Fig. 1. Receiver operator characteristic (ROC) curve for threshold difference. The false-positive rate is plotted against the true-positive rate for the difference in threshold between a subject's two ears. as derived from the pure-tone audiogram. Curves for the single frequencies 250 Hz to 8 kHz range from the worst case. 250 Hz, to the best case. 2 kHz. Curves for the other frequencies lay between these two curves and were omitted for clarity. The third curve in the Figure. an average of the best four frequencies-1 to 8 kHz. was more effective than any single frequency.

 The data were stored in a data base manager (Foxbase Plus, Fox Software, Inc., Perrysburg, Ohio) and analyzed by statistical software (yMed, Ming Telecomputing Inc., Lincoln Center, Mass. and Epistat, Tracy L Gustafson, MD, Round Rock, Texas), all of which were run on a microcomputer (Compaq Deskpro, Compaq Computer Corporation, Houston, Texas).

Results

 Figure 1 shows the results in the form of receiver-operator-characteristic (ROC) curves (ROC curves are reviewed in reference 4). The true-positive rate is the percentage of patients in the tumor group who are correctly identified by a given cut off criterion. The false-positive rate is the percentage of patients who are falsely identified as having an acoustic tumor by a given cutoff criterion. The greater the distance the ROC curve is from a diagonal line beginning at the origin and extending to the right at a 45 degree angle, the more efficient the test at distinguishing between the two groups.

Figure 1 shows the results for the hearing difference at 250 Hz, the least effective frequency for distinguishing between groups, and 2000 Hz, the most effective frequency. Using the operating position of a false-positive rate of 0.10, the true-positive rate for 2000 Hz was 0.75, compared with a true-positive rate for 250 Hz of 0.58 (chi-square = 14.57, df = 1, p = 1.35E-4). The rank order in efficiency was as follows: 1, 2000 Hz; 2, 4000 Hz; 3, 1000 Hz; 4, 8000 Hz; 5, 500 Hz, and 6, 250 Hz.

Averaging multiple frequencies was more effective than using a single frequency. We used an average of the four most effective frequencies, 1000 to 8000 Hz, which is the curve to the upper left of the Figure. Using the operating position of a false-positive rate of 0.10, the true-positive rate for the four-frequency average was 0.82 compared with a true-positive rate for 2.0 kHz of 0.75 (chi-square = 2.40, df = 1, p = 0.122), and compared with a true-positive rate for 250 Hz of 0.58 (chi-square = 29.23, df = 1, p = < 1.0E-7).

 Table 1. Additional tumors found and incremental costs of screening 100 patients for acoustic tumor using the average threshold difference at 1000, 2000, 4000, and 8000 Hz 0.75 (chi-square = 2.40, df = 1, p = 0.122), and compared with a true-positive rate for 250 Hz of 0.58 (chi-square = 29.23, df = 1, p = < 1.0E-7).

Strategy	Tumors detected	Cost of ABRs and MRIs per tumor detected (1)	Incremental cost per incremental tumor detected (1)
20 dB ABR	69.9%	$3,916.59
15 dB ABR	75.0%	$6,053.47	$41,581.59
10 dB ABR	80.1%	$8,323.18	$44,089.10
5 dB ABR	84.4%	$14,589.82	$146,280.30
20 dB MRI, 5-20 dB ABR	92.4%	$18,365.60	$47,368.86
5 dB MRI	93.8%	$40,836.14	$2,896,179.92

Choosing a Cut-off Criterion

How do we decide what cut-off criterion to use for determining if we should order additional diagnostic tests to rule out acoustic tumor? The knee point, which is 10 dB for the average of 1000 to 8000 Hz in Fig. 1, is the best balance between the true-positive and false-positive rate.5 Using the knee point assumes that the cost of a false-negative is the same as the cost of a false-positive, an assumption we will not make, because clinicians value avoiding a false-negative much higher than the value of avoiding a false-positive. To consider the effect of using a cutoff with a higher false-positive rate in order to get a higher true-positive rate, we examined the incremental costs for different cut-off criteria.

Table 1 shows the incremental cost of screening 100 patients for acoustic tumor, assuming the prevalence of tumor is 0.01. The first column shows six different strategies; the first four strategies are different cutoff criteria for average difference in hearing for frequencies 1.0, 2.0, 4.0, and 8.0 kHz. If the patient has an average threshold difference between ears that is equal to or exceeds the criterion, then the patient has an ABR. If the ABR is positive, the patient has an MRI. The fifth strategy, labeled 20 dB MRI, 5 to 20 dB ABR, means that patients with a difference of 20 dB or greater have an MRI, and patients with a difference of 5 to 20 dB have an ABR. Again, patients with positive ABRs have a MRI. The sixth strategy, labeled 5 dB MRI, means that patients with a difference of 5 dB or greater have an MRI. This sixth strategy is the benchmark for the maximum number of tumors one can expect to detect using audiograms alone as a screening tool.

Column two of the Table shows the percentage of tumors that were detected by the respective strategy. Column three shows the cost per tumor detected, which was obtained by dividing the total cost of the strategy by the number of tumors detected per 100 patients. Column four shows the incremental cost per incremental tumor detected, which was obtained by dividing the difference in cost per tumor found between two strategies by the difference in tumors detected. This is a measure of the cost of how much more are we spending per additional tumor detected if we chose a strategy that will detect more tumors (for a discussion of incremental cost, see reference 4).

We need to address the question, what is the upper limit of incremental cost that we will accept? Many clinicians have already established a cost per tumor detected by ordering magnetic resonance scans to evaluated patients with sudden sensorineural hearing loss syndrome for acoustic tumor. The probability that one of these patients has an acoustic tumor is about 0.01.6 The cost of working up one patient is on the order of $1300 ($40 to $200 for a clinician's evaluation, $45 to $75 for an audiogram, and $900 to $1200 for a MRI). It would cost about $130,000 to order 100 MRIs in order to detect the one patient with an acoustic tumor. One many consider using $130,000 as an upper limit of incremental cost. This is in line with the ratio between the cost of a false-negative and a false-positive for detecting colon cancer (reviewed in reference 3).

The first strategy of using a criterion of 20 dB involves spending about $3900 for ABRs and MRIs for every tumor detected. The second strategy of a criterion of 15 dB has an incremental cost for detecting 5.1% more tumors of about $41,600. We accept using the 15 dB criterion, since the incremental cost is less than our limit. The third strategy of a cutoff criterion of 10 dB has an incremental cost for finding another 5.1% more tumors of about $44,000, which is less than our incremental cost limit. We accept the 10 dB criterion as being more effective than a 15 dB criterion. The fourth strategy of a cutoff criterion of 5 dB has an incremental cost for finding 4.3% more tumors of about $146,300, which exceeds our upper limit for incremental cost. We reject the 5 dB criterion as not being effective. By similar reasoning we also reject strategy six as not being effective, since the incremental cost of almost $2,900,000 dwarfs our upper limit by twentyfold. Having rejected strategy four, we compared strategy five to strategy three to get the incremental cost of strategy five. With this comparison we get an incremental cost of $81,645.69, which is less than our upper limit for incremental cost. We conclude that strategy five best achieves our goals of finding as many acoustic tumors as possible without exceeding our arbitrary guidelines for incremental cost.

Sensitivity Analysis

We did a sensitivity analysis to see over what range of ABR charges our decision to use a 20 dB criterion for MRI combined with a 5 to 20 dB criterion for ABR would remain valid. To summarize, our decision would remain valid over a wide range of ABR and MRI charges and over a wide range of values for ABR sensitivity and specificity. One exception that we may consider using is the fourth strategy, a 5 dB criterion followed up by ABR if ABR sensitivity-0.97, a sensitivity thought reasonable in early reports.' We chose to use a more modest sensitivity of 0.90 in our example, because this is consistent with our clinical experience. The other exception was that we should refer all patients for MRI if the probability of tumor >0.10, which would be based on information from the patient's clinical history.

Table I points out that we should consider a sensitivity of 1.00 as unachievable in the diagnosis of acoustic tumors. Most acoustic tumor surgeons have had patients referred to them with asymptomatic tumors and who had undergone scans for reasons unrelated to their tumor. The maximum percentage of tumors that we can diagnose using audiograms is 94%. Clinicians must accept the concept that a diagnosis of acoustic tumor will be missed from time to time. The goal of following the fifth strategy, stated earlier, is primarily to diagnose as many tumors as possible and only secondarily to avoid wasting money. The clinician can improve on the sensitivity of audiogram screening by using information in the history and physical examination such as unilateral tinnitus, and distortion of words while using the telephone to refer patients for further tests. Strategy five should be used when the earlier probability of acoustic tumor is 0.01, such as in sudden sensorineural hearing loss syndrome, and probably in cases of stable unilateral hearing loss and unilateral tinnitus. MRIs should be used to evaluate patients with a previous probability greater than about 0.10, such as those with a family history of neurofibromatosis 2 (probability of tumor, 0.5), and in cases of progressive hearing loss over a period of months or years.

 In the absence of a clinical history that includes the auditory and vestibular system, clinicians should consider using a hearing asymmetry criterion for recommending further tests to evaluate the risk of acoustic tumor. We recommend a criterion for referral for MRI of an average difference of-20 dB at 1.0, 2.0, 4.0, and 8.0 kHz and a criterion for referral for ABR of a difference of 5 to 20 dB. Patients should be referred for MRI if the clinical history indicates a risk of acoustic tumor that is greater than 10%.

I wish to thank Ms. Theresa A. Skalabrin, MA, for her considerable assistance.

 1. Welling DB, Glasscock ME, Woods CI, Jackson CG. Acoustic neuroma: a cost-effective approach. OTOLARYNGOL HEAD NECK SURG 1990;103:36470.

2. Mangham CA. Decision analysis of auditory brainstem responses and rotational vestibular tests in acoustic tumor diagnosis. OTOLARYNGOL HEAD NECK SURG 1987;96:229.

3. Mangham CA. Progressive sensorineural hearing loss in adults. In: Meyers AD, Eiseman B, eds. Cost-effective otolaryngology, Philadelphia: BC Decker Inc, 1990:5975.

4. Weinstein MC, Fineberg HV. Clinical decision analysis. Philadelphia: WB Saunders, 1980:114261.

5. Connell FA, Koepsell TD. Measures of gain in certainty from a diagnostic test. Am J Epidemiol 1985;121:74453.

6. Shaia FT, Sheehy JL. Sudden sensorineural hearing impairment: a report of 1220 cases. Laryngoscope 1976;86:38998.

7. Selters WA, Brackmann DE. Acoustic tumor detection with brain stem electric response audiometry. Arch Otolaryngol 1977; 103:1817.

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