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The Effect of Hysterectomy on the Age at Ovarian Failure
Vol. 49, No. 2, February 1988 Printed in U.S.A.
FERTILITY AND STERILITY Copyright e 1988 The American Fertility Society
The Effect of Hysterectomy on the Age at Ovarian Failure
To the Editor: The recent article by Siddle et al. 1 claims a causative relation between the age at hysterectomy and the age of ovarian failure in women aged 44 years or younger at ovarian failure. The basis of their argument is the statistically significant correlation (r = 0.62) they found in 33 such women between age at hysterectomy (a) and age at ovarian failure (t =a +f). Here, f represents the number of years from hysterectomy to ovarian failure. The authors' correlation is that of a and t, but a more appropriate one is that between a and f. It can be shown with this type of data that, even if r(a, f) is negative, r(t, a) will always be positive. The actual value depends on the ratio of the standard deviations of a and f. For example, if the ratio is unity and r(f, a) = -0.5, then r(t, a) = +0.5. Reading from the authors' graph and then calculating f for all 90 women gives r (a, f) = -0.54. That is, as age at hysterectomy increases, the time to ovarian failure actually decreases. It also should be mentioned that the correlation coefficient is a measure of linear association between two variables. Large correlations do not
imply causation. It should only be calculated when the variables involved can be reasonably assumed to have normal distributions. This is clearly not possible for the dichotomized data in the authors' Figure 3 (shown herewith). The authors discuss the time to ovarian failure in 90 women in which that had occurred. However, other women from their clinic will no doubt have had a hysterectomy, albeit not yet ovarian failure. Such women generate censored failure times that could have been used to estimate the median age at ovarian failure using survival analysis techniques. 2 On a separate point, why do the authors use the Mann-Whitney test to compare the age at ovarian failure in normal menopause and hysterectomized women? Quoting of means and standard deviations of these groups suggests that at-test would be more appropriate.
David Machin, M.Sc. John D. Williams, M.Sc. Medical Statistics and Computing University of Southampton Southampton General Hospital Southampton, England August 10, 1987 REFERENCES
RELATIONSHIP BETWEEN INTERVAL TO OVARIAN
1. Siddle N, Sarrel P, Whitehead M: The effect of hysterec-
FAILURE AND AGE AT HYSTERECTOMY
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15
tomy on the age at ovarian failure: identification of a subgroup of women with premature loss of ovarian function and a literature review. Fertil Steril47:94, 1987 2. Pocock SJ: Clinical trials: A Practical Approach. Chichester, Wiley, 1983
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Machin and Williams have completely misrepresented the reason for our conclusions. 1 They state that the reason for our conclusions-the previously unacknowledged observation that postsurgical ovarian failure in hysterectomized patients with bilateral ovarian conservation occurs at a significantly earlier age than in women undergoing spontaneous natural menopause-was a positive significant correlation between age at hysterectomy and age at ovarian failure. This is a completely erroneous evaluation of our observations. The reason for Fertility and Sterility
our conclusions was, in fact, a significantly reduced age of ovarian failure in a noncensored group of posthysterectomized women compared with another group of women undergoing a spontaneous natural menopause. Machin and Williams enter into a detailed exposition of what they view as the erroneous basis for our original correlations, claiming that these are at the root of our eventual conclusions. Nevertheless, the fact seems to have been completely ignored that we only performed these correlations (see Figure 3 of our original paper, shown here) to highlight the presence of another separate subgroup of hysterectomized women: those undergoing a shorter interval than the remainder between ovarian failure and surgery. This division was evidenced by the original frequency distribution of the interval to ovarian failure in the posthysterectomized women. However, in accordance with Machin and Williams' original suggestions, we have recomputed the correlation (using Spearman's rank correlation coefficient) of age at hysterectomy against interval to ovarian failure for the group and find it to be -0.71 (N = 90, P < 0.001), agreeing with their finding of a reciprocal relationship. How does this assist in their argument? It does not invalidate our original conclusions and, from a probability plot of the original frequency data, we find significant evidence of platykurtosis (g 2 = -2.96 ± 0.30; P < 0.001), which is a characteristic of bimodal distributions. 2 We consider that this is confirmatory evidence of our conclusion that hysterectomy can result in early ovarian failure. Two additional points raised require attention. The Mann-Whitney U-test of ages of ovarian failure may have been better represented on a figure illustrating medians rather than means, in accord with the use of a nonparametric test. However, it should be clear to any numerate biologist-and certainly to a medical statistician-that a suitable nonparametric test is applicable in any circumstance where a parametric test can be used, although not vice versa. Thus, we defend our use of the Mann-Whitney U-test since, although the sample size we were using may have been larger than "conventionally" analyzed using such a method, there was some evidence of skewness, making a parametric procedure less valid unless transformed data was used. We should also like to point out that our use of the Kruskal-Wallis nonparametric ANOVA in the original article was used to highlight any potential variation due to disease etiology upon ovarian failure. We did not attempt to make any definitive statement about these factors, as this is Vol. 49, No. 2, February 1988
clearly inappropriate with retrospective data. In fact, we went to great lengths in our discussion to point out that a detailed prospective study would be required before such a statement could be made. Thus, the point that survival analysis, such as the application of Cox's regression model, could have been used is, a somewhat misplaced observation because such conclusions were not our original intention. Such data as were presented were totally inappropriate for such a technique, which should be applied to data from prospective studies designed with suitable a priori hypotheses.
Malcolm I. Whitehead, M.R.C.O.G. King's College School of Medicine and Dentistry King's College London Denmark Hill, London September 30, 1987 REFERENCES 1. Siddle N, Sarrel P, Whitehead M: The effect of hysterec-
tomy on the age at ovarian failure: identification of a subgroup of women with premature loss of ovarian function and a literature review. Fertil Steril 4 7:94, 1987 2. Sokal RR, Rohlf FW: Biometry. San Francisco, Freeman, 1981
Comment
The short but succinct letter from the University of Southampton (Medical Statistics and Computing) is "statistically" illuminating. It addresses the selection of statistical methods, interpretation, and the presentation of data. The correspondents question the choice of different ranges for the scales, and the decision to log the data in Figure 3 of the Siddle et al. article. The motif selected by the authors for Figure 3 does seem to obfuscate comparisons between the two groups. It would also be logical to assume that some correlation would exist between age of hysterectomy and ovarian failure. As age at hysterectomy increases, one would expect that time onset to ovarian failure would decrease. Correlation does not prove causation. In fact, it is difficult to understand why group II (age > 45 years at ovarian failure) would not show the same natural correlation. From a clinical point of view, biochemical evidence of elevated gonadotropins should be the gold standard of ovarian failure, or at least compensated ovarian failure rather than "symptoms" of estrogen deficiency. This is especially true in the study group where the menstrual endpoint has been lost. Without this biochemical marker, it is difficult to mark the time onset of ovarian failure. The retort by the authors is equally provocative and illuminating. This type of exchange is essential Letters-to-the-editor
379
FERTILITY AND STERILITY Copyright e 1988 The American Fertility Society
The Effect of Hysterectomy on the Age at Ovarian Failure
To the Editor: The recent article by Siddle et al. 1 claims a causative relation between the age at hysterectomy and the age of ovarian failure in women aged 44 years or younger at ovarian failure. The basis of their argument is the statistically significant correlation (r = 0.62) they found in 33 such women between age at hysterectomy (a) and age at ovarian failure (t =a +f). Here, f represents the number of years from hysterectomy to ovarian failure. The authors' correlation is that of a and t, but a more appropriate one is that between a and f. It can be shown with this type of data that, even if r(a, f) is negative, r(t, a) will always be positive. The actual value depends on the ratio of the standard deviations of a and f. For example, if the ratio is unity and r(f, a) = -0.5, then r(t, a) = +0.5. Reading from the authors' graph and then calculating f for all 90 women gives r (a, f) = -0.54. That is, as age at hysterectomy increases, the time to ovarian failure actually decreases. It also should be mentioned that the correlation coefficient is a measure of linear association between two variables. Large correlations do not
imply causation. It should only be calculated when the variables involved can be reasonably assumed to have normal distributions. This is clearly not possible for the dichotomized data in the authors' Figure 3 (shown herewith). The authors discuss the time to ovarian failure in 90 women in which that had occurred. However, other women from their clinic will no doubt have had a hysterectomy, albeit not yet ovarian failure. Such women generate censored failure times that could have been used to estimate the median age at ovarian failure using survival analysis techniques. 2 On a separate point, why do the authors use the Mann-Whitney test to compare the age at ovarian failure in normal menopause and hysterectomized women? Quoting of means and standard deviations of these groups suggests that at-test would be more appropriate.
David Machin, M.Sc. John D. Williams, M.Sc. Medical Statistics and Computing University of Southampton Southampton General Hospital Southampton, England August 10, 1987 REFERENCES
RELATIONSHIP BETWEEN INTERVAL TO OVARIAN
1. Siddle N, Sarrel P, Whitehead M: The effect of hysterec-
FAILURE AND AGE AT HYSTERECTOMY
• •
15
tomy on the age at ovarian failure: identification of a subgroup of women with premature loss of ovarian function and a literature review. Fertil Steril47:94, 1987 2. Pocock SJ: Clinical trials: A Practical Approach. Chichester, Wiley, 1983
• • • •
••
•
•
• •
•
•
Reply of the Author:
•
••
•
-·- --... --· .. . -... .. --· -· ·-· •
••
•
• • •
•
•• •
•
0 25
30
35
• •••
40
•
•
•
45
AGE AT HYSTERECTOMY (yrs)
378
Letters-to-the-editor
50
55
Machin and Williams have completely misrepresented the reason for our conclusions. 1 They state that the reason for our conclusions-the previously unacknowledged observation that postsurgical ovarian failure in hysterectomized patients with bilateral ovarian conservation occurs at a significantly earlier age than in women undergoing spontaneous natural menopause-was a positive significant correlation between age at hysterectomy and age at ovarian failure. This is a completely erroneous evaluation of our observations. The reason for Fertility and Sterility
our conclusions was, in fact, a significantly reduced age of ovarian failure in a noncensored group of posthysterectomized women compared with another group of women undergoing a spontaneous natural menopause. Machin and Williams enter into a detailed exposition of what they view as the erroneous basis for our original correlations, claiming that these are at the root of our eventual conclusions. Nevertheless, the fact seems to have been completely ignored that we only performed these correlations (see Figure 3 of our original paper, shown here) to highlight the presence of another separate subgroup of hysterectomized women: those undergoing a shorter interval than the remainder between ovarian failure and surgery. This division was evidenced by the original frequency distribution of the interval to ovarian failure in the posthysterectomized women. However, in accordance with Machin and Williams' original suggestions, we have recomputed the correlation (using Spearman's rank correlation coefficient) of age at hysterectomy against interval to ovarian failure for the group and find it to be -0.71 (N = 90, P < 0.001), agreeing with their finding of a reciprocal relationship. How does this assist in their argument? It does not invalidate our original conclusions and, from a probability plot of the original frequency data, we find significant evidence of platykurtosis (g 2 = -2.96 ± 0.30; P < 0.001), which is a characteristic of bimodal distributions. 2 We consider that this is confirmatory evidence of our conclusion that hysterectomy can result in early ovarian failure. Two additional points raised require attention. The Mann-Whitney U-test of ages of ovarian failure may have been better represented on a figure illustrating medians rather than means, in accord with the use of a nonparametric test. However, it should be clear to any numerate biologist-and certainly to a medical statistician-that a suitable nonparametric test is applicable in any circumstance where a parametric test can be used, although not vice versa. Thus, we defend our use of the Mann-Whitney U-test since, although the sample size we were using may have been larger than "conventionally" analyzed using such a method, there was some evidence of skewness, making a parametric procedure less valid unless transformed data was used. We should also like to point out that our use of the Kruskal-Wallis nonparametric ANOVA in the original article was used to highlight any potential variation due to disease etiology upon ovarian failure. We did not attempt to make any definitive statement about these factors, as this is Vol. 49, No. 2, February 1988
clearly inappropriate with retrospective data. In fact, we went to great lengths in our discussion to point out that a detailed prospective study would be required before such a statement could be made. Thus, the point that survival analysis, such as the application of Cox's regression model, could have been used is, a somewhat misplaced observation because such conclusions were not our original intention. Such data as were presented were totally inappropriate for such a technique, which should be applied to data from prospective studies designed with suitable a priori hypotheses.
Malcolm I. Whitehead, M.R.C.O.G. King's College School of Medicine and Dentistry King's College London Denmark Hill, London September 30, 1987 REFERENCES 1. Siddle N, Sarrel P, Whitehead M: The effect of hysterec-
tomy on the age at ovarian failure: identification of a subgroup of women with premature loss of ovarian function and a literature review. Fertil Steril 4 7:94, 1987 2. Sokal RR, Rohlf FW: Biometry. San Francisco, Freeman, 1981
Comment
The short but succinct letter from the University of Southampton (Medical Statistics and Computing) is "statistically" illuminating. It addresses the selection of statistical methods, interpretation, and the presentation of data. The correspondents question the choice of different ranges for the scales, and the decision to log the data in Figure 3 of the Siddle et al. article. The motif selected by the authors for Figure 3 does seem to obfuscate comparisons between the two groups. It would also be logical to assume that some correlation would exist between age of hysterectomy and ovarian failure. As age at hysterectomy increases, one would expect that time onset to ovarian failure would decrease. Correlation does not prove causation. In fact, it is difficult to understand why group II (age > 45 years at ovarian failure) would not show the same natural correlation. From a clinical point of view, biochemical evidence of elevated gonadotropins should be the gold standard of ovarian failure, or at least compensated ovarian failure rather than "symptoms" of estrogen deficiency. This is especially true in the study group where the menstrual endpoint has been lost. Without this biochemical marker, it is difficult to mark the time onset of ovarian failure. The retort by the authors is equally provocative and illuminating. This type of exchange is essential Letters-to-the-editor
379