Improving Reporting of Follow-Up Data

AMERICAN JOURNAL OF OPHTHALMOLOGY® FKANK W . N E W E L L ,

Publisher and

Editor-in-Chief

Tribune Tower, Suite 1415, 435 North Michigan Ave., Chicago, Illinois 60611 EDITORIAL BOARD

Thomas M. Aaberg, Milwaukee Mathea R. Allansmith, Boston Douglas R. Anderson, Miami Charles J. Campbell, New York Ronald E. Carr, New York Claes H. Dohlman, Boston Fred Ederer, Bethesda Eugene Helveston, Indianapolis Frederick A. Jakobiec, New York

Herbert E. Kaufman, New Orleans Steven G. Kramer, San Francisco Carl Kupfer, Bethesda Irving H. Leopold, Irvine Robert Machemer, Durham A. Edward Maumenee, Baltimore Irene H. Maumenee, Baltimore Edward W. D. Norton, Miami G. Richard O'Connor, San Francisco Arnall Pätz, Baltimore

Deborah Pavan-Langston, Boston Steven M. Podos, New York Stephen J. Ryan, Los Angeles David Shoch, Chicago Bruce E. Spivey, San Francisco Bradley R. Straatsma, Los Angeles H. Stanley Thompson, Iowa City Gunter K. von Noorden, Houston George O. Waring, Atlanta

Published monthly by the Ophthalmic Publishing Company Tribune Tower, Suite 1415, 435 North Michigan Avenue, Chicago, Illinois 60611 A . EDWARD MAUMENEE, President; DAVID SHOCH, Vice President; FRANK W. NEWELL, Secretary and Treasurer; EDWARD W. D . NORTON, BRUCE E . SPIVEY, BRADLEY R. STRAATSMA

Directors:

IMPROVING REPORTING O F FOLLOW-UP DATA In reading the results of a carefully performed clinical study, one frequently encounters a summary statement such as the following: "One hundred ten patients with disease x were observed for one to three years (mean follow-up, 24.0 months). Twenty-five of the 110 patients (22.7%) became blind during the followup period." Unfortunately, statements like this are not as informative as they sound and often better use of the data could have been made. Indeed, the type of summary illustrated above may even be misleading, especially if interpolations (such as approximating the blindness incidence rate as 11% per year) and comparisons are made using the results as stated. To illustrate the problem with condensing follow-up information in the above Reprint requests to Argye Hillis, Ph.D., Department of Ophthalmology, Wilmer Institute, Johns Hopkins University School of Medicine, Baltimore, MD 21205.

fashion, consider an investigator who looks at his results on the hypothetical disease mentioned in the first paragraph. He, too, has 110 patients, with follow-up ranging from one to three years and an average follow-up of 24.0 months. He finds that 52 (47.2%) of his 110 patients become blind. Understandably he concludes that he has found a higher rate than that previously reported. Unfortunately, both the original 22.7% and his 47.2% may be nonsense. I f the proper analysis were employed the two investigators might report identical blindness rates. Suppose that both experiments are perfect, that we can be omniscient for a moment and know the "true" risk of blindness for x disease. To simplify the illustration further, assume each patient comes in on the exact anniversary of diagnosis. Let the risk of blindness be zero, 20%, and 100% for years one, two, and three respectively. The first investigator observed five patients who were seen only at the end of the first year, 100 with two years of 250

EDITORIAL

VOL. 93, NO. 2 follow-up, and five who were followed up for three years. None of the group observed for only one year went blind. Of the next 100 patients 20 went blind. In the group observed for three years, one patient went blind in the second year and the other four in the third year. The investigator therefore observed that 25 of his 110 patients became blind during follow-up for a "rate" of 24.6%. His arithmetic is correct and the reported average follow-up (24 months) was also correctly computed. The second investigator's arithmetic is also correct, but 50 of his patients have one year of follow-up, ten have two, and 50 were observed for three years. None of his first 50 patients are blind; 20% (two) of the two-year cohort and all of the last 50 patients are blind, yielding a rate of 52 of 110 or 47.2% blindness. Superficially, it appears that the second group of patients is going blind more rapidly, but if the two sets of data were analyzed correctly using a failure time ("life table") analysis the results are identical. Both sets of data then give the correct cumulative rates of blindness: zero, 20%, and 100% for years one, two, and three respectively. Although life tables occasionally appear in the published ophthalmologic reports and they are the standard method for 1

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anlayzing follow-up information, ophthalmologists tend to overlook the advantages of this method of analysis. Life tables are easy to compute and interpret. They are simply a mathematical representation of an intuitively logical approach. Furthermore, they provide a way to compare the results of different investigations with variable follow-up periods. A second and slightly more complicated example illustrates the method. Suppose the data are as shown in the Table. The probability that a patient who can see at the beginning of a specified interval will "survive" the interval (that is, pass through without going blind) is shown in the next to the last column. The proportion of patients who can see at the end of the interval is shown in the last column. The probability that a patient who enters the study able to see will still see at the end of the nth year is equal to the chance he "survives" the first year and the second year and the third year and so forth up through the nth year. The cumulative survival rate for the nth year is easily shown to be the product of the interval survival rates for years one through n, as shown in the Table. The cumulative survival for time zero (start of the study) is not shown on the Table, but always equals one. One advantage of life table analysis is

TABLE L I F E TABLE COMPUTATION (HYPOTHETICAL EXAMPLE)

n

a

b

c

d

e

f

Year (Interval)

No. of Patients at Risk (Able to See) at Start of Interval

No. of Patients Becoming Blind During Interval

No. of Patients Without Follow-up After Interval ("Withdrawals")

Blindness Rate for Interval

Interval Survival

Cumulative Survival to End of Interval

1 2 3 4 5

20 19 15 10 9

1 4 3 0 2

0 0 2 1 0

(b/a) 0.05 0.21 0.20 0.00 0.22

(1-d) 0.95 0.79 0.80 1.00 0.78

(e x £,.,) 0.95 0.75 0.60 0.60 0.47

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that the method utilizes the full information on patients followed up for various lengths of time. Patients who entered the study too late to be observed for the full time of the analysis may be included simply by considering them at risk for as long as they were observed, provided that certain assumptions can be made. One requirement is that there must be good reason to believe that in the future the blindness rate for these patients will be the same as the rate observed for patients with longer follow-up. Such patients are usually called "withdrawals" in life table terminology because they are withdrawn from the computations for certain time intervals. Clearly they are not withdrawn from the study, however. In the example of the Table, two patients had only three years of follow-up and one patient completed only four years. True dropouts are a different problem from the group of "withdrawals" described above and may lead to serious bias. Patients who refuse to be examined and patients who for unknown reasons fail to return must be presumed to have blindness rates after dropout that are different from the non-dropouts. Such patients may have failed to return because they have gone blind or, conversely, they may be doing so well that they do not find it necessary to see the ophthalmologist. If the two withdrawals in year 3 of the example were actually patients lost to follow-up before the date of analysis, all that would be known about the number of patients going blind in the interval would be that it was somewhere between three (as shown) and five. Since no method (including life tables) can adjust for the bias inherent in failure to obtain complete follow-up, every effort must be made to keep each patient under observation for the full duration of the study and to determine the outcome for any patient who fails or refuses to return. Life tables are usually presented in the

FEBRUARY, 1982

MONTHS OF FOLLOW - UP

Figure. Cumulative event rates of visual acuity less than 6/240 (5/200) at two or more visits for all patients. (From DRS Research Group. ) 1

form of a graph. Either the cumulative proportion with an "event" or the proportion "surviving" without an event may be illustrated. The Figure is a life table that appeared in T H E JOURNAL several years ago. It shows the development of low vision at four-month intervals in patients with diabetic retinopathy. With a little practice, ophthalmologists can become familiar with the life table approach. The above explanation is intended only as a general introduction to the ideas and more complete expositions written especially for physicians are available. Almost any biostatistician should be able to assist with the required computations and simple methods are available for computing confidence intervals for the rates and for comparing two or more curves. The method is widely accepted in other medical fields and should become standard practice in ophthalmology. 1

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ARG YE HILLIS

Baltimore, Maryland REFERENCES 1. Diabetic Retinopathy Study Research Group: Preliminary report in effects of photocoagulation therapy. Am. J. Ophthalmol. 81:383, 1976. 2. Armitage, P.: Statistical Methods in Medical Research. Survivorship tables. New York, John Wiley and Sons, 1971, chap. 14. 3. Peto, R., Pike, M. C , Breslow, N. E . , Cox, D. R., Howard, S. V., Mantel, N., McPherson, K., Peto, J . , and Smith, P. G.: Design and analysis of

CORRESPONDENCE

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randomized clinical trials requiring prolonged observation of each patient. II. Analysis and examples. Br. J. Cancer 35:1, 1977. 4. Cutler, S. J . , and Ederer, F.: Maximum utilization of the life table method in analyzing survival. J. Chronic Dis. 8:699, 1958.

CORRESPONDENCE Letters to the Editor must be typed double-spaced on 8V2 x 11-inch bond paper, with lVî-inch margins on all four sides, and limited in length to two manuscript pages. Ophthalmic Drugs With Similar Packaging Editor: In light of the current interest in the hazards of similarly packaged ophthalmic drugs, that is, the accidental dispensing or use of the wrong medication, " 1 would like to point out the similar packaging of two sets of ocular medications. The first ones (Fig. 1) are the "federal supply system" versions of 1% atropine sulfate and 1% tropicamide eyedrops manufactured by Alcon. The containers have the same size and shape, as well as red tops and labels with very similar inscriptions in small type. Even the federal stock numbers are somewhat similar. Tropicamide is a short-acting mydriatic (one to four hours) whereas the effect of atropine can last many days. Moreover, atropine has a more serious potential for systemic toxicity, including dryness of the mouth, fever, urinary retention, and even convulsions. I have recently been informed of an incident in a military hospital where "dilating drops" were administered by paramedical staff who confused these two drugs. For approximately five days, several patients received atropine instead of tropicamide. Undoubtedly, many patients suffered prolonged and unwarranted mydriasis and cycloplegia. To the best of my knowledge, no systemic side effects occurred. 1

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Fig. 1 (Katz and Foer). Atropine sulfate and tropicamide ophthalmic solutions.

The other source of possible confusion is the similar packaging of bacitracin and atropine sulfate ocular ointments (Fig. 2), manufactured by Lilly. The containers have similar inscriptions except that the words "Atropine Sulfate 1 percent" appears in red and "Bacitracin" appears in black. This too is a potential source of confusion and accidental atropine poisoning. Ideally, these drugs should be packaged in a more easily distinguishable manner; in the meantime ophthalmologists and their staffs must be alert to the possibility of this hazardous mixup. NORMAN N. K. KATZ, M.D. E L L E N G. FOER

Washington, D.C., and Bethesda, Maryland

Fig. 2 (Katz and Foer). Bacitracin and atropine sulfate ointments.