## 4.3.10. Environmental epidemiology - II. Quantifying disease and associations

Authors: Eva Sugeng and Lily Fredrix

Reviewers: Ľubica Murínová and Raymond Niesink

Learning objectives

You should be able to

- describe measures of disease.
- calculate and interpret effect sizes fitting to the epidemiologic study design.
- describe and interpret significance level.
- describe stratification and interpret stratified data.

1. Measures of disease

Prevalence is the proportion of a population with an outcome at a certain time point (e.g. currently, 40% of the population is affected by disease Y) and can be calculated in cross-sectional studies.

Incidence concerns only new cases, and the cumulative incidence is the proportion of new cases in the population over a certain time span (e.g. 60% new cases of influenza per year). The (cumulative) incidence can only be calculated in prospective study designs, because the population needs to be at risk to develop the disease and therefore participants should not be affected by the disease at the start of the study.

Population Attributable Risk (PAR) is a measure to express the increase in disease in a population due to the exposure. It is calculated with this formula:

2. Effect sizes

2.1 In case of dichotomous outcomes (disease, yes versus no)

Risk ratio or relative risk (RR) is the ratio of the incidence in the exposed group to the incidence in the unexposed group (Table 1):

The RR can only be used in prospective designs, because it consists of probabilities of an outcome in a population at risk. The RR is 1 if there is no risk, <1 if there is a decreased risk, and >1 if there is an increased risk. For example, researchers find an RR of 0.8 in a hypothetical prospective cohort study on the region children live in (rural vs. urban) and the development of asthma (outcome). This means that children living in rural areas have a 0.8 lower risk to develop asthma, compared to children living in the urban areas.

Risk difference (RD) is the difference between the risks in two groups (Table 1):

Odds ratio (OR) is the ratio of odds on the outcome in the exposed group to the odds of the outcome in the unexposed group (Table 1).

The OR can be used in any study design, but is most frequently used in case-control studies. (Table 1) The OR is 1 if there is no difference in odds, >1 if there is a higher odds, and <1 if there is a lower odds. For example, researchers find an OR of 2.5 in a hypothetical case-control study on mesothelioma cancer and occupational exposure to asbestos in the past. Patients with mesothelioma cancer had 2.5 higher odds on being occupational in the past exposed to asbestos compared to the healthy controls.

The OR can also be used in terms of odds on the disease instead of the exposure, the formulae is then (Table 1):

For example, researchers find an odds ratio of 0.9 in a cross-sectional study investigating mesothelioma cancer in builders working with asbestos comparing the use of protective clothing and masks. The builders who used protective clothing and masks had 0.9 odds on having mesothelioma cancer in comparisons to builders who did not use protective clothing and masks.

Table 1: concept table to use for calculation of the RR, RD, and OR

| Disease/outcome + | Disease/outcome -
Exposure/determinant + | A | B
Exposure/determinant - | C | D

2.2 In case of continuous outcomes (when there is a scale on which a disease can be measured, e.g. blood pressure)

Mean difference is the difference between the mean in the exposed group versus the unexposed group. This is also applicable to experimental designs with a follow-up to assess increase or decrease of the outcome after an intervention: the mean at the baseline versus the mean after the intervention. This can be standardized using the following formulae:

The standard deviation (SD) is a measure of the spread of a set of values. In practice, the SD must be estimated either from the SD of the control group, or from an ‘overall’ value from both groups. The best-known index for effect size is Cohens 'd'. The standardized mean difference can have both a negative and a positive value (between -2.0 and +2.0). With a positive value, the beneficial effect of the intervention is shown, with a negative value, the effect is counterproductive. In general, an effect size of for example 0.8 means a large effect.

3. Statistical significance and confidence interval

Effect measurements such as the relative risk, the odds ratio and the mean difference are reported together with statistical significance and/or a confidence interval. Statistical significance is used to retain or reject null hypothesis. The study starts with a null hypothesis assumption, we assume that there is no difference between variables or groups, e.g. RR=1 or the difference in means is 0. Then the statistical test gives us the probability of getting the outcome observed (e.g. OR=2.3, or mean difference=1.5) when in fact the null hypothesis is true. If the probability is smaller than 5%, we conclude that the observation is true and we may reject the null hypothesis. The 5% probability corresponds to a p-value of 0.05. A p-value cut-off of p<0.05 is generally used, which means that p-values smaller than 0.05 are considered statistically significant.

The 95% confidence interval. A 95% confidence interval is a range of values within which you can be 95% certain that the true mean of the population or measure of association lies. For example, in the hypothetical cross-sectional study on smoking (yes or no) and lung cancer, an OR of 2.5 was found, with an 95% CI of 1.1 to 3.5. That means, we can say with 95% certainty that the true OR lies between 1.1 and 3.5. This is regarded statistically significant, since the 1, which means no difference in odds, does not lie within the 95% CI. If researchers also studied oesophagus cancer in relation to smoking and found an OR of 1.9 with 95% CI of 0.6-2.6, this is not regarded statistically significant, since 95% CI includes 1.

4. Stratification

When two populations investigated have a different distribution of, for example, age and gender, it is often hard to compare disease frequencies among them. One way to deal with that is to analyse associations between exposure and outcome within strata (groups). This is called stratification. Example: a hypothetical study to investigate differences in health (outcome, measured with number of symptoms, such as shortness of breath while walking) between two groups of elderly, urban elderly (n=682) and rural elderly (n=143) (determinant). No difference between urban and rural elderly was found, however there was a difference in the number of women and men in both groups. The results for symptoms for urban and rural elderly are therefore stratified by gender (Table 2). Then, it appeared that male urban elderly have more symptoms than male rural elderly (p=0.01). The difference is not significant for women (p=0.07). The differences in health of elderly living an urban region are different for men and women, hence gender is an effect modifier of our association of interest.

Table 2. Number of symptoms (expressed as a percentage) for urban and rural elderly stratified by gender. Significant differences in bold.

number of symptoms | Women | Men
| Urban | Rural | Urban | Rural
None | 16.0 | 30.4 | 16.2 | 43.5
One | 26.4 | 30.4 | 45.2 | 47.8
Two or more | 57.6 | 39.1 | 37.8 | 8.7
N | 125 | 23 | 74 | 23
p-value | 0.07 | 0.01