Roman Rouzier Ae

Charles Coutant

A E Be ´ne ´dicte Lesieur

A E Chafika

Mazouni Ae

Roberto Incitti Ae

Rene ´natowicz Ae

Lajos Pusztai

R Rouzier
email: roman.rouzier@tnn.aphp.fr

Á B Lesieur

Á C Coutant

Á C Mazouni

Á L Pusztai

R Incitti

R Natowicz

Direct comparison of logistic regression and recursive partitioning to predict chemotherapy response of breast cancer based on clinical pathological variables

Keywords: Breast cancer, Prediction, Pathological complete response, Logistic regression model, Recursive partitioning model

The purpose was to compare logistic regression model (LRM) and recursive partitioning (RP) to predict pathologic complete response to preoperative chemotherapy in patients with breast cancer. The two models were built in a same training set of 496 patients and validated in a same validation set of 337 patients. Model performance was quantified with respect to discrimination (evaluated by the areas under the receiver operating characteristics curves (AUC)) and calibration. In the training set, AUC were similar for LRM and RP models (0.77 (95% confidence interval, 0.74-0.80) and 0.75 (95% CI, 0.74-0.79), respectively) while LRM outperformed RP in the validation set (0.78 (95% CI, 0.74-0.82) versus 0.64 (95% CI, 0.60-0.67). LRM model also outperformed RP model in term of calibration. In these real datasets, LRM model outperformed RP model. It is therefore more suitable for clinical use.

Introduction

The use of adjuvant chemotherapy is influenced by three important considerations. These include estimation of risk of relapse (prognosis), probability of sensitivity to therapy (response prediction) and risk of adverse events from treatment. Several prognostic risk prediction models exist that combine various clinical and pathological variables into a prognostic score [START_REF] Chollet | Is Nottingham prognostic index useful after induction chemotherapy in operable breast cancer?[END_REF][START_REF] Diblasio | Use of nomograms to predict the risk of disease recurrence after definitive local therapy for prostate cancer[END_REF][START_REF] Eastham | Nomograms as predictive models[END_REF][START_REF] Kattan | Comparison of Cox regression with other methods for determining prediction models and nomograms[END_REF][START_REF] Kattan | Nomograms are superior to staging and risk grouping systems for identifying high-risk patients: preoperative application in prostate cancer[END_REF][START_REF] Kattan | A tool for predicting breast carcinoma mortality in women who do not receive adjuvant therapy[END_REF][START_REF] Pusztai | Technology insight: Emerging techniques to predict response to preoperative chemotherapy in breast cancer[END_REF][START_REF] Ravdin | Computer program to assist in making decisions about adjuvant therapy for women with early breast cancer[END_REF][START_REF] Rouzier | Nomograms to predict pathologic complete response and metastasis-free survival after preoperative chemotherapy for breast cancer[END_REF][START_REF] Rouzier | Development and validation of nomograms for predicting residual tumor size and the probability of successful conservative surgery with neoadjuvant chemotherapy for breast cancer[END_REF][START_REF] Shariat | Can nomograms be superior to other prediction tools?[END_REF][START_REF] Shariat | Comparison of nomograms with other methods for predicting outcomes in prostate cancer: a critical analysis of the literature[END_REF][START_REF] Chun | Initial biopsy outcome prediction-head-to-head comparison of a logistic regression-based nomogram versus artificial neural network[END_REF]. Adjuvant online is perhaps the most commonly employed and the most user friendly among these tools (www.adjuvantonline.org) [START_REF] Ravdin | Computer program to assist in making decisions about adjuvant therapy for women with early breast cancer[END_REF]. We previously developed a similar clinical pathological variable based chemotherapy response prediction model [START_REF] Rouzier | Nomograms to predict pathologic complete response and metastasis-free survival after preoperative chemotherapy for breast cancer[END_REF]. This model was built by using data from patients who received preoperative, neoadjuvant chemotherapy and therefore tumor response to treatment could be directly measured. Our clinical response prediction nomogram was subsequently validated on two sets of independent cases from two different institutions and proved to be rather accurate [START_REF] Rouzier | Nomograms to predict pathologic complete response and metastasis-free survival after preoperative chemotherapy for breast cancer[END_REF]. However, there are several different mathematical ways to combine variables into a multivariable predictor. The most often used model is logistic regression that is a form of generalized linear models and allows one to predict a discrete outcome, such as group membership (i.e. response versus no response or recurrence versus no recurrence), from a set of dependent variables that may be continuous, discrete, dichotomous, or a mix of any of these. Variables are combined in a linear manner. However, non-linear models may be more pertinent for some situations. Recursive partitioning is an example of nonlinear predictors. In recursive partitioning, data are divided on the basis of the possession of specified attributes. In contrast to logistic regression, recursive partitioning is a nonparametric type of analysis that repeatedly subdivides data into smaller and smaller subgroups based on characteristics that predict the desired endpoint. The goal is to construct subgroups that, ideally, consist entirely of subjects with one endpoint category or another. Recursive partitioning, unlike logistic regression is nonlinear in its parameters, and would have an advantage if the true relationship between the variables and the outcome of interest is nonlinear. However, if the true relationship is linear, then recursive partitioning may be inferior to linear models because it is based on assumptions that are too general. Several studies have compared the performance of linear and non-linear predictors in model building, however few studies compared the performance of distinct models built from the same data and tested on independent validation sets [START_REF] Kattan | Comparison of Cox regression with other methods for determining prediction models and nomograms[END_REF][START_REF] Kattan | Nomograms are superior to staging and risk grouping systems for identifying high-risk patients: preoperative application in prostate cancer[END_REF][START_REF] Shariat | Can nomograms be superior to other prediction tools?[END_REF][START_REF] Shariat | Comparison of nomograms with other methods for predicting outcomes in prostate cancer: a critical analysis of the literature[END_REF]. Comparing various strategies for multivariable model development may allow a better understanding of the strengths and limitations of these models.

The goal of the current work, was to compare our previously reported logistic regression model using clinical variables to predict pathologic complete response to preoperative chemotherapy with a non-linear recursive partitioning model that was built from the same discovery set (n = 496) and tested on the same validation set (n = 337).

Materials and methods

In institutional clinical databases, we identified 496 patients from the Institut Gustave Roussy (IGR) in Villejuif, France, and 337 women from the University of Texas M.D. Anderson Cancer Center (MDACC) in Houston, Texas, United States, diagnosed with breast cancer and treated with an anthracycline-based primary chemotherapy. All the women gave informed written consent to therapeutic procedures and to the analysis of data related to their malignancy in accordance with Institutional Review Board institutional guidelines and the Declaration of Helsinki. The cohort treated at IGR included 496 patients who received 3 or 4 courses of anthracycline-based preoperative chemotherapy and was used as training set to develop the predictive models. The second cohort included 337 patients treated at MDACC with 4 courses of anthracycline-based preoperative chemotherapy and was used as a validation set. The clinical and histological characteristics were prospectively recorded into databases. The largest tumor dimension at clinical examination was recorded as the tumor diameter. Histologic grade, defined according to the modified Scarff, Bloom, and Richardson system described by Contesso et al. [START_REF] Contesso | The importance of histologic grade in long-term prognosis of breast cancer: a study of 1,010 patients, uniformly treated at the Institut Gustave-Roussy[END_REF], was used at IGR, and the modified Black's nuclear grade was used at MDACC. All the patients underwent axillary lymph node dissection and mastectomy or segmental mastectomy. Patients without residual invasive tumor or with only strictly in situ carcinoma were classified as having pathological complete response (pCR) in the breast.

Patient characteristics and chemotherapy modalities have been reported previously [START_REF] Rouzier | Nomograms to predict pathologic complete response and metastasis-free survival after preoperative chemotherapy for breast cancer[END_REF]. Table 1 describes the characteristics of the population, as well as tumor and histological findings on the 496 patients of the training set and on the 337 patients of the validation set. Patients had operable breast cancer: 3 (1%), 293 (59%), 161 (32%) and 39 (8%) patients had T0-1, T2, T3 and T4 tumors in the training set and 13 (4%), 109 (32%), 90 (27%) and 125 (37%) patients had T0-1, T2, T3 and T4 tumors in the validation set. Forty-three percent and 25% of patients had a negative clinical nodal status in the training set and the validation set, respectively. Twenty-nine percent and 46% of patients had estrogen receptor (ER) negative tumors in the training set and the validation set, respectively. Seven percent, 57, and 36% in the training set and 5, 40, and 55% in the validation set had grade 1, grade 2, and grade 3 tumors, respectively. Eighty-nine percent and 95% of patients had ductal tumors in the training set and the validation set, respectively.

In order to develop a well-calibrated logistic regressionbased nomogram and a recursive partitioning model, we built these models in a training cohort and validated them in an independent validation cohort. We tested clinicopathological characteristics (age, tumor size, nodal status, histologic type and grade, ER status, multifocality and number of courses of preoperative chemotherapy) in a multivariate analysis for association with pCR. The performance of the multivariable model was assessed with respect to discrimination and calibration. Discrimination (i.e. whether the relative ranking of individual predictions was in the correct order) was quantified with the the area under (AUC) the receiver-operating characteristic curve (ROC) which can range from 0 to 1 (1 indicating perfect concordance, 0.5 indicating no association and 0 indicating perfect discordance) [START_REF] Hanley | The meaning and use of the area under a receiver operating characteristic (ROC) curve[END_REF].

Calibration corresponds to the agreement between observed outcome frequencies and predicted probabilities. Results are displayed as a calibration curve that shows the relationship between the observed outcome frequencies and the predicted probabilities for groups of patients defined by quartiles in the logistic regression model or by the final leaf in the recursive partitioning model. A calibration curve can be approximated by a regression line with intercept a and slope b. These parameters can be estimated in an LRM with the event as outcome and the linear predictor as the only covariate. Well-calibrated models have a = 0 and b = 1. Therefore, a sensible measure of calibration is a likelihood ratio statistic testing the null hypothesis that a = 0 and b = 1. The statistic has a v 2 distribution with 2 degrees of freedom (unreliability [U]-statistic). Individual predictions were either calculated from nomograms or were obtained from the original data for the RP model. We also evaluated average error (for quartiles) [E average (E aver )] and maximal error (for individual predictions) [E maximal (E max )] between predictions and observations obtained from a calibration curve. This gives an idea of model performance when extrapolated to new patient populations. This is of particular importance for clinical practice because probabilities are announced to patients without a confidence interval. To indicate a probability, ±maximal error or average error is more appropriate than providing only a probability.

All analyses were performed using the R package with the Design, Hmisc, Rpart and Verification libraries (http:// lib.stat.cmu.edu/R/CRAN/).

Results

Models development

Both models were developed from the same data set (IGR) including 496 patients. Forty-five (9%) patients had pathological complete response (pCR) and 451 (91%) had residual disease in this training set. In multivariate logistic regression analysis, initial T stage (TNM), ER status, grade, number of course of preoperative chemotherapy were independently associated with pCR. We added age to the final model because it improved the calibration of the logistic regression model. The equation of probability of achieving pCR was P = 1/(1 ? exp (-X)). Where X = -5.85766 ? 3 * V1 -0.02247 * V2 -0.46632 * V3 ? 0.91987 * V4 -0.85084 * V5 and V1 was the number of preoperative course (3 or 4), V2 was age in years, V3 was T of TNM classification (0, 1, 2, 3 or 4), V3 was histological grade (1, 2 or 3), and V5 was estrogen receptor status (0 or 1).

This clinical response prediction prediction model is freely accessible online [START_REF] Rouzier | Nomograms to predict pathologic complete response and metastasis-free survival after preoperative chemotherapy for breast cancer[END_REF] at http://www.mdanderson.org/ care_centers/breastcenter/dIndex.cfm?pn=448442B2-3EA5-4BAC-98310076A9553E63.

An example of the screen is shown on Fig. 1. The website also includes a calculator to estimate probability of breast conserving surgery and probability of residual tumor less than 3 cm after neoadjuvant chemotherapy. We next developed a recursive partitioning model. Recursive partitioning analysis created a tree that used grade, ER status, age and number of cycles of preoperative chemotherapy. The tree is represented in Fig. 2.

Comparison of the two pCR prediction models

We compared the discrimination and the calibration of the two distinct models in both the original training data and independent validation data set. The validation set included 337 patients from MDACC, the rate of pCR and residual disease were 12.7% (43 patients) and 87.3% (296 patients), respectively.

Discrimination

In the training set, the AUC of the ROC curve obtained with the logistic regression model and with the recursive partitioning model were similar, 0.77 (95% CI, 0.74-0.80; P \ 10 -3 ) and 0.75 (95% CI, 0.74-0.79; P \ 10 -3 ), respectively (Table 2; Fig. 3). In the validation set, the AUC of the ROC curve for the logistic regression model remained good, 0.78 (95% CI, 0.74-0.82; P \ 10 -3 ), however the AUC of the ROC curve for the recursive partitioning model was lower: 0.64 (95% CI, 0.60-0.67) (Table 2; Fig. 4).

Calibration

We evaluated the calibration of the two models on the validation set. The calibration of the logistic regression model was excellent with no statistical difference between predicted probability and observed probability (P = 0.24). The average difference (E aver ) and maximal difference (E max ) in predicted and calibrated probabilities were 1.6 and 1.6.10 -14 %, respectively. The calibration of the recursive partitioning model was less good. However, there was also no statistical difference between predicted probability by the recursive partitioning tree and observed probability (P = 0.12). The average difference (E aver ) and maximal difference (E max ) in predicted and calibrated probabilities were 6.3 and 27.5%, respectively, (Table 2; Fig. 5).

Discussion

In these real datasets, the logistic regression model predicted breast tumor chemosensitivity to primary chemotherapy was better than recursive partitioning. This finding is of particularly interest because the goal of these models is to develop a predictive model for clinical use and the highest possible accuracy should be the primary objective. Several mathematical models are available to combine variables into multivariate predictors and one method might be better than the other in particular situations [START_REF] Chollet | Is Nottingham prognostic index useful after induction chemotherapy in operable breast cancer?[END_REF][START_REF] Diblasio | Use of nomograms to predict the risk of disease recurrence after definitive local therapy for prostate cancer[END_REF][START_REF] Eastham | Nomograms as predictive models[END_REF][START_REF] Kattan | Comparison of Cox regression with other methods for determining prediction models and nomograms[END_REF][START_REF] Kattan | Nomograms are superior to staging and risk grouping systems for identifying high-risk patients: preoperative application in prostate cancer[END_REF][START_REF] Kattan | A tool for predicting breast carcinoma mortality in women who do not receive adjuvant therapy[END_REF][START_REF] Rouzier | Nomograms to predict pathologic complete response and metastasis-free survival after preoperative chemotherapy for breast cancer[END_REF][START_REF] Rouzier | Development and validation of nomograms for predicting residual tumor size and the probability of successful conservative surgery with neoadjuvant chemotherapy for breast cancer[END_REF][START_REF] Shariat | Can nomograms be superior to other prediction tools?[END_REF][START_REF] Shariat | Comparison of nomograms with other methods for predicting outcomes in prostate cancer: a critical analysis of the literature[END_REF][START_REF] Chun | Initial biopsy outcome prediction-head-to-head comparison of a logistic regression-based nomogram versus artificial neural network[END_REF]. In his study, we compared not only discrimination but also calibration of both a logistic regression-based nomogram and a recursive partitioning-based model. The logistic regression model that we developed is based on five input variables, including age, ER status, histologic grade, T stage and number of preoperative course. The recursive partitioning model includes age, ER status, grade and number of courses of preoperative of chemotherapy. Age was added in the logistic regression model even though it was non significant in univariate analysis because it improved calibration of that model. The development of logistic regression is easier than recursive partitioning. On the other hand, the tree that results from recursive partitioning allows an easy visualization of the decision steps and it is more easily interpretable in the biological context. The recursive-partitioning tree in Fig.

2 shows for example that ER status is useful to distinguish chemosensitive low grade tumors but not high grade tumors. In the literature, there are reports of head-to head comparison between logistic regression and other models such as artificial neural networks or recursive partitioning when applied to training data and used for model building [START_REF] Kattan | Comparison of Cox regression with other methods for determining prediction models and nomograms[END_REF][START_REF] Shariat | Comparison of nomograms with other methods for predicting outcomes in prostate cancer: a critical analysis of the literature[END_REF][START_REF] Chun | Initial biopsy outcome prediction-head-to-head comparison of a logistic regression-based nomogram versus artificial neural network[END_REF]. However, few studies are able to compare the performance of such competing models in independent validation sets of patients. Our results indicate that the AUC under the ROC curve of the logistic regression-based nomogram 0.77 (95% CI, 0.74-0.80) was similar to the AUC of the recursive partitioning 0.75 (95% CI, 0.74-0.79) in the training set. The small 2% difference in predictive accuracy does not imply that the use of the nomogram instead of the recursive partitioning in 1,000 patients will result in 20 additional (2%) correctly classified patients (while this is the common belief [START_REF] Chun | Initial biopsy outcome prediction-head-to-head comparison of a logistic regression-based nomogram versus artificial neural network[END_REF]). Accuracy, or the predictive ability of a model, has two major components, discrimination and calibration. The AUC is similar to the c-index, which is a measure of discrimination, or the ability to separate two patients. The c-index is independent of the prior probability of each outcome. The c index computation requires only that the algorithm produce an ordinally-scaled relative predictive score, not a true probability. The c-statistic is the probability that, for a randomly selected pair of subjects, one with favorable outcome (pCR in our study) and the other with unfavorable outcome (residual disease), the person with favorable outcome will have the higher estimated probability according to the model. Therefore, the c-index reflects how accurate is the model to correctly predict, between two patients, which one will have the best outcome. In a prospective validation, calibration, or how well the predicted probabilities reflect actual risk, is another aspect of accuracy that is not captured by the c-index. A model could discriminate well but lack even internal calibration if the fitted scores do not reflect the true probability of an event. Actually, a well calibrated model will also be discriminant. Our results demonstrate these elements. In our data, the logistic regression model was better calibrated and was therefore a better predictor of the probability of pCR as shown in Figs. 4, 5 and Table 2. These observations are in keeping with previous studies that demonstrated that treebased models do not provide an improvement in predictive accuracy over logistic or Cox regression model [START_REF] Kattan | Comparison of Cox regression with other methods for determining prediction models and nomograms[END_REF][START_REF] Shariat | Comparison of nomograms with other methods for predicting outcomes in prostate cancer: a critical analysis of the literature[END_REF].

In conclusion, we demonstrate that the logistic regression-based nomogram that we previously reported is slightly more accurate than recursive partitioning.

Fig. 1

 1 Fig. 1 Example of screen from the computer program to predict pathological complete response after preoperative chemotherapy for breast cancer

Fig. 2

 2 Fig. 2 Recursive partitioning model developed from our training set to predict pathological complete response after preoperative chemotherapy for breast cancer

Fig. 3 Fig. 4

 34 Fig. 3 Receiver operating characteristics (ROC) curves of the logistic regression model and the recursive partitioning model for the 496 patients of the training set

Fig. 5

 5 Fig. 5 Calibration plot of the logistic regression model and the recursive partitioning model for the 337 patients of the validation set

Table 1

 1

	Clinical and
	pathological data for the 496
	patients of the training set and
	the 337 patients of the
	validation set

Table 2

 2 Comparison of logistic regression model and recursive partitioning model to predict chemotherapy response of breast cancer based on clinical pathological variables according to discrimination and calibration These two models were built from the same training set and tested on the same validation set. IGR Institut Gustave Roussy, MDACC M.D. Anderson cancer center, Nb number, E difference in predicted and calibrated probabilities between calibration and AUC, E max maximal error, E aver average error, AUC Area under the ROC curve, ROC receiver operating characteristic, CI confidence interval, a E max for individual predictions, b E aver for quartiles

	Models	Nb of patients	Discrimination	Calibration
			AUC (95% CI)	P value	E max	a (%)	E aver	b (%)
	Logistic regression model
	Training set (IGR cohort)	496	0.77 (0.74-0.80)	Not adequate
	Validation set (MDACC cohort)	337	0.78 (0.74-0.82)	0.24	10 -14	1.6
	Recurssive partitioning model
	Training set (IGR cohort)	496	0.75 (0.74-0.79)	Not adequate
	Validation set (MDACC cohort)	337	0.64 (0.60-0.67)	0.12	27.5		6.3

  E = difference in predicted and calibrated probabilities between calibration and AUC, E max = maximal error, E aver = average error, AUC = Area under the ROC curve, ROC = receiver operating characteristic

		1.0
		0.8
	Actual Probability	0.2 0.4 0.6
		0.0
		0.0	0.2	0.4	0.6	0.8	1.0
			Predicted Probability
			Model		Calibration plot (p value)	E max (%)	E aver (%)
		Ideal line
		Logistic regression model		0.24	10 -14	1.6
		Recursive partitioning model	0.12	27.5	6.3

Breast Cancer Res Treat (2009) 117:325-331


Roger L Milne
email: rmilne@cnio.es

Ana Osorio

Teresa Ramón

Montserrat Cajal

Adriana Baiget

Eduardo Lasa

Miguel Diaz-Rubio

Trinidad Hoya

Alex Caldés

Roger L Milne Ae

Ana Osorio Ae

Teresa Ramo ´n Y Cajal

A E Montserrat

Baiget Ae

Adriana Lasa

Ae Eduardo Diaz-Rubio

Miguel Ae

Hoya De La

Trinidad Ae

Calde

Alex Ae

´ae Teule

La ´zaro Conxi

Ignacio Blanco Ae

Judith Ae

Balman

A E Gessamı ´sa ´nchez-

Olle ´ae

Ana Vega

A E Ana

Blanco Ae

Isabel Chirivella

A E Eva

Esteban Esteban Carden

Mercedes Ae

Dura

Eladio Ae

Ae Eduardo Velasco

Martı ´nez De Duen

A E Marı ´a-

Isabel Tejada

Dolores Miramar

A E Marı ´a-Teresa

Calvo Ae

Carmen Guille ´n-Ponce

Raquel Ae

Ae Carlos Salazar

Roma ´n San

Miguel Urioste Ae

Javier Ae

Benı ´tez

Á M Urioste

Á J Benı ´tez

T Ramo

M Baiget

Á A Lasa

E Diaz-Rubio

M De La Hoya

Á T Calde

A Teule

´á I Blanco

J Balman

Á G Sa

Á A Blanco

Fundacio ´n Pu

Á E Esteban Carden

Á E Martı ´nez De Duen

Á C Guille ´n-Ponce

M Dura

Á E Velasco

E Martı ´nez De Duen

M.-I Tejada

M.-D Miramar

M.-T Calvo

R Salazar

C San

M Urioste

Parity and the risk of breast and ovarian cancer in and mutation carriers

Keywords: Parity, Breast cancer, Ovarian cancer, BRCA1, BRCA2

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

P = 0.9 for women under age 40), and this trend was highly consistently observed for carriers of mutations in each gene. There was no evidence of an association between breast cancer risk and age at first birth for parous BRCA1 or BRCA2 mutation carriers (P-trend C 0.3). The power to detect associations with ovarian cancer risk was much lower, especially for BRCA2 mutation carriers. Nevertheless, having a live-birth was associated with protection for BRCA1 mutation carriers (HR = 0.41, 95%CI = 0.18-0.94, P = 0.03), and a strong and consistent protective effect of age at first birth was observed for parous carriers of mutations in both genes (HR = 0.65, 95%CI = 0.52-0.83, P \ 0.001). This is the third independent study to find that, as in the general population, parity appears to be associated with protection from breast cancer in women with mutations in BRCA1 and BRCA2.

Introduction

The incomplete penetrance of mutations in the breast and ovarian cancer susceptibility genes BRCA1 and BRCA2 suggests that there are other genetic and/or environmental factors that modify the risk of these cancers in female mutation carriers. Additional evidence of risk modifiers includes the general observation that estimates of penetrance tend to be higher in studies of multiple-case families than in studies of families of cases unselected for family history [START_REF] Antoniou | Average risks of breast and ovarian cancer associated with BRCA1 or BRCA2 mutations detected in case series unselected for family history: a combined analysis of 22 studies[END_REF], as well as the more recent finding that the proportion of breast cancer phenocopies (cases of cancer in non-carrier members of a mutation-carrying family) is greater than that expected according to the disease incidence in the general population [START_REF] Goldgar | BRCA phenocopies or ascertainment bias?[END_REF][START_REF] Gronwald | Phenocopies in breast cancer 1 (BRCA1) families: implications for genetic counselling[END_REF][START_REF] Smith | Phenocopies in BRCA1 and BRCA2 families: evidence for modifier genes and implications for screening[END_REF]. Both results suggest that other genetic and/or non-genetic factors may accumulate in some families and influence the risk of cancer in carriers and non-carriers alike. More specific evidence of the existence of non-genetic modifiers, of breast cancer risk in particular, comes from the consistent observation that the penetrance of BRCA1 and BRCA2 mutations has increased over the last century [START_REF] Antoniou | Average risks of breast and ovarian cancer associated with BRCA1 or BRCA2 mutations detected in case series unselected for family history: a combined analysis of 22 studies[END_REF][START_REF] Milne | The average cumulative risks of breast and ovarian cancer for carriers of mutations in BRCA1 and BRCA2 attending genetic counselling units in Spain[END_REF][START_REF] Tryggvadottir | Population-based study of changing breast cancer risk in Icelandic BRCA2 mutation carriers, 1920-2000[END_REF][START_REF] King | Breast and ovarian cancer risks due to inherited mutations in BRCA1 and BRCA2[END_REF][START_REF] Narod | Increasing incidence of breast cancer in family with BRCA1 mutation[END_REF]. Environmental or lifestyle factors, rather than genetic factors, are most likely to explain this trend.

The identification of these risk-modifying factors for mutation carriers is important for several reasons. Firstly, providing these women with information about what they can do with respect to environmental and lifestyle factors to reduce their risk of cancer may be an important complement to screening programs, and a possible alternative to invasive prophylactic surgical interventions. Secondly, the incorporation of these factors into penetrance estimation will lead to more accurate risk modelling and therefore better informed genetic counselling.

It is not clear whether established risk factors for breast and/or ovarian cancer in the general population, such as parity [START_REF] Kelsey | Reproductive factors and breast cancer[END_REF][START_REF] Elmasry | Ovarian cancer aetiology: facts and fiction[END_REF], act as risk modifiers in carriers of mutations in BRCA1 and BRCA2. Various studies have investigated such factors as modifiers, but all are subject to potential biases due to the way in which mutation carriers are recruited, and few definitive conclusions have been reached [START_REF] Milne | Breast cancer risk modifiers[END_REF]. While prospective studies of cohorts of unaffected carriers are considered best placed to clarify this issue, these will take time to accumulate a sufficient number of incident cancer cases for analysis. It is therefore important that, at least until results from prospective studies become available, the largely retrospective data at hand are taken advantage of to make appropriate inference. Results that are consistently observed across multiple studies are likely to be most reliable.

It has been established in the general population that an increasing number of children is associated with protection from both breast and ovarian cancer [START_REF] Kelsey | Reproductive factors and breast cancer[END_REF][START_REF]Breast cancer and breastfeeding: collaborative reanalysis of individual data from 47 epidemiological studies in 30 countries, including 50302 women with breast cancer and 96973 women without the disease[END_REF][START_REF] Whittemore | Characteristics relating to ovarian cancer risk: collaborative analysis of 12 US casecontrol studies. II. Invasive epithelial ovarian cancers in white women. Collaborative ovarian cancer group[END_REF]. Later age at first birth is associated with increased risk of breast cancer [START_REF] Kelsey | Reproductive factors and breast cancer[END_REF], but possibly a reduced risk of ovarian cancer [START_REF] Whittemore | Characteristics relating to ovarian cancer risk: collaborative analysis of 12 US casecontrol studies. II. Invasive epithelial ovarian cancers in white women. Collaborative ovarian cancer group[END_REF]. Parity has been evaluated as a breast cancer risk modifier in a number of studies of mutation carriers [START_REF] Cullinane | Effect of pregnancy as a risk factor for breast cancer in BRCA1/BRCA2 mutation carriers[END_REF][START_REF] Gronwald | Influence of selected lifestyle factors on breast and ovarian cancer risk in BRCA1 mutation carriers from Poland[END_REF][START_REF] Jernstrom | Pregnancy and risk of early breast cancer in carriers of BRCA1 and BRCA2[END_REF][START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF][START_REF] Antoniou | Parity and breast cancer risk among BRCA1 and BRCA2 mutation carriers[END_REF][START_REF] Kotsopoulos | Age at first birth and the risk of breast cancer in BRCA1 and BRCA2 mutation carriers[END_REF][START_REF] Rebbeck | Modification of BRCA1-and BRCA2-associated breast cancer risk by AIB1 genotype and reproductive history[END_REF], with largely contradictory results. There are fewer published studies of modifiers of ovarian cancer risk [START_REF] Gronwald | Influence of selected lifestyle factors on breast and ovarian cancer risk in BRCA1 mutation carriers from Poland[END_REF][START_REF] Mclaughlin | Reproductive risk factors for ovarian cancer in carriers of BRCA1 or BRCA2 mutations: a case-control study[END_REF][START_REF] Antoniou | Reproductive and hormonal factors, and ovarian cancer risk for BRCA1 and BRCA2 mutation carriers: results from the International BRCA1/ 2 carrier cohort study[END_REF]. We aimed to assess parity (ever parous, number of full-term pregnancies and age at first full-term pregnancy) as a modifier of breast cancer risk and ovarian cancer risk in carriers of mutations in BRCA1 and BRCA2 recruited by 13 genetic counselling centres in Spain.

Methods

Subjects

All female carriers of deleterious mutations in BRCA1 and BRCA2 recruited at 13 genetic counselling centres in Spain (see Table 1) were considered eligible. These included: (1) 799 mutation carriers recruited by 12 centres between 1995 and 2006 from the 319 families included in our previous penetrance study [START_REF] Milne | The average cumulative risks of breast and ovarian cancer for carriers of mutations in BRCA1 and BRCA2 attending genetic counselling units in Spain[END_REF]; (2) 235 mutation carriers from 235 families in which, as at 31st December, 2006, they were the only individual that had tested positive (which meant that they were excluded from the penetrance study, [START_REF] Milne | The average cumulative risks of breast and ovarian cancer for carriers of mutations in BRCA1 and BRCA2 attending genetic counselling units in Spain[END_REF]); (3) 89 mutation carriers from 42 families recruited by the Hospital Vall d'Hebron in Barcelona between 2005 and 2008; and (4) 107 obligate carriers (untested women with at least one decendent and one other non-decendent blood relative who had tested positive for the same mutation) from families recruited at all 13 centres.

Family selection, mutation testing and other data collection methods have been described previously [START_REF] Milne | The average cumulative risks of breast and ovarian cancer for carriers of mutations in BRCA1 and BRCA2 attending genetic counselling units in Spain[END_REF]. Briefly, the youngest member affected with breast and/or ovarian cancer from families with multiple cases of these cancers was generally the first tested for mutations in BRCA1 and/or BRCA2. When a mutation was detected, that specific mutation was tested for in additional family members. Mutations were defined as deleterious if they were classified as clinically important by the Breast Information Core (BIC, http://research.nhgri.nih.gov/bic/) or they met other widely accepted criteria [START_REF] Milne | The average cumulative risks of breast and ovarian cancer for carriers of mutations in BRCA1 and BRCA2 attending genetic counselling units in Spain[END_REF]. Information Associations with the risk of breast and ovarian cancer were assessed separately for each of the parity variables considered, by estimating hazard ratios (HR) and their corresponding 95% confidence intervals (CI) using weighted multivariable Cox proportional hazards regression with robust estimates of variance [START_REF] Antoniou | A weighted cohort approach for analysing factors modifying disease risks in carriers of high-risk susceptibility genes[END_REF]. For each mutation carrier, we modelled the time to diagnosis of breast or ovarian cancer from birth, censoring at the first of the following events: bilateral prophylactic mastectomy, bilateral prophylactic oophorectomy, breast cancer diagnosis, ovarian cancer diagnosis, death and date last known to be alive. For the analysis of breast cancer, subjects were considered affected if their age at censoring corresponded to their age at diagnosis of breast cancer and unaffected otherwise. For the analysis of ovarian cancer, subjects were considered affected if their age at censoring corresponded to their age at diagnosis of ovarian cancer and unaffected otherwise. Weights were assigned separately for the breast and ovarian cancer analyses, by affection status, age and gene mutated, so that the weighted observed incidence rate agreed with established estimates [START_REF] Antoniou | Average risks of breast and ovarian cancer associated with BRCA1 or BRCA2 mutations detected in case series unselected for family history: a combined analysis of 22 studies[END_REF], summarized as ''external rates'' in Antoniou et al. [START_REF] Antoniou | A weighted cohort approach for analysing factors modifying disease risks in carriers of high-risk susceptibility genes[END_REF]. The age categories considered were\25, 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, 60-64, 65-69 and C70, with the first three categories combined for the ovarian cancer analysis due to the small number of affected women observed. These weights have been shown to correct for the bias inherent in the oversampling of affected women due to the ascertainment criteria applied [START_REF] Antoniou | A weighted cohort approach for analysing factors modifying disease risks in carriers of high-risk susceptibility genes[END_REF].

We evaluated associations with parity (nulliparous, parous), number of live-births (0, 1, 2, 3, C4) and age at first live-birth (15-19, 20-24, 25-29, C30), with trends assessed for the latter two based on the corresponding continuous variables. For the analysis of categories of age at first livebirth, 20-24 was used as the reference group because it was the most common. All these measures were modelled as time-varying variables. Additional independent variables included in all analyses were year of birth (\1930, 1930-1939, 1940-1949, 1950-1959, 1960-1969, C1970) and centre (as defined above and presented in Table 2). Heterogeneity in HRs by age was assessed based on the Waldstatistic P-value corresponding to the interaction term for the variable in question and age (dichotomized into \40, C40). Mutation carriers from the present study included in previous studies of parity as a modifier of cancer risk by the International BRCA1/2 Carrier Cohort Study (IBCCS) [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF][START_REF] Antoniou | Reproductive and hormonal factors, and ovarian cancer risk for BRCA1 and BRCA2 mutation carriers: results from the International BRCA1/ 2 carrier cohort study[END_REF] were excluded and weights recalculated in sensitivity analysis. The influence of survival bias was evaluated by repeating all analyses (based on recalculated weights) after excluding affected women who were genetically tested more than 3 years after their breast cancer diagnosis, or more than 1 year after their ovarian cancer diagnosis.

All statistical analyses were carried out using Stata: Release 10 [START_REF] Statacorp | Stata Statistical Software: Release 10[END_REF]. Robust estimates of variance were calculated using the cluster subcommand, applied to an identifier variable unique to each family. All P-values were two-sided and those less than 0.05 were considered statistically significant.

Results

Of the 626 eligible BRCA1 mutation carriers and 604 eligible BRCA2 mutation carriers, 515 (82%) and 503 (83%), respectively, were included in the analyses of parity as a risk modifier. Details are given in Table 1. These were members of 253 and 246 families, respectively. The distribution of the number of carriers per family were very similar for BRCA1 and BRCA2 mutations, with, overall, 51% of families with just one member, 23% with two, 13% with three, 6% with four, 3% with five, 2% with six, 1% with seven and less than 1% of families with eight or more members represented in the dataset. Table 2 summarises the characteristics of included mutation carriers according to affection status, and gene mutated. For ovarian cancer, but not breast cancer, affected mutation carriers tended to be older than unaffected mutation carriers, regardless of the gene mutated (both P \ 0.001). For carriers of mutations in both genes and for both cancers, affected women tended to be born before unaffected women (all P B 0.001).

Associations with breast cancer risk

Results from the multivariable analysis of the three parity variables and breast cancer risk are summarized in Table 3. The results for ever being parous and number of live-births were very similar for carriers of mutations in BRCA1 and BRCA2, with HR estimates below 1, although none were statistically significant (all P C 0.08). After combining mutation carriers in both genes, the estimated HR associated with ever having had a live-birth was 0.74 (95% confidence interval [CI] = 0.55-1.01, P = 0.06), and that associated with each live-birth was 0.87 (95%CI = 0.77-0.98, P = 0.02). Analyses stratified by age suggested that this association with number of live-births was only apparent in women aged 40 and above (HR = 0.81, 95%CI = 0.70-0.94, P = 0.004 vs. HR = 0.99, 95%CI = 0.83-1.18, P = 0.9 for women under age 40). While the difference in HR by age was not statistically significant (P = 0.1), this result was consistently observed for BRCA1 mutation carriers (HR = 0.82, 95%CI = 0.69-0.98, P = 0.03 for women aged 40 and above and HR = 1.02, 95%CI = 0.81-1.29, P = 0.9 for younger women) and BRCA2 mutation carriers (HR = 0.81, 95%CI = 0.63-1.04, P = 0.09 and HR = 0.97, 95%CI = 0.74-1.28, P = 0.8, respectively). We observed no evidence of an association between breast There were 67 mutation carriers that were included in a previous study of parity and breast cancer risk by the IBCCS [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF], 38 with mutations in BRCA1 and 29 with mutations in BRCA2. Excluding these made no substantial difference to the results obtained. The estimated HR per live-birth was 0.86 for BRCA1 mutation carriers, 0.90 for BRCA2 mutation carriers and 0.87 (P = 0.03) for all carriers combined. The corresponding HR estimates for women aged less than 40 were 0.96, 1.03 and 0.97, respectively, while those for women aged 40 and above were 0.82, 0.83 and 0.81 (P = 0.008), respectively. There were 299 affected mutation carriers who were diagnosed with breast cancer more than 3 years prior to their mutation testing, 154 with mutations in BRCA1 and 145 with mutations in BRCA2. Excluding these similarly made no substantial difference to the results obtained. The estimated HR per live-birth was 0.77 for BRCA1 mutation carriers, 0.88 for BRCA2 mutation carriers and 0.79 (P = 0.002) for all mutation carriers combined.

Associations with ovarian cancer risk

Results from the multivariable analyses of the three parity variables and ovarian cancer risk are also summarized in Table 3. For BRCA1 mutation carriers, ever having had a live-birth was associated with reduced risk of ovarian cancer (HR = 0.41, 95%CI = 0.18-0.94, P = 0.03). There was some evidence of a dose-response effect, with BRCA1 mutation carriers with four or more children at even lower estimated risk relative to those with no children (HR = 0.15, 95%CI = 0.04-0.56, P = 0.005), but the trend per birth was not statistically significant (HR = 0.80, 95%CI = 0.61-1.05, P = 0.1). There was no evidence of association with number of live-births for BRCA2 mutation carriers (all P C 0.3). Age at first birth appeared to be inversely associated with ovarian cancer risk, with very similar HR estimates for BRCA1 and BRCA2 mutation carriers (P-trend = 0.001 and 0.1 for BRCA1 and BRCA2 mutation carriers, respectively). The estimated HRs for carries of mutations in both genes combined, per 5 years of age, was 0.65 (95%CI = 0.52-0.83, P \ 0.001).

There were 116 mutation carriers that were included in a previous study of parity and ovarian cancer risk by the IBCCS [START_REF] Antoniou | Reproductive and hormonal factors, and ovarian cancer risk for BRCA1 and BRCA2 mutation carriers: results from the International BRCA1/ 2 carrier cohort study[END_REF], 59 with mutations in BRCA1 and 57 with mutations in BRCA2. Excluding these gave slightly stronger evidence of the associations reported above. For BRCA1 mutation carriers the estimated HRs were 0.32 (P = 0.01) for ever having had a live-birth and 0.74 (P = 0.04) per live-birth. The estimated HR associated with increments of 5 years in age at first birth was 0.64 (P = 0.004) for BRCA1 mutation carriers, 0.46 (P = 0.02) for BRCA2 mutation carriers and 0.60 (P = 0.001) for all carriers combined. There were 55 affected mutation carriers who were diagnosed with ovarian cancer more than 1 year prior to their mutation testing, 36 with mutations in BRCA1 and 19 with mutations in BRCA2. Results were consistent after excluding these women. For BRCA1 mutation carriers the estimated HRs were 0.29 (P = 0.007) for ever having had a live-birth and 0.72 (P = 0.08) per live-birth. The estimated HR associated with increments of 5 years in age at first birth was 0.58 (P = 0.03) for BRCA1 mutation carriers, 0.78 (P = 0.5) for BRCA2 mutation carriers and 0.65 (P = 0.04) for all carriers combined. It should be noted that there was likely to be over-fitting of these latter models due to the small number of affected women in this reduced sample set (37 and 16 for BRCA1 and BRCA2 mutation carriers, respectively).

Discussion

Parity and breast cancer risk

We have evaluated the effect of parity on the risk of breast cancer in 515 BRCA1 mutation carriers and 503 BRCA2 mutation carriers in Spain. After adjusting for study centre and year of birth, we observed evidence that parity is associated with protection from breast cancer in BRCA1 and BRCA2 mutation carriers. Each live-birth was associated with an estimated 13% risk reduction. We observed no evidence of an association with age at first birth. The results from previous studies of the possible effect of parity on breast cancer risk in BRCA1 and BRCA2 mutation carriers have been mixed. They are summarized in Table 4. Jernstrom et al., [START_REF] Jernstrom | Pregnancy and risk of early breast cancer in carriers of BRCA1 and BRCA2[END_REF] pooled data from carriers of mutations in both genes (although 80% had mutations in BRCA1) and found that parous carriers were at an estimate 71% increased risk of breast cancer compared with nulliparous carriers. They also observed a trend effect, with an estimated 24% increased risk per full-term pregnancy. This result was not replicated in a subsequent study by the same group, based on a much larger set of mutation carriers from 55 international collaborating centres [START_REF] Cullinane | Effect of pregnancy as a risk factor for breast cancer in BRCA1/BRCA2 mutation carriers[END_REF], most (73%) in North America. They observed that for women with a BRCA1 mutation, having four or more children was associated with reduced breast cancer risk compared with being nulliparous. In contrast, among BRCA2 carriers, increasing parity was associated with an increased risk of breast cancer (15% per live-birth). A third study by some of the same authors [START_REF] Gronwald | Influence of selected lifestyle factors on breast and ovarian cancer risk in BRCA1 mutation carriers from Poland[END_REF], reported that for Polish BRCA1 mutation carriers, each live-birth was associated with an estimated 20% increased risk of breast cancer. All three studies matched unaffected carriers to affected carriers on year of birth, country and gene mutated and estimated odds ratios (OR) using condition logistic regression.

The IBCCS, a predominantly European consortium, has more recently published their analysis of parity as a potential modifier of breast cancer risk in mutation carriers [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF]. They obtained similar results for carriers of mutations in BRCA1 and BRCA2. In a pooled analysis, they observed no effect associated with being parous, but among parous women, estimated that each live-birth was associated with a statistically significant 14% decrease in risk. This effect was only observed in women over age 40 years. This group also evaluated the effect of age at first live-birth and found marginally statistically significant evidence that it differed between BRCA1 and BRCA2 mutation carriers [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF]. While for BRCA1 mutation carriers, having a child later in life appeared to be associated with protection, the opposite seemed to be the case for BRCA2 mutation carriers. Antoniou et al. [START_REF] Antoniou | Parity and breast cancer risk among BRCA1 and BRCA2 mutation carriers[END_REF] subsequently carried out a very similar analysis of a smaller set of mutation carriers from the United Kingdom and found that ever being parous was associated with an estimated 56% reduced risk for all mutation carriers combined, but again, only for women over age 40. For women of all ages, there was marginal evidence of a trend of decreasing risk with increasing parity. They also observed evidence that in parous BRCA2 mutation carriers, risk is higher for those who have their first child later. Both these studies estimated HR using weighted Cox regression, adjusting for year of birth and other covariates.

Two other studies have examined the effect of age at first birth on breast cancer risk in mutation carriers. Rebbeck et al. [START_REF] Rebbeck | Modification of BRCA1-and BRCA2-associated breast cancer risk by AIB1 genotype and reproductive history[END_REF] studied mostly (83%) BRCA1 mutation carriers and observed that those who had their first birth earlier were at reduced risk of breast cancer. Most recently, members of the aforementioned international consortium applied their matched case-control design to the largest set of mutation carriers studied to date [START_REF] Kotsopoulos | Age at first birth and the risk of breast cancer in BRCA1 and BRCA2 mutation carriers[END_REF]. They found no evidence of an association for all carriers combined and reported that this result was consistent in stratified analyses by gene mutated.

Our results are consistent with those of the two other European studies that applied the same analytic approach [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF][START_REF] Antoniou | A weighted cohort approach for analysing factors modifying disease risks in carriers of high-risk susceptibility genes[END_REF]. This approach allows all mutation carriers with complete data to be included, in contrast to the majority of the other studies in which up to 40% of carriers were excluded because no matched-pair was found [START_REF] Cullinane | Effect of pregnancy as a risk factor for breast cancer in BRCA1/BRCA2 mutation carriers[END_REF][START_REF] Kotsopoulos | Age at first birth and the risk of breast cancer in BRCA1 and BRCA2 mutation carriers[END_REF]. The consistent results from these three independent studies suggest that, as for women in the general population, parity is associated with protection from breast cancer for women at high risk of the disease due to mutations in BRCA1 and BRCA2. This finding may be particularly relevant to unaffected mutation carriers who are concerned about the impact pregnancy may have on their own breast cancer risk.

While our results are also consistent with there being no association between age at first birth and breast cancer risk in mutation carriers, the power of our study in this regard was limited (as discussed further, below), and the estimated HRs for trend are in the same (opposing) directions as those reported by the two European studies [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF][START_REF] Antoniou | Parity and breast cancer risk among BRCA1 and BRCA2 mutation carriers[END_REF]. It is therefore difficult to reach any definitive conclusions in this regard.

Parity and ovarian cancer risk

Regarding ovarian cancer risk, after adjusting for study centre and year of birth, we observed marginal evidence that for BRCA1 mutation carriers, ever having had a livebirth is associated with protection. We also observed that for parous BRCA1, and possibly BRCA2, mutation carriers, later age at first birth is associated with protection.

Three studies have evaluated parity as a modifier of ovarian cancer risk in mutation carriers. A Polish study of 300 BRCA1 mutation carriers found no evidence of association with number of live-births [START_REF] Gronwald | Influence of selected lifestyle factors on breast and ovarian cancer risk in BRCA1 mutation carriers from Poland[END_REF]. The previously mentioned international consortium studied 3,223 mutation carriers, and observed that while women with BRCA1 mutations (84% of their sample) appeared to be protected from ovarian cancer both by ever having had full-term pregnancy (OR = 0.67, 95%CI = 0.46-0.96, P = 0.03) and with increasing parity (OR = 0.87 per birth, 95%CI = 0.79-0.95, P = 0.003), parous BRCA2 mutation carriers were at increased risk (OR = 2.74, 95%CI = 1.18-6.41, P = 0.02) [START_REF] Mclaughlin | Reproductive risk factors for ovarian cancer in carriers of BRCA1 or BRCA2 mutations: a case-control study[END_REF]. The authors did not assess age at first birth as a risk modifier. Finally, the IBCCS has recently reported on their study of larger sample of 2,281 BRCA1 and 1,038 BRCA2 mutation carriers [START_REF] Antoniou | Reproductive and hormonal factors, and ovarian cancer risk for BRCA1 and BRCA2 mutation carriers: results from the International BRCA1/ 2 carrier cohort study[END_REF]. It also observed evidence that among parous BRCA1 mutation carriers, ovarian cancer risk decreased with each live-birth after the first (P = 0.002), but that risk was also reduced for those who were nulliparous, relative to those who had had just one live-birth (P = 0.02). No definitive conclusions were reached regarding the effect of parity for BRCA2 mutation carriers. No evidence of an association with ovarian cancer risk was seen for age at first birth.

Our finding that later age at first birth is associated with reduced risk of ovarian cancer in mutation carriers is consistent with what has been observed in the general population, based on two large [START_REF] Adami | Parity, age at first childbirth, and risk of ovarian cancer[END_REF][START_REF] Riman | Risk factors for invasive epithelial ovarian cancer: results from a Swedish casecontrol study[END_REF] (and a combined analysis of smaller [START_REF] Whittemore | Characteristics relating to ovarian cancer risk: collaborative analysis of 12 US casecontrol studies. II. Invasive epithelial ovarian cancers in white women. Collaborative ovarian cancer group[END_REF]) population-based case-control studies, although inconsistent findings have been reported from much smaller, hospital-based studies [START_REF] Whittemore | Characteristics relating to ovarian cancer risk: collaborative analysis of 12 US casecontrol studies. II. Invasive epithelial ovarian cancers in white women. Collaborative ovarian cancer group[END_REF][START_REF] Booth | Risk factors for ovarian cancer: a case-control study[END_REF][START_REF] Polychronopoulou | Reproductive variables, tobacco, ethanol, coffee and somatometry as risk factors for ovarian cancer[END_REF]. Further investigation is warranted to clarify this issue.

Study biases and limitations

Our study, like those of the IBCCS and the UK group [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF][START_REF] Antoniou | Parity and breast cancer risk among BRCA1 and BRCA2 mutation carriers[END_REF][START_REF] Antoniou | Reproductive and hormonal factors, and ovarian cancer risk for BRCA1 and BRCA2 mutation carriers: results from the International BRCA1/ 2 carrier cohort study[END_REF], sought to account for the potential biases inherent in these studies of a highly selected and related sample of mutation carriers by modelling time from birth to diagnosis of breast or ovarian cancer in carriers using weighted Cox regression. Weights were calculated to correct for the overrepresentation of affected individuals, assuming that the age-specific incidence rates for breast and ovarian cancer in carriers of mutations in both genes estimated by Antoniou et al. [START_REF] Antoniou | Average risks of breast and ovarian cancer associated with BRCA1 or BRCA2 mutations detected in case series unselected for family history: a combined analysis of 22 studies[END_REF] are applicable [START_REF] Antoniou | A weighted cohort approach for analysing factors modifying disease risks in carriers of high-risk susceptibility genes[END_REF]. Our recent study of the penetrance of mutations in BRCA1 and BRCA2 in Spanish multiple-case families indicated that this assumption is valid [START_REF] Milne | The average cumulative risks of breast and ovarian cancer for carriers of mutations in BRCA1 and BRCA2 attending genetic counselling units in Spain[END_REF]. That our results were maintained after excluding prevalent cases suggests that survival bias was not present.

While we attempted to include obligate carriers wherever possible, in general, a mutation carrier had to be genetically tested in order to be included in the analysis. A further potential bias in this study would therefore be present if affected and unaffected women were influenced by parity in different ways in terms of their decision to undergo genetic testing. It may be, for example, that women who have already been diagnosed with breast or ovarian cancer are more influenced in this decision by whether or not they have children (at potential genetic risk of the disease), than are unaffected women and this may result in bias in HR estimation. However, it could be hypothesized that this would tend to bias HR estimates in the direction of increased risk associated with being parous, rather than towards the observed protection.

One of the limitations of our study was that we measured time to cancer diagnosis and age at first birth in years, rather than months or days. This would have reduced the power to detect associations, but is unlikely to have introduced bias in HR estimation. Another potential limitation was that we were not able to adjust for potential confounding factors such as education level and other hormonal risk factors because we did not systematically collect this information on all mutation carriers. However, other studies were able to adjust for most of these factors and found that this had little impact on parity-associated HR estimates for breast and ovarian cancer [START_REF] Andrieu | Pregnancies, breast-feeding, and breast cancer risk in the international BRCA1/2 carrier cohort study (IBCCS)[END_REF][START_REF] Mclaughlin | Reproductive risk factors for ovarian cancer in carriers of BRCA1 or BRCA2 mutations: a case-control study[END_REF]. Finally, the number of mutation carriers with ovarian cancer was relatively low, particularly with regard to BRCA2, and so the corresponding results should be interpreted with greater caution.

Conclusions

This is the third independent study to find that, as in the general population, parity appears to be associated with protection from breast cancer in women with mutations in BRCA1 and BRCA2. Nevertheless, results have not been consistent across all studies and their retrospective designs imply a number of potential biases. Prospective studies of mutation carrier cohorts are therefore likely to be highly informative in this regard.

Parity also appears to confer protection from ovarian cancer, at least for BRCA1 mutation carriers. Whether this is the case for BRCA2 mutation carriers remains to be confirmed. It may be that later age at first birth is associated with protection from ovarian cancer in both BRCA1 and BRCA2 mutation carriers, as has been observed in the general population, but again, this finding requires confirmation in independent studies.

Table 1

 1 Number of eligible and included carriers of mutations in BRCA1 and BRCA2, by centre

	Centre a	Carriers from families included		Sole mutation	Total		Proportion of
		in the penetrance study [5]		carriers b		(all mutation	eligible mutation
		Tested		Obligate				carriers)		carriers included
		Included/eligible c	Included/eligible c	Included/eligible c	Included/eligible c
		BRCA1	BRCA2	BRCA1 BRCA2 BRCA1	BRCA2 BRCA1	BRCA2	BRCA1 (%) BRCA2 (%)
	CNIO	69/84	4/121	1/7	3/6	35/37	20/26	105/128 117/153	82	76
	Sant Pau	63/64	69/72	12/16	7/8	11/11	7/7	86/91	83/87	95	95
	HCSC	63/72	52/57	1/16	0/11	14/15	20/20	78/103	72/88	76	82
	ICO	41/43	57/58	7/9	4/4	4/4	3/3	52/56	64/65	93	98
	Vall d'Hebron d							60/68	25/27	88	93
	FPGMX	49/58	6/8	0/3	0/0	10/12	0/1	59/73	6/9	81	67
	Valencia	6/6	43/43	0/0	4/4	3/3	3/5	9/9	50/52	100	96
	Valladolid	4/17	1/8	2/4	0/2	16/27	31/50	22/48	32/60	46	53
	Castello ´n	12/12	12/12	3/3	1/1	0/0	0/0	15/15	13/13	100	100
	Barakaldo	5/5	18/18	0/0	1/2	0/0	0/0	5/5	19/20	100	95
	Zaragoza	9/10	5/6	0/0	0/0	5/5	4/7	14/15	9/13	93	69
	Elche	7/7	7/7	0/2	2/2	1/1	1/1	8/10	10/10	80	100
	Salamanca	2/5	3/6	0/0	0/1	0/0	0/0	2/5	3/7	40	43
	Total (all centres) 330/383 367/416 26/60	22/41	99/115	89/120	515/626 503/604	82	83
	a The 13 participating centres were the Centro Nacional de Investigaciones Oncolo ´gicas, Madrid (CNIO); the Hospital de la Santa Creu i Sant
	Pau, Barcelona (Sant Pau); the Hospital Clı ´nico San Carlos, Madrid (HCSC); the Instituto Catala ´n de Oncologı ´a, Barcelona (ICO); the Hospital
	Vall d'Hebron, Barcelona (Vall d'Hebron); the Fundacio ´n Pu ´blica Galega de Medicina Xeno ´mica, Santiago de Compostela (FPGMX); the
	Hospital Clı ´nico Universitario de Valencia, Valencia (Valencia); the Instituto de Biologı ´a y Gene ´tica Molecular, Valladolid (Valladolid); the
	Hospital Provincial de Castello ´n, Castello ´n (Castello ´n); the Hospital de Cruces, Barakaldo-Bizkaia (Barakaldo); the Hospital Universitario
	Miguel Servet, Zaragoza (Zaragoza); the Hospital General Universitario de Elche, Elche (Elche); and the Centro de Investigacio ´n del Ca ´ncer,
	Salamanca (Salamanca)
	b Sole mutation carriers in their respective families (not included in the penetrance study; [5])
	c All identified female mutation carriers were considered eligible, but only those with complete data were included in the analyses
	d Carriers from Vall d'Hebron were not included in the penetrance study [5]. These included 4 of 5 eligible obligate BRCA1 mutation carriers
	and 1 eligible obligate BRCA2 mutation carrier

Table 2

 2 Distribution of mutation carriers according to study centre (CENTRE), censoring age (AGE) and year of birth (YOB), by affection status, type of cancer and gene mutated

		BRCA1 mutation carriers, n (%)		BRCA2 mutation carriers, n (%)
		Breast cancer		Ovarian cancer	Breast cancer		Ovarian cancer
		Affected	Unaffected	Affected	Unaffected	Affected	Unaffected	Affected	Unaffected
	CENTRE*
	CNIO	61 (22)	44 (18)	15 (21)	90 (20)	64 (22)	53 (25)	11 (31)	106 (23)
	Sant Pau	46 (17)	40 (17)	9 (12)	77 (17)	43 (15)	40 (19)	6 (17)	77 (16)
	HCSC	35 (13)	43 (18)	13 (18)	65 (15)	35 (12)	37 (17)	5 (14)	67 (14)
	ICO	31 (11)	21 (9)	5 (7)	47 (11)	32 (11)	32 (15)	5 (14)	59 (13)
	Vall d'Hebron	29 (11)	31 (13)	5 (7)	55 (12)
	FPGMX	28 (10)	31 (13)	13 (18)	46 (10)
	Valencia					32 (11)	18 (8)	3 (9)	47 (10)
	Others a	46 (17)	29 (12)	13 (18)	62 (14)	83 (28)	34 (16)	5 (14)	112 (24)
	P-value b	0.3		0.3		0.01		0.8
	AGE
	\25	6 (2)	23 (10)	0 (0)	29 (7)	2 (1)	21 (10)	0 (0)	23 (5)
	25-29	23 (8)	24 (10)	0 (0)	47 (11)	17 (6)	27 (13)	0 (0)	44 (10)
	30-34	54 (20)	34 (14)	6 (8)	82 (19)	44 (15)	36 (17)	1 (3)	79 (17)
	35-39	57 (21)	34 (14)	6 (8)	85 (19)	62 (21)	23 (11)	0 (0)	85 (18)
	40-44	61 (22)	35 (15)	12 (16)	84 (19)	58 (20)	25 (12)	3 (9)	80 (17)
	45-49	36 (13)	28 (12)	17 (23)	47 (11)	44 (15)	23 (11)	5 (14)	62 (13)
	P-value c	0.2		\0.001		0.2		\0.001
	YOB
	\ 1930	12 (4)	13 (5)	5 (7)	20 (5)	16 (6)	9 (4)	6 (17)	19 (4)
	1930-39	20 (7)	14 (6)	13 (18)	21 (5)	32 (11)	20 (9)	13 (37)	39 (8)
	1940-49	54 (20)	32 (13)	18 (25)	68 (15)	54 (19)	20 (9)	9 (26)	65 (14)
	1950-59	87 (32)	45 (19)	24 (33)	108 (24)	93 (32)	39 (18)	4 (11)	128 (27)
	1960-69	68 (25)	53 (22)	9 (12)	112 (25)	71 (25)	40 (19)	3 (9)	108 (23)
	C1970	35 (13)	82 (34)	4 (5)	113 (26)	23 (8)	86 (40)	0 (0)	109 (23)
	P-value c	\0.001		\0.001		\0.001		\0.001

a Includes Valencia for carriers of mutations in BRCA1, and includes Vall d'Hebron and FPGMX for carriers of mutations in BRCA2 b P-value calculated using Pearson's Chi-squared test c P-value calculated using logistic regression on the continuous variable cancer risk and age at first birth for parous BRCA1 or BRCA2 mutation carriers (both P-trend C 0.3).

Table 3

 3 Estimated hazard ratios (HR) for breast and ovarian cancer associated with parity variables, for BRCA1 and BRCA2 mutation carriers

		Breast cancer		Ovarian cancer
		BRCA1 mutation carriers	BRCA2 mutation carriers	BRCA1 mutation carriers	BRCA2 mutation carriers
		HR a (95%CI); P-value	HR a (95%CI); P-value	HR a (95%CI); P-value	HR a (95%CI); P-value
	Parity
	Nulliparous	1.00	1.00	1.00	1.00
	Parous	0.82 (0.55-1.20); 0.3	0.66 (0.39-1.12); 0.1	0.41 (0.18-0.94); 0.03	0.62 (0.10-3.97); 0.6
	Number of live-births
	0	1.00	1.00	1.00	1.00
	1	0.93 (0.60-1.46); 0.8	0.69 (0.36-1.34): 0.3	0.33 (0.12-0.95): 0.04	0.87 (0.11-6.79); 0.9
	2	0.83 (0.54-1.27); 0.4	0.68 (0.38-1.22); 0.2	0.40 (0.17-0.94); 0.04	0.36 (0.05-2.92); 0.3
	3	0.64 (0.36-1.17); 0.1	0.54 (0.26-1.10); 0.09	0.74 (0.28-1.99); 0.6	0.61 (0.08-4.96); 0.6
	C4	0.64 (0.32-1.25); 0.2	0.72 (0.29-1.77); 0.5	0.15 (0.04-0.56); 0.005	1.87 (0.19-18.4); 0.6
	Trend (per live-birth)	0.88 (0.76-1.02); 0.08	0.88 (0.71-1.08); 0.2	0.80 (0.61-1.05); 0.1	1.21 (0.59-2.46); 0.6
	Age at first live-birth
	15-19	0.81 (0.41-1.60); 0.5	0.83 (0.30-2.30); 0.7	0.85 (0.30-2.43); 0.8	0.78 (0.11-5.46); 0.8
	20-24	1.00	1.00	1.00	1.00
	25-29	0.76 (0.48-1.19); 0.2	1.15 (0.68-1.95); 0.6	1.07 (0.51-2.27); 0.9	0.70 (0.18-2.72); 0.6
	C30	0.65 (0.38-1.11); 0.1	1.16 (0.57-2.38); 0.7	0.40 (0.16-1.02); 0.06	0.26 (0.05-1.35); 0.1
	Trend (per 5 years)	0.90 (0.73-1.11); 0.3	1.13 (0.83-1.54); 0.4	0.65 (0.49-0.85); 0.001	0.63 (0.35-1.13); 0.1
	CI confidence interval

a Adjusting for year of birth and study centre

Table 4

 4 Summary of published studies of parity as a modifier of breast cancer risk in BRCA1

	mutation carriers
	and BRCA2

a Number of affected carriers/number of unaffected carriers (gene in which a mutation is carried in parenthesis) b RR estimate of relative risk associated with the exposure, CI

Breast Cancer Res Treat (2010) 119:221-232

Breast Cancer Res Treat (2010) 119:221-232

Acknowledgments We thank the patients and families without whose generous participation this study would not have been possible. We also thank Alicia Barroso and Fernando Ferna ´ndez who conducted the genetic testing at the Centro Nacional de Investigaciones On-colo´gicas; Guillermo Pita for information technology support; Marina Polla ´n and Fernando Artalejo from the Universidad Auto´noma de Madrid; M. Carmen Alonso, Consol Lo ´pez and David Fisas from the Hospital de la Santa Creu i Sant Pau; Daniel Fortuny, Neus Gadea, and Orland Dı ´ez from Hospital Vall d'Hebron; Vicenta Garce ´s from the Hospital Clı´nico Universitario de Valencia, Pascual Bolufer from the Laboratorio de Biologı´a Molecular, Hospital La Fe de Valencia; Dolores Salas and Dolores Cuevas from the Grupo de Ca´ncer Hereditario, Comunidad Valenciana. This work was partly supported by a grant from the Fondo de Investigacio´n Sanitario [PI081120]. TC, MdH and ED-R were supported by the RTICC (RD06/0020/0021), Instituto de Salud Carlos III, Spanish Ministry of Science and Innovation and a grant from the Fundacio´n de Investigacio´n Me´dica Mutua Madrilen˜a (FMMA/06). The work at the Instituto Catala´n de On-cologı´a was supported by grants ISCIII-RETIC RD06/0020/1051 and 2005SGR00018. The Fundacio ´n Pu ´blica Galega de Medicina Xeno

´mica -SERGAS component of this work was partially supported by grants from the Ministerio de Sanidad y Consumo (PI052275) and the Xunta de Galicia (PGIDIT06BTF910101PR) to AV. AB has a fellowship from the Instituto de Salud Carlos III. The work at the Instituto de Biologia y Genetica Molecular was partly supported by the Hereditary Cancer Prevention Programme of the Regional Government of Castilla y Leo ´n, and grant PI06/1102 (Fondo de Investigacio´n Sanitaria, Instituto de Salud Carlos III). The work at the Hospital de Cruces was funded by the grant BIO07/CA/006.