have changed over the years. It could be that compared
with what was observed at one instance, the physical strength of the
woman who fell might be different in another situation, so the original
observation that her age alone was responsible for her frailty and her
fall could not hold true for another person. Such was the logic of a
group of logicians who are referred to as deductive logic; in
\href{http://physics.weber.edu/carroll/honors/logic.htm}{deductive}
logic, one would start with a general theory and then one would explain
a particular phenomenon. In health and environmental epidemiology, when
we aim to explain a health occurrence, we tend to use what is referred
to as inductivo-deductive logic; this means, we start with an
observation, and then we formulate a theory, and then on the basis of
that theory, holding that conditions of the world might change, we tend
to predict occurrences. Then we search for specific observations to
refute our theories. Why should we aim to refute our theories? This is
because if we frame theories and search or observe only those
observations that tend to support our theories, then we fall for a
fallacy of circular logic and we do not have rooms for alternative
theories or better more explanatory theories that can explain the
phenomena. For example, think of the previous example where the old lady
slipped on ice and broke her hip. We observed this single fact that an
elderly lady slipped on ice and broke her hip. From here, we could argue
that an icy pavement alone is the cause of her hip fracture and we could
come to a theory that icy pavements are the sole causes of hip fractures
(we can call this theory ice pavement theory). Then, using this theory
as our basis of further statements, we would claim that icy pavements
are causes of hip or other organ fractures and injuries, and we could
continue to support our theory by finding out or actively seeking cases
of people who went out and slipped on icy pavements and injured
themselves. On the other hand, if we were to come across one single
situation where an old woman, of same age and who was wobbly, were to
come out and would break her hip falling on a soft surface, that wold
refute our theory. Logicians call this approach as falsifying our
hypotheses. To logicians, a single case of falsifying a hypothesis is
more important than consistently proving that our hypothesis is correct.
This idea of falsification of hypothesis was extended further with the
theory of
\href{http://philosophyfaculty.ucsd.edu/faculty/rarneson/Courses/popperphil1.pdf}{conjecture
and refutation by Karl Popper (this is a PDF)}. Karl Popper argued that
we can explain the same phenomenon by invoking a number of different
explanations that are our theories. We should then examine each of these
theories by framing hypotheses. We should aim at falsifying the
hypotheses till the one that cannot be falsified. The hypothesis that
would be failed to prove true would be the best explanation till that
hypothesis too, can be deemed to be wrong by another set of findings.
Thus, science becomes an infinite set of iterations in search of the
best explanation.



\subsection*{Concepts of Hypothesis
Testing}\label{concepts-of-hypothesis-testing}

We use this concept everyday in our scientific literature by using the
test of hypotheses. As shown in the following table, we start with a
null hypothesis and aim to reject the null hypothesis with our findings.\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Observation & Null True & Null False\tabularnewline
\midrule
\endhead
Reject Null & Type I Error & Correct\tabularnewline
Fail to reject Null & Correct & Type II Error\tabularnewline
\bottomrule
\end{longtable}



As can be seen in the above figure, Type I error occurs when we falsely
reject the null hypothesis, and Type II error occurs when falsely fail
to reject the null hypothesis. This is referred to as alpha error and
this is how we control for the play of chance. Imagine you are
conducting a study on the association of second hand environmental
tobacco smoke and lung cancer. Your theory may be that compared with
those who do not have lung cancer, those who have lung cancer may have
higher level of exposure to environmental tobacco smoke. A counter
argument to your theory (that environmental tobacco smoke causes lung
cancer) and specific hypothesis (that if we were to compare the
environmental tobacco smoke measurements, we would find the levels
higher on average among those who have suffered from lung cancer than
those who weren't all other things being equal) would be that the levels
of ETS would be no more higher among those with lung cancer than those
without and that, even if you were to find such an association, that
association would be a chance finding. The way to rule out whether what
you found was a chance finding would be to specify beforehand that
chance can explain the findings but also specify the level of that
chance. By convention, this is set at 5\%. Then, after you complete data
collection and analysis, you test what is the probability that what you
found could be explained by chance alone or under the conditions of the
null. This value is referred to as p-value. Again, as with the alpha
error, the p-value is set at 5\% level. However, do not use the p-value
as a cut-off between what is significant and what is not significant.
Overemphasis on p-values as the arbiter of ``significance'' leads to a
malpractice referred to as
\href{http://psychology.wikia.com/wiki/P-hacking}{p-hacking}.

\subsection*{Controlling for Chance, Bias, and Confounding
~Variables}

{\label{576698}}

In order to validate causal inference (``X is a cause of Y'', for
example, ``Air Pollution causes Asthma'') you will need to first
establish that the association is a real association, and then you will
need to examine that the nature of such association is one of cause and
effect. In order to arrive at a point of real association (i.e., not
spurious association), you will need to establish that the association
you observe is not due to:

\begin{enumerate}
\tightlist
\item
  Chance (we have just stated that you can rule out the play of chance
  by using p-values and setting up hypotheses testing)
\item
  You will need to eliminate biases
\item
  You will need to control for potential confounding variables.
\end{enumerate}

\subsection*{Concept of Bias}

{\label{395119}}

The second step is to eliminate biases. Biases are defined as systematic
errors in the observation or conduct of a study. For a comprehensive
review of
biases,~\href{http://www.bmj.com/about-bmj/resources-readers/publications/epidemiology-uninitiated/4-measurement-error-and-bias}{see
this link}. For example, Mustafa Al-Zoughool and ~colleagues conducted a
case control study (we will learn about these types of studies later) to
test the association between exposure to environmental tobacco smoke and
lung cancer~\cite{Al_Zoughool_2013}. In order to study this association, they
interviewed 44 out of 1200 lung cancer patients from different hospitals
in Montreal over four years, and randomly sampled 430 people free from
lung cancer for the same time period. They obtained information about
exposure to ETS from proxy respondents. What could be a problem about
the relationship between ETS and lung cancer if information about
exposure to ETS were to be taken like this? The information obtained
from the respondents might not be reliable, as those people with lung
cancer, if they suspected that ETS were responsible for their lung
cancer would be more accurate or would likely ~to be over cautious in
responding or recalling ETS exposure than those in the control arm. As
information obtained from these two groups would be different in each
arm, this difference is likely to introduce a bias. This bias is
referred to as ``recall bias'' A recall bias is a form
of~\textbf{information bias}. Other forms of biases are referred to as
``selection bias'', where the investigators differently recruit
participants in the studies based on the aims of the study and the
theory that they would like to test. For example, in the case control
study on the association between ETS and lung cancer, if the lung cancer
patients were all recruited from those areas or those neighbourhoods
where they were likely to be exposed to heavy ETS (say low income
neighbourhoods or those neighbourhoods with high smoking rates), and the
control patients were selected or recruited from those neighbourhoods
where they were less likly to be exposed to smoking, then this would be
an example of selection bias. You will need to pay attention to these
possibilities when you read a research study.~

You cannot eliminate selection and information biases at the end of the
study or you cannot examine their impacts at the end of the conduct of
the study, you can only eliminate biases at the planning stage of a
study design. We will discuss this in the section on study designs.~

\subsection*{Concept of Confounding
Variables}

{\label{542045}}

The third alternative explanation for the association between an
exposure and a health outcome could be due to confounding variables. A
confounding variable is referred to as a variable that is associated
both with the exposure of interest and the outcome of interest but that
variable should not come in the causal pathway (see the following
figure)

\par\null\selectlanguage{english}
\begin{figure}
\centering
\includegraphics{https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Simple_Confounding_Case.svg/1200px-Simple_Confounding_Case.svg.png}
\caption{{Confounding Variable}}
\end{figure}

(Source:~\url{https://upload.wikimedia.org/wikipedia/commons/thumb/b/b8/Simple\_Confounding\_Case.svg/1200px-Simple\_Confounding\_Case.svg.png})

The above diagram shows that in the association between X and Y, Z is a
confounding variable. As you can see, Z is associated with both X and Y,
but Z does not come in a causal connection that links X and Y. For
example, in Nordic countries, Eero Pukkala and colleagues studied
airline pilot who were considered to be at high risk of developing skin
cancer as they flew over the poles and were exposed to high energy
cosmic rays~\cite{Pukkala_2002}. If you were to study this association,
that is flying as an occupation and risk of death from cancer, you'd
have to include gender as a confounding variable. Men are more likely to
fly transcontinental aircrafts, and
\href{https://www.cancer.gov/about-cancer/understanding/statistics}{men
are also more likely to die from cancers}.~

You can control for confounding in many different ways. Before beginning
a study, you can identify potential confounding variables, and then you
can either restrict participants so that a potential confounding
variable would be controlled for. In the airline pilot and cancer study,
for example, you would only consider men. You could also match on
specific variables. In case of the airline pilot and risk of cancer
deaths, for example, you could take same number of men and women or the
same proportion of men and women in the comparison arms. You can also
control the role of potential confounding variables by conducting
stratified analysis or conducting multivariable analysis. We will
examine these examples in the section on data analysis for
epidemiology.~

\subsection*{Hill's Criteria or
Considerations}

{\label{689538}}

In exploring the relationship between an exposure and a health outcome,
if you can rule out the play of chance, eliminate biases before or at
the stage of study design, and control for confounding variables either
at the stage of study design or during the analysis of data, then you
have established that the exposure has a valid association with the
outcome. But what will help us to understand the nature of this
association that this association is one of cause and effect?~

This answer is not easy and as it happens, there is no easy way to
understand this. One approach might be to consider several criteria and
examine them to judge whether the association might be one of cause and
effect. The reason this type of association is important is because if
you know that X is a cause of Y, then you can state that if X is
eliminated or if X is removed or if X is controlled for, then there
would be a certain level in the diminution of Y as well. This is the
basis of \href{http://www.sehn.org/ppfaqs.html}{precautionary principle}
that is used in Environmental and Occupational health. Precautionary
principle is a principle that states that even if we do not know the
full extent of the association, if we know that some exposure will lead
to an adverse health outcome, then a precaution can be taken to remove
or restrict or eliminate that factor to protect human health.~

It'd be easy if we were to adopt a list of items that we could check
off. Something similar along this lines was provided by the British
Occupational Health statistician Sir Austin Bradford Hill in 1965, and
these are referred to as Hill's Criteria~\cite{Hill_2015}. Hill stated
the following ``considerations'' for assessing whether an association
might be one of cause and effect. These are:

\begin{enumerate}
\tightlist
\item
  Strength of Association. -- The stronger an association is, the more
  likely that this is one of cause and effect (we will review this
  concept in the next section)
\item
  Specificity. -- If X is a cause of Y, then there should be a one on
  one association between X and Y. This is not always true.
\item
  Consistency. -- If X is a cause of Y, then this association should be
  observed in different situations and under different conditions,
  different studies.
\item
  Temporality. -- If X is a cause of Y, then X must precede Y. This is a
  reasonable and valid clause and indeed, one that is necessary
  condition for X to be a cause of Y.
\item
  Biological Gradient. -- In Environmental and Occupational health we
  refer this to as dose response gradient. By this, we mean that if X is
  a cause of Y, then, as the dosage or the amount of exposure to X
  increases, this will also cause a corresponding increase in the
  outcome or Y. This association is sometimes linear, but it does not
  have to be a linear association. We will review this concept when we
  will study the concepts of environmental health risk assessment.~
\end{enumerate}

So, this summarises the concepts of causation and causal inference.
Causality is intuitive and in health sciences, we have more than one
cause for a health outcome. You can think of causes as models where many
causes biologically interact to form what is referred to as ``sufficient
cause''; each cause in a sufficient cause is a component cause and a
component cause that has to be present in every sufficient causal model
is referred to as necessary cause. In order for an exposure E to be a
cause of an health outcome O, E has to fulfil that it has a
statistically valid association. This is done by ruling out chance,
eliminating biases, and controlling for confounding variables. Finally,
whether such an association is one of cause and effect is also
determined by considering different situations as outlined by Sir Austin
Hill, referred to as HIll's criteria.~

\subsection*{Measurement in
Epidemiology}

{\label{566096}}

We will now discuss the different measures we use in Epidemiology. There
are measures of disease occurrence and measures of association. We
discuss three measures of disease occurrence -- incidence, prevalence,
and standardised rates. We will discuss two measures of exposure-outcome
association -- relative and absolute rates, and odds ratios.~

\subsection*{Concepts of Incidence and
Prevalence}

{\label{895996}}

\href{https://www.nimh.nih.gov/health/statistics/prevalence/index.shtml}{Prevalence}
is defined as the proportion of population who suffer from or who have a
particular disease condition or a health condition. Prevalence is given
by the following formula:

\(\frac{Number\ of\ Individuals\ with\ Disease}{Total\ Population\ }\ \) multiplied by a base population, something like 1000,
or 10, 000.

Consider two towns A \& B, with populations of 1000 and 2000; ~let's say
that it is reported that 15 people in town A and 20 people in town B
have diarrhoea and E.coli infection from contamination of drinking
water. Which township has more disease? If we do not know the total
population of each township, it may appear that indeed more people have
disease in town B, but once we consider the population of each town, we
see a different situation:

\par\null\selectlanguage{english}
\begin{longtable}[]{@{}llll@{}}
\toprule
Town & Number of diarrhoea & Population & Prevalence/1000\tabularnewline
\midrule
\endhead
A & 15 & 1000 & 15 per 1000\tabularnewline
B & 20 & 2000 & 10 per 1000\tabularnewline
\bottomrule
\end{longtable}

As you can see even though there were more people with diarrhoea in town
B, the prevalence of diarrhoea was less in Town B than in Town A.~

While prevalence provides you an idea of the probability or the
likelihood of a
disease,~\href{https://www.health.ny.gov/diseases/chronic/basicstat.htm}{incidence}
provides you with the idea as to how fast the disease is developing, or
an idea as to the hazard associated with the disease. The word hazard
here indicates the chance that someone who is disease free up till now
will develop the disease or the health condition under study. For this,
we need to start with individuals who are free from the disease under
study and a sense of time through which they are followed. This is the
concept of person-time. If I person is followed for 1 year, we have 1
person-year. If 10 persons are followed for 1 year, we have 10
person-years. If 100 persons are followed for 1 year, we have 100
person-years. This is same as if 10 persons were to be followed for 10
years, as there would be 10 persons * 10 ~years = 100 person-years. This
will be the denominator and on the numerator we will estimate the number
of new cases of the disease. Such as measure is referred to as incidence
density rate or simply incidence rate per 1000 person-years or how many
person-years we consider.~

Imagine you want to study a study heart diseases among young people
(5-16 years of age) in a population P for five years. Let us say it is a
small community of 1000 young people, so P = 1000. In the five ~years
you study them, 50 children were diagnosed with heart disease. No one
died in the community and so you have 5000 person-years (1000 people
followed for five years will be 5000 person-years). Can you estimate the
incidence rate of heart disease in this community?

\par\null\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
Population Size & 1000\tabularnewline
\midrule
\endhead
Follow up time & 5 years\tabularnewline
Person-years & 5000 person-years\tabularnewline
Number of cases & 50\tabularnewline
Incidence & 50/5000 or 10 per 1000 person-years\tabularnewline
\bottomrule
\end{longtable}

So, incidence and prevalence estimate two different entities. Prevalence
is suited for long term conditions to give you an idea of the magnitude
of the problem, and incidence provides you an idea of the force at which
a condition is developing in the population.~

\subsection*{Concepts of Age-standardisation and Standardised Incidence
Rate}

{\label{850069}}

Sometimes, we are interested to know whether difference in the age or
other structures in the two populations might be influencing the
difference in the rates we find. In order to assess this situation, we
need age-specific rates of the two or more populations that we'd like to
compare and another population whose age structure we know. This method
is referred to as age-standardisation. This is particularly useful in
situations where we investigate clusters of cases of diseases in
environmental health. For example, imagine you have received reports
that cancer incidence rate has increased in a particular township since
the introduction of a new plant. How do you know that whether the rates
that are being reported are really too high when compared with the rest
of the country? This is where standardisation of the rates become an
important concept to learn.~

We will first illustrate this concept using UK cancer data and then we
will illustrate the point of standardised rates using data sets from the
NZ Ministry of Health for cancer cases for the years 2013, 2014, and
2015.~\href{http://www.health.govt.nz/publication/selected-cancers-2013-2014-2015}{You
can obtain the data sets from here}. We will first illustrate by
calculating age-standardised rates for breast cancers and then we will
compare the ASRs for Leukemia, and melanoma, the two cancers that are
linked to environmental variables.~

In order to calculate age standardised rates of diseases we need to
conduct the following steps:

\begin{enumerate}
\tightlist
\item
  Obtain or calculate the age-specific rates
\item
  Obtain SEGI population or another standardised population. You can
  find \href{http://www.who.int/healthinfo/paper31.pdf}{SEGI population
  here (PDFdocument)}.~
\item
  Multiply each age-band of the age-specific rate with the number for
  the corresponding age band in the SEGI population
\item
  Add up the numbers in the product column
\item
  This number you obtained in step 4 is the age-standardised rate
\end{enumerate}

We will illustrate this idea with an example. We have obtained data for
all cancer incidence rates for UK between the years 2012-2014. Below, in
Table 1, we have presented this data. You can see that for some age
groups, cancer rates among women are lower than that for men, and for
others, the rates are higher. How do we know whether, for all cancers,
the rates are higher among men?~

\par\null\par\null\selectlanguage{english}
\begin{table}[h!]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCC}
Age Range & Males & Females \\
0 to 04 & 20.4 & 18.3 \\
05 to 09 & 12.6 & 10 \\
10 to 14 & 12.6 & 11.7 \\
15 to 19 & 20.7 & 20.6 \\
20 to 24 & 31.2 & 35.5 \\
25 to 29 & 49 & 75.7 \\
30 to 34 & 64 & 109.4 \\
35 to 39 & 83 & 161.9 \\
40 to 44 & 123.4 & 257 \\
45 to 49 & 209.6 & 412.7 \\
50 to 54 & 373.2 & 574.8 \\
55 to 59 & 698 & 731.8 \\
60 to 64 & 1178.2 & 994.3 \\
65 to 69 & 1743.4 & 1283 \\
70 to 74 & 2363.7 & 1530.1 \\
75 to 79 & 2904.9 & 1832.9 \\
80 to 84 & 3260.9 & 2100 \\
85 to 89 & 3643.2 & 2260.7 \\
90+ & 3654.6 & 2114.1 \\
\end{tabulary}
\caption{{This table ~shows the all cancer incidence for UK, male and female,
{\label{955330}}%
}}
\end{table}The first column provides the age group in five year intervals. The
second column provides age-specific incidence rates for men. The third
column provides age-specific incidence rates for women. If we plot these
figures, we get the following figure:

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/cases-crude-all-I14-0/cases-crude-all-I14-0}
\caption{{Comparison of Age-specific cancer rates, UK, 2012-2014, taken from the
website (publicly available data,
see~\url{http://www.cancerresearchuk.org/health-professional/cancer-statistics/incidence/age\#heading-Zero})
{\label{183914}}%
}}
\end{center}
\end{figure}

As can be seen in the above figure, Male rates are higher in the older
age groups, but for younger age groups, rates of cancer among women is
marginally higher than that among men. But this figure, however
informative, does not answer the question: ``are overall rates of cancer
among men higher than that among women?''

In order to answer this question, we will standardise the rates using
the WHO world standard population as a standardising population. ~In
Table 2, we present the results of the standardised rates:

\par\null\selectlanguage{english}
\begin{table}[h!]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCC}
Age Range & Males & Females & WHO World Standard & Counts for Males & Counts for Females \\
0 to 04 & 20.4 & 18.3 & 8.86 & 0.0 & 0.0 \\
05 to 09 & 12.6 & 10 & 8.69 & 0.0 & 0.0 \\
10 to 14 & 12.6 & 11.7 & 8.6 & 0.0 & 0.0 \\
15 to 19 & 20.7 & 20.6 & 8.47 & 0.0 & 0.0 \\
20 to 24 & 31.2 & 35.5 & 8.22 & 0.0 & 0.0 \\
25 to 29 & 49 & 75.7 & 7.93 & 0.0 & 0.01 \\
30 to 34 & 64 & 109.4 & 7.61 & 0.0 & 0.01 \\
35 to 39 & 83 & 161.9 & 7.15 & 0.01 & 0.01 \\
40 to 44 & 123.4 & 257 & 6.59 & 0.01 & 0.02 \\
45 to 49 & 209.6 & 412.7 & 6.04 & 0.01 & 0.02 \\
50 to 54 & 373.2 & 574.8 & 5.37 & 0.02 & 0.03 \\
55 to 59 & 698 & 731.8 & 4.55 & 0.03 & 0.03 \\
60 to 64 & 1178.2 & 994.3 & 3.72 & 0.04 & 0.04 \\
65 to 69 & 1743.4 & 1283 & 2.96 & 0.05 & 0.04 \\
70 to 74 & 2363.7 & 1530.1 & 2.21 & 0.05 & 0.03 \\
75 to 79 & 2904.9 & 1832.9 & 1.52 & 0.04 & 0.03 \\
80 to 84 & 3260.9 & 2100 & 0.91 & 0.03 & 0.02 \\
85 to 89 & 3643.2 & 2260.7 & 0.63 & 0.02 & 0.01 \\
90+ & 3654.6 & 2114.1 & 0.63 & 0.02 & 0.01 \\
 &  &  & Total Count & 0.36 & 0.32 \\
 &  &  & SIR & 1.12 &  \\
\end{tabulary}
\caption{{This table shows the estimation of standardised incidence ratio (SIR)
among males and females for all cancers, in UK, 2012-2014
{\label{107225}}%
}}
\end{table}Overall, after age adjustment, males have higher rates of cancer (for
all cancers) than females. The ratio between the total counts for males
and females is referred to as standardised incidence ratio and is given
in this case by 1.12;~

\subsection*{Call to Action}

{\label{175116}}

Now it's your turn. I have provided you the following table, where you
can plug in the numbers as I have shown above and based on your
calculations, can you tell if the Maoris in New Zealand have higher or
lower rates of melanoma? If so, by how much? (In answering this
question, fill in the empty cells using a hand calculator and calculate
the standardised incidence ratio)

\par\null\selectlanguage{english}
\begin{table}[h!]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCCCC}
Age Group & M\selectlanguage{polish}ā\selectlanguage{english}ori Age-Specific rate & Non-M\selectlanguage{polish}ā\selectlanguage{english}ori Age-specific rate & World Standard Population & Probability for M\selectlanguage{polish}ā\selectlanguage{english}oris & Count for M\selectlanguage{polish}ā\selectlanguage{english}ori & Prob for Non-M\selectlanguage{polish}ā\selectlanguage{english}ori & Count for Non-M\selectlanguage{polish}ā\selectlanguage{english}ori \\
0 to 4 & 0.0 & 0.0 & 8.86 &  &  &  &  \\
5 to 9 & 0.0 & 0.0 & 8.69 &  &  &  &  \\
10 to 14 & 0.0 & 0.0 & 8.6 &  &  &  &  \\
15 to 19 & 1.5 & 2.5 & 8.47 &  &  &  &  \\
20 to 24 & 0.0 & 5.4 & 8.22 &  &  &  &  \\
25 to 29 & 0.0 & 12.8 & 7.93 &  &  &  &  \\
30 to 34 & 7.5 & 19.8 & 7.61 &  &  &  &  \\
35 to 39 & 9.9 & 36.4 & 7.15 &  &  &  &  \\
40 to 44 & 9.3 & 40.2 & 6.59 &  &  &  &  \\
45 to 49 & 5.1 & 52.1 & 6.04 &  &  &  &  \\
50 to 54 & 16.0 & 80.9 & 5.37 &  &  &  &  \\
55 to 59 & 24.4 & 80.6 & 4.55 &  &  &  &  \\
60 to 64 & 32.3 & 133.8 & 3.72 &  &  &  &  \\
65 to 69 & 13.3 & 139.7 & 2.96 &  &  &  &  \\
70 to 74 & 39.1 & 197.5 & 2.21 &  &  &  &  \\
75 to 79 & 0.0 & 217.7 & 1.52 &  &  &  &  \\
80 to 84 & 59.5 & 258.9 & 0.91 &  &  &  &  \\
85 + & 0.0 & 270.0 & 0.63 &  &  &  &  \\
 &  &  &  &  &  &  &  \\
 &  &  &  &  &  &  &  \\
 &  &  &  &  &  &  &  \\
\end{tabulary}
\caption{{This is a spreadsheet where we will estimate the rate of melanoma (year
2013) for Maoris and non-Maori population in New Zealand and use the WHO
World Standard Population to calculate the Standardised Incidence Ratio;
your task is to fill in the blank cells using a calculator
{\label{304310}}{\label{304310}}%
}}
\end{table}\subsection*{Measures of Association: Relative Risk and Odds
Ratios}

{\label{778724}}

Exposure outcome linkages are measured using risk ratios, odds ratios,
and impact of exposure on outcomes are measured using impact fractions
and population attributable risk percents. Incidence rates are measures
of risk in the population. In Environmental Epidemiological cohort
studies, two or more incidence rates are compared between those who are
not exposed and those who are exposed. The resulting ratio is referred
to as incidence rate ratios, or relative risks. Absolute risk refers to
the difference between the exposed and non-exposed population in the
incidence of the health outcome. Here is an example.

Imagine you are studying the association between ETS and Asthma in
primary school-age children and for this purpose you have decided to
compare two populations. Population A (N = 200) is exposed to ETS and
Population B (N = 300)~is not exposed to ETS. You have followed both the
populations for five years and have tallied the number of new Asthma
cases in those five years among primary school children for both groups.
The results of your study are shown in the following table:

\par\null\selectlanguage{english}
\begin{table}[h!]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCCCC}
Exposure Status & Population & Follow up Time & Person-years & Asthma Cases & Incidence & Relative Risk \\
Exposed to ETS & 200 & 5 & 1000 & 50 & 0.05 & 5 \\
Not Exposed to ETS & 300 & 5 & 1500 & 15 & 0.01 &  \\
 &  &  &  &  &  &  \\
 &  &  &  &  &  &  \\
 &  &  &  &  &  &  \\
 &  &  &  &  &  &  \\
 &  &  &  &  &  &  \\
 &  &  &  &  &  &  \\
 &  &  &  &  &  &  \\
\end{tabulary}
\caption{{This is a summary table of a study on the association between ETS and
Asthma in primary school aged children The follow-up time was measured
in years and the incidence was measured per 100-person-years.~
{\label{421105}}{\label{421105}}%
}}
\end{table}As can be seen in Table 4, you studied 200 children for five years for a
total of 1000 person-years and had 50 Asthma cases. This resulted in an
incidence rate of 5 per 100 person-years (do the math yourself), and for
the non-exposed group, you had 300 children followed for five years for
a total of 1500 person-years and in the five years, you found 15
children with Asthma. This resulted in an incidence rate of 1 per 100
person-years. The ratio between the two rates was 5.0 and is referred to
as Relative Risk or Rate Ratio (RR).~

\subsection*{Concepts of Attributable Risk and Population Attributable
Risk}

{\label{506348}}

In this same study, you found that there were 4 per 100 person-year more
cases of Asthma in the group that was exposed to environmental tobacco
smoke. This figure is referred to as ``Attributable Risk'' or the excess
risk of Asthma in a population exposed to ETS. If ETS were to be
completely or 100\% eradicated from the exposed group, by how much
percent would the Asthma incidence be reduced? This would depend on two
factors: the relative risk of association between ETS and Asthma but
also on the existing prevalence of exposure to ETS. Let us imagine that
this was a real study and that we found that the RR of the relationship
between ETS and Asthma was 5.0. Soliman et.al. (2004) estimated that in
the 2000s, the prevalence of ETS in the US was about
25\%~\cite{Soliman_2004}. They also found that this figure dropped from
35\% in the 1990s to 25\% by 2000. If we were to use the 25\% as the
estimated prevalence of exposure to ETS, then we can use these two
figures to estimate the population attributable risk percent or PAR\% --
this figure would indicate the proportion by which childhood asthma
would decrease if ETS were to be completely removed. The formula is
given as follows:

\textbf{\emph{PAR = P}}\textsubscript{\textbf{\emph{e~}}}\textbf{\emph{*
(RR}}\textsubscript{\textbf{\emph{e~}}}\textbf{\emph{- 1) / {[}1 +
P}}\textsubscript{\textbf{\emph{e~}}}\textbf{\emph{*
(RR}}\textsubscript{\textbf{\emph{e~}}}\textbf{\emph{-1){]}}}

Where,~

PAR = Population Attributable Risk

P\textsubscript{e~}= Prevalence of Exposure

RR\textsubscript{e~}= Relative Risk of the association between Exposure
and Disease

If we were to plug this formula to our own situation where
RR\textsubscript{e} = 5.00 and P\textsubscript{e~}= 0.25, then we would
have:

PAR = 0.2 or in terms of percents, PAR\% = 20\%

This states that if we were to eliminate the ETS altogether in a
population where the prevalence of ETS was 25\%, it would lead to a 20\%
reduction in Asthma in the children.

\subsection*{Call to action}

{\label{884995}}

By how much would childhood asthma be reduced if the prevalence was
35\%? What does this tell us?

You can see that if the prevalence of the exposure would be high, the
corresponding decrease in the disease condition as a result of the
exposure would be high as well. This is the strength of evidence of the
association between a risk factor and a disease.~

\subsection*{Concepts of Odds Ratio}

{\label{394068}}

Another common measure for the association between an exposure and a
disease is Odds Ratio. Odds refers to a ratio of probabilities. Suppose
we toss a coin. The probability of the head is 0.5, and the probability
of the coin not falling head is (1 - 0.5) = 0.5. Odds refers to the
ratio of probability of an event happening and the complementary
probability of an event not occurring. Here, in the coin example, the
ratio of probability of heads versus not head is 1:1, or even. In other
situations, you will have other odds.~

\subsection*{Call to Action}

{\label{525937}}

Take the Rugby matches between Crusaders and Hurricanes
(\href{http://www.rugbydata.com/superrugby/crusaders/hurricanes/}{for
stats, check this site}). ~According to the site, for the 28 matches
that the Crusaders played against the Hurricanes, Crusaders won 16 of
those 28 matches, and three of those matches were drawn, so let's say
Crusaders won 16 out of the remaining 25 matches. What is the Odds of
Crusaders Win Against Hurricanes? Can you figure out?

Answer: Odds are 16:9 in favour of the Crusaders

We use this concept of Odds and comparison of Odds in Epidemiology. In
order to study rare diseases, the exposure and outcome associations
between rare diseases such as cancers. Torres-Duran and colleagues
conducted a case control study (we will learn about different types of
study designs in the next section) of exposure to Radon gas in the
residential area and risk of lung cancer among non-smokers in
Spain~\cite{Torres_Duran_2014}. Before we dive in to the results of that
study, let's see how odds ratios work.~

\par\null\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Exposure & Number with disease & Number without disease\tabularnewline
\midrule
\endhead
Exposed & A & B\tabularnewline
Not Exposed & C & D\tabularnewline
Total & A+C & B+D\tabularnewline
\bottomrule
\end{longtable}

Let us imagine a study where A+C number of people with a certain disease
were compared with B+D number of people without the disease. We would
like to find an association of Exposure with this disease. We see that
out of A+C number of people with the disease, A number of people were
exposed. So the probability of exposure for people with the disease was
A/(A+C), and the probability of non-exposure was C/(A+C). If we put
these two numbers together, we can see that the odds of Exposure for
people with the disease was A:C. Similarly, if we follow the same logic
of exposure for people who did not have the disease (``without
disease''), we can see that their odds of exposure would be B:D. The
odds ratio (OR) as a measure of the association between the exposure and
the disease would be given by A:C / B:D, and would be equivalent of A *
D / B * C or the cross product ratio.~

We now apply this logic to the following table of Radon Gas exposure and
Lung Cancer:

\par\null\selectlanguage{english}
\begin{table}[h!]
\centering
\normalsize\begin{tabulary}{1.0\textwidth}{CCCCC}
Radon Exposure & Cases & Controls &  &  \\
>=200 Bcq/cu.m & 85 & 80 &  &  \\
<= 100 Bcq/cu.m & 36 & 73 &  &  \\
Total & 121 & 153 &  &  \\
Odds of exposure & 2.36 & 1.1 &  &  \\
Odds Ratio & 2.15 &  &  &  \\
 &  &  &  &  \\
 &  &  &  &  \\
 &  &  &  &  \\
 &  &  &  &  \\
\end{tabulary}
\caption{{Illustration of the principles of Odds Ratio in a case-control study of
exposure to residential radon gas and development of lung cancer.~
{\label{631532}}%
}}
\end{table}As can be seen in the Table 5, cases had higher odds than controls to be
exposed to residential radon gas in excess of 200 bcq per cubic metres.
In this case, Odds Ratios are relative risk estimates of the association
between exposure and outcomes. In this case, we can state that Radon gas
is a risk factor for lung cancer with a relative risk estimate of 2.15,
this is a crude Odds Ratio. We use the Odds Ratio in this situation as
we would use the RR and we can calculate the reduction in lung cancer
prevalence if we were to reduce the exposure to Radon gas to zero.~

\subsection*{Epidemiological Study
Designs}

{\label{587746}}

These different measures of association are obtained on the basis of
epidemiological studies. In environmental and occupational epidemiology,
we do not test the results of interventions as Environment is the source
of exposure. Hence, we conduct different types of epidemiological
studies: ecological studies (secondary data analyses from primary data),
case control studies either by themselves or case control studies that
are nested within cohort studies, and cohort studies.~

Ecological studies are those where data in aggregated forms are
correlated. This is in the form of regression analyses or testing of
linear models. Imagine you want to test your theory that Air Pollution
causes Asthma. You would test your hypotheses that those who are exposed
to poor air quality are more likely to get admitted to hospitals with
Asthma related issues, or if nothing, Asthma symptoms would worsen
during periods of poor air quality. In order to test this hypothesis,
you would set up a study where you would correlate air quality
indicators and rate or likelihood of hospital admissions with Asthma and
related symptoms.~

Ecological studies are useful for being relatively inexpensive but they
cannot provide definite information about causes and effects. This is
because while they are useful for population based aggregated
associations, the results from ecological studies cannot be extended to
individuals. For example, while using Air quality data and aggregated
hospital admissions, one can state that poor air quality is a risk
factor for Asthma related hospital admissions, it does not follow that
every time there is a drop in the air quality, an individual residing in
the area where the air quality worsened would be at higher risk of
hospital admission. This is referred to as
\href{http://www.socialresearchmethods.net/kb/fallacy.php}{ecological
fallacy}.~

\par\null\selectlanguage{english}
\begin{figure}
\centering
\includegraphics{http://study.com/cimages/multimages/16/cross_sectional_research_study.png}
\caption{{Cross sectional Surveys}}
\end{figure}

Cross sectional surveys, source:
http://study.com/academy/lesson/cross-sectional-research-definition-examples-quiz.html

Cross sectional surveys are studies where a group of people are surveyed
or interviewed at a given point in time or an extended period of time.
While cross-sectional surveys are relatively inexpensive, these studies
have limited values in terms of establishing cause and effect
relationships.~

\par\null

\includegraphics{https://www.ebmconsult.com/content/images/Stats/Case\%20Control\%20Study\%20Design\%20Diagram.png}
Case control study design, source:
https://www.ebmconsult.com/articles/case-control-study-biostatistics

\par\null

Case control studies are those studies where odds of exposure for cases
are compared with the odds of exposure for controls. Cases and controls
are as similar as possible, and the rule is that, if the controls were
to develop the outcome of interest, then they would be labelled as
cases.~

\par\null

\includegraphics{http://www.ciphi.ca/hamilton/Content/images/epma/maCCCS02.gif}
Cohort Study design

Cohort studies are those where people are stratified into exposed and
non-exposed groups and then they are followed through in time. For each
cohort, the rate of occurrrence of the outcome are noted and these are
compared using the rate ratio or relative risk estimate.~

Retrospective cohort studies are those where the exposure and outcomes
are ascertained at the same time, although it is presumed that the
exposure preceded the outcome. Retrospective cohort studies are useful
study designs for occupational epidemiological studies.

A case control study can be nested within a prospective or a
retrospective or even within the scope of a cross-sectional survey. This
is also referred to as serological study.~

\subsection*{Analysis of Epidemiological
Studies}

{\label{184139}}

We analyse the results of the different epidemiological studies using
different strategies. Our analysis depends on the nature of the outcomes
we aim to study and the objectives of our study. In ecological study
design, where air pollution and asthma health effects are studied, we
use linear regression. for example, \ldots{}. In case control and
crosssectional surveys where we aim to regress the odds of exposure for
those with and without outcomes, we use logistic regression. In logistic
regression, \ldots{}. In cohort studies, were time dependent events are
modelled, we use survival analysis and a particular type of linear model
referred to as Cox Proportional Hazards model. Here we model hazards
that are defined as the instantaneous likelihood of the occurrence of an
event.~

The goal of each of these analyses would be to adjust for the potential
confounding variables and also to understand whether the effect of an
exposure would vary by the levels of a third variable.~

\subsection*{Summary}

{\label{859935}}

This was a review of the essential epidemiological principles we use in
Environmental Health. To recapitulate, in Environmental Health, we study
environmental epidemiology. We discuss cause and causal inference as the
goals of most environmental epidemiological studies. Unlike in daily
life, the notion of cause and effect in health sciences is not intuitive
in the sense that there can be more than one cause for a particular
health outcome in populations. Hence we need to discuss the causal
models in the form of sufficient and necessary causes. In order to
assess whether an asociation is causal, we need to first establish that
the exposure and the outcome have a valid association. This is done on
the basis of ruling out the play of chance, elimination of bias in the
conduct of the study, and controlling for confounding variables. Then,
we can use considerations as explained by Sir Austin Bradford Hill to
evaluate if the nature of association is one of cause and effect. We
measure distribution of diseases using prevalence and incidence and we
can measure the impact of the association between an exposure and an
outcome using relative risk or risk ratios, hazard ratios, and odds
ratios. We can study public health impacts by estimating attributable
risks and population attributable risks or impact fractions. Impact
fractions can add up to more than or less than 100\% as there can be
overlaps between exposure variables. In order to arrive at the measures
of association, or measures of occurrence of health outcomes, we need to
design a range of epidemiological studies. Ecological studies,
cross-sectional surveys, case control studies, and cohort studies are
used to assess the association between an exposure and an outcome. Each
type of study generate data that can be analysed using a range of
analytical processes: these include linear modelling and linear
regression, logistic regression, Cox Proportional Hazards modelling and
survival analysis.~

\selectlanguage{english}
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\bibliography{bibliography/converted_to_latex.bib%
}

\end{document}

