**8. References**


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In practice, it might be difficult to collect families with a mutation-carrier proband. However, with the emergence of large international consortiums such as the Breast and Colon Cancer Family Registries, the planning of studies using designs POP+ and CLI+ is now quite feasible. Therefore, the use of 200 families in the CLI+ design, as specified in our simulation study, seems to provide a reasonable sample size; however, the efficiency gains with more families

There are potential limitations to our study. First, we assumed the Weibull distribution, chosen to model the penetrance function because of flexible modeling of the baseline hazard function which includes constant, increasing or decreasing hazard functions. There might be potential for model misspecification. Kopciuk et al. (2009) employed the generalized log-Burr model for more flexible modeling as it includes the Weibull model or the log-logistic model as special cases (Lawless, 2003), where the Weibull model has a monotonic functional form of the hazard whereas the log-logistic model does not. The baseline hazard can be also modeled semiparametrically using a step function while assuming proportional hazards. Second, between-family heterogeneity in allele frequencies and baseline hazards can lead to bias in parameter estimates based on the homogeneous models. A random effect model would allow us to take between-family heterogeneity into account while avoiding a great number of family-specific parameters. Finally, familial correlation is a common feature of family data due to the unobserved genetic or environmental risk factors shared within families. We did not explicitly model within-family dependencies, instead, we accommodated a robust variance estimator. However, ignoring familial correlation can lead to biased estimates of the model parameters, and so to biased disease risks (Choi et al., 2008). Relating to other work, several authors have adopted mixed effect models for binary outcomes in family studies (Heagerty, 1999; Pfeiffer et al., 2008; Zheng et al., 2010). Shared frailty models can allow us to model times to onset data from families while explicitly modeling familial correlation. We are planning to

This research was supported by the Canadian Institutes of Health Research-Interdisciplinary Health Research Team, Grant no. 43821, the Institutes of Genetics and Population and Public Health of the Canadian Institutes of Health Research, Grant no. 110053 and the Natural

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**7. Acknowledgment**

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