PREVALENCE RATIO AND PREVALENCE ODDS RATIO IN CROSS-SECTIONAL STUDIES

By: Syndi Siahaan, Nurul Hidayah, Hafsah Amalia, Adhella Menur

A cross-sectional study is an observational study in which all data from each subject is collected at a single point in time. It is considered more affordable and feasible than longitudinal studies, as it does not require following patients over time. Traditionally, a cross-sectional study has been used to determine the prevalence of a disease or condition, defined as the proportion of a population with a specific characteristic at a given time. This is why a cross-sectional study is also referred to as a “prevalence study.” However, it can also analyze the association between two or more variables, providing an analytical approach. This makes a cross-sectional study a valuable option for exploring associations, especially in preliminary investigations or when resources are limited. Of note, the interpretation of the analysis requires caution regarding the potential association of disease duration with exposure status (survival bias).
The cross-sectional analysis results are often presented as Prevalence Ratio (PR), which measures and compares disease prevalence between two groups. The Odds Ratio (OR), a result commonly presented in case-control studies, can also be applied in cross-sectional studies, where it is referred to as the Prevalence Odds Ratio (POR). There has been a debate about whether the OR should be exclusively used for case-control studies, with some authors reporting that when disease prevalence is high, the POR tends to overestimate the PR. This article will summarize how PR and POR are applied in cross-sectional studies.

Figure 1. Cross-sectional studies design – take a “snapshot” of the proportion of individuals in the population that are,
for example, diseased and non-diseased at one point in time.

What to Choose: Cross-Sectional or Case-Control Studies

Cross-sectional and case-control studies are commonly used in analytical observational study designs. As mentioned before, in a cross-sectional study, data on exposure and outcomes (disease or condition) are collected simultaneously from each subject at one point in time (Figure 1). The analysis compares outcomes prevalence between exposed and unexposed individuals or the exposure levels between those with and without the disease or condition. Although cross-sectional studies are often more practical to conduct, they have several limitations. They are not suitable for conditions with low prevalence, as such studies require a large sample size. Additionally, the findings depend on the disease’s duration since data is collected only once. While cross-sectional studies can identify associations, they cannot determine causal relationships because it is unclear whether the disease or the exposure occurred first.

Figure 2. Case-control studies design.

When studying the development of a condition or disease with low prevalence, a case-control study is more commonly used. This design compares a case group (individuals with the disease) to a control group (individuals without the disease) (Figure 2). Data on past exposures for both groups are collected retrospectively through medical records or laboratory results.

Table 1. Choosing a cross-sectional or case-control study according to research questions.

Choosing between cross-sectional and case-control studies depends on the research questions; therefore, developing a specific research question is essential. Table 1 lists several research question types with the appropriate study design.

Measuring Association in Cross-Sectional Studies: Prevalence Ratio and Prevalence Odds Ratio

Table 2. The elements of a 2×2 table for analyzing epidemiological studies.

Notes: a is defined as individuals exposed and have the disease, b is individuals exposed but do not have the disease, c is individuals not exposed but have the disease, d is individuals not exposed and do not have the disease, a + b is total of exposed individuals, c + d is total of unexposed individuals, a + c is total of individuals with the disease, and b + d is total of individuals without the disease.

Measures of association are utilized to compare the association between a specific exposure and the outcomes. Note that evidence of an association does not imply that the relationship is causal; the association may also be artifactual or non-causal. To measure the association, analysis of epidemiological studies is performed using a 2×2 table, as shown in Table 2.

(1) Outcome =”Yes”

Prevalence ratio (PR) is analogous to the risk ratio (RR) of cohort studies. PR is interpreted as “exposed individuals have a disease or condition XX times greater than unexposed individuals.” Based on the Table 2, PR can be calculated as follows:

(2) Outcome =”No”

From this formula, we can see that the two equations are not reciprocal to each other. The denominators for both equations are fixed populations. This differs from the Prevalence Odds Ratio (POR), where the equations are reciprocal using different outcomes. POR represents the odds that an outcome will occur given a particular exposure compared to the odds of the outcome occurring without that exposure. The formula is as follows:

(1) Outcome = “Yes”
(2) Outcome =”No”

A POR value equal to 1 means the exposure is not associated with the disease. A POR greater than 1.0 indicates a positive association, and a POR less than 1.0 indicates a negative, or protective, association. Authors sometimes misinterpret POR with statements like “exposed individuals have XX times higher probability or risk of disease or condition.” Such statements are incorrect because the odds are not a ratio of probabilities or risks, and cross-sectional designs cannot evaluate risk. The correct language is “exposed individuals have XX times greater odds of disease or condition.”

Figure 3. Comparison between PR and POR based on the prevalence of the outcome [adapted from the comparison between RR and OR by Soto A, Cvetkovic-Vega A., 2020, DOI: 10.25176/RFMH.v20i1.2555]. POR tend to overestimate the strength of association when outcomes prevalence ≥10%.

The literature is rich with articles discussing the advantages and disadvantages of PR versus POR and de-bating the ‘appropriate’ measure of association. Cvetkovic-Vega et al. introduced the concept that the measure of association in a cross-sectional study can be either PR or POR, depending on the initial observation of the outcome prevalence. It is considered that when the outcome prevalence is greater than or equal to 10%, PR should be used as the appropriate measure of association in cross-sectional studies. Using POR in these cases would overestimate the PR value. When the prevalence of the outcome is below 10%, POR and PR are closer to each other; hence POR may be used. However, some researchers argue that PR is more recommended for cross-sectional studies with analytical purposes.

The potential cause-effect relationship between the variables may provide consideration for selecting between PR and POR. When there is a reasonable assumption about which variable is the exposure and which is the outcome, it is convenient to compare the prevalence of the effect between exposed and non-exposed individuals and calculate the PR. When the causal relationship between the variables is unclear, POR has the advantage of maintaining the same numerical value regardless of its position in the contingency (2×2) table. For acute disease studies, PR is the preferred measure of association. For chronic disease studies or studies of long-lasting risk factors, POR is the preferred measure of association.

Case Example

In this case example, we cite research by Tamhane et al. (2016) on the association of race sex with hypertension control status. Descriptive characteristics are shown in Table 3.

Table 3. Descriptive characteristics according to hypertension control status by Tamhane et al. (2016).

Table 4 below shows the results of PR and POR from the study. Using POR results in an overestimation of the strength of the association. For instance, in the White-female group, when ‘Hypertension control = Yes’ was modeled (‘No’ as the reference group), POR was 2.63, while PR was 1.48.

Table 4. Prevalence Ratio (PR) and Prevalence Odds Ratio (POR) to measure the association between race sex and hypertension control.

In this case, since the prevalence of the outcome (hypertension control) is ≥10% (54.4%, 380/699), reporting PR was deemed more appropriate than POR due to the considerable overestimation of the association’s strength by POR.

Conclusion

To conclude, choosing the appropriate study design depends on the research question. In cross-sectional studies, measuring association can be done using either PR or POR based on the initial observation of the prevalence and characteristics of the outcomes (disease or condition). Employing proper statistical methods in the analysis is crucial to avoid inappropriate estimates and interpretations. While using PR is generally recommended, reporting POR in cross-sectional studies is acceptable as long as authors interpret POR correctly as the ratio between odds or for conditions or diseases with low prevalence.

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