Publication of the International Union Against Cancer Publication de l’Union Internationale Contre le Cancer Int. J. Cancer: 73, 1–9 (1997) r 1997 Wiley-Liss, Inc. EFFECT OF PARITY AND AGE AT DELIVERY ON BREAST CANCER RISK IN SLOVENIAN WOMEN AGED 25–54 YEARS Chris ROBERTSON1*, Maja PRIMIC-ZAKELJ2, Peter BOYLE1 and Chung-Cheng HSIEH3 1Division of Epidemiology and Biostatistics, European Institute of Oncology, Milan, Italy 2Institute of Oncology, Epidemiology and Cancer Prevention Unit, Ljubljana, Slovenia 3University of Massachusetts, Cancer Center, Two Biotech, Worcester, MA In 1988, a case-control study on breast cancer and oral contraceptives with 624 cases and 624 matched controls in the age range 25–54 years was undertaken in Slovenia. This analysis assesses the relationship between parity and breast cancer risk: the relative importance of age at first birth, age at subsequent births and total parity. We also evaluate whether a dual effect of an increased risk immediately after childbirth followed by a long-term benefit exists. Three logistic regression models were used. Age at first delivery is an important breast cancer risk factor: among parous women it was associated with a 5.3% increase/year in the odds of breast cancer. Multiparity was not shown to be an independent risk factor. Age at subsequent deliveries was associated with a 1% increase in risk for every 1 year increase of age at any birth, but this contribution to the risk was not significant. In the analysis stratified by parity the most important influence is with the age at first birth. We find no evidence of an effect on the odds of breast cancer associated with the age at the second, or later, births. We do find that there is an increased risk associated with the birth of the first child followed by a longer term protective effect. A post-menopausal woman has a reduced breast cancer risk compared with a pre-menopausal woman of the same age, adjusting for the same number of deliveries and ages at these deliveries. Int. J. Cancer 73:1–9, 1997. r 1997 Wiley-Liss, Inc. Slovenia was one of the participating centers in the international case-control study (in 7 locations of the world performed in late 1960s) demonstrating that the risk of breast cancer is decreased in women who have their first child at an early age (MacMahon et al., 1970; Ravnihar et al., 1971). There is still no consensus about the effect of subsequent pregnancies. Some studies indicate that multiparity has an independent protective effect against breast cancer (Kelsey et al., 1993), while later re-analyses of the 7-countries study suggested that age at any birth was an independent risk indicator (albeit smaller than that for age at first delivery) and that the parity effect was determined by the age of occurrence of the component pregnancies (Trichopoulos et al., 1983). Some authors have suggested that age at last pregnancy may be even more important than age at the first one (Kalache et al., 1993; Kvale and Heuch, 1987), but this finding has recently been questioned (Hsieh et al., 1996). Several studies have demonstrated that a full-term pregnancy exerts a short-term adverse influence and a long-term beneficial influence on breast cancer risk (Kelsey et al., 1993; Lambe et al., 1994; Hsieh et al., 1994). In 1988, a new case-control study was undertaken in Slovenia to evaluate further the relationship between breast cancer and oral contraceptive use in the age range 25–54 years using a generalpopulation control group for the first time (Primic Zakelj et al., 1995). In addition to the data on oral contraceptives and classical risk factors, data on timing of all deliveries were also collected and evaluated. The main purpose of the present analyses is to assess the relationship among parity, age at delivery and breast cancer risk. We focus on 1) the relative importance of age at first birth; 2) the effect of age at subsequent births; and 3) the effect of total parity on breast cancer risks in young Slovenian women. Furthermore, we evaluate whether a dual effect of pregnancy exists whereby the birth of the first child is associated with an increased risk of breast cancer followed by a long-term protective effect. Three related approaches were used (Trichopoulos et al., 1983; Hsieh and Lan, 1996; Rosner et al., 1994) and are described in the Appendix. Each has a slightly different emphasis for modeling the effect of age at any birth on breast cancer risk and provides separate contributions to our understanding of the joint effects of parity and age at delivery. The simplest approach is a logistic regression model with separate terms for the age at any delivery and each separate delivery (Trichopoulos et al., 1983). A stratified model comparing uni- and nulli-parous women only to investigate whether the effects of parity and age at first delivery are modified by age at diagnosis is an extension of the simple model (Hsieh and Lan, 1996). In the proposed adaption of the Rosner et al. (1994) model, the variables in the model are the durations since the births until the age at diagnosis. This implies that age is a modifying factor for parity and is also an extension of the model of Trichopoulos et al. (1983). SUBJECTS AND METHODS Cases and controls Women from the whole of Slovenia, aged between 25 and 54 years, with breast cancer confirmed histologically and/or cytologically between January 1, 1988, and December 31, 1990, were included as cases. They were eligible if they had been permanent residents of Slovenia since 1965, if they had not had previous cancer (except non-melanoma skin cancer) and if they were considered psychologically competent to participate in such a study. Cases were identified at the Institute of Oncology in Ljubljana and 4 Slovenian general hospitals at the time of patient admission for diagnosis and/or primary treatment. Of 647 eligible cases, 23 refused to participate, resulting in a participation rate of 94.4%. For every case, one control was randomly selected from the Population Registry of Slovenia. Each control date of birth was matched to the case month and year of birth, and the control had to live in the same commune (60 in Slovenia) as the case. The mean age of cases and controls was 45 years. Other eligibility criteria were the same as for the case patients. Controls were contacted first by a letter; if they did not respond, they were contacted by telephone or a second letter (if their name was not in the telephone directory) within 2 weeks after the first letter was sent. If they did not answer the second invitation, or refused, or if they did not meet the selection criteria, another control was selected at random from the Population Registry. Of 624 potential first controls, 21 could not be traced and 71 were not eligible. The ineligibles arose because of violations of the entry criteria: 59 had not been residents Contract grant sponsor: Associazione Italiana per la Ricerca sul Cancro. *Correspondence to: Division of Epidemiology and Biostatistics, European Institute of Oncology, via Ripamonti 435, 20141 Milan, Italy. Fax: 139 2 57489813. E-mail: [email protected] Received 14 January 1997; Revised 20 May 1997 2 ROBERTSON ET AL. in Slovenia since 1965, 8 had another cancer and 4 were considered psychologically incapable of completing the study. From 532 eligible controls, 93 refused to be interviewed. These 185 controls were subsequently replaced by second (130) or subsequent (55) choices. Data collection Most patients (82.4%) were interviewed on the wards during their stay in the hospital for primary treatment, while 97 were interviewed during follow-up visits and 13 at home. Controls were visited and interviewed at home. The interviews were performed by 2 specially trained nurses; in most instances the matched pair (case and control) was interviewed by the same nurse. The interview lasted for approximately 30 min. It gathered data on basic demographic characteristics, education, reproductive and contraceptive history, family history of breast cancer, medical history and some other characteristics. Clinical data were collected from medical records. To assist better recall, a calendar was used on which oral contraceptive use and reproductive events since menarche were recorded. The date of diagnosis was taken to be the date of the first visit to the outpatient clinic that the biopsy that turned out to be positive was performed or the date of admission to the hospital on which biopsy was performed and proved positive. For every control a pseudo-diagnosis date was determined, the date on which she was exactly the same age as the case at diagnosis. All the data were collected prior to this date. For this study, each pregnancy that ended after 24 weeks was considered as ending with delivery. A woman was considered menopausal if her last period was more than 6 months before diagnosis/pseudo-diagnosis. Statistical methods The mathematical framework of the models is presented in the Appendix. Multivariate logistic regression was used for the estimation of relative risk (Breslow and Day, 1980). As this is a matched case-control study, conditional logistic regression was used. Nulliparous and uni-parous women are compared directly, as are uni-parous and bi-parous women (Lambe et al., 1994; Hsieh and Lan, 1996). In this case the matching is broken and an unconditional logistic regression model used, with age at diagnosis/ interview included in the model. This was especially important for the comparison of nulli-parous and uni-parous women, as there were only 62 parity eligible pairs, i.e., matched pairs with the case being either nulli-parous or uni-parous and the control also of parity 0 or 1. Adjustment was made for education, age at menarche, menopausal status, age at menopause and family history of breast cancer (mother) (Primic Zakelj et al., 1995). Adjusted and unadjusted values are presented. Results are presented as odds ratios (OR) and the corresponding 95% confidence intervals (95% CI). The analyses were performed for all the women together and for some characteristics also by the following age groups: 25–34, 35–44 and 45–54 years old. The first model considers that the risk of breast cancer is related to the age at birth of any child, together with indicator variables denoting the number of deliveries (Trichopoulos et al., 1983). When the analysis was performed for parous women, only parity eligible pairs were included and conditional logistic regression used. The second part is an extension of the first and considers interactions with parity and age at any birth and age at diagnosis (Lambe et al., 1994; Hsieh and Lan, 1996). Also, it is stratified by parity, and only adjacent parities are analyzed. Separate analyses were carried out to estimate the effect of age at first birth among women with parity 0 or 1, and to estimate the effect of age at second birth among women with parity 1 or 2. This analysis will reveal if the effects of parity and age at the birth of a child are modified by the age at diagnosis. The third part is also an extension of the first part and considers that the risk of breast cancer is related to the number of years from TABLE I – SUMMARY INFORMATION ABOUT THE WOMEN IN THE STUDY Number of children (% of cases and controls) Case Control 0 1 2 3 41 Total 7.5 6.3 26.1 22.8 50.2 53.2 11.4 14.3 4.8 3.5 624 624 Delivery Age (years) at delivery of children 1 Case Control 2 Case Control 3 Case Control 4 Case Control Age (years) at menopause Case Control Age (years) at menarche Case Control Number Mean Standard deviation Minimum Maximum 577 585 23.8 22.9 4.33 4.00 13 16 39 41 414 443 27.5 26.9 4.59 4.27 18 18 42 43 101 111 30.3 29.6 5.13 4.32 21 19 42 44 30 22 32.1 32.3 4.92 4.90 23 24 43 39 123 154 47.3 46.8 4.25 4.18 32 32 54 54 623 623 13.8 13.9 1.83 1.80 9 10 20 19 Education (number of years at school) (% of cases and controls) Case Control 1–8 9–12 131 Total 40.1 36.7 41.5 48.7 18.4 14.6 624 624 TABLE II – ESTIMATED EFFECTS OF AGE AT ANY BIRTH USING THE TRICHOPOULOS ET AL. (1983) MODEL Parity 1 Parity 2 Parity 3 Parity 41 Age at first delivery centered on 23 Age at second delivery centered on 27 Age at third delivery centered on 30 Age at fourth delivery centered on 32 Estimate1 SE Estimate2 SE 20.1141 20.2177 20.4049 0.3197 0.0467 0.2515 0.2291 0.2694 0.3806 0.0186 20.1099 20.1635 20.4029 0.1963 0.0445 0.2573 0.2347 0.2753 0.3911 0.0192 0.0060 0.0206 0.0061 0.0209 0.0330 0.0345 0.0417 0.0352 20.0360 0.0609 20.0434 0.0618 1These estimates were obtained from a conditional logistic regression and were not adjusted for any other variables.–2Conditional logistic regression adjusted for education, family history of breast cancer, age at menarche, menopausal status and age at menopause. menarche, the number of years since the birth of any child and the number of years from menopause, together with indicator variables for the birth of the first and subsequent children and for menopausal status (Rosner et al., 1994; Rosner and Colditz, 1996). RESULTS Summary information is presented in Table I. The number of deliveries ranges from 0 to 7 for both cases and controls. The percentage of cases who are nulli-parous is 7.5% and the corresponding percentage for the controls is 6.3%. There are slightly more deliveries among controls and, up to the third delivery, the controls are slightly younger, on average, at each delivery than cases. There PARITY, AGE AT DELIVERY AND BREAST CANCER RISK 3 TABLE III – DISTRIBUTION OF CASES AND CONTROLS WHO WERE NULLI-PAROUS OR UNI-PAROUS BY AGE AT DELIVERY AND CURRENT AGE Current age (years) Nulli-parous 25–34 Cases Controls OR 95% CI 35–44 Cases Controls OR 95% CI 45–54 Cases Controls OR 95% CI Uniparous: age at delivery (years) 13–19 20–24 25–29 30–41 5 4 1.00 — 4 3 0.95 0.12–7.58 9 10 0.58 0.11–3.15 7 2 2.61 0.31–22.02 — — — — 18 17 1.00 — 7 7 0.99 0.28–3.44 15 16 0.91 0.35–2.41 17 13 1.26 0.47–3.37 12 5 2.19 0.63–7.57 24 18 1.00 — 2 11 0.14 0.03–0.70 37 34 0.81 0.38–1.76 28 24 0.87 0.39–1.98 25 17 1.10 0.46–2.63 TABLE IV – WEIGHTED AVERAGES OF THE ODDS RATIOS ACCORDING TO DIFFERENT INTERVALS AFTER THE FIRST DELIVERY BASED ON THE DIFFERENCE BETWEEN 5-YEAR CATEGORIES OF CURRENT AGE AND AGE AT FIRST DELIVERY Years after delivery 0–10 OR 95% CI 11–20 OR 95% CI 211 OR 95% CI 1No Uni-parous: age at delivery (years) Nulli-parous 13–19 —1 — 1.00 — 20–24 25–29 30–41 0.86 1.56 1.39 0.18–4.16 0.45–5.35 0.46–4.20 1.00 — 0.51 0.86 1.03 1.51 0.22–1.14 0.49–1.51 0.55–1.92 0.70–3.25 1.00 — 0.32 0.81 0.82 0.11–0.91 0.41–1.60 0.37–1.82 —1 — observations here. is no difference in the age at menarche between cases and controls nor is there any difference in age at menopause, although a greater percentage of controls are post-menopausal, 24.7% compared with 19.7%. There was a family history of breast cancer among first-degree relatives in 6.4% of cases and 4.0% of controls. The first analysis was restricted to parous women and is based on model 1 in the Appendix, without the interaction term. It looked for the independent ‘‘main effects’’ of age at first delivery (continuous variable) and multiparity (defined as 2 or more deliveries). The coefficient for age at first delivery is statistically significantly different from zero ( p 5 0.0017) and implies a 5.3% (95% CI 2.0–8.8) increase in the odds of breast cancer for every 1-year increase in age at first delivery. The comparison of multiparity with uniparity has a relative risk of 0.96 (95% CI 0.72–1.28) implying that, on average, pregnancies beyond the first do not convey significant additional protection against breast cancer. The relative risk for the interaction between multiparity and age at first birth was not significantly different from zero, at 1.03/year (95% CI 0.96–1.10; p 5 0.40). From the model (Appendix model 2) exploring whether age at any delivery is an independent determinant of breast cancer risk, after controlling for parity we estimated regression coefficients (Table II). The coefficient for age at first birth implies a 4.4% (95% CI 1.01–8.56) increase in the odds of breast cancer for every 1 year increase in age at first delivery. The coefficients for age at subsequent deliveries were smaller than that for the first birth and non-signficant. Since they showed no substantial or systematic variation, they were combined into a common OR of 1.01/year (95% CI 0.98–1.04), implying that for every 1-year increase of age at any delivery after the first the odds of breast cancer increase by 1% ( p 5 0.40). To evaluate the hypothesis of a dual effect of pregnancy on breast cancer risk the analysis was first restricted to nulli-parous and uni-parous study subjects (210 cases and 181 controls) (Hsieh and Lan, 1996). The distribution of nulli-parous and uni-parous cases and controls by age at diagnosis and age at delivery and age-specific odds ratios are presented in Table III. The CIs are all wide as there are few observations; the pattern of the odds ratios is important. All age groups have lower odds ratios compared with nulli-parous women of the same age if the birth of the child was early, at 13–24 years. If the delivery was later (25–41 years), then there was an elevated OR relative to nulliparous women, particularly among the younger ages at diagnosis. Table IV shows that within each strata of years since delivery, uni-parous women have reduced ORs of breast cancer, compared with nulli-parous women, if the delivery was at a younger age but that the odds increase with increasing age at first delivery. Although individually not significant, the ORs are elevated soon after the delivery for uni-parous women with late delivery compared with nulli-parous women. The regression coefficients from model 3 in the Appendix (Hsieh and Lan, 1996) are presented in Table V. The interactions with age at diagnosis are included to investigate the relationship between age at first birth and age at diagnosis. A reduction in the odds of breast cancer by 0.85 (95% CI 0.51–1.43) was found for women having one full-term pregnancy at age 23 compared with nulliparous women. Age at first birth is the only significant effect ( p 5 0.0260), and then only in the unadjusted model. The predicted ORs of breast cancer relative to nulli-parous women are plotted in Figure 1. These show a transient increase in the odds soon after the first birth particularly among women with older age at delivery. The odds decline as the number of years since the birth increases. The estimated break-even point of about 15–20 years after delivery is consistent with the previous estimates (Hsieh and Lan, 1996). Bi-parous and uni-parous women were compared. The regression coefficients obtained from model 4 in the Appendix are presented in Table V. No evidence suggests any effect of age at second birth over and above the effect of age at first birth. The distribution of cases and controls and age-specific ORs by age at diagnosis over the age groups at second delivery are presented in Table VI. The ORs for bi-parous women are in general lower than for uni-parous women, though there is a tendency for ORs to increase with older age at second delivery in age groups 35–44 and 45–54 years. However, none of the ORs are significantly different from zero and there is no evidence of an effect of age at second birth. The parameter estimates for model 5 in the Appendix are presented in Table VII. The most important effects are age at first birth, parity and menopausal status. At menopause there is a 40% reduction in the odds ( p 5 0.03) compared with pre-menopausal women of the same age, parity and ages at childbirth. Relative to a ROBERTSON ET AL. 4 FIGURE 1 – Age at first birth and years since the birth. This graph shows the predicted odds ratios of breast cancer based upon the Hsieh and Lan (1996) model for nulli- and uni-parous women. The horizontal line corresponds to nulli-parous women, who have an odds ratio of 1. There is a separate predicted line for women with 1 birth only at ages 20, 25, 30 and 35. TABLE V – REGRESSION COEFFICIENT ESTIMATES: MODELING WITH INTERACTION TERMS Parity 1 vs. 0 Parity Age at 1st delivery4 Parity 1 3 age5 Age at 1st delivery 3 age Parity 2 vs. 1 Age at 1st delivery Age at 1st delivery 3 age Parity 2 Age at 2nd delivery7 Parity 2 3 age Age at 2nd delivery 3 age Estimate1 SE Estimate2 SE Hsieh and Lan estimate3 20.1713 0.0544 20.0408 20.0031 0.2541 0.0244 0.0380 0.0038 20.1597 0.0364 20.0412 20.0028 0.2634 0.0263 0.0391 0.0040 21.0945 0.0686 0.0144 20.0011 0.0405 20.0005 20.0995 0.0003 0.0232 20.0003 0.0188 0.0031 0.1507 0.0211 0.0224 0.0035 0.0292 0.0004 20.1069 0.0027 0.0256 20.0005 0.0196 0.0032 0.1530 0.0213 0.0225 0.0036 —6 —6 20.3962 0.0182 4.7 3 1026 20.0002 1These estimates were obtained from an unconditional logistic regression (see text) and were not adjusted for any variables other than age.–2Unconditional logistic regression (see text) adjusted for age, education, family history of breast cancer, age at menarche, menopausal status and age at menopause.– 3Taken from Hsieh and Lan (1996).–4Age at 1st delivery centered on 23.–5Age at interview centered at 45.–6Estimate not quoted.–7Age at 2nd delivery centered on 27. nulli-parous women with the same age at menarche and menopause, a women with parity 1 will have an instantaneous increase in the odds of breast cancer at the delivery ( p 5 0.02), but thereafter the odds will decrease by 5.2%/year ( p 5 0.002). In this way a first delivery is associated with an increased risk initially but with a longer term protection. There is no significant effect of a second delivery over and above the first ( p 5 0.55). Predicted odds ratios are presented in Figures 2–4 for a number of scenarios of deliveries, including nulli-parous. All were based on an age at menarche of 12 and an age at menopause of 50. These are predictions based on a linear model, and their utility depends on the adequacy of the model. Figure 2 looks at the effect of age at first birth among women with only one birth. Relative to a women with one birth at age 18, the later the first birth the greater the odds but PARITY, AGE AT DELIVERY AND BREAST CANCER RISK 5 TABLE VI – DISTRIBUTION OF UNI-PAROUS AND BI-PAROUS CASES AND CONTROLS BY AGE AT SECOND DELIVERY AND CURRENT AGE Current age (years) Uni-parous 25–34 Cases Controls OR 95% CI 35–44 Cases Controls OR 95% CI 45–54 Cases Controls OR 95% CI Bi-parous: age at second delivery (years) 18–24 25–29 30–34 351 20 15 1.00 — 8 8 0.75 0.23–2.48 5 11 0.34 0.10–1.19 1 3 0.25 0.02–2.63 — — — — 51 41 1.00 — 29 35 0.67 0.35–1.27 50 62 0.65 0.37–1.13 32 25 1.02 0.53–1.99 11 6 1.45 0.49–4.28 92 86 1.00 — 35 39 0.83 0.48–1.43 73 76 0.89 0.57–1.38 50 45 1.04 0.63–1.71 19 22 0.81 0.41–1.60 TABLE VII – REGRESSION COEFFICIENT ESTIMATES: MODELING DURATION FROM EVENTS Estimate1 Years since menarche3 Years since first delivery4 Parity 11 Years since second delivery4 Parity 21 Years since menopause4 Post menopause SE Estimate2 SE 0.0542 0.0336 0.0534 0.0341 20.0540 0.0170 20.0534 0.0175 1.0167 0.4095 0.0081 0.0152 0.9962 0.4173 0.0068 0.0152 20.2059 0.2823 20.1683 0.2846 20.0017 0.0393 0.0017 0.0395 20.4940 0.2314 20.5141 0.2333 1These estimates were obtained from a conditional logistic regression and were not adjusted for any other variables.–2Conditional logistic regression adjusted for education and family history of breast cancer.–3Two women had unknown age at menarche, and the pairs were omitted. This parameter should be interpreted with care; see Appendix.–4These variables all take the value zero if the event has not occurred. only after the birth. Relative to a women with one birth, nulliparous women have smaller odds but only in the period following the birth, as the risk for nulli-parous women increases steadily throughout their life until menopause, while for parous women the increase following the first birth is at a much reduced rate. Relative to a woman with one birth at 18, a woman with one birth only at age 28 is predicted to have a constant increased risk after the birth. The lines are parallel after the birth because the only difference between the 2 women is the time since the birth of their only children, which for fixed time has a constant effect. A similar picture can be seen with 2 births (Fig. 3). The drop in the OR associated with the second birth is not precisely estimated and is not significantly different from zero. Figure 4 shows a comparison of one late birth with 2 late births; apart from an instantaneous slight reduction in OR associated with the second birth, there is little long-term effect. In all graphs the important conclusion is that the first birth is associated with a transient increase in risk of breast cancer relative to a nulli-parous woman of the same age and age at menarche. This lasts for about 15–20 years following the birth. For women with 2 births within 3 years the transient increase in risk lasts for a slightly shorter time. DISCUSSION As in most epidemiological studies, our study shows that age at first delivery is an important breast cancer risk factor. Among parous women it was associated with a 5.3% increase in the odds of breast cancer for every 1 year increase in age at first birth, which is close to the figure of 5.1% reported by Trichopoulos et al. (1983). This is compatible with the observations from animal experiments of pregnancy-induced irreversible terminal differentiation of mammary epithelium (Russo et al., 1982; 1990). The interaction term between multiparity and age at first birth among parous women was not significant in our study. The estimated increase in the odds of 2.7%/year is similar to that of Trichopoulos et al. (1983) (2.2%) but has a larger standard error, partly as a consequence of the smaller sample size here. Our finding does not contradict the hypothesis that multiparity is modifying the effect of age at first delivery. The estimated increase in the odds of breast cancer associated with age at delivery of the first child of 4.4%/year is comparable to estimates reported by Trichopoulos et al. (1983) (3.5%) and Decarli et al. (1996) (4.7%). Age at subsequent deliveries was associated with a 1% increase in risk for every 1 year increase of age at any birth. Again, this estimate is similar to those estimated by Trichopoulos et al. (1983) (0.9%) and Decarli et al. (1996) (0.7%). This demonstrates that our data give comparable results to other studies and that only the age at first birth is important in our data. We find no significant independent effect of parity, which is unusual. Part of the reason for this is that few of the cases in our study are nulli-parous (7%) compared with, for example, 16% in Italy (Decarli et al., 1996) and 19% in Sweden (Lambe et al., 1994). The most important influence of age at any birth is with age at first birth. We find no evidence of an effect associated with age at second birth when comparing uni-parous and bi-parous women. The parameter estimates in Table IV are consistent with those presented by Hsieh and Lan (1996). The assertion that age at diagnosis is a modifying factor for age at first birth receives limited support, as one of the interactions involving age at diagnosis are significant. Rosner et al. (1994) and Rosner and Colditz (1996) used cohort data and modeled breast cancer incidence rates. As case-control data are used here, there is no information on incidence rates; however, the ORs that can be derived from Table VI are similar to those derived from Rosner et al. (1994) and Rosner and Colditz (1996). By using the year since the birth, age at diagnosis is assumed to modify the effect of parity but not the age of delivery (Robertson and Boyle, 1997), in contrast to the Hsieh and Lan (1996) model, in which age modifies both effects. The odds of breast cancer increase instantaneously at the delivery of the first child but thereafter increase at a reduced rate compared with before the birth. Our results are consistent with a short-term increase in breast cancer risk associated with the first birth (Hsieh and Lan, 1996). Overall, nulli-parous women are at the greatest long-term risk, but FIGURE 2 FIGURE 3 PARITY, AGE AT DELIVERY AND BREAST CANCER RISK 7 FIGURE 4 – Nulli-parous, uni-parous and bi-parous women (Rosner et al., 1994). This graph shows the predicted odds ratio of breast cancer for nulli-parous women, or women with 1 birth at 35, or women with 2 births at ages 35 and 38 only relative to a woman with 2 births at ages 20 and 23. The horizontal line is the odds ratio for a women with 2 births at ages 20 and 23. The dotted curve corresponds to nulli-parous women. within the child-bearing years nulli-parous women are predicted to have a lower risk than parous women. This is the period when risk of breast cancer is small; in older ages there is a much greater risk of breast cancer among nulli-parous women. Evidence of a small effect of age at second and subsequent births has been reported (Trichopoulos et al., 1983; Lambe et al., 1994; Rosner et al., 1994). No significant effect of age at second and subsequent births was detected in this analysis. It is unlikely that selection, recall or confounding bias could explain this result. Most cases (96.2%) registered in The Cancer Registry of Slovenia were interviewed, and parity status certainly did not influence the response rate of general population controls. A calendar was used to improve recall, and major confounding variables were taken into FIGURE 2 – Nulli-parous and uni-parous women (Rosner et al., 1994). This graph shows the predicted odds ratios of breast cancer for nulli-parous women, or women with 1 birth only relative to a woman with 1 birth at age 18. The horizontal line is the odds ratio for a woman with 1 birth at age 18. The 2 lines with a step in them correspond to women with 1 birth at age 28 and 1 birth at 38. The dotted curve corresponds to nulli-parous women. FIGURE 3 – Nulli-parous and bi-parous women (Rosner et al., 1994). This graph shows the predicted odds ratios of breast cancer for nulli-parous women, or women with 2 births only relative to a woman with 2 births at ages 20 and 23. The horizontal line is the odds ratio for a woman with 2 births at ages 20 and 23. The 2 lines with a step in them correspond to women with 2 births at ages 30 and 33 and 2 births at ages 40 and 43. The dotted curve corresponds to nulli-parous women. account in the analysis. As the magnitude and sign of the estimates of the effects obtained here are consistent with previously published estimates, the most likely scenario is that our study sample was not large enough to detect the small additional effects of age at deliveries subsequent to the first one on the risk of breast cancer. The value of the statistical modeling is that we are able to assess the joint effects of births and the age at which these births occur. The models may be viewed in increasing order of complexity. Those of Trichopoulos et al. (1983) are the simplest, as they do not have interaction effects betewen age and the births. The other 2 models do have such effects. These models are used to investigate whether age modifies the effects of parity and age at first and subsequent births. We have significant evidence to support this effect with respect to the birth of the first child but not the age at the delivery. The Tricholoulos et al. (1983) model does not incorporate any transient effects and in this instance should be viewed as a necessary preliminary model. Each model can be seen from a slightly different point of view and each provides related contributions to the estimation of the effects of parity and the age at which the births occur on the risk of breast cancer (Robertson and Boyle, 1997). ACKNOWLEDGEMENTS This work was conducted within the framework of support from the Associazione Italiana per la Ricerca sul Cancro (Italian Association for Cancer Research). 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RUSSO, J., TAY, L.K. and RUSSO, I.H., Differentiation of the mammary gland and susceptibility to carcinogenesis. Breast Cancer Res. Treat., 2, 5–73 (1982). TRICHOPOULOS, D., HSIEH, C.-C., MACMAHON, B., LIN, T.M., LOWE, C.R., MIRRA, A.P., RAVNIHAR, B., SALBER, E.J., VALAORAS, V.G. and YUSA, S., Age at any birth and breast cancer risk. Int. J. Cancer, 31, 701–704 (1983). APPENDIX: MODELS FOR THE EFFECT OF AGE AT ANY BIRTH Trichopoulos et al. (1983) published a model for estimating the effects of age at any birth on breast cancer risk. The age at diagnosis for cases and age at interview for controls is denoted by t. We let ti represent the age at the time of the ith birth, and assume that there are s births. The age ti is not defined if there are less than i births for i 5 l, . . ., s. The first model uses only parous women and can be written as 11 2 p2 5 µ 1 g (t 2 t*) 1 b p 1 a (t 2 t*) p ln 1 2 2 1 1 1 1 a2 (t1 2 t*) 1 p21 . (1) Age is centered on t*. The term (t1 2t1*)p21 is used to investigate if multiparity (2 or more births) interacts with age at first birth. This model is extended to investigate the separate contributions of all births. 11 2 p2 5 µ 1 g (t 2 t*) 1 b p p ln 1 1 11 11 2 p2 5 µ 1 g (t 2 t*) 1 b p p ln 1 1 11 1 a1 (t1 2 t*) 1 p11 1 d1 (t 2 t*) p1 1 r1 (t 2 t*) (t1 2 t*) 1 p11 . ln (2) The variables pi1 are indicator variables taking the value 1 if there are greater than or equal to i births and zero otherwise. The term (ti 2 t*i )pi1 serves to ensure that there is no contribution to the model for ai from women with fewer than i births. Also, if s 5 0, as it will be for nulli-parous women, the terms in a and b do not contribute to the model. The estimates for this model are presented in Table I. The term b1 represents the effect of one or more births, where the first is at age t1*, and b2 represents the additional effect of 2 or more births, where the second is at age t*. 2 An increase in age at first birth of 1 year is associated with an increase in the log odds of being a case of a1 units, and a2 represents the effect of the age at second birth given, the age at first birth. Hsieh and Lan (1996) investigated the effect of the age at which women gave birth through a time-dependent model of disease risk. They also developed their model through a stratification to compare parity 1 with parity 0, and parity 2 with parity 1. For (3) This model includes differential terms for the age at diagnosis for cases or interview for controls, for nulli-parous and uni-parous women, and this is the means by which time-dependent effects are included. If the estimated effects of d or r are significantly different from zero then there is evidence that age modifies the effects of a birth (d), or the effect of the age at that birth (r). The predicted odds ratios in Figure 1 are obtained from the above equation. In the comparison of uni-parous with bi-parous women the model is extended: 11 2 p2 5 µ 1 g (t 2 t*) 1 b p p 1 b2 P2 1 · · · 1 bs ps1 1 a1 (t1 2 t*)p 1 11 1 a2 (t2 2 t*) 2 p21 1 · · · 1 as (ts 2 t* s ps1) . nulli-parous vs. uni-parous women, their model for estimating the effect of age at any birth on breast cancer risk is: 1 2 21 1 a1 (t1 2 t*) 1 1 a2 (t2 2 t*) 2 p21 1 d2 (t 2 t*) p21 (4) 1 r1 (t 2 t*)(t1 2 t*) 1 1 r2(t 2 t*)(t2 2 t*)p 2 21. This model has time-dependent effects for the age at second birth over and above the time-dependent effects for the age at the first birth. These are stratified models and are extensions to model 2, restricted to 2 births. The parameter estimates for models 3 and 4 are presented in Table IV. Rosner et al. (1994) published a modification of a mathematical model for breast cancer incidence that was originally published by Pike (1987). Subsequently, they developed a log incidence model (Rosner and Colditz, 1996). These models are more involved than the ones of Hsieh and Lan (1996) and of Trichopoulos et al. (1987) in that they are based on the concept of breast tissue aging. Both of these models were developed for cohort studies where estimates of incidence can be obtained. We propose to adapt the Rosner et al. (1994) model for use in case-control studies. PARITY, AGE AT DELIVERY AND BREAST CANCER RISK The model for breast cancer incidence at age t, I(t), is written as I(t) 5 [d(t)]k, where d(t) denotes the breast tissue age at calender age t, and k is an exponent determined by the rate of increase of breast cancer incidence with breast tissue age. Breast tissue age is written as a linear function: d(t) 5 g1 (t 2 t0) 1 b1 p11 1 b2 p21 1 a1(t 2 t1) p11 1 a*[(t 2 t2) p21 1· · ·1 (t 2 ts) ps1] 1 g2 pm 1 g3(t 2 tm) pm . 2 Age at menarche is denoted t0 and in nulli-parous women breast tissue is assumed to age at a rate of g1 a year since menarche. There is no aging of the breast tissue before menarche. The variable pm is an indicator of menopausal status and takes the value 1 for post-menopausal women (0 otherwise). Age at menopause is denoted tm and is defined for post-menopausal women only. This model also assumes a common effect for the length of time since the second and subsequent births, denoted a*. 2 We use a model similar to the Rosner and Colditz (1996) model: 11 2 p2 5 µ 1 g (t 2 t ) 1 b p p ln 1 0 1 11 1 b2 p2 1 a1(t 2 t1) p11 1 a*[(t 2 t2) p21 1· · ·1 (t 2 ts) ps1] 2 1 g2 pm 1 g3(t 2 tm) pm . (5) 9 This is not an attempt to model the odds of being a case as a function of breast tissue age but an attempt to model breast cancer risk at a particular age as a function of the number of years since the births. Essentially, we propose to use the functional form of the model to relate the number of years since an event to the log odds of breast cancer. The parameter estimates are in Table VI. This model is also an extension to (2), with the effects of births after 3 constrained to be equal, in that an interaction with age and parity is included. It is important not to overinterpret this model within a casecontrol study. As cases and controls are matched for age and as there are terms in the model for age some parameters are not identifiable. Specifically, the coefficient g1 will just give the effect of age at menarche (with a negative sign), rather than the time from menarche. Furthermore, for a fixed age at menarche a 1-year increase in years since menarche is the same as a 1-year increase in age, which cannot be estimated within a case-control study. Thus when we compare the effect of different patterns of birth the age at menarche is always constant and so the number of years since menarche is the same in the comparison groups. The other terms all involve age through an interaction, and these are estimable and interpretable within a case-control setting (Hsieh and Lan, 1996; Breslow and Day, 1980).