Many of the scientific research questions in veterinary and human medicine addresses causal relationships (i.e. knowing what causes individuals to develop a particular disease or health outcome). We need to understand these causal relationships to prevent disease and improve diagnosis and treatment. For example:
In order to answer these and other questions, we need to be aware of the difference between association and causation. Association is a statistical measure of the strength of the relationship between exposure and outcome. We can say, for example, that there is an association between the presence of antibodies to Toxoplasma gondii in people and mental illnesses, but we can’t say definitively that toxoplasmosis causes people to become crazy cat ladies. Causation is not straightforward and is the subject of many philosophical debates. A useful working definition is that from Rothman and Greenland (2005, P S144):
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With all this controversy around causation, it is not surprising that epidemiologists have turned to checklists for making causal inference. The most widely used list of causal criteria in epidemiology is based on a paper by Sir Austin Bradford-Hill that was published in 1965. The criteria, often called ‘Hill’s Criteria’, are frequently used as a checklist for causation and as such, they warrant further attention. However, to be fair to Hill, he never called them criteria nor did he want them to be thought of as a checklist.
What is the strength of the association between the cause and effect?
The first factor Hill considered was the strength of association. This is often incorrectly interpreted as saying weak associations are less likely to be causal. What Hill actually meant was that when the association is stronger, it is more difficult to explain this away by bias or confounding. However, this should not be taken to mean that small measures of association are automatically biased or non-causal.
Have similar results been shown in other studies?
Hill’s second viewpoint was that the observed association should have consistency across different types of studies and in different populations. For example, at the time of Hill’s paper being written, the relationship between smoking and lung cancer had been shown in at least 29 retrospective studies and seven prospective studies. Hill argued that the consistency allowed one to infer that the association was unlikely to be due to a consistent error. However, he was quick to point out that different results from different studies do not invalidate the first. Furthermore, one should not consider a set of results as inconsistent when some results are statistically significant and others are not. It is entirely possible for studies to get the same estimate for the strength of the association, but differ in the level of statistical significance due to difference in the standard errors or size of the study sample.
Is the association limited to a specific group of people or diseases?
Hill then proposed that specificity should be the third characteristic that was considered. Specificity means that if an association is limited to a specific group of people or specific diseases, this adds weight to the argument of causation. Clearly, this cannot be considered as a general rule. For example, it would be ridiculous to suggest that the evidence that smoking causes lung cancer is weakened by the fact we have found smoking is associated with other diseases.
Does the cause precede the effect?
The first factor Hill considered was the strength of association. This is often incorrectly interpreted as saying weak associations are less likely to be causal. What Hill actually meant was that when the association is stronger, it is more difficult to explain this away by bias or confounding. However, this should not be taken to mean that small measures of association are automatically biased or non-causal.
Is an increased in exposure associated with an increase in response?
An association might be causal if one could demonstrate a biological gradient; that is, the likelihood or severity of the outcome is greater with a higher dose of exposure. For example, the death-rate from lung cancer increases with the number of cigarettes smoked daily. Hill did concede that in observational studies it is difficult to demonstrate a dose-response relationship because, for example, the number of cigarettes smoked daily likely varies over time. Furthermore, some relationships are not linear meaning that there may be threshold effects or inconsistent patterns in the relationship.
Is the association consistent with existing knowledge?
Another factor we should consider when deciding if an association is causal is plausibility or does it make ‘biological sense’. Biological plausibility provides a strong argument for causation if it is present. However, when there is absence of biological plausibility should not be seen as a reason to exclude a causal relationship as it may be a new one to science or medicine (something Hill himself acknowledges). Despite Hill acknowledging that we should not dismiss an association as non-causal because it seems implausible the association should not be in conflict with the general knowledge. That is, the association should be coherent with the other evidence. The requirement for coherence is vague and, in many ways, not substantially different to biological plausibility. Furthermore, the whole process of science is frequently challenging what we previously thought of as facts. Do not forget that people once thought the world was flat and the sun circled the earth!
Is the evidence based on a robust study design?
Hill also noted that, on occasion, it is possible to find experimental or semi-experimental evidence for a causal association. Therefore, evidence from controlled randomized trials of interventions provides the best evidence for a causal relationship. However, it is not generally possible to perform experiments on humans in which possible disease-producing agents are administered or risk behaviours encouraged. There is good evidence that alcohol consumption during pregnancy harms the fetus, but it would be considered highly unethical to run an experiment where you asked groups of pregnant women to drink.
How many lines of evidence lead to the same conclusion?
The coherence criterion asks whether epidemiological findings are consistent with what is known from other sources of evidence, such as laboratory studies, pathology, or biological mechanisms. When population-level associations align with experimental or mechanistic evidence, our confidence that an effect is real is strengthened. However, Hill cautioned that a lack of laboratory evidence does not invalidate an epidemiological association. Many true causal relationships were recognised through population studies long before the underlying biological mechanisms were understood. Coherence therefore supports causal inference when present
Are there similar relationships with other exposures or disease?
Another point made by Hill was that in some circumstances an association might be considered causal by analogy. This means that a similar relationship could have been observed with another exposure and/or disease. Hill gave the example that the known effects of the drug thalidomide would accept evidence that another drug could cause birth defects. In the veterinary sphere, bovine spongiform encephalopathy (BSE) and scrapie/transmissible mink encephalopathy make us more willing to accept the existence of similar diseases in other species like variant Creutzfeldt-Jakob’s disease in people.
Does removal of a cause decrease the risk of the effect?
The reversibility criterion considers whether disease frequency or severity decreases when a suspected cause is reduced or eliminated. If an exposure truly contributes to disease, we would expect that removing it, or introducing an effective intervention, leads to improvement in outcomes at the individual or population level. Evidence of reversibility can come from intervention studies, policy changes, or natural experiments. However, absence of reversibility does not necessarily rule out causation, particularly when disease processes are irreversible, have long latency periods, or when exposure has already caused permanent damage.
If we cannot use a defined checklist, then how can we assess causation between an exposure and an outcome? To answer this question, consider the following quote from Rothman and Greenland (2005):
“Although there are no absolute criteria for assessing the validity of scientific evidence, it is still possible to assess the validity of a study. What is required is much more than the application of a list of criteria. Instead, one must apply thorough criticism, with the goal of obtaining a quantitative evaluation of the total error that afflicts the study. This type of assessment is not one that can be done easily by someone who lacks the skills and training of a scientist familiar with the subject matter and the scientific methods that were employed. Neither can it be applied readily by judges in court, nor by scientists who either lack the requisite knowledge or who do not take the time to penetrate the work.”
The first step towards understanding causal relationships is to establish whether the ‘amount’ of disease in a group of individuals who are exposed to the potential risk factor is different the occurrence of disease in a group that were not exposed to the potential risk factor. To express this formally, we can ask ‘Does the frequency of disease occurrence (measured using prevalence, incidence, or odds) differ between the exposed group and the non-exposed group?” The ‘exposure’ that we are interested in is called a risk factor if we believe it increases disease or a protective factor if we believe it decreases disease. For example:
If we identify risk factors that are causally associated with an increased likelihood of disease and those that are causally associated with a decreased likelihood of disease, then we are in a good position to make recommendations about health management. Much of epidemiological research is concerned with identifying and quantifying the effect of risk factors on the likelihood of disease. It is important that we have a group of individuals without the exposure for comparison because diseases are usually multifactorial and so we would expect at least some of the unexposed population to develop disease. For example, we have pretty good evidence that smoking causes lung cancer and we would therefore expect the frequency of lung cancer to be higher in smokers. However, people can still develop lung cancer for other reasons like exposure to high levels of air pollution in crowded cities or working in buildings with asbestos. As epidemiologists, we are interested in how much greater the disease occurrence is in the exposed versus unexposed.
In epidemiology, we often relate disease occurrence with exposure to a particular agent. If both disease status and exposure status are binary variables (yes or no), we can construct a table that reports the number of individuals in each of the four exposure-disease categories (a, b, c and d cells).
In this ‘standard’ format of a two-by-two table, disease status is presented in the columns and exposure status in the rows. Letters a, b, c and d represent the number of individuals exposed and diseased, exposed and non-diseased, non-exposed and diseased, and non-exposed and non-diseased, respectively. In some textbooks, you may find the disease status in the rows and exposure in the columns; therefore, it is not important to memorize what a, b, c and d mean, but to understand the logic behind a two-by-two table.
To illustrate how this works, consider a study looking to determine if consumption of raw milk is associated with brucellosis. The study involved 5000 people; 2,200 drank raw milk and 2,800 did not. During the study period, there were 1,800 cases of brucellosis, of which 1,000 occurred in people who had consumed raw milk.
To assess whether there is an association between raw milk consumption and brucellosis, we have to determine whether there is an increased risk of disease in the group exposed to a particular agent (in this case raw milk consumption) compared to a non-exposed group. We can calculate the risk of disease in both exposed and non-exposed individuals using incidence risk. The incidence risk in the exposed group (Re) is:
And, the incidence risk in the non-exposed group (R0) is:
For reasons that will become apparent later, it is also good to calculate the incidence risk in the study population. The incidence risk in the study population was:
Having calculated these three values, we will now calculate measures of association to determine the strength of the relationship between consumption of raw milk and brucellosis. The next step is to calculate our risk ratio which is simply dividing the two values. In this case, because we are using incidence risk as our measure of disease frequency in the exposed and non-exposed groups, the risk ratio we calculate will be the incidence risk ratio.
For our example, this would be 0.45 / 0.29 = 1.55. In other words, the incidence risk of disease in individuals who consumed raw milk was 1.55 times greater than for individuals who did not. If our study had instead measured prevalence, incidence rate, or odds, then we could calculate the prevalence risk ratio, incidence rate ratio, and odds ratio, respectively.
The risk ratio provides an estimate of how many times more likely exposed individuals are to experience disease compared with non-exposed individuals. If the incidence risk ratio equals one, then the risk of disease in the exposed and non-exposed groups are equal and there is no association between them. If the risk ratio is greater than one, then exposure increases the risk of disease, with greater departures from one indicative of a stronger effect. If the risk ratio is less than one, exposure reduces the risk of disease and exposure is said to be protective; the greater the departure from one, the stronger the protective effect.
We also often calculate the 95% confidence interval around the risk ratio value, which is basically a measure of how confident we are that our estimate of the risk ratio accurately reflects the true value for the population.
For example, if we had a risk ratio of 2.05 with a 95% confidence interval of 0.39 to 3.71, that basically means that we are 95% confident the true point value of the risk ratio in the population falls somewhere within that range.
We would consider this risk ratio to be statistically insignificant because the ranges spans the values for protective effect (0 to <1), no effect value (1), and risk factor (>1 to ∞) and so we can’t make any robust conclusion about the relationship between the exposure and the outcome.
However, if the 95% confidence interval had a narrower range at 1.74 to 2.36, then we are pretty confident that is indeed a risk factor since the entire range of potential values lies in the risk factor range (>1 to ∞). We would say that this is a statistically significant risk factor. It is also important to note that the farther away the risk ratio is from 1 in either direction, the stronger the association.
RR > 1: Occurrence of disease in the exposed group is greater than in the unexposed group. The risk factor is associated with an increased risk of disease
RR = 1: Occurrence of disease in the exposed and unexposed groups is identical. There is no association between the disease and the risk factor
RR < 1: Occurrence of disease in the exposed group is less than in the unexposed group. The risk (protective) factor is associated with a decreased risk of disease
Measures of effect aim to quantify how much of the disease can be attributed to a certain exposure or, in other words, how much a disease could be prevented in a population if the exposure is eliminated (assuming of course that the relationship between exposure and disease is causal). In the association between exposure and disease there is generally a risk of disease (incidence risk) in the total population, in the exposed group and in the non-exposed group. If we want to know how much of the disease could be prevented by controlling for a given exposure, we have to subtract the risk observed in the non-exposed group because it represents the baseline or background risk in the population. There are two main types of measures i) measures of effect in the exposed group; and ii) measures of effect in the whole population.
Attributable risk tells us how much disease can be attributed to exposure in the exposed group and, therefore, preventable if we could control for exposure. Imagine that exposure to an agent is causing disease, but disease is also occurring in the non-exposed group. You want to know how much of the disease in the exposed group is due to exposure. We calculate the attributable risk (risk difference) as follows:
The result is interpreted as the incidence risk in the exposed individuals that is due to exposure. In other words, it represents the amount of disease that we can hope to reduce in the exposed group if exposure were eliminated completely.
We can also express the attributable risk as a proportion of the risk in the exposed group. The measure is known as the attributable fraction and is calculated as follows:
This result is interpreted as the proportion of the disease risk in the exposed group that is due to exposure. In other words, it represents the proportion of disease that we can hope to reduce in the exposed group if exposure were eliminated completely.
When the exposure of interest prevents disease, such as vaccination, it makes more sense to talk about the ‘number needed to treat’ rather than the risk difference. The number needed to treat is defined as follows:
For example, if sheep vaccinated against Salmonella have 5/100 (0.05) fewer deaths than the untreated group (risk difference). The number of sheep that need to be vaccinated in order to prevent one death is 20 (1/0.05). If it costs $5 per sheep to vaccinate and the cost of a death is only $60 then it would not be economically viable for a farmer to implement a vaccination programme.
The population attributable risk tells us how much disease can be attributed to exposure in the population (not only in the exposed group). Our interest now is not to assess the effect that controlling for exposure would have on the exposed group, but the effect that controlling for exposure would have on the entire population. To calculate the population attributable risk, we need to subtract the observed risk of disease in the non-exposed group to the risk of disease observed in the total population:
The result is interpreted as the incidence risk in the population that is due to exposure. In other words, it represents the amount of disease that we can hope to reduce or prevent in the population if the exposure were eliminated completely. The graphical representation is very similar, but the difference is that instead of the risk of disease in the exposed group, the total risk of disease (risk in exposed + risk in non-exposed) is used.
We can also express this measure as a proportion, which is called a population attributable fraction (PAF). The PAF is calculated as follows:
This result is interpreted as the proportion of the disease risk in the population that is due to exposure. In other words, it represents the proportion of disease that we can hope to reduce or prevent in the population if exposure were eliminated completely.
The following is an extreme example to show the difference between the attributable risk for the exposed group and the attributable risk for the total population. A study investigated the association between people exposed to atomic bomb radiation and the development of cancer. In total, there were 50 people exposed to radiation: 45 of them developed cancer; while from 10,000 people non-exposed to this radiation, 500 developed cancer. The two-by-two table would look like this:
This shows that if we could prevent exposure to atomic bomb radiation, we could eliminate 94.4% of the cancer in the people that are exposed. However, only 7.8% of cancer in the total population could be eliminated because very few people in the population had been exposed to this kind of radiation. Therefore, the impact of preventing exposure at the population level is much lower than in the exposed group.
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