Figure 95.1. Characteristics of a screening test: sensitivity, specificity, and predictive value.

WHAT INFLUENCES THE SENSITIVITY, SPECIFICITY, AND PREDICTIVE VALUE?

The sensitivity and specificity of a given screening test are in part dependent on where we are in our biological capabilities of identifying preclinical stages for a given disease and our technological abilities to develop a good screening test, but they can also be affected by what is called the criterion of positivity, that is, the cutoff value that is used to define an “abnormal” screening test. Lowering this criterion or making it less stringent—that is, setting the criterion of positivity for a screening for hypertension, for example, as a single systolic blood pressure of 120 mm Hg—will increase the sensitivity of the screening test and decrease the false negatives because everyone with hypertension will be picked up by the screen. But it will also lower the specificity of the test and increase the false positives in that many normotensive people will screen positive using this criterion. Similarly, raising the criterion or making it more stringent—that is, setting the criterion for positivity to 160 mm Hg—will mean that a higher proportion of those with hypertension will test negative on the screening test (decreased sensitivity and increased false negatives), but more individuals who are truly normotensive will screen negative (increased specificity and decreased false positives). The predictive value of a positive test is only slightly affected by changes in the sensitivity and specificity of the test, but it can be increased primarily by effecting an increase in the underlying prevalence of the preclinical disease in the screened population by, for example, targeting the screening program to a group at higher risk of developing the disease by nature of their risk factor profile (such as in the case above, screening older women or those with a positive family history of breast cancer or a personal history of benign breast disease).

BIAS IN THE INTERPRETATION OF SCREENING RESULTS

In evaluating the effectiveness of a screening program—that is, whether the screening program is effective in reducing morbidity or mortality from the disease—the screened and unscreened populations need to be comparable with respect to all other factors affecting the course of the disease besides the screening program itself. One source of bias that is of particular importance in the interpretation of the results of a screening program is lead time bias related to the amount of time by which the diagnosis of the disease has been advanced as a direct result of the screening program. Since screening is applied to asymptomatic individuals, every case picked up by screen is diagnosed earlier than if the diagnosis had been based on waiting for clinical symptoms to develop. If that estimate of lead time is not taken into account when comparing mortality outcomes between screened and unscreened groups, survival from diagnosis may appear to be longer for the screened group only because the diagnosis was made earlier in the course of disease. Lead time bias can be addressed by comparing the age-specific death rates in the screened and nonscreened groups rather than by comparing the length of survival from diagnosis to death.

MEASUREMENT OF DATA: MEASURES OF DISEASE FREQUENCY AND MEASURES OF ASSOCIATION

Question 2:

For each statement below, choose the measure of disease frequency that best describes each disease frequency:

Prevalence

Incidence

Standardized morbidity ratio

Age-specific measure

Age-adjusted measure

    1. At the initial study examination, 17 persons per 1000 had evidence of coronary heart disease.

    2. At the initial study examination, 31 persons aged 45–62 had evidence of coronary heart disease per 1000 persons examined in this age group.

    3. At the initial study examination, men and women had the same prevalence of coronary heart disease, after controlling for differences in age between the groups.

    4. During the first 8 years of the study, 45 persons developed coronary heart disease per 1000 persons who entered the study free of disease.

    5. During the first 8 years of the study, the observed frequency of angina pectoris in heavy smokers was 1.6 times as great as the expected frequency based on nonsmokers.

MEASURES OF DISEASE FREQUENCY

It is necessary for any epidemiological investigation to be able to quantify the occurrence of disease by measuring the number of affected individuals given the size of the source population and the time period during which the data were collected, allowing the direct comparison of disease frequencies in two or more groups of individuals. The measures of disease frequency most frequently used are incidence and prevalence. As shown in box 95.1, prevalence represents a snapshot of the status of the population at a point in time and is calculated as the number of existing cases of a disease divided by the size of the total population at that specified time. Incidence, on the other hand, represents the development of disease and is calculated as the number of new cases of a disease that developed during a specified period of time divided by the population at risk of being a new case of the disease. The measures of disease frequency can be calculated for the population as a whole or can be specific to a particular category or subgroup of the population such as an age-specific or gender-specific frequency. When two or more populations are being compared, these measures can also be adjusted for baseline differences between the populations, such as an age- or gender-adjusted frequency, or the observed cases in a population can be compared to the number of cases that would be expected based on previous experience or another population (standardized morbidity ratio).

    Thus, the correct answers for Question 2 would be:

    1. At the initial study examination, 17 persons per 1000 had evidence of coronary heart disease: PREVALENCE

    2. At the initial study examination, 31 persons aged 45 to 62 had coronary heart disease per 1000 persons examined in this age group: AGE-SPECIFIC PREVALENCE

    3. At the initial study examination, men and women in the study had the same prevalence of coronary heart disease, controlling for differences between the groups with respect to age: AGE-ADJUSTED PREVALENCE

    4. During the first 8 years of the study, 45 persons developed coronary heart disease per 1000 persons who entered the study free of disease: INCIDENCE

    5. During the first 8 years of the study, the observed frequency of angina pectoris in heavy smokers was 1.6 times as great as the expected frequency based on nonsmokers: STANDARDIZED MORBIDITY RATIO

Box 95.1 MEASURES OF DISEASE FREQUENCY IN EPIDEMIOLOGICAL STUDIES

Calculation of Measures of Disease Frequency

Question 3:

At the beginning of 2012, 800 people diagnosed with diabetes lived in a city that had a midyear population estimated at 10,000. During that year, 200 new cases of diabetes were diagnosed in the city, and 40 people died of complications of diabetes.

    1. What was the incidence per 1000 of diabetes during 2012?

    2. What was the prevalence per 1000 of diabetes on January 1, 2012?

    3. What was the prevalence per 1000 of diabetes on December 31, 2012?

    4. What was the mortality per 1000 from diabetes during 2012?

    5. If the prevalence of diabetes in 2012 was less than the prevalence of diabetes in 2010, could this be due to a change in the incidence rate, a change in the duration of the disease, or both?

    The definitions given in box 95.1 provide the information needed to calculate each of the individual measures of incidence and prevalence. Often the population is provided as a midyear estimate, and in that case the “population at risk” is the same as the total population. With regard to their interrelationship, prevalence—the proportion of the population that has a disease at a point in time—depends on both the rate of development of new disease during the period of time (incidence) as well as the duration of the disease from onset to termination (such as cure or death). Thus, a change in prevalence from one population to another or one time period to another can reflect a change in incidence, a change in the duration of the disease, or both.

    Thus, the answers to Question 3 would be:

    1. Incidence of diabetes during 2012 = 200/10,000 = 20/1000

    2. Prevalence of diabetes on January 1, 2012 = 800/10,000 = 80/1000

    3. Prevalence of diabetes on December 31, 2012 = (800 + 200–40)/10,000 = 96/1000

    4. Mortality from diabetes in the population during 2012 = 40/10,000 = 4/1000

    5. If the prevalence of diabetes in 2012 were less than the prevalence of diabetes in 2010, this could be due to a change in the incidence rate, a change in the duration of the disease, or changes in both.

MEASURES OF ASSOCIATION

Whereas the calculation of appropriate measures of disease frequency is the basis for the description and the comparison of populations, it is also efficient and informative to combine the two frequencies being compared into a single summary parameter that estimates the association between the exposure and the risk of developing the outcome. This can be accomplished by calculating either the ratio of the measures of disease frequency for the two populations, which indicates how much more likely on a relative scale one group is to develop a disease than another, or the difference between the two measures of disease frequency, which indicates on an absolute scale how much greater the frequency of disease is in one group compared with the other. These two measures of association are referred to broadly as relative risk and attributable risk.

    The relative risk (RR) estimates the magnitude of the association between the exposure and disease and represents the likelihood of developing the outcome in the exposed group relative to those who are not exposed. In a cohort study or randomized trial, this is defined as the ratio of the incidence in the exposed group (Ie) divided by the corresponding incidence of disease in the nonexposed (Io) group; the RR is a measure of the strength of the association between the exposure and the disease. If there is no association between the exposure and disease, that is, under the null hypothesis, the RR will equal 1. Values >1 indicate that those who are exposed have an increased risk of developing the outcome, and values less than one, a decreased risk.

    The attributable risk (AR) among the exposed provides information about the absolute effect of the exposure or the excess risk of disease in those exposed compared with those nonexposed. Again, in a cohort study or randomized trial, this measure is defined as the difference between the incidence rates in the exposed and nonexposed groups, calculated as Ie – Io. If there is no association between the exposure and the disease, that is, under the null hypothesis, the AR will equal 0. Assuming there is a causal relationship between the exposure and the disease and that the AR is >0, its value indicates the number of cases of the disease among the exposed that can be attributed to the exposure itself, or alternatively, the number of cases of the disease among the exposed that could be eliminated if the exposure were eliminated. As such, the AR is useful as a measure of the public health impact of a particular exposure.

    The AR can also be expressed as a percentage, calculated as AR% = AR/Ie × 100, in order to estimate the proportion of the disease among the exposed that is attributable to the exposure, or the proportion of the disease in that group that could be prevented by eliminating the exposure. In addition, for clinical purposes, the number needed to treat (NNT) to prevent one case of the outcome can be calculated, as the inverse of the absolute value of the AR, or NNT = 1/AR.

    The RR and AR provide very different but complementary types of information. The RR is a measure of the strength of the association between an exposure and disease and provides information that can be used to judge whether a valid observed association is likely to be causal. In contrast, the AR provides a measure of the public health impact of an exposure, assuming that the association is one of cause and effect.

Calculation of Measures of Association

Question 4:

A randomized trial was conducted of a new statin drug to assess its potential benefit on death from coronary heart disease. A total of 4000 patients were entered into the study, 2000 allocated to the active statin and 2000 to placebo. Of the 2000 assigned to the statin, 200 of these died from coronary heart disease in the 5-year median duration of follow-up; of the 2000 assigned to placebo, 300 died from coronary heart disease. What is the magnitude of the association between the statin and death from coronary heart disease? What is the potential public health impact of this drug? What is the number needed to treat to prevent one coronary heart disease death?

    Figure 95.2 presents the 2 × 2 table summarizing the randomized trial data from Question 4. The RR, calculated as the incidence of the outcome (dying from coronary heart disease) in the exposed (those assigned to statin) divided by the incidence in the nonexposed (those assigned to placebo), is 200/2000 divided by 300/2000 or 0.67. This means that those assigned to the statin had 67% of the risk, or 33% less risk (1 – 0.67), of dying from coronary heart disease during this period than those assigned to placebo. The AR, calculated as the incidence in the exposed minus the incidence in the nonexposed, is 200/2000–300/2000 or –0.05. This means that if statins are causally related to the prevention of coronary heart disease mortality, 5 per 100 of the coronary heart disease deaths in the placebo group could have been prevented by use of this statin. Taking the inverse of this AR, 1/0.05, provides the number needed to treat, or 20, indicating that we would need to treat 20 patients with this statin over 5 years (the median duration of follow-up) to prevent one death from coronary heart disease.

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