chapter questions
Introduction
One of the major challenges to an epidemiologist is presentation of research findings in a meaningful and interpretable manner. Much of the basic vocabulary in this context is termed measures of effect in “epi-speak.” An effect measure is “[a] quantity that measures the effect of a factor on the frequency or risk of a health outcome. Three such measures are ATTRIBUTABLE FRACTIONS, which measure the fraction of cases due to a factor; risk and rate differences, which measure the amount a factor adds to the risk or rate of a disease; and risk and rate ratios, which measure the amount by which a factor multiplies the risk or rate of disease.” 1
This chapter will extend the discussion of an odds ratio (OR) and a relative risk (RR). Classified as measures of relative effects, these two measures were defined and illustrated elsewhere in the text. Several additional measures of effect, useful when one is evaluating the potential implications of an exposure–disease association, are introduced. For the science of public health, correct extrapolation of the findings of individual studies to the larger population is critical. Armed with knowledge of the measures presented in this chapter, public health practitioners can be more effective in planning programs, delivering resources, and evaluating proposed interventions.
We will also demonstrate that the exposure–disease association can have quite different implications for risk to the individual and impact upon the population. A risk that is relatively modest for the individual can be very meaningful for the population. Thus, individuals may be less inclined to lower their risk factor status for a particular adverse health outcome when quality of life is reduced; from the population perspective, public health officials may be more inclined to advocate for reduction of that same risk factor. An example will be provided later in the chapter.
Absolute Effects
One of the simplest ways to compare the disease burden in two groups is to calculate the absolute difference in disease frequency. This type of comparison also is referred to as a difference measure of association, or attributable risk . 2 An absolute effect may be based on differences in incidence rates, cumulative incidence, prevalence, 3 or mortality. 4 An attributable risk is also known as a rate difference or risk difference . 3 , 5
Risk Difference
|
I e |
= Incidence rate of disease in exposed group |
|
I ne |
= Incidence rate of disease in nonexposed group |
Measures of risk differences aid in assessing the impact of a component cause, which is one of a set of multiple causes linked to a particular effect. With respect to the issue of component causes in epidemiology, Rothman’s comments are particularly relevant:
· A cause is an act or event or a state of nature which initiates or permits, alone or in conjunction with other causes, a sequence of events resulting in an effect . A cause which inevitably produces the effect is sufficient. The inevitability of disease after a sufficient cause calls for qualification: disease usually requires time to become manifest, and during this gestation, while disease may no longer be preventable, it might be fortuitously cured, or death might intervene … Most causes that are of interest in the health field are components of sufficient causes but are not sufficient in themselves … Causal research focuses on components of sufficient causes, whether necessary or not. 6 ( p 588 )
Along the lines of Rothman’s statements, it is asserted elsewhere in this book that many chronic diseases, for example, coronary heart disease (CHD), result not from a single exposure but rather from the combined influences of several exposures, such as environmental and lifestyle factors, that operate over a long time period. Therefore, removal of only one of the exposures (e.g., high serum cholesterol) that leads to a chronic disease (i.e., CHD) would not result in complete elimination of the disease; other risk factors would still be operative and contribute to the rate of disease. One approach to estimate the realistic potential impact of removing an exposure from the population is to calculate the risk difference in disease frequency (i.e., incidence rates) between the exposed and the nonexposed groups. According to Rothman, a risk difference “represents the incidence rate of disease with the exposure as a component cause.” 3 ( p 35 )
Risk difference : The difference between the incidence rate of disease in the exposed group (Ie) and the incidence rate of disease in the nonexposed group (Ine); risk difference = Ie — Ine. 5
As mentioned earlier, the measure of disease frequency used in the determination of absolute effects may be incidence density, cumulative incidence, prevalence, or mortality. Thus, to be perfectly accurate, when the measure of disease frequency is cumulative incidence, the term risk difference could be used. When incidence density measures are used as the measure of disease frequency, the term rate difference is most appropriate. For prevalence and mortality, the most precise terms would be prevalence difference and mortality difference , respectively. Regardless of the measure of disease frequency used, the basic concept of absolute effects is the same: The measure of disease frequency among the nonexposed group is subtracted from the measure of disease frequency among the exposed group.
As an example, hip fractures (often among persons with osteoporosis) pose a significant public health burden for the elderly population. ( Figure 9–1 illustrates osteoporosis.) In 2002, there were an estimated 44 million U.S. adults with osteoporosis or low bone mass. 7 Investigators at the Mayo Clinic in Rochester, Minnesota, examined seasonal variations in fracture rates, comparing the rates during winter with those during summer. 8 For women younger than age 75, the incidence Ie of fractures per 100,000 person-days was highest in the winter (0.41), and the incidence Ine was lowest in the summer (0.29). The risk difference between the two seasons (Ie – Ine) was 0.41 – 0.29, or 0.12 per 100,000 person-days.
FIGURE 9–1 Osteoporosis: A risk factor for fractures.
Population Risk Difference
|
I p |
= Overall incidence rate of disease in a population |
|
P e |
= Proportion of the population exposed |
|
P ne |
= Proportion of the population not exposed |
Population risk difference is defined as a measure of the benefit to the population derived by modifying a risk factor. This measure addresses the question of how many cases in the whole population can be attributed to a particular exposure. To understand fully the concept of population risk difference, consider that the incidence rate (risk) of disease in the population (denoted by the symbol IP), for the simplest case of a dichotomous exposure (exposed or nonexposed), is made up of four components: the incidence rate (risk) of disease in the exposed group (Ie); the incidence rate (risk) of disease in the nonexposed group (Ine); the proportion of the population exposed (Pe); and the proportion of the population not exposed (Pne). The nonexposed group is sometimes called the reference group. The relationship among the four components may be expressed by the following formula:
Ip = (Ie)(Pe) + (Ine)(Pne)
Ignore, for the moment, the proportion exposed (Pe) and the proportion not exposed (Pne). If one were to remove the effects of exposure associated with higher rates of disease, the overall rate of disease in the population then would be expected to decrease to the rate observed among the nonexposed, or reference, group. Thus, subtraction of the rate (risk) of disease among the nonexposed (Ine) from the rate of disease among the population (IP) provides an indication of the potential impact of a public health intervention designed to eliminate the harmful exposure.
Population risk difference : The difference between the rate (risk) of disease in the nonexposed segment of the population (Ine) and the overall rate (IP).
Just as for the risk difference, the measures of disease frequency used to calculate population risk differences may be generalized to include the cumulative incidence (risk), incidence density (rates), prevalence, or mortality. Remember: Risk difference is the risk in the exposed minus the risk in the non-exposed; population risk difference is the risk in the population minus the risk in the nonexposed subset of the population.
As another example, nonsteroidal anti-inflammatory drugs (NSAIDs) are the most frequently used drugs in the United States, with 111 million prescriptions filled annually and an estimated cost of about $2 billion annually for over-the-counter NSAIDs. 9 The risks associated with use of NSAIDs include significant upper gastrointestinal bleeding; especially among older persons. 10 To examine the association of NSAID usage and peptic ulcer disease among elderly persons, Smalley et al. 11 determined the incidence rate of serious ulcer disease among users and nonusers of NSAIDs. The study was based on 103,954 elderly Tennessee Medicaid recipients followed from 1984 to 1986. A total of 1,371 patients were hospitalized with peptic ulcer disease after 209,068 person-years of follow-up. The incidence (density) rate of peptic ulcer disease in the study population (IP) was calculated to be 6.6 per 1,000 person-years [(1,371/209,068) × 1,000]. The rate (Ine) among nonusers of NSAIDs was only 4.2 per 1,000 person-years. The population risk difference (IP Ine) was 6.6 – 4.2, or 2.4 per 1,000 person-years. The risk difference may be computed also: It was known that the observed incidence rate (Ie) of peptic ulcer disease among users of NSAIDs was 16.7 per 1,000 person-years. Therefore, the risk difference (Ie – Ine) was 16.7 – 4.2, or 12.5 per 1,000 person-years.
Relative Effects
Interpretation of the absolute measures of effect can sometimes be enhanced when expressed relative to a baseline rate. For example, an RR provides an estimate of the magnitude of an association between exposure and disease. 5 Such a ratio also can be described as a relative effect. Note that all relative effects contain an absolute effect in the numerator.
Previously, we defined RR as the ratio of the cumulative incidence rate in the exposed (Ie) to the cumulative incidence rate in the nonexposed (Ine), or Ie/Ine. This is actually a simplification of the true formula for RR, in which the numerator is Ie – Ine (the risk difference). If one divides both terms in the numerator by Ine, one is left with the formula (Ie/Ine) – (Ine/Ine). The first term, Ie/Ine, was previously defined as the RR. Because any number (or variable) divided by itself is 1, the second term becomes 1, and the expression becomes RR = 1. Typically the = 1 is ignored. Occasionally, however, one may encounter statements such as “30% greater risk among the exposed”; this statement implies that the RR ratio of Ie/Ineis 1.3 but that the 1 has been subtracted. The interpretation is exactly the same. RRs between 1.0 and 2.0 sound bigger when stated as a percentage, however (e.g., 1.3 versus 30%).
Etiologic Fraction
One of the conceptual difficulties with RR is that the rate of disease in the referent (nonexposed) group is not necessarily 0. In fact, for a common disease that is theorized to have multiple contributing causes, the rate may still be quite high in the referent group as a result of other causes in addition to the exposure of interest. One implication of multiple contributing causes is that, even in the absence of exposure to the single factor of interest, a number of cases still would have developed among the nonexposed population. An approach to estimating the effects due to the single exposure factor is to compute the etiologic fraction . It is defined as the proportion of the rate in the exposed group that is due to the exposure. Also termed attributable proportion or attributable fraction, it can be estimated by two formulas. To estimate the number of cases among the exposed that are attributable to the exposure, one must subtract from the exposed group those cases that would have occurred irrespective of membership in the exposed population.
|
Etiologic fraction = ( I e − I ne )I e |
(Eq. 1) |
Note that the difference between Equation 1 and RR is the rate in the denominator—Ie instead of Ine. The numerator represents an acknowledgment that not all the cases among the exposed group can be fairly ascribed to the exposure; some fraction would have occurred anyway, and this fraction is estimated by the rate in the nonexposed group. This formula can be applied to data from cohort or cross-sectional studies. The appropriate measures of disease frequency must be utilized: cumulative incidence, incidence density, or mortality from cohort studies or prevalence of disease from cross-sectional studies.
With a little arithmetic, it is possible to express Equation 1 , the formula for etiologic fraction, in another convenient form. If one considers Equation 1 as two separate fractions, one obtains 1 − (Ine/Ie). Note that (Ine/Ie) is merely the reciprocal of the original definition of RR. Thus, one is left with 1 − −(1/RR). If one expresses the 1 as RR/RR, the formula requires only an estimate of RR, obviously beneficial for those situations in which the actual incidence rates are unknown ( Equation 2 ). Thus, this formula may be applied when the data at hand, whether from a report or a published article, include only the summary measures. More important, because the OR provides an estimate of RR, this formula is applicable to data from case-control studies.
|
Etiologic fraction = ( RR − 1 )RR |
(Eq. 2) |
For example, what fraction of peptic ulcer disease in elderly persons is attributable to NSAIDs? Recall from the previous example that Ine was 4.2 and Ie was 16.7 per 1,000 person-years. 11 The risk difference was computed to be 16.7 – 4.2, or 12.5 per 1,000 person-years. The etiologic fraction from Equation 1 is 12.5 + 16.7, or 74.9%. Thus, roughly three-fourths of the cases of peptic ulcer disease that occurred among NSAID users were attributed to that exposure.
To demonstrate that both formulas are equivalent, one may compute the etio-logic fraction using Equation 2 . To do this, one must first compute the RR. In this example the answer is 16.7 + 4.2, or 3.98. The etiologic fraction is therefore 2.98 divided by 3.98. Both formulas should yield the same answer, an outcome that the reader may wish to verify.
In general, low RRs equate to a low etiologic fraction, and high RRs equate to a high etiologic fraction. A reasonable question to ask at this point is: What does risk difference reveal beyond what one could already infer from the RR? Perhaps this question is best answered with an illustration. Take the case of two diseases, A and B, and two exposure factors, X and Y. The rate of disease A is 2 per 100,000 per year among individuals exposed to factor X and 1 per 100,000 per year among those not exposed to factor X. The rate of disease B is 400 per 100,000 per year among individuals exposed to factor Y and 200 per 100,000 per year among those not exposed to factor Y. Therefore, for either disease the RR associated with the relevant exposure is 2 (i.e., 2 ÷ or 400 ÷ 200). Exposure factors X and Y both appear to pose a significant health hazard, a doubling of risk of disease. Consider what is obtained by examining the risk difference: For disease A the risk difference is 2 − 1 or 1 per 100,000 per year, and for disease B the risk difference is 400 – 200 or 200 per 100,000 per year. Although the RRs for factor X and factor Y are the same, the risk differences for the two factors are quite disparate. If one were to design an intervention to improve public health, the RRs for factors X and Y would not be terribly informative. The risk difference calculations would suggest, however, that control of exposure Y might pay greater dividends than control of exposure X (ignoring, for the moment, critical issues such as cost and feasibility).
Population Etiologic Fraction
As we have seen, from the perspective of those with a disease, the etiologic fraction gives an indication of the potential benefit of removing a particular exposure to a putative disease factor. That is, does a particular exposure account for 5% of the etiology of the disease or 95%? An alternative perspective to consider is that of the population. The population etiologic fraction provides an indication of the effect of removing a particular exposure on the burden of disease in the population. A possible scenario is one in which a dichotomous (present or absent) exposure factor is associated with risk of disease and 25% of the population is exposed to the factor. As was pointed out earlier, the total rate of disease in the population may be thought of as a weighted average of the rate of disease among the 25% of the population exposed and the rate of disease among the 75% of the population not exposed. (Note that the concept of a weighted average is applied to the direct method of age adjustment.) If the offending exposure is reduced, the lower limit of disease rate that can be achieved is the background rate observed among the nonexposed segment of the population. Again, two formulas for the population etiologic fraction will be presented.
The population etiologic fraction (also termed the attributable fraction in the population) represented by Equation 3 is the proportion of the rate of disease in the population that is due to the exposure. It is calculated as the population risk difference divided by the rate of disease in the population.
|
Population etiologic fraction = ( I P − I ne )I P |
(Eq. 3) |
As an example, consider again the study of NSAIDs and peptic ulcer disease among elderly persons. 11 Inewas 4.2, IP was 6.6 per 1,000 person-years, and the population risk difference was computed to be 6.6 + 4.2, or 2.4 per 1,000 person-years. For this example, the population etiologic fraction is (2.4/6.6) × 100 = 36.4%. Therefore, if everyone in the population stopped taking NSAIDs, the rate of peptic ulcer disease would decrease by more than one-third. Notice that compared with the etiologic fraction of those with the disease, this value of 36.4% is far less than the etiologic fraction of 74.9%.
When the incidence rate in the population is unknown, an alternative formula ( Equation 4 ) may be applied. This formula requires information about two components: the RR of disease associated with the exposure of interest, and the prevalence of the exposure in the population (Pe).
|
Population etiologic fraction = P e ( RR − 1 )p e ( RR − 1 ) + 1 × 100 |
(Eq. 4) |
Case-control studies do not allow an estimation of disease rates in the total population or in the nonexposed population and, therefore, the Equation 3 population etiologic fraction cannot be used. Equation 4 , however, lends itself to interpretation of data from case-control studies because the OR can be substituted for RR. The missing piece of information is the prevalence of the exposure in the population. Recall from the chapter titled “Study Designs: Ecologic, Cross-Sectional, Case-Control” that the purpose of a control group is to provide an estimate of the expected frequency of the exposure of interest. With certain assumptions, the frequency of exposure among the control group can be used to approximate the overall frequency of exposure in the population.
Example 1: Given that the prevalence (Pe) of current NSAID use in the study by Smalley et al. 11 was 0.13, compute the population etiologic fraction using Equation 4 . The RR had been previously determined to be 3.98. Plugging the values for RR and Pe into Equation 4 , one obtains:
0.13 ( 3.98 − 1 )0.13 ( 3.98 − 1 ) + 1 × 100 = 0.3871.387 × 100 = 27.9%
This answer is slightly lower than the results obtained by using Equation 3 for the population etiologic fraction because the prevalence figure Pe did not include former or indeterminate users of NSAIDs. Mathematically the two formulas yield the same result, however.
Example 2: Suppose you are dealing with an exposure that confers a high RR for disease (e.g., RR = 20), but the prevalence (Pe) of the exposure in the population is low (e.g., 1 per 100,000). Compare the etiologic fraction with the population etiologic fraction using these data. Compute the etiologic fraction using Equation 2 . We obtain:
20 − 120 × 100 = 95%
From Equation 4 , we obtain:
0.00001 ( 20 − 1 )0.00001 ( 20 − 1 ) + 1 × 100 = 0.019%
Thus, 95% of the cases that occurred among the exposed were attributable to the exposure. Because the exposure was rare in the population, however, it contributed little to the total disease rate.
These two examples illustrate that the impact of an exposure on a population depends upon:
· •• the strength of the association between exposure and resulting disease.
· •• the overall incidence rate of disease in the population.
· •• the prevalence of the exposure in the population.
One may also infer that exposures of high prevalence and low RR can have a major impact on the public’s health. For example, an individual’s risk of cardiovascular disease mortality associated with an elevated serum cholesterol level may be low. That is, the etiologic fraction is low. However, because a substantial proportion of the population has high cholesterol (i.e., hypercholesterolemia has a high prevalence), the benefit to the population from reducing cholesterol could be substantial. In contrast, the foregoing example of a rare exposure with a high RR for disease demonstrates that a single exposure factor can account for the vast majority of cases of disease among the exposed but that removal of that particular exposure from the population will have little impact on the overall incidence of disease.
Statistical Measures of Effect
In addition to the preceding methods of expressing epidemiologic study results (absolute and relative effects), epidemiologists frequently employ and rely on statistical tests to help interpret observed associations. An illustration of statistical tests arises from a study of the effects of passive smoking (by parents) on the prevalence of wheezing respiratory illness among their children. 12 The results indicate that mothers who smoked at the time of the survey were 1.4 times more likely to report wheezing respiratory illness among their children than mothers who did not smoke. The reasons for this outcome may be as follows:
· 1. Passive smoking by a parent does, in fact, increase children’s risk of wheezing respiratory illness.
· 2. Some additional exposure has not been properly allowed for in the analysis.
· 3. The results represent nothing more than a chance (random) finding.
Only after options 2 and 3 have been ruled out can one reasonably conclude that passive smoking increases children’s risk of wheezing respiratory illness.
Significance Tests
Underlying all statistical tests is a null hypothesis , usually stated as, “There is no difference in population parameters among the groups being compared.” The parameters may consist of the prevalence or incidence of disease in the population. For example, the prevalence or incidence might represent an actual count of cases of disease identified by surveillance programs, or by other means such as positive serological evidence of infection from elevated antibody titers. A discussion of the particular statistical test to be employed, the choice of which is determined by a number of considerations, is beyond the scope of this book. Suffice it to say that in deciding whether to fail to reject or to reject the null hypothesis, a test statistic is computed and compared with a critical value obtained from a set of statistical tables. The significance level is the chance of rejecting the null hypothesis when, in fact, it is true.
The P Value
The P value indicates the probability that the findings observed could have occurred by chance alone. The converse is not true: A nonsignificant difference is not necessarily attributable to chance alone. For studies with a small sample size, the sampling error is likely to be large, which may lead to a nonsignificant test even when the observed difference is caused by a real effect.
Confidence Interval
A confidence interval (CI) is a statistical measure that is considered by many epidemiologists to be more meaningful than a point estimate; the latter is a single number—for example, a sample mean, an incidence rate, or an RR—that is used to estimate a population parameter. A CI is expressed as a computed interval of values that, with a given probability, contains the true value of the population parameter. 1 The degree of confidence is usually stated as a percentage; the 95% CI is commonly used. Although it is beyond the scope of this book to demonstrate how to construct CIs, it is important, nonetheless, to know how to interpret them. A CI can be interpreted as a measure of uncertainty about a parameter estimate (e.g., a mean, OR, RR, or incidence rate).
· •• In terms of utility, a 95% CI contains the “true” population estimate 95% of the time.
· •• Thus, if one samples a population 100 times, the 95% CI will contain the true estimate (i.e., the population parameter) 95 times. Alternatively, if one were to repeat the study 100 times, one would observe the same outcome 5 times just by chance.
· •• CIs are influenced by the variability of the data and the sample size.
The hypothetical example presented in Table 9–1 reports the OR for a case-control study with three different sample sizes. The exposure, disease, study population, and survey instrument are the same in all three cases. In fact, everything is identical except for the size of the study groups.
Table 9–1 Odds Ratios, P Values, and 95% Confidence Intervals for a Case-Control Study with Three Different Sample Sizes
|
|
Sample Size
|
||
|
Parameter Computed |
20 |
50 |
500 |
|
OR |
2.00 |
2.00 |
2.000 |
|
P |
0.50 |
0.20 |
0.001 |
|
95% CI |
0.5, 7.7 |
0.9, 4.7 |
1.5, 2.6 |
Perhaps the first sample size was obtained for a small-scale pilot study. Twenty cases and 20 controls are included. An OR of 2 is observed, but the 95% CI includes 1; the results are therefore consistent with no association. Suppose, alternatively, that one is able to study 50 per group instead of only 20. The same point estimate of association is observed, and the 95% CI also includes the null value of 1. The degree of precision of the magnitude of the OR is improved; the interval is narrower, but the results are still not statistically significant. In the final scenario there are unlimited resources, and one is able to study 500 individuals in each group. With this extra effort and expense, the same study results are obtained: an OR of 2. The larger sample size has allowed for a more precise estimate of the effect to be obtained (the 95% CI is narrower). The outcome is now statistically significant, as the null value of 1 is now excluded from the 95% CI for the OR. The point to be made is that the estimate of an effect from an epidemiologic study is not necessarily incorrect just because the sample size is small; a small sample size merely may not produce precise results (i.e., there is a wide CI around the estimate of effect).
Clinical Versus Statistical Significance
The preceding discussion of statistical significance should suggest to the reader that P values are only a part of the evaluation of the validity of epidemiologic data.
One also should be aware of an important caveat of large sample sizes: Small differences in disease frequency or low magnitudes of RR may be statistically significant. Such minimal effects may have no clinical significance, however. For example, suppose an investigator conducted a survey among pregnant women in urban and suburban populations to assess folic acid levels. Furthermore, suppose that there were 2,000 women in each group, that the average folic acid levels differed by 1.3%, and that this difference was statistically significant. In this example, the sample size was large enough to detect subtle differences in exposure; biologically and clinically, such small differences may be quite insignificant.
The converse of the large sample size issue is that, with small samples, large differences or measures of effect may be clinically important and worthy of additional study. Thus, mere inspection of statistical significance could cause oversight. The lack of statistical significance may simply be a reflection of insufficient statistical power to detect a meaningful association. Statistical power is defined as, “… the ability of a study to demonstrate an association if one exists. The power of a study is determined by several factors, including the frequency of the condition under study, the magnitude of the effect, the study design, and sample size.” 1 One example of the magnitude of the effect is how large a relative risk is found, that is, whether RR = 1, 5, or 10.
Another problem inherent in the use of statistical significance testing is that it may lead to mechanical thinking. In his Cassel Memorial Lecture to the Society for Epidemiologic Research Annual Meeting in June 1995, Rothman 13 noted that John Graunt’s famous epidemiologic contributions were made in the absence of a knowledge of statistical significance testing.
Evaluating Epidemiologic Associations
The ability to evaluate critically epidemiologic associations reported in the literature is a realistic and attainable goal for the public health practitioner. Although the basic skills to perform such an evaluation are covered in this book, there is no substitute for practice. As an aid to the reader, five key questions that should be asked are presented below.
Could the Association Have Been Observed by Chance?
The major tools that are used to answer this question are statistical tests. Although any public health practitioner should have a basic understanding of biostatistics, he or she should not underestimate the value of a competent biostatistician as a source of help. A small P value (i.e., highly significant result) for an observed association should provide some assurance that the results were not obtained simply by chance, but one must always remember that a very small P value does not imply that the association is real.
Could the Association Be Due to Bias?
The term bias refers to systematic errors, and is discussed in detail elsewhere in this text. At this point it is sufficient to say that one should critically evaluate how the study groups were selected, how the information about exposure and disease was collected, and how the data were analyzed. Errors at any of these stages may lead to results that are not valid.
Could Other Confounding Variables Have Accounted for the Observed Relationship?
Confounding refers to the masking of an association between an exposure and an outcome because of the influence of a third variable that was not considered in the design or analysis. The issue of confounding and how to control it is covered elsewhere in this book. Based on one’s understanding of the natural history and epidemiology of a disease, one needs to consider whether important known confounding factors have been omitted from the study.
To Whom Does This Association Apply?
Although population-based samples are important in epidemiologic research, and although these sampling procedures enhance the likelihood of generalizability of results, they do not guarantee such an outcome. Furthermore, in some situations a great deal can be learned from an unrepresentative study sample. If a study has been properly conducted among a certain stratum of the population, for example, white women between the ages of 55 and 69 who live in the state of Iowa, then one could certainly generalize to other white women who live in the Midwest. If the diets of the women in Iowa are indicative of the diets of American women of this age group, however, then any observed diet–disease associations may apply to a much broader population.
In addition to the representativeness of the sample, many investigators believe that participation rates are crucial to the validity of epidemiologic findings. Participation rates, the percentage of a sample that completes the data collection phase of a study, must be at a sufficiently high level. For example, some top-tier public health journals may not publish a report in which the participation rate was less than 70%. Ironically, high participation rates do not necessarily ensure generalizability, and in certain circumstances generalizability may be high even if participation rates are low. Consider a study of a potential precursor of colorectal cancer: the rate of proliferation of cells in the rectal mucosa. Measurement of the proliferation rate of the rectal epithelium requires a punch biopsy, obtainable as part of a sigmoidoscopy or colonoscopy procedure. Suppose one conducts a case-control study of patients with adenomatous polyps (a known precursor of colorectal cancer) and controls free from colon polyps or cancer. Cases are found to have significantly higher rates of rectal cell proliferation than the controls. Because of the invasive nature of the procedure, however, the participation rates are only 10% among the eligible cases and 5% among eligible controls. Does this necessarily mean that the findings cannot be generalized? The key issue is whether the exposure of interest influenced the decision process of the eligible cases and controls to participate. In this example, it is difficult to imagine how an unmeasured characteristic, such as the rate of rectal cell proliferation, could possibly influence participation. Therefore, despite participation rates that usually would be regarded as unacceptable, one may still be able to generalize the findings, especially the underlying biology, to a broader population.
Does the Association Represent a Cause-and-Effect Relationship?
The answer to this question is determined by careful consideration of each of Hill’s criteria of causality. 14 These criteria are: strength of the association, temporality, dose-response, consistency, biologic plausibility, specificity, analogy, and coherence.
Models of Causal Relationships
Drawing upon the concepts presented earlier in the chapter, this section introduces models of disease causation. Relationships between suspected disease-causing factors and outcomes fall into two general categories: not statistically associated and statistically associated. 15 Among statistical associations are non-causal and causal associations. Possible types of associations are formatted in Figure 9–2 .
We have already considered the role of statistical significance in evaluating an association and noted that evaluation of statistical significance is used to rule out the operation of chance in producing an observed association; a nonstatistically associated (independent) relationship is shown in box A of the diagram (left side).
FIGURE 9–2 Map of possible associations between disease-causing factors and outcomes.
Source: Data from B MacMahon and TF Pugh, Epidemiology Principles and Methods. Boston, MA: Little, Brown and Company; 1970.
As shown in Figure 9–2 , a statistical association may be either noncausal or causal. What is meant by a noncausal (secondary) association? Suppose factor C is related to disease outcome A. The association may be due to the operation of a third factor B that is related to both C and A. Thus, the association between C and A is secondary to the association of C with B and C with A. For example, periodontal disease (C) is associated with chronic obstructive pulmonary disease (A). 16 One possible explanation for this association is the secondary association of smoking (B) with both periodontal disease (C) and chronic obstructive pulmonary disease (A). This model suggests that the increased risk of chronic obstructive pulmonary disease associated with periodontal disease is related to the role that smoking may play as a cofactor in both conditions. Here is a map of a secondary association: C ← B → A. 1
With respect to causal associations, the relationship between factor and outcome may be indirect or direct. An indirect causal association involves the operation of an intervening variable, which is a variable that falls in the chain of association between C and A. An illustration of an indirect association is the postulated relationship between low education levels (C) and obesity (A) among men. 17 Men who have lower education levels tend to be more obese than those who have higher education levels. It is plausible that the relationship between C and A operates through the intervening variable of lack of leisure time physical activity (B). An indirect association involves an intervening variable in the association between C and A. This relationship may be formatted as follows: C → B → A. 1 Note that the arrow between C and B has been reversed in contrast with an indirect noncausal association.
Multiple Causality
The foregoing section provided models of causality that employ more than one factor. As stated earlier in this chapter, the measure risk difference implies multivariate causality by isolating the effects of a single exposure from the effects of other exposures. The example on NSAIDs examined the difference between risk of peptic ulcer among users and nonusers of NSAIDs, where the risk difference was 12.5 per 1,000 person-years. The risk of peptic ulcer caused by other exposures was 4.2 per 1,000 person-years.
The issue of disease causality is exceedingly complicated. To describe exposure–disease relationships, epidemiologists have developed complex models of disease causality. These models acknowledge the multifactor causality of diseases, even those that seem to have “simple” infectious agents. Often, these models involve an ecologic approach by relating disease to one or more environmental factors. “The requirement that more than one factor be present for disease to develop is referred to as multiple causation or multifactorial etiology.” 18 ( p 27 ) Examples of several influential models are the:
· •• epidemiologic triangle
· •• web of causation
· •• wheel model
· •• pie model
Web of causation
The web of causation is “… a popular METAPHOR for the theory of sequential and linked multiple causes of diseases and other health states.” 1 The web of causation implicates broad classes of events and represents an incomplete portrayal of reality. 15 Although the web of causation for most diseases is complex, one may not need to understand fully the causality of any specific disease in order to prevent it. An example of the web of causation of avian influenza is provided in Figure 9–3 . Follow the infection of the human host from the virus reservoir in wild birds. As of 2007, the virus had not mutated into a form that could be spread readily from person to person.
Wheel model
The wheel model is similar to the epidemiologic triangle and web of causation with respect to involving multiple causality ( Figure 9–4 ). Observe that the model explains the etiology of disease by calling into play host and environment interactions. Environmental components are biologic, social, and physical. The circle designated as “host” refers to human beings or other hosts affected by a disease. The circle called “genetic core” acknowledges the role that genetic factors play in many diseases. The wheel model de-emphasizes specific agent factors and, instead, differentiates between host and environmental factors in disease causation. The biologic environment is relevant to infectious agents, by taking into account the environmental dimensions that permit survival of microbial agents of disease.
FIGURE 9–3 The web of causation for avian influenza.
FIGURE 9–4 The wheel model of man–environment interactions.
Source: Modified with permission from JS Mausner and S Kramer, Mausner & Bahn Epidemiology: An Introductory Text, 2nd ed. Philadelphia, PA: W.B. Saunders Company;1974, p 36.
A wheel model may be used to account for the occurrence of childhood lead poisoning. 18 In this example, preschool children are typical hosts. The physical environment provides many opportunities for lead exposure from lead-based paint in older homes, playground equipment, candy wrappers, and other sources. Some children ingest paint chips from peeling surfaces as a result of pica, the predilection to eat nonfood substances. Because lead-based paints often are located in poorer neighborhoods that have substandard housing, the social environment is associated with childhood poisoning. Limited access to medical care in such communities may restrict screening of preschool children for lead exposure. Elimination of childhood lead poisoning requires visionary public health leadership to advocate for detection of lead-based paints and other sources of environmental lead exposure as well as the implementation of screening programs. Such efforts will help to protect vulnerable children against the sequelae of lead poisoning.
Pie model
Another model of multiple causality (multicausality) is the causal pie model. 19 As Figure 9–5 shows, the model indicates that a disease may be caused by more than one causal mechanism (also called a sufficient cause), which is defined as “a set of minimal conditions and events that inevitably produce disease.” 19 (p S144) Each causal mechanism is denoted in Figure 9–5 by the numerals I through III. An example of different causal mechanisms for a disease is provided by the etiology of lung cancer: lung cancer caused by smoking; lung cancer caused by exposure to ionizing radiation; and lung cancer caused by inhalation of carcinogenic solvents in the workplace.
FIGURE 9–5 Three sufficient causes of disease.
Source: From KJ Rothman and S Greenland, Causation and causal inference in epidemiology, Am J Public Health,2005; vol 95, p S145. Reprinted with permission from the American Public Health Association.
Rothman and Greenland note that, “A given disease can be caused by more than one causal mechanism, and every causal mechanism involves the joint action of a multitude of component causes.” 19 (p S145) The component causes, or factors, are denoted by the letters shown within each pie slice. A single letter indicates a single component cause. A single component could be common to each causal mechanism (shown by the letter A that appears in each pie); in other cases, the component causes for each causal mechanism could be different for each mechanism (shown by the letters that differ across the pies). Returning to the lung cancer example, a common factor that could apply to all causal mechanisms for lung cancer is a genetic predisposition for cancer. Several other component causes might be different for each causal mechanism involved in the etiology of lung cancer.
In models of multicausality, most of the identified component causes are neither necessary nor sufficient causes (defined in the section on absolute effects). Accordingly, it is possible to prevent disease when a specific component cause that is neither necessary nor sufficient is removed; nevertheless, when the effects of this component cause are removed, cases of the disease will continue to occur.
Conclusion
This chapter covered two new measures of effect—absolute and relative effects—that may be used as aids in the interpretation of epidemiologic studies. In addition, the chapter presented guidelines that should be taken into account when one is interpreting an epidemiologic finding. Absolute effects, the first variety of which is called risk differences, are determined by finding the difference in measures of disease frequency between exposed and nonexposed individuals. A second type of absolute effect, called population risk difference, is found by computing the difference in measures of disease frequency between the exposed segment of the population and the total population. Relative effects are characterized by the inclusion of an absolute effect in the numerator and a reference group in the denominator. One type of relative effect, the etiologic fraction, attempts to quantify the amount of a disease that is attributable to a given exposure. The second type of relative effect, the population etiologic fraction, provides an estimate of the possible impact on the population rates of disease that can be anticipated by removal of the offending exposure. With respect to interpretation of epidemiologic findings, one should be cognizant of the influence of sample size upon the statistical significance of the results. Large sample sizes may lead to clinically unimportant, yet statistically significant, results; small sample sizes may yield statistically nonsignificant results that are clinically important. Therefore, we presented a series of five questions that should be asked when one attempts to interpret an epidemiologic observation. The chapter closed with a discourse on causal models, which may be particularly instructive when trying to interpret epidemiologic data.