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Increased Incidence of Choroidal Malignant Melanoma and the Use of Inappropriate Statistical Methods: Reply
VOL. 90, NO. 2
CORRESPONDENCE
authors' finding of a single plant in the United States with this number of cases when the single trial expectation is as stated is not surprising. The statistical way out of this difficulty of covert multiple testing is to take the complete set of cases for a large population, and test the randomness of their distribution by standard methods. This has been done for endemic disease, for example leukemia, but can clearly miss small point sources that provide only a small proportion of the total cases. Nevertheless it is mandatory to deal with the effect of multiple trials, whether overt or covert, in statistical analyses where the positive findings have been arrived at by other means than a systematic survey. The alternative is to seek for more data. A continuation of the occurrence of cases in the plant would clinch the matter, as would discovery of similar groups of cases in comparable plants. Without confirmatory data, or the conduct of appropriate statistical tests, the proposition that the current findings are of statistical significance is an error. JOHN A. H. LEE, M.D. Seattle, Washington Reply Editor: Dr. Lee makes the point that out of all the industrial plants in the United States, it is likely that at least one of them might fortuitously have had five cases of choroidal malignant melanoma and that our study may have been but a description of such a fortuitously occurring cluster, identified not as a result of a systematic survey whose hypotheses had been formulated a priori, but rather as a result of multiple overt and covert examinations of different data bases by different investigators. The implication would be that we have studied, after its discovery, the
273
cluster of choroidal malignant melanoma cases that could have been expected to have occurred by chance alone. Dr. Lee additionally notes that the alternative to dealing with the effect of these multiple overt and covert data examinations, on the calculation of the probability fraction upon which is based the inference that a statistically significant excess number of choroidal malignant melanomas has occurred, is " to seek more data. A continuation of the occurrence of cases in the plant would clinch the matter ... " Although our account of the chronology of events that led to our data collection may not have made it sufficiently clear, this is precisely what we have observed and what we have attempted to describe. Our efforts began with the identification in late 1976 of two cases of choroidal malignant melanoma from a list of purported ocular tumors occurring at the plant. We submitted to the National Institute for Occupational Safety and Health a contract proposal, dated January 27, 1977 (quoted from our proposal), to undertake "a screening examination of the Belle chemical workers" to address the question, "Is there an increased incidence of malignant melanomas of the choroid, ciliary body or iris in this population?" About this same time, we reported the two cases in a letter to the editor of the New England Journal of Medicine, the implicit statement being that we would hope that additional cases of choroidal malignant melanoma discovered at other chemical plants might be reported if the medical community were made aware of our observations. This resulted in a letter, dated April 7, 1977, from physicians with the National Institutes of Health reporting to us Case 3. Later in 1977, review of company medical records uncovered Case 4. Case 5 was discovered in April 1978 during our ophthalmologic survey. We believe that these last three cases, discovered after our initiation of
274
AMERICAN JOURNAL OF OPHTHALMOLOGY
plans to study this plant further, are in the nature of "a continuation of occurrence of cases" suggested by Dr. Lee to "clinch the matter." We noted in our article our reasons for believing our observed and calculated expected number of choroidal malignant melanoma cases to be conservative estimates of the actual occurrence of choroidal malignant melanomas and its expectation in the plant population. Although there is no statistical way to settle the point to everyone's satisfaction, we believe that the true level of probability is closer to our stated level than Dr. Lee's letter would suggest. We agree with Dr. Lee that the discovery of similar cases in comparable plants would add greatly to support the conclusions we have drawn from our data. DANIEL M. ALBERT, M.D.
Boston, Massachusetts ALEXANDER BLAIR SMITH, M.D. AND SANFORD
S. LEFFINGWELL, M. D.
AUGUST, 1980
and engaging style, the author tells of the adjustment problems that plagued him after the accident. The book provides numerous helpful hints and suggestions of how to cope with the loss of stereopsis and restriction of the field of vision. The teaching of how to use clues of monocular depth perception reflects the aviation and engineering background of the writer. There are also useful chapters on driving, driver and pilot licensing standards in different states, and how to take care of a prosthesis, the socket, and the remaining good eye. This warm, personal, and often humorous essay by someone who has mastered a difficult situation and resumed an active life in which flying plays a major part is recommended to all patients who have recently lost one eye. Ophthalmologists who read this book will be in a better position to advise their patients on how to cope with a bewildering and initially frightening handicap. GUNTER K. VON NOORDEN
Cincinnati, Ohio
BOOK
REVIEWS
A Singular View, revised. By Frank B. Brady. Oradell, New Jersey, Medical Economics, Co., 1979. Hardcover, 129 pages, foreword, publisher's notes, 22 black and white figures. $15.50 Most of us enjoy sight with both eyes and give little thought to the complexities of everyday activities encountered by those who have to make a sudden transition to monocular vision. This manual for the newly one-eyed was written by an aviation engineer who had lost one eye during a bizarre accident caused by a duck crashing through the windshield of a plane in which he was co-pilot. In a breezy
Congenital and Acquired Color Vision Defects. By Joel Pokorny, Vivianne G. Smith, Guy Verriest, and A. J. L. G. Pinckers. New York, Grune and Stratton, 1979. Hardcover, 409 pages, preface, references, index, 129 black and white figures. $33.50 Forewords to scholarly works, as a rule, are laudatory. The foreword to this work, by Professor W. D. Wright, is no exception. In this case, however, the foreword could have doubled as an unbiased review. This book is destined to serve as a key reference in its area and, to a lesser extent, as a text as well. It is a splendid addition to the published clinical and visual science material. The first two chapters summarize radiometric and photometric measures; the third reviews "physiological and theoretical bases of
CORRESPONDENCE
authors' finding of a single plant in the United States with this number of cases when the single trial expectation is as stated is not surprising. The statistical way out of this difficulty of covert multiple testing is to take the complete set of cases for a large population, and test the randomness of their distribution by standard methods. This has been done for endemic disease, for example leukemia, but can clearly miss small point sources that provide only a small proportion of the total cases. Nevertheless it is mandatory to deal with the effect of multiple trials, whether overt or covert, in statistical analyses where the positive findings have been arrived at by other means than a systematic survey. The alternative is to seek for more data. A continuation of the occurrence of cases in the plant would clinch the matter, as would discovery of similar groups of cases in comparable plants. Without confirmatory data, or the conduct of appropriate statistical tests, the proposition that the current findings are of statistical significance is an error. JOHN A. H. LEE, M.D. Seattle, Washington Reply Editor: Dr. Lee makes the point that out of all the industrial plants in the United States, it is likely that at least one of them might fortuitously have had five cases of choroidal malignant melanoma and that our study may have been but a description of such a fortuitously occurring cluster, identified not as a result of a systematic survey whose hypotheses had been formulated a priori, but rather as a result of multiple overt and covert examinations of different data bases by different investigators. The implication would be that we have studied, after its discovery, the
273
cluster of choroidal malignant melanoma cases that could have been expected to have occurred by chance alone. Dr. Lee additionally notes that the alternative to dealing with the effect of these multiple overt and covert data examinations, on the calculation of the probability fraction upon which is based the inference that a statistically significant excess number of choroidal malignant melanomas has occurred, is " to seek more data. A continuation of the occurrence of cases in the plant would clinch the matter ... " Although our account of the chronology of events that led to our data collection may not have made it sufficiently clear, this is precisely what we have observed and what we have attempted to describe. Our efforts began with the identification in late 1976 of two cases of choroidal malignant melanoma from a list of purported ocular tumors occurring at the plant. We submitted to the National Institute for Occupational Safety and Health a contract proposal, dated January 27, 1977 (quoted from our proposal), to undertake "a screening examination of the Belle chemical workers" to address the question, "Is there an increased incidence of malignant melanomas of the choroid, ciliary body or iris in this population?" About this same time, we reported the two cases in a letter to the editor of the New England Journal of Medicine, the implicit statement being that we would hope that additional cases of choroidal malignant melanoma discovered at other chemical plants might be reported if the medical community were made aware of our observations. This resulted in a letter, dated April 7, 1977, from physicians with the National Institutes of Health reporting to us Case 3. Later in 1977, review of company medical records uncovered Case 4. Case 5 was discovered in April 1978 during our ophthalmologic survey. We believe that these last three cases, discovered after our initiation of
274
AMERICAN JOURNAL OF OPHTHALMOLOGY
plans to study this plant further, are in the nature of "a continuation of occurrence of cases" suggested by Dr. Lee to "clinch the matter." We noted in our article our reasons for believing our observed and calculated expected number of choroidal malignant melanoma cases to be conservative estimates of the actual occurrence of choroidal malignant melanomas and its expectation in the plant population. Although there is no statistical way to settle the point to everyone's satisfaction, we believe that the true level of probability is closer to our stated level than Dr. Lee's letter would suggest. We agree with Dr. Lee that the discovery of similar cases in comparable plants would add greatly to support the conclusions we have drawn from our data. DANIEL M. ALBERT, M.D.
Boston, Massachusetts ALEXANDER BLAIR SMITH, M.D. AND SANFORD
S. LEFFINGWELL, M. D.
AUGUST, 1980
and engaging style, the author tells of the adjustment problems that plagued him after the accident. The book provides numerous helpful hints and suggestions of how to cope with the loss of stereopsis and restriction of the field of vision. The teaching of how to use clues of monocular depth perception reflects the aviation and engineering background of the writer. There are also useful chapters on driving, driver and pilot licensing standards in different states, and how to take care of a prosthesis, the socket, and the remaining good eye. This warm, personal, and often humorous essay by someone who has mastered a difficult situation and resumed an active life in which flying plays a major part is recommended to all patients who have recently lost one eye. Ophthalmologists who read this book will be in a better position to advise their patients on how to cope with a bewildering and initially frightening handicap. GUNTER K. VON NOORDEN
Cincinnati, Ohio
BOOK
REVIEWS
A Singular View, revised. By Frank B. Brady. Oradell, New Jersey, Medical Economics, Co., 1979. Hardcover, 129 pages, foreword, publisher's notes, 22 black and white figures. $15.50 Most of us enjoy sight with both eyes and give little thought to the complexities of everyday activities encountered by those who have to make a sudden transition to monocular vision. This manual for the newly one-eyed was written by an aviation engineer who had lost one eye during a bizarre accident caused by a duck crashing through the windshield of a plane in which he was co-pilot. In a breezy
Congenital and Acquired Color Vision Defects. By Joel Pokorny, Vivianne G. Smith, Guy Verriest, and A. J. L. G. Pinckers. New York, Grune and Stratton, 1979. Hardcover, 409 pages, preface, references, index, 129 black and white figures. $33.50 Forewords to scholarly works, as a rule, are laudatory. The foreword to this work, by Professor W. D. Wright, is no exception. In this case, however, the foreword could have doubled as an unbiased review. This book is destined to serve as a key reference in its area and, to a lesser extent, as a text as well. It is a splendid addition to the published clinical and visual science material. The first two chapters summarize radiometric and photometric measures; the third reviews "physiological and theoretical bases of