808
LETTERS TO THE EDITOR METHODS AND INTERPRETATION OF TWIN CONCORDANCE DATA
To the Editor: In the July 1974 issue of the Journal Smith presented a comprehensive review of methods for analyzing data on traits and diseases in twins [1]. He emphasized the desirability of using the proband concordance rate without mentioning the realities which sometimes make its use impossible. He recognized no advantage in using the casewise rate, which is in fact designed to deal with some of those realities. The proband method is a valuable theoretical construction based on the assumption of specific conditions of diagnostic ascertainment [2]. When these conditions are not met or when the nature of the ascertainment process cannot be specified, the casewise or pairwise rates may be more realistic measures of concordance. The use of these rates has been discussed by Gottesman and Shields [3, p 341]. The proband rate is directly comparable to the population prevalence and does not vary with completeness of ascertainment. Yet information obtained from twin samples by the proband concordance rate often has neither of those properties. In many twin samples doubly and singly ascertained pairs cannot be clearly and completely distinguished, in which case the obtained rate differs from the proband rate by an unknown amount. Also, even the proband rate is not constant unless ascertainment in the secondary cases (cotwins of the probands) is complete. This variation is specified in Smith's table 4 by the coefficient of PR in case 6, 7nc'. And finally, whatever the ascertainment level in the cotwins, the proband rate is not directly comparable with the reference population unless the same ascertainment level, qT'c, obtains in both, which is very often not true. In using the casewise rate an investigator makes no pretense of distinguishing doubly and singly ascertained pairs. The information discarded is often valueless and in the analysis of prerecorded data the distinctions cannot be made. One simply counts all concordant pairs twice in both the numerator and denominator of the rate [3]. In a twin registry covering a defined population, if they are known to be affected, cotwins of cases are themselves index cases. The casewise rate then is identical with the best approximation of the proband rate. This is true of any twin sample in which index cases and affected cotwins are detected in one and the same ascertainment operation. Errors that may be concealed in such situations by assuming a valid proband concordance rate have been graphed [4]. When the extent of ascertainment can be determined by reference to a reliable independent source, these rates can be corrected by dividing them by the ascertainment proportion. When ascertainment is very low, no pair is likely to be doubly ascertained. In that situation, assuming diagnostic evaluation of all cotwins, the pairwise rate, in which each concordant pair is counted once, is equivalent to the proband concordance rate. Under these conditions, if the sampling situation is not appropriate for the proband rate the pairwise rate is a more meaningful designation. Any compari-
LETTERS TO THE EDITOR
809
son of this rate with prevalence in the reference population requires knowledge of or assumptions about ascertainment in both the twins and the population. This is true for the proband rate as well as the pairwise rate. ZDENEK HRUBEC'
AND
GORDON ALLEN2
REFERENCES 1. SMITH C: Concordance in twins: methods and interpretations. Am J Hum Genet 26:454-466, 1974 2. CROW JF: Problems of ascertainment in the analysis of family data, in Genetics and the Epidemiology of Chronic Diseases, edited by NEEL JV, SHAW MW, SCHULL WJ, Public Health Service Publication no. 1163, Washington, D.C., U.S. Department of Health, Education and Welfare, 1965 3. GOTTESMAN II, SHIELDS J: Schizophrenia and Genetics. New York, Academic Press, 1972 4. HRUBEC Z: The effect on diagnostic ascertainment in twins on the assessment of the genetic factor in disease etiology. Am J Hum Genet 25:15-28, 1973 1 National Research Council, Washington, D.C. National Institute of Mental Health, Bethesda, Maryland.
2
Familial Wilms's Tumor To the Editor: The report of Juberg et al. [1] on familial Wilms's tumor is fascinating and important, but we wish to record an objection to the authors' application of our concepts [2 ] in the interpretation of their data. With respect to the presence of a hereditary tumor in the offspring of normal parents the situation is no different from those previously recorded instances of childhood tumors in sibs born to unaffected parents. For example, for retinoblastoma in the absence of a positive family history the recurrence risk for unaffected parents with one affected child is of the order of magnitude of 5%-10% [3]. As the authors themselves point out, gonadal mosaicism is a likely explanation for unaffected parents of two or more cases and is certainly more probable than the scant risk (< 1/10,000) that a subsequent sib would be affected in the absence of a predisposing gene. Since Wilms's tumor has been so highly lethal until recent times, affected sibs with unaffected parents are the most frequent familial manifestation of the predisposing gene. The concordance rate for identical twins generally is given by us as the product, hereditary fraction X penetrance, in which the latter is provided by the expression 1- e-", where m -mean number of tumors in genetic cases. If we presume that the tumor in the family of Juberg et al. [1] is genetic, then expected concordance in the twins is simply 1 - e-m, or, according to our estimate for Wilms's tumor, 6357o, as noted by the authors themselves. Therefore in 37% of cases where a twin
LETTERS TO THE EDITOR METHODS AND INTERPRETATION OF TWIN CONCORDANCE DATA
To the Editor: In the July 1974 issue of the Journal Smith presented a comprehensive review of methods for analyzing data on traits and diseases in twins [1]. He emphasized the desirability of using the proband concordance rate without mentioning the realities which sometimes make its use impossible. He recognized no advantage in using the casewise rate, which is in fact designed to deal with some of those realities. The proband method is a valuable theoretical construction based on the assumption of specific conditions of diagnostic ascertainment [2]. When these conditions are not met or when the nature of the ascertainment process cannot be specified, the casewise or pairwise rates may be more realistic measures of concordance. The use of these rates has been discussed by Gottesman and Shields [3, p 341]. The proband rate is directly comparable to the population prevalence and does not vary with completeness of ascertainment. Yet information obtained from twin samples by the proband concordance rate often has neither of those properties. In many twin samples doubly and singly ascertained pairs cannot be clearly and completely distinguished, in which case the obtained rate differs from the proband rate by an unknown amount. Also, even the proband rate is not constant unless ascertainment in the secondary cases (cotwins of the probands) is complete. This variation is specified in Smith's table 4 by the coefficient of PR in case 6, 7nc'. And finally, whatever the ascertainment level in the cotwins, the proband rate is not directly comparable with the reference population unless the same ascertainment level, qT'c, obtains in both, which is very often not true. In using the casewise rate an investigator makes no pretense of distinguishing doubly and singly ascertained pairs. The information discarded is often valueless and in the analysis of prerecorded data the distinctions cannot be made. One simply counts all concordant pairs twice in both the numerator and denominator of the rate [3]. In a twin registry covering a defined population, if they are known to be affected, cotwins of cases are themselves index cases. The casewise rate then is identical with the best approximation of the proband rate. This is true of any twin sample in which index cases and affected cotwins are detected in one and the same ascertainment operation. Errors that may be concealed in such situations by assuming a valid proband concordance rate have been graphed [4]. When the extent of ascertainment can be determined by reference to a reliable independent source, these rates can be corrected by dividing them by the ascertainment proportion. When ascertainment is very low, no pair is likely to be doubly ascertained. In that situation, assuming diagnostic evaluation of all cotwins, the pairwise rate, in which each concordant pair is counted once, is equivalent to the proband concordance rate. Under these conditions, if the sampling situation is not appropriate for the proband rate the pairwise rate is a more meaningful designation. Any compari-
LETTERS TO THE EDITOR
809
son of this rate with prevalence in the reference population requires knowledge of or assumptions about ascertainment in both the twins and the population. This is true for the proband rate as well as the pairwise rate. ZDENEK HRUBEC'
AND
GORDON ALLEN2
REFERENCES 1. SMITH C: Concordance in twins: methods and interpretations. Am J Hum Genet 26:454-466, 1974 2. CROW JF: Problems of ascertainment in the analysis of family data, in Genetics and the Epidemiology of Chronic Diseases, edited by NEEL JV, SHAW MW, SCHULL WJ, Public Health Service Publication no. 1163, Washington, D.C., U.S. Department of Health, Education and Welfare, 1965 3. GOTTESMAN II, SHIELDS J: Schizophrenia and Genetics. New York, Academic Press, 1972 4. HRUBEC Z: The effect on diagnostic ascertainment in twins on the assessment of the genetic factor in disease etiology. Am J Hum Genet 25:15-28, 1973 1 National Research Council, Washington, D.C. National Institute of Mental Health, Bethesda, Maryland.
2
Familial Wilms's Tumor To the Editor: The report of Juberg et al. [1] on familial Wilms's tumor is fascinating and important, but we wish to record an objection to the authors' application of our concepts [2 ] in the interpretation of their data. With respect to the presence of a hereditary tumor in the offspring of normal parents the situation is no different from those previously recorded instances of childhood tumors in sibs born to unaffected parents. For example, for retinoblastoma in the absence of a positive family history the recurrence risk for unaffected parents with one affected child is of the order of magnitude of 5%-10% [3]. As the authors themselves point out, gonadal mosaicism is a likely explanation for unaffected parents of two or more cases and is certainly more probable than the scant risk (< 1/10,000) that a subsequent sib would be affected in the absence of a predisposing gene. Since Wilms's tumor has been so highly lethal until recent times, affected sibs with unaffected parents are the most frequent familial manifestation of the predisposing gene. The concordance rate for identical twins generally is given by us as the product, hereditary fraction X penetrance, in which the latter is provided by the expression 1- e-", where m -mean number of tumors in genetic cases. If we presume that the tumor in the family of Juberg et al. [1] is genetic, then expected concordance in the twins is simply 1 - e-m, or, according to our estimate for Wilms's tumor, 6357o, as noted by the authors themselves. Therefore in 37% of cases where a twin
