In epidemiological research, we are usually interested in how certain interventions or exposures are associated with outcomes; for example, is there an association between paternal age and retinoblastoma in the offspring? [10]. There are several statistical approaches that can be used to quantify associations, either as a ratio or as a difference, depending on the study design and statistical method used (Table 1.2).

The ratio of cumulative incidences of exposed and unexposed individuals (or between treated and untreated patients) is the relative risk (RR). For example, in the Netherlands, the RR of retinoblastoma in children conceived by in vitro fertilization is between 4.9 and 7.2. This implies that the risk of getting retinoblastoma is between 4.9 and 7.2 times higher for children conceived after IVF than naturally conceived children.

The ratio of incidence densities of unexposed and exposed patients (or between treated and untreated patients) is the hazard ratio (HR), which has a similar interpretation as the RR.  This measure is often used in relation to mortality because we are generally interested not only in the proportion of patients that die but also in the time from baseline (diagnosis or start of treatment) until death. A special application of HR is the ratio of the observed to the expected number of cases (O/E ratio). In this case, the observed incidence density is calculated for the study population, and this is compared to the expected incidence density derived from a population registry (e.g. cancer registration). For example, in a study of lifetime risks of common cancers among 144 hereditary retinoblastoma survivors, 41 cancer deaths were observed, whereas only 7.58 deaths due to cancer were expected. This data can be expressed as a standardized mortality ratio of 5.41 [11].

P _l prevalence group 1, P ₂ prevalence group 2, C I cumulative incidence, C I _l CI group 1, C I ₂ CI group 2, I D incidence density, I D _l ID group 1, I D ₂ ID group 2, O / E ratio observed to expected ratio, R C T randomized controlled trial $X _ { 1 } = $ mean score group 1; $X _ { 2 } = $ mean score group 2

The odds ratio (OR) is the most commonly reported measure of association in the literature due to the fact that this is the statistic that can be derived from the popular logistic regression analysis. The OR is the ratio of the odds of outcome of interest between the exposed and the unexposed. Generally speaking, the OR is a good approximation of the RR or HR.

Differences in risks (RD) are preferably reported as outcomes in randomized controlled trials. The RD is easy to interpret and can be used to calculate the number of patients needed to treat (NNT) to prevent one extra event (e.g., death) compared to the standard treatment or placebo. The NNT can be calculated as the inverse of RD (1/RD). A related concept is that of the number needed to screen (NNS). This refers to the number of patients needed to be screened to prevent one extra event compared to the situation without a screening program. The NNS, thus, depends on the predictive probability of the screening test as well as on the efficacy of treatment for people that are diagnosed with that screening test. The value of routine neuroimaging screening of pineoblastoma in retinoblastoma patients is uncertain and a point of discussion [12].

For scores on interval scales, such as quality-of-life, differences in mean scores between exposed and unexposed participants are the most important measure of interest. These can be derived from independent samples t-test of general linear models (e.g., linear regression analysis).

When interpreting an outcome, we do not only want to know the numerical value of the point estimate but also the precision with which it has been assessed. In other words, can we be confident that the outcome is not just a chance finding? The usual standard for accepting an outcome as being beyond chance is p (probability) < 0.05. A more informative description is provided by the 95% confidence interval (CI). The rough interpretation of the 95% CI is that there is a 95% probability that the real value lies within the confidence interval.

Statistical significance and the width of confidence intervals are strongly dependent on the sample size of a study. This means that in very large samples, weak (and potentially unimportant) associations can be statistically significant. In contrast, in small samples, strong (and potentially important) associations are sometimes not statistically significant. Such findings should, of course, not be dismissed as being irrelevant. Instead, they should be replicated in larger study populations. Associations, although statistically significant, need not be clinically important. Therefore, interpretation of findings should never solely rely on statistical significance.