Analytic epidemiology is concerned with testing hypotheses. Measures of association are typically derived for case-control and cohort studies (see Chapter 13), to assess the relationship between specific exposures and disease. These tests will establish if an association exists and the strength of that association. If an association does exist, we say that the specific exposure represents a risk factor for the disease.
The focus on exposures takes a broad view that reflects contemporary concerns including lifestyle practices such as smoking, substance abuse, drinking alcohol or coffee and eating foods high in cholesterol or salt; occupational hazards, such as repetitive tasks or heavy lifting; environmental influences, such as second-hand smoke, toxic waste and sunlight; and specific interventions, such as exercise, medications or treatment modalities. These exposures increase or decrease the likelihood of developing certain disorders or influence the ultimate outcome of a disorder. For example, smoking and sunlight are considered risk factors that increase the chance of developing cancer.18,19 Stroke patients with comprehension deficits have an increased risk of poor therapeutic outcomes.20 Exercise and higher fitness level in men with diabetes are associated with reduced risk of mortality from cardiovascular disease.21
This is a fundamental process in the determination of prognosis, as we attempt to predict outcomes based on patient characteristics. As with all measures of association, risk does not necessarily mean that the exposure causes the outcome.
Relative versus Absolute Effects
Analyses of association are based on a measure of effect that looks at the frequency of disease among those who were and were not exposed to the risk factor. A relative effect is a ratio that describes the risks associated with the exposed group as compared with the unexposed. An absolute effect is the actual difference between the rate of disease in the exposed and unexposed groups, or the difference in the risk of developing the disease between these two groups. To illustrate the concepts of relative and absolute effect, suppose we purchased two books, one costing $3 and the other $6. The absolute difference is $3, whereas the relative difference is that the second book is twice as expensive as the first. Therefore, the relative effect is based on the absolute effect, but takes into account the baseline value. Analogously, we can use measures of incidence of disease in exposed and unexposed groups to determine both relative and absolute effects of particular exposures.
The most common measure of relative effect is relative risk (RR), which indicates the likelihood that someone who has been exposed to a risk factor will develop the disease, as compared with one who has not been exposed. Relative risk is defined as the ratio of incidence of disease among the exposed subjects to the incidence of disease among the unexposed. Measures of relative risk are appropriate for use with cohort studies.
To determine risk, data are typically organized in a 2 × 2 table, called a contingency table, as shown in Figure 28.1. The vertical columns in the table represent the classification of disease status (the outcome), and the horizontal rows represent exposure status. To facilitate consistency in presentation and calculation, the cells in the table are designated a, b, c, and d, as shown in the figure. Therefore, cell a represents those who have the disease and were exposed, cell b represents those who do not have the disease and were exposed, and so on. The marginal totals for each row and column represent the total numbers of individuals who were exposed (a + b) and were not exposed (c + d), and the total numbers who have the disease (a + c) and do not have the disease (b + d). The sum of all four cells is the total sample size (N).
General format for a 2 × 2 contingency table, showing frequencies for disease and exposure.
For a cohort study, we can obtain cumulative incidence estimates for the exposed (CIE) and unexposed (CI0) groups. The cumulative incidence for the exposed group is the number of cases of the disease among the total exposed sample, or a/(a + b). The cumulative incidence for the unexposed group is the number of cases of the disease among the total unexposed sample, or c/(c + d).∗ Therefore,
If the incidence rates of the outcome are the same for the exposed and unexposed groups, the relative risk is 1.0, indicating that the exposure presents no excess risk for the outcome. Therefore, a relative risk greater than 1.0 indicates an increased risk, and a relative risk less than 1.0 means that the exposure decreases the risk of developing the disorder.
To illustrate this application, consider the data shown in Table 28.1 A for a cohort study of the risk of hip fracture associated with leisure time physical activity.22 Data were taken from longitudinal studies over six birth cohorts. For this example, we will look at a subsample of 130 women. The research question is: Does physical activity reduce the risk of hip fracture in elderly women?
TABLE 28.1RELATIVE RISK: DATA FOR A COHORT STUDY SHOWING THE RELATIONSHIP BETWEEN PHYSICAL ACTIVITY AND RISK OF HIP FRACTURE IN WOMEN ||Download (.pdf) TABLE 28.1 RELATIVE RISK: DATA FOR A COHORT STUDY SHOWING THE RELATIONSHIP BETWEEN PHYSICAL ACTIVITY AND RISK OF HIP FRACTURE IN WOMEN
Our first step is to determine what proportion of patients who exercised sustained a hip fracture. This is the incidence of hip fracture among exercisers, 48 out of 98, or 49%. Then we determine what proportion of sedentary patients sustained a hip fracture. This is the incidence of hip fracture for those who did not exercise, 20 out of 32, or 63%. Relative risk is the ratio of these two proportions:
This tells us that the risk of hip fracture was decreased among nonsedentary women; that is, those who were active at least 2 hours/week were 0.78 times as likely (less likely) to have a hip fracture as compared with those who were sedentary.
Confidence Intervals for Relative Risk
An important assumption in any research study is that we can draw reasonable inferences about population characteristics based on sample data. This assumption holds true for epidemiologic studies as well. When a risk estimate is derived from a particular set of subjects, the researcher will use that estimate to make generalizations about expected behaviors or outcomes in others who have similar exposure histories. Therefore, it is important to determine a measure of true effect using a confidence interval (see Chapter 18). For example, as shown in Table 28.1B, with an observed relative risk of 0.78 for the association between hip fracture and physical activity, the 95% confidence interval is 0.560 to 1.097. This interval represents a range of values within which the true population effect is expected to fall.
Confidence intervals can also be used to provide information about statistical significance by referring to the null value for relative risk, which is 1.0. We look to see if the null value is included within the 95% confidence interval. If the null value is contained within the confidence interval, and we are 95% confident that the interval contains the true population value, then we cannot rule out 1.0 as the population value. Therefore, the estimate is not considered significant. If the null value is not contained within the interval, the estimate is considered significant; that is, we are 95% sure that the null value is not the true population value. In our example, the 95% confidence interval is 0.56 to 1.097. As this interval contains the null value of 1.0, we would state that the observed association is not statistically significant at the .05 level. Therefore, we must conclude that, although the RR value shows a reduced risk for hip fracture with physical activity, this value could have occurred by chance.
Chi-square can also be used as a test of significance, to determine if the proportions differ across categories in a crosstabulation (see Chapter 25). In this example, the value of chi-square results in p = .184 (see Table 28.1B), which is not significant. This confirms the conclusion drawn from the confidence interval analysis, with a parallel interpretation. Chi-square tells us that the proportion of individuals with and without hip fracture who were in the two physical activity groups was not different from what would be expected just by chance.
A case-control study differs from a cohort study in that subjects are purposefully chosen based on the presence or absence of disease (cases or controls) and therefore, we cannot determine the rate of incidence of the disease (see Chapter 13). Relative risk is not an appropriate measure for case-control studies because we cannot calculate cumulative incidence. The relative risk can, however, be estimated using an odds ratio (OR), which is calculated using the formula
The odds ratio is interpreted in the same way as relative risk, with a null value of 1.0.
Consider the data shown in Table 28.2A. These data are from a case-control study which examined the risk for developing plantar fasciitis associated with body mass index (BMI).23 The researchers assembled a sample of 50 cases and 100 controls, with a 1 : 2 match on age and gender. Among the cases, 29 individuals had a BMI over 30 (considered obese); among the controls, 17 subjects had a BMI over 30. The crude odds ratio for these data is
TABLE 28.2ODDS RATIO: CASE-CONTROL DATA SHOWING THE RELATIONSHIP BETWEEN BODY MASS INDEX (BMI) AND RISK OF PLANTAR FASCIITIS ||Download (.pdf) TABLE 28.2 ODDS RATIO: CASE-CONTROL DATA SHOWING THE RELATIONSHIP BETWEEN BODY MASS INDEX (BMI) AND RISK OF PLANTAR FASCIITIS
This means that the odds of developing plantar fasciitis are almost seven times greater for those who are obese than for those who are not. In other words, being obese appears to increase the risk of developing plantar fasciitis.
Confidence Intervals for the Odds Ratio
Confidence intervals can also be generated for the odds ratio to determine the significance of the ratio as an estimate of population values. As shown in Table 28.2B, the confidence interval for the relationship between plantar fasciitis and BMI is 3.13 to 14.51. This interval does not contain the null value of 1.0, and therefore, this represents a significant odds ratio.
Chi-square can also be used to determine if the proportion of individuals varies across categories. This outcome is shown in Table 28.2B, confirming the significant outcome of the confidence interval analysis.
Confounding and Effect Modification
Quite often, in the analysis of the association between a risk factor and disease, researchers seek to infer a potential causal relationship between the two. The researcher also recognizes, however, that in a study of association, cause and effect cannot be readily established (as it can in an experimental study) because other factors may contribute to the observed relationship. Alternatively, we may see no association because other factors actually obscure the relationship between exposure and outcome.
In some cases, these extraneous variables provide information important to understanding how the association varies across different subgroups, such as age or gender. In other situations, such variables create a bias in the interpretation, interfering with the true association being studied. These two complications of analysis are called confounding and effect modification.
The simplest type of analyses are based on crude data. These are data concerning the exposure status and outcome status of all subjects regardless of any other risks or characteristics. Although analyses based on crude data are often reported in the literature, most studies also require more complicated analyses to evaluate the role of other factors in the relationship of exposure and outcome. These analyses are accomplished through stratification or multivariate methods and provide adjusted measures of association. Researchers must consider the potential influence of confounding and effect modification in all analyses and account for them in the design or analysis of data as much as possible.
Confounding variables can be thought of as nuisance variables. Confounding is introduced when extraneous variables interfere with the observed association between the exposure and outcome. A confounder is a variable that (1) is associated with the exposure, (2) is a risk factor for the disease independent of the exposure, and (3) is not part of the causal link between the exposure and the disease (Figure 28.2A). In other words, a confounding variable is associated with the predictor variable, but may also be a risk factor for the outcome variable, and therefore must be ruled out. Confounding occurs when the exposure can become confused or distorted by the extraneous variable.
A. Relationship between exposure and outcome, both related to a confounding variable. B. Relationship between receiving influenza vaccine and mortality in elders, confounded by functional status.
Example. To illustrate this concept, Jackson and co-workers24 examined the association between risk of mortality and receiving influenza vaccine in elders over 65 years. They studied 252 cases who died during an influenza season and 576 age-matched controls. The crude odds ratio for this relationship was 0.76 (95% Cl 0.47, 1.06), indicating that receiving the vaccine decreased the risk of death. The researchers were interested, however, in the potentially confounding effect of limited functional status, which (1) would be associated with not getting the vaccine, (2) would be a risk factor for mortality, and (3) is not a causal link between the vaccine and mortality. When they adjusted for the effect of functional limitations, the odds ratio was lowered to 0.59 (95% Cl 0.41, 0.83). Because older individuals who have functional limitations would be less likely to visit a clinic to get the vaccine, and mortality is also related to functional decline, the crude odds ratio was an underestimate of the protective nature of the vaccine on mortality. When function is taken into account, the actual risk of death is lower. If there were no discrepancy between the crude and unconfounded estimates, there would be no confounding. The degree of discrepancy is indicative of the extent to which function confounded the original data. By eliminating the effect of functional status, a stronger (and significant) relationship was seen between getting the vaccine and decreased mortality.
Adjusting for Confounders. Confounding variables may or may not be present in a study, depending on the source population and how subjects are chosen. When confounding is present, the statistical outcome may not be documenting the true causal factor. A method commonly used to adjust for a potential confounder is stratification, in which the comparison between exposure and disease is done at specific levels of the potential confounder. When a study mentions that researchers "controlled" or "adjusted" for a factor in the analysis, they have tried to remove the effect of that variable as a confounder.
To evaluate the effect of confounding in an analysis, the researcher must collect information on the potentially confounding variable. If the investigator in the vaccine study did not collect data on the subjects' functional status, the analysis of the confounder would not have been possible. Therefore, the researcher must be able to predict what variables are possible confounders. It is conceivable that several confounding factors will be operating in one study. In addition to controlling for confounding in the analysis, researchers can use design strategies, such as matching or homogeneous subjects, to control for these effects (see Chapter 9). For instance, in the study of influenza vaccine, if we were to restrict subjects to only those who were functionally independent, then function would not be a confounding factor.
Age and gender are often considered potential confounders in epidemiologic studies because of their common association with disease and disability, as well as being related to the presence of many exposures. Other common confounders are socioeconomic status, education level, marital status, weight, and cognitive status.
In contrast to confounding, effect modification occurs when the presence of one variable modifies the association between an exposure and outcome. Where a confounder is a nuisance that needs to be controlled to get an accurate estimate of an association, an effect modifier is a real effect that helps explain the biologic relationship between the exposure and outcome.25 Researchers attempt to cancel the effect of a confounding variable in the design or analysis of a study. Effect modifiers are studied so they can be reported.
An effect modifier will interact with the exposure and disease variables in such a way as to present a constant effect. It is a natural phenomenon that exists independent of the study design and will always be a factor in interpretation of risk. Effect modifiers tend to be biologically related to the variables being studied.
Example. Researchers have studied the association between diabetes and risk of endometrial cancer, with many conflicting results. Friberg et al26 hypothesized that this relationship could be misunderstood because of major modifiers such as physical activity. They studied a cohort of over 36,000 women over 7 years and found a relative risk of endometrial cancer of 2.37, adjusted for age, for women diagnosed with diabetes as compared to women without diabetes.
They then stratified the sample by physical activity (see Table 28.3). For diabetics with high physical activity, they found a RR for endometrial cancer of 1.06 as compared to those without diabetes who were active. Therefore, physically active diabetics were essentially at no increased risk of cancer. For diabetics with low physical activity, however, they found a RR of 2.67. The risk associated with endometrial cancer increased by more than two times for those who did not exercise. The fact that the risk estimates are different for each stratum indicates that physical activity interacts with diabetes as an effect modifier; that is, the association between diabetes and endometrial cancer is significantly modified by physical activity.
TABLE 28.3ASSOCIATION OF DIABETES AND ENDOMETRIAL CANCER STRATIFIED BY PHYSICAL ACTIVITY: ILLUSTRATION OF EFFECT MODIFICATION ||Download (.pdf) TABLE 28.3 ASSOCIATION OF DIABETES AND ENDOMETRIAL CANCER STRATIFIED BY PHYSICAL ACTIVITY: ILLUSTRATION OF EFFECT MODIFICATION
| || ||Number of Cases ||RR (95% CI) |
|Total Sample || |
|2.37 (1.51–3.74) |
|High Physical Activity || |
|1.06 (0.43–2.60) |
|Low Physical Activity || |
|2.67 (1.58–4.53) |
When data are stratified, separate risk estimates are calculated for each stratum; however, it is usually more useful to consider a single overall estimate that reflects the association between exposure and disease with the confounding factor taken into account. Several statistical techniques can be used to accomplish this, although the most commonly used procedures belong to a set of estimates proposed by Mantel and Haenszel.27 The Mantel-Haenszel pooled risk estimate provides a weighted summary value that can be used to report the relative risk associated with a specific exposure adjusted for the confounding variable. When the Mantel-Haenszel estimate differs from the crude risk estimate, it is the Mantel-Haenszel estimate that should be reported. It is most appropriately used when the stratum-specific relative risks are uniform, that is, when there is no effect modification. Formulas used to calculate Mantel-Haenszel estimates of relative risk for case-control and cohort studies are given in Table 28.4. The numerators and denominators in these formulas represent the sum of the expressions for each stratum.
TABLE 28.4MANTEL-HAENSZEL POOLED ESTIMATES FOR RELATIVE RISK FOR COHORT AND CASE-CONTROL STUDIES ||Download (.pdf) TABLE 28.4 MANTEL-HAENSZEL POOLED ESTIMATES FOR RELATIVE RISK FOR COHORT AND CASE-CONTROL STUDIES