Chapter 6. Diagnostic Testing

• The sensitivity of a diagnostic test is the likelihood that persons with the disease of interest will have positive test results.
• The specificity of a diagnostic test is the likelihood that persons who do not have the disease of interest will have negative test results.
•  Positive predictive value measures the likelihood of having the disease of interest among those whose diagnostic test results are positive.
•  Negative predictive value is the likelihood of not having the disease of interest among those whose diagnostic test results are negative.
•  Likelihood ratios can be used to measure the extent to which the likelihood of the disease of interest is changed by the results of a diagnostic test.
• The area under a receiver operating characteristic (ROC) curve can be used to assess the performance of a diagnostic test.
• Screening for a particular disease is conducted in order to detect the disease at an earlier stage than would occur through routine methods.
• An error in the evaluation of a screening test, known as lead time bias, can occur when persons with disease detected by screening appear to live longer simply because of the earlier recognition of their illnesses.
• An error in the evaluation of a screening test, known as length-biased sampling, can occur when persons with disease detected by screening appear to live longer simply because they have more slowly progressing illnesses.

The results of the mammogram were not normal, and the radiologist suggested that a breast biopsy be performed. The family practitioner notified the patient of the abnormal mammogram and referred her to a surgeon, who concurred that physical examination of the breast was normal. Based on the mammographic abnormality, however, the surgeon and the radiologist agreed that fine-needle aspiration (FNA) of the abnormal breast under radiologic guidance was indicated. Evaluation of the FNA specimen by a pathologist revealed cancer cells, and the patient was scheduled for further surgery the following week.

The practice of clinical medicine is the artful application of science. A seemingly straightforward chain of decisions by the physicians in the Patient Profile ultimately led to the diagnosis of breast cancer and subsequent treatment. In practice, however, the process of clinical reasoning can be extremely complex. Each decision made by the clinicians in the Patient Profile included the possibility that information was incorrect. Sir William Osler eloquently described the difficulties of clinical decision making in 1921:

The problems of disease are more complicated and difficult than any others with which the trained mind has to grapple. . . Variability is the law of life. As no two faces are the same, so no two bodies are alike, and no two individuals react alike and behave alike under the abnormal conditions which we know as disease. This is the fundamental difficulty in the education of the physician, and one which he (or she) may never grasp. . Probability is the guide of life.

The clinical decision-making process is based on probability. For example, in the Patient Profile the clinician knew that a 54-year-old woman with a normal breast examination had a low probability of having breast cancer (~0.3%). An abnormal screening mammogram increased the likelihood of having breast cancer to perhaps 13%. The radiologist may have predicted a slightly lower or higher probability of breast cancer being present based on the particular mammographic findings. A positive FNA test increased the probability of having breast cancer to about 64%. Again, based on the characteristics of this patient’s FNA specimen, such as the appearance of the nucleus or the nuclear/cytoplasmic ratio, the estimate of the probability of breast cancer being present may be raised or lowered slightly. Furthermore, different pathologists may reach different conclusions when interpreting the same microscopic specimen: some pathologists may state that cancer cells are definitely present, whereas others may report that the specimen is suspicious for the presence of cancer.

Figure 6–1 is a diagrammatic representation of stages in the diagnostic process that ultimately led to a diagnosis of breast cancer in the woman in the Patient Profile. The likelihood of confirming the existence of a particular disease at any point in time is given on the horizontal axis. At the far left, the probability of the presence of disease is 0, and at the far right, the probability is 100%. Based on each new meaningful piece of information, the likelihood that a particular disease is present moves toward 0 or 100%. In the Patient Profile, the probability of breast cancer for the patient increased from near 0 to almost 67% during the diagnostic work-up. The purpose of a diagnostic test is to move the estimated probability of the presence of a disease toward either end of the probability scale, thereby providing information that will alter subsequent diagnostic or treatment plans. When the estimated probability of a disease being present is close to 0, the disease can be ruled out; when the estimated probability is close to 100%, the presence of disease is confirmed.

Although diagnostic procedures such as x-rays or biopsies are often considered laboratory tests, almost all approaches to gathering clinical information can be regarded as tests. A patient’s responses to questions during history taking or the presence or absence of physical findings influence the clinician’s estimation of the probability of a particular disease being present. In the Patient Profile, if the patient’s sister and mother had been previously diagnosed with breast cancer, the patient’s likelihood of having breast cancer prior to any tests could have been as high as 1%. If a palpable breast lump had been present on physical examination, the likelihood that the patient had cancer could have been estimated to be 20–40% prior to the mammogram. Experienced diagnosticians typically form hypotheses early in an encounter with a patient and then direct the history and physical examination in an effort to refine the estimated probabilities of a relatively small number of diseases.

Tests may be performed for many reasons. In the preceding discussion, attention was focused on determining the probability that a disease was present. Tests also may be used to assess the severity of an illness, predict disease outcome, or monitor response to therapy. Regardless of the purpose of a test, it is important to remember that the test is used to estimate the probability of an outcome.

In a perfect world, medical tests would always be correct. For example, women could undergo a diagnostic test that would unequivocally determine whether breast cancer was present and the test would have no side effects. A positive test result would indicate that cancer was present and a negative test result would indicate that cancer was absent. In reality, however, every test is fallible.

Consider a test that has only positive or negative results. After the test is performed, one of four possible scenarios will occur, as demonstrated in Figure 6–2. For the purposes of this discussion, “true” disease status is determined by the most definitive diagnostic method, referred to as a “gold standard.” For example, the gold standard for breast cancer diagnosis might be histopathologic confirmation of cancer in a surgical specimen. In cell a of Figure 6–2, the disease of interest is present and the test result is positive, a true-positive result. In cell d, the disease is absent and the test result is negative, a true-negative result. In both of these cells, the test result agrees with the actual status of the disease. Cell b represents individuals without the disease who have a positive test result. Since these test results incorrectly suggest that the disease is present, they are considered to be false-positives. Individuals in cell c have the disease but have negative test results. These results are designated false-negatives because they incorrectly suggest that the disease is absent.

Any diagnostic test can be evaluated in this manner. The first step in the evaluation of a test is determining the “true” status of the disease. For the FNA test, we could compare results obtained from FNA with results obtained if every woman subsequently underwent a surgical excisional biopsy procedure (ie, removal and histopathologic examination of the tissue in question). This procedure, the gold standard, is considered to represent the true status of the disease.

Just such a comparison of FNA results with excisional biopsy was made in 114 consecutive women with normal physical examinations and abnormal mammograms; patients received an FNA followed by a surgical excisional biopsy of the same breast (Bibbo et al, 1988). The results of the comparison are given in Figure 6–3.

Sensitivity and specificity are terms used to describe the validity of the FNA test relative to the surgical excisional biopsy.

Substituting data from Figure 6–3, the sensitivity of the FNA test is

The greater the sensitivity of a test, the more likely the test will detect persons with the disease of interest. For the FNA test, 93% of all the patients with breast cancer had positive test results. Tests with great sensitivity are useful clinically to rule out the presence of a disease. That is, a negative result would virtually exclude the possibility that the patient has the disease of interest.

Substituting data from Figure 6–3, the specificity of the FNA test is

The greater the specificity of a test, the more likely it is that persons without the disease of interest will be excluded from consideration of having the disease. Very specific tests often are used to confirm the presence of a disease. If the test is highly specific, a positive test result would strongly suggest the presence of the disease of interest.

Sensitivity and specificity are descriptors of the accuracy of a test. Two measures concerning the estimation of the probability of the presence or absence of disease are the positive predictive value (PV+) and the negative predictive value (PV–).

The PV+ is the percentage of persons with positive test results who have the disease. The calculation of the PV+ for the FNA test described in Figure 6–3 is

The average probability of breast cancer among women in this sample prior to the FNA test was 15 affected women out of 114 total women, or 13%. After the FNA test, the probability of breast cancer for a woman with a positive test result increased to 64%.

For the FNA test data in Figure 6–3, the PV– is

Before the FNA was performed, the average likelihood of not having breast cancer among women in this sample was 99 unaffected women out of 114 total women, or 87%. After a negative FNA result, the probability of not having breast cancer increased to 99%.

Now that the post-FNA probability of disease has been calculated for either a positive or negative test result, the usefulness of the FNA test for a patient with a nonpalpable breast lesion can be considered. A positive test result increased the probability of breast cancer from 13% to 64%. Whether the probability of breast cancer is 13% or 64%, further work-up is indicated. Both before and after a positive FNA result, the clinician would conclude that the likelihood of breast cancer was too great to forego a test such as a surgical biopsy, which would provide the most definitive diagnosis.

A negative test result, however, would reduce the probability that breast cancer is present to 1% (100% - PV– = 1%). The decision could be made to defer surgical biopsy and repeat mammographic and physical examinations in several months for women with abnormal mammograms but normal FNAs, accepting a 1 in 100 risk of mistakenly delaying treatment of an existing cancer. A more aggressive approach would be to perform a surgical biopsy on every woman with an abnormal mammogram. The basis of this decision would be that a probability of breast cancer of 1% is too high not to proceed with a surgical biopsy. The advantage of performing an FNA on patients with abnormal mammograms is that the vast majority of these women could be spared the increased morbidity and expense associated with a surgical biopsy.

In addition to recognizing that all tests are fallible, it is important to appreciate that the usefulness of a test changes as the clinical situation changes. Specifically, the pretest probability of the presence of disease in an individual, or the prevalence of disease in a population, greatly influences the predictive value. The concept of variable test performance can be illustrated by comparing the use of FNA in women with mammographically detected breast lesions but without palpable breast masses to the use of FNA in women with breast masses found on physical examination (Figure 6–4).

Note that the prevalence of breast cancer in these two groups, which is the same as the average pretest probability of the presence of disease, was higher among the women with palpable masses (38%) than among the women without palpable masses (13%). Although the FNA test had identical specificity and sensitivity in these two clinical situations, the PV+ of the test was 64% for women without palpable masses, but 88% for women with palpable masses. The PV+ rose with an increase in the pretest probability of disease. Therefore, it was easier to confirm the presence of breast cancer in a woman with increased baseline likelihood of disease.

The PV– was 99% when FNA was used for women without palpable masses, but decreased to 96% when used for women with palpable masses. The PV– decreased as the pretest probability of the presence of disease increased; it becomes easier to exclude a disease as the pretest prevalence of disease decreases. The differences in predictive value between these two populations result only from the difference in the pretest probability of the presence of disease.

Does the difference in predictive values described in Figure 6–4 have clinical implications? As discussed previously, among women with nonpalpable lesions, a negative FNA test result (PV– = 99%) could reduce the probability of the presence of disease to 1%, and therefore obviate the need for a surgical biopsy. In the group with palpable masses, after a negative FNA test result, the probability of breast cancer still would be 4%, which might warrant further testing, for example, a surgical biopsy. If neither a positive nor a negative test result would change subsequent management, the use of FNA among women with palpable lumps should be questioned.

In this chapter the use of FNA was analyzed as a method for detecting breast cancer, assuming that the test’s report would indicate either “cancer present” or “cancer absent.” The dichotomous classification of clinical findings as positive or negative is commonplace and useful. Examples of dichotomous results are a positive or negative history of pain in a breast, the presence or absence of a palpable breast mass on physical examination, and a normal or abnormal alkaline phosphatase level (a serum marker of bone or liver disease). In reality, however, test results often occur along a continuum. Breast pain, for example, can be negative, intermittent, or continuous. The size of a breast mass is usually measured in centimeters. A serum alkaline phosphatase level may range along a continuous scale. In general, the more extreme the value of a continuous test result, the greater the likelihood that the result reflects a laboratory error or an abnormality in the patient.

The results of the FNA test often are classified as follows:

• 1. Insufficient material to adequately assess presence or absence of malignant cells
• 2. Benign (no malignant cells present)
• 3. Suspicious (atypical cells present but not definitely malignant)
• 4. Malignant cells present.

Whether each of these four possible results is considered a positive or negative test result influences the assessment of test performance. In both the clinical series of patients with breast abnormalities presented above (see Figure 6–4), the patients with inadequate specimens were considered to have negative test results. Another important decision concerning FNA is whether to classify women with suspicious or atypical results as positive or negative. The ramifications of this decision were explored in an evaluation of the test among women with palpable breast masses. That evaluation of FNA, shown in Figure 6–5, employs two different assumptions: (1) suspicious FNA results were considered to be positive, and (2) suspicious FNA results were considered to be negative. Note that the sensitivity of FNA decreased and the specificity increased when women with suspicious FNA findings were considered to have negative test results.

This is an example of changing the cutoff point, which is the point at which a test result is considered to change from negative to positive. In Figure 6–5, in which suspicious FNA results were treated as positive, the cutoff point was considered to be between normal FNAs and suspicious FNAs. When suspicious FNA results were considered to be negative, a cutoff point between a suspicious FNA result and a malignant FNA result was chosen. Moving the cutoff point changes the test’s sensitivity, specificity, and positive and negative predictive values, and hence the way in which the test is used.

As illustrated in Figure 6–5, with a cutoff point set between the categories of benign and suspicious, a negative FNA result would reduce the probability of breast cancer, but with the resulting chance of breast cancer at 4%, a biopsy may still be warranted. A positive FNA result would increase the likelihood of cancer to 88%, but still would not absolutely confirm the diagnosis. Alternatively, by setting the cutoff point between the categories of suspicious and malignant (a more stringent requirement for a test result to be considered positive), the PV+ of the test becomes 100%. This could be useful clinically, because women with a positive FNA result would require no further diagnostic tests prior to definitive treatment (at a minimum, removal of the breast mass). Indeed, many clinicians believe that a positive FNA test result precludes the need for surgical excisional biopsy, thereby saving the patient an additional procedure and reducing the cost of treatment.

Another set of measures is useful in the interpretation of diagnostic tests. These measures are referred to as likelihood ratios (LR). An LR is the probability of a particular test result for a person with the disease of interest divided by the probability of that test result for a person without the disease of interest. For tests such as FNA, which can be classified into dichotomous results, LRs are defined for either positive or negative test results. The likelihood ratio for a positive test result (LR+) is the probability of a positive test result for a person with the disease of interest divided by the probability of a positive test result for a person without the disease. Mathematically, the LR+ is calculated as

in which sensitivity and specificity are expressed as proportions rather than as percentages. The smallest possible value of the LR+ occurs when the numerator is minimized (sensitivity = 0), producing an LR+ of zero. The maximum value of the LR+ occurs when the denominator is minimized (specificity = 1, so 1 - specificity = 0), resulting in an LR+ of positive infinity. An LR+ of one indicates a test with no value in sorting out persons with and without the disease of interest, since the probability of a positive test result is equally likely for affected and unaffected persons. Values of the LR+ greater than one correspond to situations in which persons affected with the disease of interest are more likely to have a positive test result than unaffected persons. The larger the value of the LR+, the stronger the association between having a positive test result and having the disease of interest.

The likelihood ratio for a negative test result (LR–) is the probability of a negative test result for a person with the disease of interest divided by the probability of a negative test result for a person without the disease. Mathematically, the LR– is calculated as

in which sensitivity and specificity again are expressed as proportions rather than as percentages. The smallest value of the LR– occurs when the numerator is minimized (sensitivity = 1, so 1 - sensitivity = 0), resulting in an LR– of zero. The largest value of the LR– occurs when the denominator is minimized (specificity = 0), resulting in an LR– of positive infinity. Just as with the LR+, an LR– with a value of one indicates a test with no value in sorting out persons with and without the disease of interest, as the probability of a negative test result is equally likely among persons affected and unaffected with the disease of interest. The smaller the value of the LR–, the stronger the association between having a negative test result and not having the disease of interest.

The calculation of LR+ and LR– can be illustrated by data on the FNA test as applied to women without palpable breast masses (see Figure 6–3). In this example, the LR+ is

and the LR– is

One of the desirable properties of the likelihood ratios is that they do not vary as a function of the prevalence of disease. This can be shown with the data presented in Figure 6–4. For women without palpable breast masses, the prevalence of disease is 13%. As just calculated, the LR+ is 11.63 and the LR– is 0.08. For women with palpable breast masses, the prevalence of disease is much greater—38%. The LR+, however, is still given by

and the LR– is still given by

Thus, in contrast to predictive values, the likelihood ratios do not vary according to the prevalence of disease.

As indicated above, the sizes of the two likelihood ratios indicate the strength of the linkage between a test result and the likelihood of disease. A diagnostic test with a large LR+ value increases the suspicion of disease for patients with positive test results. The larger the size of the LR+, the better the diagnostic value of the test. Although somewhat arbitrary, an LR+ value of 10 or greater is often perceived as an indication of a test of high diagnostic value. The FNA test with an LR+ of 11.63, therefore, satisfies this criterion.

Similar reasoning applies to the LR–, except in the opposite direction. A diagnostic test with a small LR– value decreases the suspicion of disease for patients with negative test results. The smaller the size of the LR–, the better the diagnostic value of the test. Again, on somewhat arbitrary grounds, an LR– value of 0.1 or less is often perceived as an indication of a test with high diagnostic value. The FNA test with an LR– of 0.08, therefore, satisfies this criterion as well.

Next, we convert the pretest probability of disease into pretest odds of disease. The pretest odds of disease are defined as the estimate before diagnostic testing of the probability that a patient has the disease of interest divided by the probability that the patient does not have the disease of interest. In the present example, the pretest odds are given by

Next the posttest odds of disease are calculated. The posttest odds of disease are defined as the estimate after diagnostic testing of the probability that a patient has the disease of interest divided by the probability that the patient does not have the disease of interest. The posttest odds of disease are calculated as the product of the pretest odds of disease and the LR+. Therefore in the present example the posttest odds are

Finally, the posttest probability of disease is calculated as

In other words, as a result of obtaining a positive test result, the estimated probability of the presence of disease has risen from 0.13 to 0.64, an almost fivefold increase in the estimated likelihood of disease.

As noted in the section on cutoff points, FNA is an example of a diagnostic test for which the results are classified in discrete categories of possible outcome. These include inadequate specimen for evaluation, benign, suspicious, and malignant. The cutoff point between positive and negative test results can be set to have either a restrictive definition of positive test results (malignant cells present) or a more inclusive definition of positive test results (either suspicious or malignant cells present). The change in cutoff point was shown to affect the sensitivity, specificity, and predictive values of the FNA test, and therefore the clinical value of the information obtained.

Other types of diagnostic tests, such as serum levels of enzymes, produce results along a continuous scale of measurement. In such a situation, there are many more options about where to set the cutoff point between a positive and a negative test result. Along the continuous scale of measurement, different cutoff points will result in differing levels of sensitivity or specificity. As a general rule, as the cutoff point rises, the sensitivity will increase, with a corresponding decrease in the specificity. A convenient summary of this relationship can be shown in a graph referred to as a receiver operating characteristic (ROC) curve. This curve derives its name from its first application—measuring the ability of radar operators to distinguish radar signals from noise. For the purposes of diagnostic testing, a graph is constructed with sensitivity (sometimes labeled as the true-positive rate) on the vertical axis, and 1 – specificity (sometimes labeled as the false-positive rate) on the horizontal axis. At each cutoff point, sensitivity and 1 – specificity will be calculated. These results then can be graphed along the full range of cutoff points, producing the ROC curve. A hypothetical example of an ROC curve is shown in Figure 6–6. In this graph, the performance of the diagnostic test is shown by the solid line. The dashed diagonal line represents a reference of a test with no diagnostic value. At every point along this dashed line, the sensitivity is equal to 1 – specificity. Note that when the sensitivity is equal to 1 – specificity, the numerator of the LR+ is equal to its denominator. That is to say, at every point along this dashed diagonal line the LR+ is equal to one, and a positive test result is equally likely for persons with and without the disease of interest. A diagnostic test that is clinically useful, therefore, will have an ROC curve that is far from this dashed diagonal line.

Another way of thinking about the ROC curve for a diagnostic test is to consider the vertical axis (sensitivity) the “signal” and the horizontal axis (1 – specificity) the “noise.” Toward the left-hand portion of Figure 6–6 there is a steep rise in sensitivity (signal), with a corresponding modest increase in 1 – specificity (noise). In other words, substantial gains can be made in sensitivity, with only modest reductions in specificity—a very favorable trade-off. However, toward the right-hand portion of Figure 6–6 the slope of the ROC curve is very flat, indicating relatively little improvement in signal for substantial increases in noise—a very unfavorable trade-off.

Given these extremes, obviously it is desirable for the area under an ROC curve to be closer to 1 than to 0.5. This principle also can be used to compare the relative values of two different diagnostic tests for a particular disease. This point is illustrated in Figure 6–7, in which the performance of two hypothetical diagnostic tests, A and B, are contrasted. The area under the ROC curve is greater for test A than for test B, indicating superior diagnostic value.

Breast cancer is a prototypical example of a progressive disease. As with most neoplasms, a breast cancer is believed to begin as a single malignant cell, which grows rapidly and forms a proliferating tumor. Over time, breast cancer cells can spread through the lymphatic system to the axillary lymph nodes and eventually to other parts of the body via the lymphatic system, the vascular system, or both. Detection of breast cancer earlier in the course of the disease decreases the likelihood that the cancer will spread to lymph nodes and other sites.

It has long been known that length of survival from time of diagnosis of breast cancer is related to the size of the tumor and the extent of spread to adjacent and remote sites. When mammography was first introduced, it was obvious that cancerous lesions in the breast—even those that could not be felt by even the most skilled clinician—could be detected with a mammogram. Researchers postulated that by screening asymptomatic women with mammography, breast cancer could be detected at an earlier stage, and therefore affected women as a group would experience increased survival. This logic seems infallible, but two important biases—lead-time bias and length-biased sampling—must be considered when evaluating any screening program.

To overcome lead-time bias and length-biased sampling, and therefore to assess the true benefit of a screening program, it is useful to measure disease-specific mortality rates within an entire population. Individuals who are randomly assigned either to a screening program or to no screening are followed to determine whether they die from the disease of interest. Such a study was performed in the 1960s by the Health Insurance Plan (HIP) of New York. In the HIP study, women were randomly assigned to receive routine care or to undergo a screening program comprised of yearly mammograms and breast examinations.

The results of that study on the usefulness of mammography as a screening tool appear in Figure 6–10. In the evaluation of any screening test, it is important to identify false-negative results. In the HIP study, in the screened group asymptomatic women with a positive result were referred for biopsy. At the time, there was no definitive or gold standard test such as FNA that could be performed on healthy women after a mammogram to determine whether cancers had been missed. An approximation of the number of false-negative screening tests (47 in this example) was derived by determining the number of cancers that arose between yearly screening examinations; these were designated “interval cancers.” If a symptomatic cancer occurred after a screening mammogram but prior to the next mammogram, it was presumed that the first mammogram was falsely negative.

In Figure 6–10, note that mammography had an excellent specificity (98%), yet the false-positive tests still outnumbered the true-positive tests by over 7 to 1 (PV+ = 12%). This means that among women with positive mammograms who were referred for surgical biopsy to obtain a definitive diagnosis, more than seven biopsies were negative for every one instance of breast cancer that was found. This high false-positive rate is related to the low prevalence of breast cancer at any single point in time in the general population. A low PV+ is fairly typical for a screening test designed to detect the presence of a disease that affects only a small proportion of persons in the source population at a given point in time. It is important, therefore, to consider the possible anxiety, expense, and morbidity associated with false-positive results when screening initiatives are introduced into the general population.

The purpose of the HIP study was to determine if repeated use of mammography could reduce breast cancer mortality. The use of a concurrent control group allowed investigators to assess the relationship between mammographic screening and mortality from breast cancer. A random assignment of women to either screening or routine care tended to balance the screened and unscreened groups with respect to factors that might affect subsequent breast cancer mortality (see discussion of randomization in Chapter 7: Clinical Trials). Evaluation of age-specific breast cancer mortality rates, rather than length of survival, diminished the possible distorting effect of lead-time bias. After the initial screening, slow-growing tumors presumably were removed from the screened women, and the effectiveness of subsequent annual mammograms in reducing breast cancer mortality was less likely to reflect length-biased sampling. The HIP researchers concluded that mammography reduced breast cancer mortality among the screened population by 30% when compared with the control group of women who were receiving routine care. The results of this landmark study, combined with findings from investigations of similar design in other countries, established the effectiveness of screening using mammography.

A list of criteria for a successful screening program is presented in Table 6–1. A screening program for breast cancer using mammography can be assessed with these criteria. Breast cancer is an important public health problem in the United States; at some time during her lifetime, one of every nine women will be diagnosed with breast cancer. Early detection allows less extensive surgical treatment and reduces morbidity and mortality from this disease. Since the incidence of breast cancer increases steadily with age, a high-risk population can be defined as any group of women 50 years of age or older. Although screening recommendations for women under age 50 remain controversial, it is widely recommended that women aged 50 or older have a mammogram once a year. Although the test does cause some discomfort, most women find the procedure acceptable. There is an extremely small risk of developing breast cancer associated with the radiation received during mammography. This risk is negligible, however, when compared with an average woman’s baseline risk of developing the disease. Finally, mammography is a relatively sensitive and specific test.

In this chapter, the principles of evaluating and interpreting diagnostic tests were introduced, using the diagnosis of breast cancer as an example. The process of reaching a diagnosis can be represented as a weighing of probabilities. When a particular diagnosis is excluded or ruled out, the probability that the disease is present is close to 0. When a particular diagnosis is confirmed, the probability that the disease is present is close to 100%. The challenge for the clinician is to collect information that will allow successive improvements in probability, until the presence of a disease is either confirmed or excluded.

All clinical information is subject to error. Accounting for the various errors that can arise in diagnostic testing allows the physician to select tests and interpret the results of those tests appropriately. One type of error is referred to as a false-negative result because the test fails to detect a disease when it is present. A test is said to be sensitive when the percentage of false-negative errors is low. A second type of error is referred to as a false-positive result because the test indicates that a disease is present when in fact it is not. A test with a low percentage of false-positive results is said to be specific.

Sensitivity and specificity are characteristics of a diagnostic test. It is useful to consider two other measures, positive predictive value (PV+) and negative predictive value (PV–), which are used to interpret the results of a diagnostic test. PV+ is the percentage of persons with a positive test result who actually have the disease of interest. PV– is the percentage of persons with a negative test result who do not have the disease of interest. Both positive and negative predictive values are heavily influenced by either the pretest probability that the patient has the disease of interest, or by the prevalence of the disease in the particular population that is tested.

In some situations, a test result has only one of two possible outcomes: positive or negative. In other circumstances, however, multiple levels of outcome or even a continuous range of values can occur. For multilevel or continuous outcome test results, a dividing line or cutoff point can be chosen to separate findings considered to be positive or negative. The choice of a cutoff value affects the sensitivity and specificity of a test, and consequently the positive and negative predictive values as well. Raising the threshold for considering a result to be positive typically will lead to a gain in specificity (fewer false-positive results) but a loss of sensitivity (more false-negative results or missed cases). On the other hand, lowering the threshold for considering a result to be positive typically will reduce the level of false-negative results (raise sensitivity) and increase the likelihood of false-positive results (lower specificity).

The performance of diagnostic tests also can be assessed by the use of likelihood ratios. The likelihood ratio for a positive test (LR+) is the probability of a positive test result for a person with the disease of interest divided by the probability of a positive test result for a person without the disease of interest. Values of the LR+ of 10 or greater are consistent with a test that provides considerable diagnostic value. The likelihood ratio for a negative test result (LR–) is the probability of a negative test result for a person with the disease of interest divided by the probability of a negative test result for a person without the disease of interest. Values of the LR– of 0.1 or smaller are consistent with a test that provides considerable diagnostic value. When combined with a pretest estimate of disease probability, the LR+ can be used to estimate the posttest probability of disease.

For diagnostic tests that produce results on a continuous scale of measurement, the performance of a test can be represented graphically by a receiver operating characteristic (ROC) curve. The area under the ROC curve serves as an overall measure of test performance, with an area of 1 indicating a perfect test and an area of 0.5 indicating a test that is unable to distinguish persons with and without the disease of interest. The respective areas under the ROC curves for two diagnostic tests for a particular disease can be used to identify the test that will provide the greater diagnostic value.

The use of tests to detect the presence of a disease at an earlier time than it would be detected through routine methods is referred to as screening. The evaluation of a screening test must take into account two types of distorting effects: lead-time bias and length-biased sampling. Lead-time bias can occur in a comparison of survival time. Screening detects cases in which the disease occurs earlier in the clinical course; therefore survival time may appear to be longer, even though the time of death is the same as if no screening had occurred. Lead-time bias may be minimized by evaluating mortality rates—rather than duration of survival—as the outcome. Length-biased sampling can occur when the screening test preferentially detects slowly progressive disease that is less likely to cause death or may result in a delayed death. Length-biased sampling can be reduced by repeated screening efforts, as slowly progressive forms of disease can be removed by the initial screening, and thus should not be overrepresented in later screenings.

A successful screening program will focus on a disease with appreciable health impact, for which early diagnosis and effective treatment can reduce the risk for significant morbidity and mortality. In addition, it is essential to define a high-risk population for whom (1) the test is acceptable and (2) the test can be administered with minimal risk. The false-negative, and particularly the false-positive, errors of the screening test should be relatively small, and the expense and morbidity of further evaluation of false-positive results must be acceptable. When evaluated using these criteria, screening using mammography is judged to be a very useful technique, at least for women over age 50.