Familial Breast and Ovarian Cancer: A Swedish Population-based Register Study

Harald Anderson1, Anna Bladström1, Håkan Olsson1,2 and Torgil R. Möller1

1 Department of Cancer Epidemiology, University Hospital, Lund, Sweden.
2 Department of Oncology, University Hospital, Lund, Sweden.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A cohort of offspring of mothers with breast or ovarian cancer diagnosed in 1958–1993 was established using Swedish population-based registers. The children (n = 158,041) were born between 1941 and 1993, and their cancer incidence was followed between 1961 and 1993. A total of 3,257 tumors in 3,102 children were found. Observed numbers of cases were compared with expected numbers based on national calendar year-, age-, and sex-specific incidences. For daughters of women with breast cancer, the standardized morbidity ratios for being diagnosed with breast cancer and ovarian cancer before age 50 years were 1.99 (95% confidence interval (CI): 1.86, 2.14) and 1.28 (95% CI: 1.05, 1.54), respectively. The corresponding figures for daughters of women with ovarian cancer were 1.79 (95% CI: 1.55, 2.07) and 2.38 (95% CI: 1.77, 3.12). The risks were raised if the mother's cancer was diagnosed at a young age, the mother had multiple breast/ovarian diagnoses, or there was a sister with breast/ovarian cancer. Among all offspring, increased risks were found for thyroid cancer, testicular cancer, and malignant melanoma, while lung cancer risk was decreased if the mother had had breast cancer. The authors developed a variance estimator for the standardized morbidity ratio to cope with overdispersion due to dependency within families.

breast neoplasms; cohort studies; family characteristics; genetic predisposition to disease; ovarian neoplasms; risk factors

Abbreviations: CI, confidence interval; SMR, standardized morbidity ratio.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
A history of breast cancer in a first degree relative generally doubles a woman's risk of breast cancer (1GoGo–3Go), and the risk is higher if the relative was diagnosed at a young age or had bilateral breast cancer. In the late 1980s and early 1990s, it became clear that in some families breast and ovarian cancer shared a common genetic predisposition. Through linkage analysis (4Go, 5Go) and, later, cloning (6Go), a gene on the long arm of chromosome 17, BRCA1, was found to be responsible for a large proportion of cancers in breast/ovarian cancer families. In 1995, another gene, BRCA2, was identified that, if mutated, renders individuals at increased risk for breast (including male breast) cancer and ovarian cancer (7Go, 8Go).

The progress in population genetics and molecular genetics of breast cancer has already had an impact on the clinical management of families with a hereditary predisposition. However, for a large proportion of families with possible dominant inheritance of breast cancer, the responsible gene(s) remain to be identified. Therefore, risk management for these families is very much dependent on assessing risk through pedigree information. Risk estimates have mainly been based on data from case-control studies, such as those conducted by Claus et al. (9Go, 10Go). The studies have been relatively small, which leads to broad confidence intervals; furthermore, most such studies are susceptible to bias due to nonresponse or due to case ascertainment through voluntarily participating probands or probands from selected hospitals.

Hemminki and Vaittinen (11Go) previously studied the risk of breast cancer and other cancers in daughters of patients with breast carcinoma for the entire population of Sweden. In the present study, we also studied the Swedish population but considered carcinoma in both sons and daughters of mothers with either breast or ovarian cancer, since these diagnoses may have a common genetic cause. We also studied in detail cancer risk in relation to bilateral breast cancer and to multiple diagnoses of breast and ovarian cancer in the mother, and in relation to the presence of breast/ovarian cancer in a sister.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Register data
The population-based Swedish cancer register was started in 1958 and has very good coverage (12Go). Among other data, the following information is registered: cancer site according to the International Classification of Diseases, Seventh Revision; pathology code; tumor number; and dates of birth, diagnosis, and death. During the period 1958–1993, there were 165,494 women with at least one primary malignant breast or ovarian cancer diagnosis, and they constituted the potential mothers or probands in this study.

Children of these women who were born in Sweden between 1941 and 1993 were identified by means of the unique personal identification numbers and registers kept by Statistics Sweden. The fertility register includes all births occurring since 1961, with identification numbers for both mother and child; hence, data on all children born in Sweden beginning in 1961 were easily obtained. In the 1960 and 1965 Swedish national censuses, information was collected by household and included identification numbers and family relationships. Hence, children living in the same households as the probands and born in 1941–1960 were identified.

Of the 165,494 probands, 81,088 had at least one child that was alive at the end of 1960 or born later. Altogether there were 158,041 children (77,263 girls and 80,778 boys) in the study cohort. To obtain information about malignant tumors in the children, we linked the cohort to the national cancer register through 1993; and to obtain times of emigration and death and thus time at risk, we linked the cohort to various Statistics Sweden population registers. Follow-up included 4.7 million person-years of observation, and a total of 3,257 tumors (of which 142 were second primaries and 13 were third primaries) were found in 3,102 children.

Relative and cumulative risks
Cancer incidence in the children was analyzed by means of the person-years method, with national Swedish incidence rates being used as the reference category, stratified by calendar year, sex, and 5-year age group. The 1960 census was carried out in autumn 1960, and therefore children who died before that time were not included. Follow-up for an individual cohort member thus started on January 1, 1961, or at birth, if later. Each individual was followed until December 31, 1993, or until the time of a second primary cancer diagnosis or the date of first emigration, if earlier.

The standardized morbidity ratio (SMR), primarily for breast and ovarian cancer, was studied as a function of various risk factors such as the mother's age at diagnosis, the current age of offspring, and incidence of breast or ovarian cancer in a sister. For every individual in the cohort, we had follow-up data on cancer incidence, death, and emigration from at least the age of 20 years, and the individual's cumulative risk of contracting cancer before the age of 50 was determined by means of the life table method. Note that this risk is an average of the person's cancer risk during the period 1961–1993, with an emphasis on the last 10 years, since most of the follow-up in the higher-risk age groups over 40 occurred during those years.

Attributable fraction
Women with mothers with (for example) breast cancer have a higher risk of breast cancer than average women. Consider the event "breast cancer before age 50." The fraction (AF) of this event attributable to the mother's having had breast cancer, for these "exposed" women, is

where Obs and Exp denote observed and expected (according to national reference rates) numbers of breast cancer cases occurring before age 50 in a cohort of women whose mothers had breast cancer, and the relative risk (RR) = Obs/Exp.

The attributable fraction of breast cancer diagnosed before age 50 in the population that may have been due to the mother's having breast cancer at any age was determined using the formula (13Go, p. 38)

where P0 denotes the proportion of exposed women, that is, those whose mothers got breast cancer, and RR is the relative risk of breast cancer before age 50 in exposed women compared with the nonexposed population. We estimated RR from the cohort analysis and P0 from the national incidence of breast cancer in the 1980s (12Go).

Time scale
Normally a woman is diagnosed with breast or ovarian cancer many years after the birth of a daughter, and in a family consulting situation, one would be interested in the daughter's risk from that calendar day forward. In a cohort study, this would correspond to starting follow-up at the date of the mother's diagnosis. The aim of this investigation was to study familial cancer in general–for example, to determine the population risk that a daughter would be diagnosed with breast cancer given that her mother had breast cancer before 50 years of age. In such a case, follow-up should start at the birth of the child or on January 1, 1961, if that date is later.

When studying the daughter's cancer risk given that a sister also has (for example) breast cancer, more time scale questions arise. In a genetic counseling situation, the most straightforward solution would be to start follow-up at the date on which the first sister in a family is diagnosed with breast or ovarian cancer. Parallel to the situation regarding a breast/ovarian cancer diagnosis in the mother only, we would include in the study base all women with a mother and a sister with known breast or ovarian cancer and start follow-up at birth or on January 1, 1961, if that date occurred later, independently of the mother's and sister's dates of diagnosis. Given that a sister (and mother) has had breast/ovarian cancer, we then assume that the relative risk of a woman's contracting breast or ovarian cancer is the same before and after the dates of her mother's and sister's diagnoses. Note that a woman may be included in the analysis both directly, by contributing follow-up time, and indirectly, as part of the "exposure" for a sister. For instance, with two daughters in a family, both will be included in the follow-up if both have breast cancer, while the one without cancer will be included if only one of the daughters has a known breast cancer diagnosis.

Overdispersion
In standard cohort analysis, one assumes independent cohort data and the statistical inference is based on Poisson-distributed observed numbers. In the present study, there is a dependence within siblings, especially in the situation where one studies the risk of cancer given that both the mother and a sister have had cancer. This does not bias the estimate of the SMR, but the estimated standard error for the SMR may be too small if the dependency among family members is not taken into account. To cope with this problem, we worked out a sampling-based standard error for the SMR (see the Appendix for details).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Composition and follow-up of the cohort
The study cohort comprised 158,041 individuals, the offspring of 81,088 mothers with a diagnosis of breast or ovarian cancer in the Swedish Cancer Registry from its start in 1958 to 1993. There were 77,263 female offspring with 55,015 mothers; 48 percent of the daughters did not have a sister, 36 percent had one sister, 12 percent had two sisters, and 4 percent had three or more sisters.

Follow-up started on January 1, 1961, and ended on December 31, 1993; and since the oldest children were born in 1941, it extended to, at most, 53 years of age. The total amount of follow-up time was 3.90 million person-years in the offspring of mothers with breast cancer and 0.90 million person-years in the offspring of mothers with ovarian cancer, distributed about equally by sex. Because of the composition of the cohort, only 22 percent of the follow-up time covered the age range of 30–40 years, and only 11 percent covered ages above 40 years.

Cancer incidence in children of mothers with breast cancer
In the studied period, there were 129,610 individuals who had a mother with breast cancer; in 43,390 individuals, the mother was below 50 years of age at her first breast cancer diagnosis, and in 86,220 individuals, the mother was aged 50 years or older at first diagnosis. Table 1 gives an overview of cancer incidence for the entire cohort and for the cohort split by mother's age at breast cancer diagnosis. There were 2,630 observed cancer cases in the entire cohort, as compared with 2,161 expected (SMR = 1.22; 95 percent confidence interval (CI): 1.17, 1.26). For breast cancer, the SMR was 1.99 (95 percent CI: 1.86, 2.14), and for ovarian cancer it was 1.28 (95 percent CI: 1.05, 1.54). The risks were more pronounced when the mother's age at diagnosis was below 50: For all cancers, the SMR was 1.30 (95 percent CI: 1.20, 1.42); for breast cancer, it was 2.69 (95 percent CI: 2.29, 3.15); and for ovarian cancer, it was 1.48 (95 percent CI: 0.93, 2.24). An increased incidence was also noted for testicular cancer (SMR = 1.27; 95 percent CI: 1.05, 1.52) and malignant melanoma (SMR = 1.26; 95 percent CI: 1.11, 1.42). The risk for thyroid cancer was increased among offspring of mothers who had breast cancer before age 50 (SMR = 1.57; 95 percent CI: 0.98, 2.37). A lowered risk was primarily found for lung cancer (SMR = 0.69; 95 percent CI: 0.50, 0.93).


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TABLE 1. Incidence of malignant tumors among offspring of Swedish women diagnosed with breast cancer between 1958 and 1993*

 
Cancer incidence in children of mothers with ovarian cancer
There were 29,499 women who had a mother with ovarian cancer. In 8,746 cases, the mother's age at diagnosis was less than 50 years, and in 20,753 cases, the mother's age was 50 years or more. Table 2 gives an overview of cancer incidence. In all, 666 cancer cases were observed as compared with 532 expected (SMR = 1.25; 95 percent CI: 1.16, 1.35). In the cohort as a whole, the SMR was 1.79 (95 percent CI: 1.55, 2.07) for breast cancer and 2.38 (95 percent CI: 1.77, 3.12) for ovarian cancer; when the mother's age at diagnosis was below 50, the SMRs were 2.92 (95 percent CI: 2.11, 3.95) and 3.70 (95 percent CI: 1.97, 6.33), respectively. Raised risks were also observed for thyroid cancer in the cohort as a whole (SMR = 1.50; 95 percent CI: 0.97, 2.21) and for colon and testis cancer when the mother had ovarian cancer before age 50 (SMR = 3.28 (95 percent CI: 1.64, 5.88) and SMR = 2.40 (95 percent CI: 1.24, 4.19), respectively).


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TABLE 2. Incidence of malignant tumors among offspring of Swedish women diagnosed with ovarian cancer between 1958 and 1993*

 
Breast and ovarian cancer incidence as a function of mother's age at diagnosis
Breast and ovarian cancer incidence among daughters was also studied in more detail as a function of the mother's age at diagnosis and the follow-up period (table 3). Considering follow-up in all age groups, the relative risk for breast cancer decreased from 4.97 (95 percent CI: 3.31, 7.19) if the mother was below 40 years of age when she got breast cancer to 1.74 (95 percent CI: 1.58, 1.91) if the mother was aged 60 years or more. A similar pattern was seen for ovarian cancer incidence among daughters of mothers with ovarian cancer (table 4): The relative risk decreased from 7.67 (95 percent CI: 2.09, 19.65) if the mother was below age 40 years at diagnosis to 2.23 (95 percent CI: 1.46, 3.27) if the mother was aged 60 years or older.


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TABLE 3. Risk of breast cancer among daughters of Swedish women with breast cancer as a function of age of follow-up and mother's age at breast cancer diagnosis*

 

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TABLE 4. Risk of ovarian cancer among daughters of Swedish women with ovarian cancer as a function of mother's age at ovarian cancer diagnosis*

 
Multiple diagnoses of breast/ovarian cancer in mothers
The Swedish cancer register is a register of diagnoses, and hence it is possible to identify daughters of women with multiple cancers (table 5). In the present data, there were 3,262 women who had a mother with more than one breast cancer diagnosis. The SMR for breast cancer in this group was 3.41 (95 percent CI: 2.68, 4.29), that is, approximately twice that obtained if the mother had one (or more) breast cancer diagnosis. If the mother had two breast cancer diagnoses and the first diagnosis had been made before she reached 50 years of age, the relative risk increased to 6.06 (95 percent CI: 3.99, 8.81). An extremely high breast cancer risk was observed when the mother had two breast cancers and the first had been diagnosed before 40 years of age (SMR = 21.3; 95 percent CI: 9.2, 41.9).


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TABLE 5. Risks of breast and ovarian cancer among daughters of Swedish women with multiple breast and ovarian cancers*

 
We also studied cases in which the mother developed both breast and ovarian cancer. There were 530 daughters of such women, and their relative risks for breast cancer and ovarian cancer were 5.94 (95 percent CI: 3.77, 8.92) and 12.2 (95 percent CI: 5.8, 22.4), respectively. With the extra requirement that the mother be under 50 years of age when she got breast cancer, there were 184 daughters left; they had seven breast cancers and one ovarian cancer compared with the 0.70 and 0.17 expected.

Mother and sister with breast/ovarian cancer
There were 478 women in the cohort who had both a mother and a sister with breast cancer (table 6), and when follow-up for every woman started at birth or on January 1, 1961, they had 11 breast cancers as compared with 4.5 expected (SMR = 2.5; 95 percent CI: 0.3, 4.6). Note that the dependency within sibships becomes especially marked here, yielding broader confidence intervals in comparison with the situation regarding independent cohort members. The number of women increased to 651 if women with a mother and a sister with breast or ovarian cancer were included. There were then 24 observed breast cancers compared with 5.9 expected and five observed ovarian cancers compared with 1.2 expected, which yields larger relative risks. If one also demanded that the mother must have had breast/ovarian cancer before age 50 years, there were 146 women in the cohort and they got 10 breast cancers and four ovarian cancers. This yields very high relative risks, but because of the dependency the standard errors are large.


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TABLE 6. Risks of breast and ovarian cancer among Swedish women with both a mother and a sister who had breast or ovarian cancer*

 
Cumulative risks of developing breast or ovarian cancer
The general population cumulative risk of breast cancer before 50 years of age was 1.6 percent in the 1980s in Sweden, and the corresponding risk for ovarian cancer was 0.3 percent. Table 7 shows the corresponding risks for women with information about cancer in their mothers and sisters. If the mother had had breast cancer, the cumulative risk for breast cancer before age 50 was 3.1 percent (95 percent CI: 2.8, 3.3) and the risk for ovarian cancer was 0.4 percent (95 percent CI: 0.3, 0.5). The risks increased when the mothers had had breast cancer at younger ages, ranging from 6.5 percent if the mother had breast cancer before age 40 to 2.6 percent if she contracted cancer from the age of 70 onward (not shown in the table). If the mother had had ovarian cancer, the risk for ovarian cancer in the daughter was 0.9 percent (95 percent CI: 0.7, 1.2), and the risk increased to 1.8 percent (95 percent CI: 1.0, 3.3) if the mother had had ovarian cancer before age 50. Breast cancer risks of 5–12 percent were found if the mother had two or more diagnoses of breast/ovarian cancer and when both the mother and a sister had breast/ovarian cancer. The highest risk for ovarian cancer, 8.4 percent (95 percent CI: 2.8, 23.9), occurred when the mother had breast or ovarian cancer before age 50 and a sister also had breast or ovarian cancer. Note that the confidence intervals for the cumulative risks are calculated assuming independence; especially for the groups based on cancer in a sister, this is not quite true, and thus the true intervals should be wider.


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TABLE 7. Cumulative risks of breast and ovarian cancer at age 50 years among Swedish women with a mother or both a mother and a sister who had breast or ovarian cancer*

 
Attributable fraction
The estimated relative risk of breast cancer before age 50 given that one's mother developed breast cancer before age 50 is 2.7, and this yields an attributable fraction of 63 percent in the "exposed" population (that is, women whose mothers had breast cancer before age 50). In the general Swedish population, 1.6 percent of women contract breast cancer before the age of 50, leading to a population attributable fraction of 2.6 percent for breast cancer under age 50. Table 8 shows the attributable fraction of breast and ovarian cancer before age 50 due to breast and ovarian cancer at any age in the mother. The general population risk of breast cancer at any age among females is 11 percent, and the corresponding relative risk that a daughter will get breast cancer before age 50 is 2.0; this yields attributable fractions of 50 percent in the exposed women and 10 percent in the population. The corresponding fractions of ovarian cancer before age 50 due to ovarian cancer in the mother are 58 percent and 3 percent, respectively, for the exposed women and women in the general population.


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TABLE 8. Attributable fractions, in the "exposed" women* (AFe) and in the entire Swedish population (AFp), of breast and ovarian cancer diagnosed before age 50 years due to breast or ovarian cancer in the mother{dagger}

 

    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
In line with many other investigations, our study demonstrates that female first degree relatives of patients with breast cancer have an increased risk of breast cancer. This risk is highly dependent on the age at diagnosis of the proband. Additionally, daughters of women with ovarian cancer have an increased risk of both ovarian cancer and breast cancer. Our study, like the one by Hemminki and Vaittinen (11Go), being a nationwide cohort investigation, was able to obtain more accurate risk estimates than most retrospective case-control studies. Furthermore, our study addressed certain issues in more depth, such as the risk among women who have both a mother and a sister affected and the risk among women whose mothers have had two primary breast cancers. It also demonstrated that daughters of women with both breast and ovarian cancer have a high risk for both breast and ovarian cancer. In addition, our study included the sons of women with breast cancer and ovarian cancer, and increased risks were seen for thyroid cancer and testicular cancer among offspring. Our analysis of the nationwide data differed from that of Hemminki and Vaittinen (11Go) in that we used a straightforward cohort approach calculating person-years at risk with age- and calendar year-specific incidence reference data, while Hemminki and Vaittinen used a more approximate method.

We estimated cumulative risks up to 50 years of age for daughters of breast and ovarian cancer patients. To our knowledge, this has not previously been done on a nationwide scale, and it may be very valuable for clinical oncogenetic practice. Presently, large discussions are taking place in the scientific community in order to define a clinical basis for genetic testing. A strong risk relation exists between breast cancer and ovarian cancer, and families with many such diagnoses often harbor mutations, especially in the BRCA1 gene (14Go). Our data on risk for a daughter in relation to her mother's age at diagnosis, as well as the high risk associated with having a mother with both breast and ovarian carcinoma, may help researchers in identifying a group of patients who should be offered genetic counseling and mutation testing. Mothers who have been diagnosed with two primary breast cancers, especially at a young age, confer a particularly extreme risk on their female offspring.

Through the nationwide Swedish database, it may be possible to identify new risk relations and possible hereditary associations (15Go). Indeed, looking backwards, our data clearly could have pinpointed the association between breast and ovarian carcinoma which, through case-control studies, was postulated in the 1980s and was further used for linkage analysis and for finding the BRCA1 gene on chromosome 17. The relations between cases of breast/ovarian cancer in young women and testicular and thyroid cancer in their offspring may provide new genetic associations for further studies. Previously, a relation between breast cancer and thyroid cancer was delineated through Cowden's syndrome and mutations in the PTEN gene (16Go, 17Go). However, in a study by Marsh et al. (18Go), the majority of families showing clustering of breast and thyroid cancer did not have the syndrome stigmata of Cowden's disease, and it was not possible to associate them with the PTEN gene. Thus, there may still be new genes to discover in relation to families harboring breast and thyroid disease and breast and testicular cancer.

According to our estimate, approximately 10 percent of the breast cancer cases diagnosed before age 50 are attributable to maternal breast cancer occurring at any age. The fraction of breast cancer patients under age 50 at diagnosis (and of European ancestry) who carry either the BRCA1 gene or the BRCA2 gene is estimated to be 3 percent (D. Easton, unpublished data). Half of a person's genes originate from the mother; hence, only about 15 percent (1.5/10) of the excess cases occurring before age 50 are due to known genes.

The unexplained excess maternal (familial) breast cancer may be due to a common lifestyle, including reproductive habits, to unknown genes, or to a combination of these factors. It is well known that women with breast cancer are more educated and of higher social class than average (19Go, 20Go), and it is probable that the same holds true for their offspring. This is supported by the fact that the offspring of women with breast cancer had substantially lower incidence of lung cancer than expected and higher incidence of malignant melanoma than expected, since smoking in Sweden is less common and sunbathing is more common among better off and well educated women than among average women. Thus, it is reasonable to believe that some of the observed excess cancer is due to social inheritance. However, it is difficult to think that such factors could explain more than 80 percent of the excess breast cancer cases below age 50 attributed to maternal breast cancer; unknown genetic factors, perhaps interacting with environmental factors, are probably also important.

Our study had certain limitations. First, it was only possible to identify children born between 1941 and 1993. Since cancer incidence was registered up to 1993, the cohort could only provide relative and cumulative risk estimates up to the age of 53 years. For tumors which normally appear in persons above 55 years of age, such as prostate cancer and most gastrointestinal cancers, risk relations may have been missed. The data suggest that the earlier the onset of breast/ovarian cancer, the more strongly genetic is the etiology. However, there were no data on cancer incidence in daughters above 53 years of age, and hence one cannot exclude the possibility that there is a genetic component that increases breast/ovarian cancer risk at higher ages in both mothers and offspring. Another limitation of this study is that it was only possible to study risks in relation to cancer incidence in first degree relatives. This may have precluded the finding of stronger familial associations in certain families with a true dominant pattern of inheritance. In the cohort analyses, the reference population comprised all women in Sweden, including those whose mothers had breast and ovarian cancer; thus, the relative risks were slightly underestimated.

However, these limitations had no major impact on our conclusions. This study demonstrates that daughters of women with breast or ovarian cancer have a doubled risk of breast cancer before age 50 years and that the risk of ovarian cancer is increased, especially if the mother has also had ovarian cancer. It is also clear that the risks are higher if the mother's disease was diagnosed at a younger age. Furthermore, very high risks are present if the mother had bilateral breast cancer at a young age or had both breast and ovarian carcinoma. Offspring, including sons, experience an increased risk of thyroid and testicular cancer–relations that may indicate associations with new predisposing genes.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Variance Estimation in Cohort Analysis with Clusters of Individuals
Let the cohort consist of M sibships (clusters) with mi, i = 1, ..., M children, and let yij and xij be the observed (Obs) and expected (Exp) numbers of cases for individual j in sibship i. The observed and expected numbers in sibship i are then and and they are independent for different sibships. The standardized morbidity ratio (SMR) may be written

with variance (V) approximated by means of the delta method:




The population sibship parameters µx, {sigma}y, {sigma}x, and {rho}y,x denote the expectation of the expected number of cases in a sibship, the standard deviations of the observed and expected numbers in a sibship, and their correlation coefficient, respectively, and they may be estimated by the corresponding moments in the sample of sibships–for example, , where is the mean of the observed number of cases per sibship. Hence, the standard error (SE) of the SMR is

In the clustered cohort analysis, confidence intervals for the SMR were determined using normal approximation; that is, a 95 percent confidence interval was calculated as SMR ± 1.96 x SE(SMR). Note that the method is also applicable in the situation where an event may occur several times in a single individual. Then the individuals constitute the clusters.

In the present study, the Poisson-based standard errors were very close to the above clustered sampling-based estimates, except for the cohorts formed by women with both a mother and a sister with cancer.


    ACKNOWLEDGMENTS
 
This study was supported by a grant from the Swedish Cancer Society.


    NOTES
 
Reprint requests to Dr. Harald Anderson, Department of Cancer Epidemiology, University Hospital, SE-221 85 Lund, Sweden (e-mail: Harald.Anderson{at}cancerepid.lu.se).


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 

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Received for publication April 28, 1999. Accepted for publication February 4, 2000.