A marginalized two-part joint model for a longitudinal biomarker and a terminal event with application to advanced head and neck cancers.

The sum of the longest diameter (SLD) of the target lesions is a longitudinal biomarker used to assess tumor response in cancer clinical trials, which can inform about early treatment effect. This biomarker is semicontinuous, often characterized by an excess of zeros and right skewness. Conditional two-part joint models were introduced to account for the excess of zeros in the longitudinal biomarker distribution and link it to a time-to-event outcome. A limitation of the conditional two-part model is that it only provides an effect of covariates, such as treatment, on the conditional mean of positive biomarker values, and not an overall effect on the biomarker, which is often of clinical relevance. As an alternative, we propose in this article, a marginalized two-part joint model (M-TPJM) for the repeated measurements of the SLD and a terminal event, where the covariates affect the overall mean of the biomarker. Our simulation studies assessed the good performance of the marginalized model in terms of estimation and coverage rates. Our application of the M-TPJM to a randomized clinical trial of advanced head and neck cancer shows that the combination of panitumumab in addition with chemotherapy increases the odds of observing a disappearance of all target lesions compared to chemotherapy alone, leading to a possible indirect effect of the combined treatment on time to death.

THE SCALABLE BIRTH-DEATH MCMC ALGORITHM FOR MIXED GRAPHICAL MODEL LEARNING WITH APPLICATION TO GENOMIC DATA INTEGRATION.

Recent advances in biological research have seen the emergence of high-throughput technologies with numerous applications that allow the study of biological mechanisms at an unprecedented depth and scale. A large amount of genomic data is now distributed through consortia like The Cancer Genome Atlas (TCGA), where specific types of biological information on specific type of tissue or cell are available. In cancer research, the challenge is now to perform integrative analyses of high-dimensional multi-omic data with the goal to better understand genomic processes that correlate with cancer outcomes, e.g. elucidate gene networks that discriminate a specific cancer subgroups (cancer sub-typing) or discovering gene networks that overlap across different cancer types (pan-cancer studies). In this paper, we propose a novel mixed graphical model approach to analyze multi-omic data of different types (continuous, discrete and count) and perform model selection by extending the Birth-Death MCMC (BDMCMC) algorithm initially proposed by Stephens (2000) and later developed by Mohammadi and Wit (2015). We compare the performance of our method to the LASSO method and the standard BDMCMC method using simulations and find that our method is superior in terms of both computational efficiency and the accuracy of the model selection results. Finally, an application to the TCGA breast cancer data shows that integrating genomic information at different levels (mutation and expression data) leads to better subtyping of breast cancers.

Large-scale whole exome sequencing studies identify two genes,CTSL and APOE, associated with lung cancer.

Common genetic variants associated with lung cancer have been well studied in the past decade. However, only 12.3% heritability has been explained by these variants. In this study, we investigate the contribution of rare variants (RVs) (minor allele frequency <0.01) to lung cancer through two large whole exome sequencing case-control studies. We first performed gene-based association tests using a novel Bayes Factor statistic in the International Lung Cancer Consortium, the discovery study (European, 1042 cases vs. 881 controls). The top genes identified are further assessed in the UK Biobank (European, 630 cases vs. 172 864 controls), the replication study. After controlling for the false discovery rate, we found two genes, CTSL and APOE, significantly associated with lung cancer in both studies. Single variant tests in UK Biobank identified 4 RVs (3 missense variants) in CTSL and 2 RVs (1 missense variant) in APOE stongly associated with lung cancer (OR between 2.0 and 139.0). The role of these genetic variants in the regulation of CTSL or APOE expression remains unclear. If such a role is established, this could have important therapeutic implications for lung cancer patients.

Evaluating colonoscopy screening intervals in patients with Lynch syndrome from a large Canadian registry.

BACKGROUND: Lynch syndrome (LS) screening guidelines originally recommended colonoscopy every 1 to 2 years, beginning between the ages of 20 and 25 years. Recent studies have questioned the benefits of these short screening intervals in preventing colorectal cancer (CRC). Our goal is to determine how colonoscopy screening intervals impact CRC in patients with LS. METHODS: We analyzed the demographics, screening practices, and outcomes of patients with LS identified through the clinic based Familial Gastrointestinal Cancer Registry at the Zane Cohen Centre, Sinai Health System, Toronto, Canada. RESULTS: A total of 429 patients with LS were identified with median follow-up of 9.2 years; 44 developed CRC. We found a positive trend between shorter screening intervals and the number of adenomas detected during colonoscopy. Any new adenoma detected at screening decreased 10-year CRC incidence by 11.3%. For MLH1 carriers, a screening interval of 1-2 years vs 2-3 years led to a 20-year cumulative CRC risk reduction of 28% and 14% in females and males, respectively. For MSH2 carriers, this risk reduction was 29% and 17%, respectively, and for male MSH6 carriers 18%. Individuals without any adenomas detected (53.4% of LS carriers) had an increased 20-year CRC risk of 25.7% and 57.2% for women and men, respectively, compared with those diagnosed with adenomas at screening. CONCLUSIONS: The recommended colonoscopy screening interval of 1-2 years is efficient at detecting adenomas and reducing CRC risk. The observation that 53.4% of LS patients never had an adenoma warrants further investigation about a possible adenoma-free pathway.

Bayesian estimation of two-part joint models for a longitudinal semicontinuous biomarker and a terminal event with INLA: Interests for cancer clinical trial evaluation.

Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., a large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using the INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.

DNA methylation profiles in the blood of newborn term infants born to mothers with obesity.

Maternal obesity is an important risk factor for childhood obesity and influences the prevalence of metabolic diseases in offspring. As childhood obesity is influenced by postnatal factors, it is critical to determine whether children born to women with obesity during pregnancy show alterations that are detectable at birth. Epigenetic mechanisms such as DNA methylation modifications have been proposed to mediate prenatal programming. We investigated DNA methylation signatures in male and female infants from mothers with a normal Body Mass Index (BMI 18.5-24.9 kg/m2) compared to mothers with obesity (BMI≥30 kg/m2). BMI was measured during the first prenatal visit from women recruited into the Ontario Birth Study (OBS) at Mount Sinai Hospital in Toronto, ON, Canada. DNA was extracted from neonatal dried blood spots collected from heel pricks obtained 24 hours after birth at term (total n = 40) from women with a normal BMI and women with obesity matched for parity, age, and neonatal sex. Reduced representation bisulfite sequencing was used to identify genomic loci associated with differentially methylated regions (DMRs) in CpG-dense regions most likely to influence gene regulation. DMRs were predominantly localized to intergenic regions and gene bodies, with only 9% of DMRs localized to promoter regions. Genes associated with DMRs were compared to those from a large publicly available cohort study, the Avon Longitudinal Study of Parents and Children (ALSPAC; total n = 859). Hypergeometric tests revealed a significant overlap in genes associated with DMRs in the OBS and ALSPAC cohorts. PTPRN2, a gene involved in insulin secretion, and MAD1L1, which plays a role in the cell cycle and tumor suppression, contained DMRs in males and females in both cohorts. In males, KEGG pathway analysis revealed significant overrepresentation of genes involved in endocytosis and pathways in cancer, including IGF1R, which was previously shown to respond to diet-induced metabolic stress in animal models and in lymphocytes in the context of childhood obesity. These preliminary findings are consistent with Developmental Origins of Health and Disease paradigm, which posits that adverse prenatal exposures set developmental health trajectories.

Two-part joint model for a longitudinal semicontinuous marker and a terminal event with application to metastatic colorectal cancer data.

Joint models for a longitudinal biomarker and a terminal event have gained interests for evaluating cancer clinical trials because the tumor evolution reflects directly the state of the disease. A biomarker characterizing the tumor size evolution over time can be highly informative for assessing treatment options and could be taken into account in addition to the survival time. The biomarker often has a semicontinuous distribution, i.e., it is zero inflated and right skewed. An appropriate model is needed for the longitudinal biomarker as well as an association structure with the survival outcome. In this article, we propose a joint model for a longitudinal semicontinuous biomarker and a survival time. The semicontinuous nature of the longitudinal biomarker is specified by a two-part model, which splits its distribution into a binary outcome (first part) represented by the positive versus zero values and a continuous outcome (second part) with the positive values only. Survival times are modeled with a proportional hazards model for which we propose three association structures with the biomarker. Our simulation studies show some bias can arise in the parameter estimates when the semicontinuous nature of the biomarker is ignored, assuming the true model is a two-part model. An application to advanced metastatic colorectal cancer data from the GERCOR study is performed where our two-part model is compared to one-part joint models. Our results show that treatment arm B (FOLFOX6/FOLFIRI) is associated to higher SLD values over time and its positive association with the terminal event leads to an increased risk of death compared to treatment arm A (FOLFIRI/FOLFOX6).

A competing risks model with binary time varying covariates for estimation of breast cancer risks in BRCA1 families.

Mammographic screening and prophylactic surgery such as risk-reducing salpingo oophorectomy can potentially reduce breast cancer risks among mutation carriers of BRCA families. The evaluation of these interventions is usually complicated by the fact that their effects on breast cancer may change over time and by the presence of competing risks. We introduce a correlated competing risks model to model breast and ovarian cancer risks within BRCA1 families that accounts for time-varying covariates. Different parametric forms for the effects of time-varying covariates are proposed for more flexibility and a correlated gamma frailty model is specified to account for the correlated competing events.We also introduce a new ascertainment correction approach that accounts for the selection of families through probands affected with either breast or ovarian cancer, or unaffected. Our simulation studies demonstrate the good performances of our proposed approach in terms of bias and precision of the estimators of model parameters and cause-specific penetrances over different levels of familial correlations. We applied our new approach to 498 BRCA1 mutation carrier families recruited through the Breast Cancer Family Registry. Our results demonstrate the importance of the functional form of the time-varying covariate effect when assessing the role of risk-reducing salpingo oophorectomy on breast cancer. In particular, under the best fitting time-varying covariate model, the overall effect of risk-reducing salpingo oophorectomy on breast cancer risk was statistically significant in women with BRCA1 mutation.

Association of Risk-Reducing Salpingo-Oophorectomy With Breast Cancer Risk in Women With BRCA1 and BRCA2 Pathogenic Variants.

IMPORTANCE: Women with pathogenic variants in BRCA1 and BRCA2 are at high risk of developing breast and ovarian cancers. They usually undergo intensive cancer surveillance and may also consider surgical interventions, such as risk-reducing mastectomy or risk-reducing salpingo-oophorectomy (RRSO). Risk-reducing salpingo-oophorectomy has been shown to reduce ovarian cancer risk, but its association with breast cancer risk is less clear. OBJECTIVE: To assess the association of RRSO with the risk of breast cancer in women with BRCA1 and BRCA2 pathogenic variants. DESIGN, SETTING, AND PARTICIPANTS: This case series included families enrolled in the Breast Cancer Family Registry between 1996 and 2000 that carried an inherited pathogenic variant in BRCA1 (498 families) or BRCA2 (378 families). A survival analysis approach was used that was designed specifically to assess the time-varying association of RRSO with breast cancer risk and accounting for other potential biases. Data were analyzed from August 2019 to November 2020. EXPOSURE: Risk-reducing salpingo-oophorectomy. MAIN OUTCOMES AND MEASURES: In all analyses, the primary end point was the time to a first primary breast cancer. RESULTS: A total of 876 families were evaluated, including 498 with BRCA1 (2650 individuals; mean [SD] event age, 55.8 [19.1] years; 437 White probands [87.8%]) and 378 with BRCA2 (1925 individuals; mean [SD] event age, 57.0 [18.6] years; 299 White probands [79.1%]). Risk-reducing salpingo-oophorectomy was associated with a reduced risk of breast cancer for BRCA1 and BRCA2 pathogenic variant carriers within 5 years after surgery (hazard ratios [HRs], 0.28 [95% CI, 0.10-0.63] and 0.19 [95% CI, 0.06-0.71], respectively), whereas the corresponding HRs were weaker after 5 years postsurgery (HRs, 0.64 [95% CI, 0.38-0.97] and 0.99 [95% CI; 0.84-1.00], respectively). For BRCA1 and BRCA2 pathogenic variant carriers who underwent RRSO at age 40 years, the cause-specific cumulative risk of breast cancer was 49.7% (95% CI, 40.0-60.3) and 52.7% (95% CI, 47.9-58.7) by age 70 years, respectively, compared with 61.0% (95% CI, 56.7-66.0) and 54.0% (95% CI, 49.3-60.1), respectively, for women without RRSO. CONCLUSIONS AND RELEVANCE: Although the primary indication for RRSO is the prevention of ovarian cancer, it is also critical to assess its association with breast cancer risk in order to guide clinical decision-making about RRSO use and timing. The results of this case series suggest a reduced risk of breast cancer associated with RRSO in the immediate 5 years after surgery in women carrying BRCA1 and BRCA2 pathogenic variants, and a longer-term association with cumulative breast cancer risk in women carrying BRCA1 pathogenic variants.

A Bayes factor approach with informative prior for rare genetic variant analysis from next generation sequencing data.

The discovery of rare genetic variants through next generation sequencing is a very challenging issue in the field of human genetics. We propose a novel region-based statistical approach based on a Bayes Factor (BF) to assess evidence of association between a set of rare variants (RVs) located on the same genomic region and a disease outcome in the context of case-control design. Marginal likelihoods are computed under the null and alternative hypotheses assuming a binomial distribution for the RV count in the region and a beta or mixture of Dirac and beta prior distribution for the probability of RV. We derive the theoretical null distribution of the BF under our prior setting and show that a Bayesian control of the false Discovery Rate can be obtained for genome-wide inference. Informative priors are introduced using prior evidence of association from a Kolmogorov-Smirnov test statistic. We use our simulation program, sim1000G, to generate RV data similar to the 1000 genomes sequencing project. Our simulation studies showed that the new BF statistic outperforms standard methods (SKAT, SKAT-O, Burden test) in case-control studies with moderate sample sizes and is equivalent to them under large sample size scenarios. Our real data application to a lung cancer case-control study found enrichment for RVs in known and novel cancer genes. It also suggests that using the BF with informative prior improves the overall gene discovery compared to the BF with noninformative prior.

Joint nested frailty models for clustered recurrent and terminal events: An application to colonoscopy screening visits and colorectal cancer risks in Lynch Syndrome families.

Joint models for recurrent and terminal events have not been yet developed for clustered data. The goals of our study are to develop a statistical framework for modelling clustered recurrent and terminal events and to perform dynamic predictions of the terminal event in family studies. We propose a joint nested frailty model for colonoscopy screening visits and colorectal cancer onset in Lynch Syndrome families. The screening and disease processes could each depend on individuals' screening history and other measured covariates and be correlated within families; our approach allows for familial correlations to affect both the visit process and the terminal event and the dependence between the two processes is specified through frailty distributions. We provide dynamic predictions of colorectal cancer risk for an individual conditional on his/her own screening history, his/her family history of screening and disease and other important clinical covariates. We apply our model to 18 Lynch Syndrome families from Newfoundland for individualized dynamic predictions of colorectal cancer risks. We demonstrate that the screening visits are non-ignorable for estimating the disease risks, and the joint nested frailty model improves dynamic prediction accuracies compared to existing joint frailty models after accounting for familial and individual screening and cancer histories.

Risks of Colorectal Cancer and Cancer-Related Mortality in Familial Colorectal Cancer Type X and Lynch Syndrome Families.

BACKGROUND: The risk of cancers is well characterized in Lynch syndrome (LS) families but has been less studied in familial colorectal cancer type X (FCCTX) families. METHODS: In this article, we compare the risk estimates of first and second colorectal cancers (CRCs) in 168 FCTTX and 780 LS families recruited through the Colon Cancer Family Registry as well as the risk of cancer-related deaths and disease-free survival (DFS) after a first CRC. Our methodology is based on a survival analysis approach, developed specifically to model the occurrence of successive cancers (ie, first and second CRCs) in the presence of competing risk events (ie, death from any causes). RESULTS: We found an excess risk of first and second CRC in individuals with LS compared to FCCTX family members. However, for an average age at first CRC of 60 years in FCCTX families and 50 years in LS families, the DFS rates were comparable in men but lower in women from FCCTX vs LS families, eg , 75.1% (95% confidence interval [CI] = 69.0% to 80.9%) vs 78.9% (95% CI = 76.3% to 81.3%) for the 10-year DFS. The 10-year risk of cancer-related death was higher in FCCTX families vs LS families, eg, 15.4% in men (95% CI = 10.9% to 19.8%) and 19.3% in women (95% CI = 13.6% to 24.7%) vs 8.9% (95% CI = 7.5% to 11.4%) and 8.7% (95% CI = 7.1% to 10.8%), respectively. CONCLUSIONS: Individuals with CRCs arising in the context of FCCTX do not experience the same improved DFS and overall survival of those with LS, and that difference may be relevant in management decisions.

Germline Mutations in the Kallikrein 6 Region and Predisposition for Aggressive Prostate Cancer.

Background: There is a need for markers that can specifically identify individuals at increased risk of harboring aggressive forms of prostate cancer (PCa). Methods: We surveyed the Kallikrein ( KLK ) region ( KLK 1-15) for single-nucleotide polymorphisms (SNPs) associated with aggressive PCa (Gleason Score ≥ 8) in 1858 PCa patients. Discovery cohorts (Swiss arm of the European Randomized Study of Screening for PCa, n = 379; Toronto, Canada, n = 540) and a validation cohort (Prostate, Lung, Colorectal and Ovarian [PLCO] screening trial, n = 939) were analyzed. Fine-mapping within the KLK region was carried out by genotyping and imputation in the discovery cohort, whereas PLCO data were provided through database of Genotypes and Phenotypes ( dbGaP ). The influence of SNPs of interest on biochemical-free survival was evaluated in a cohort of localized PCa from the International Cancer Genome Consortium (ICGC; n = 130) analyzed with next-generation sequencing. Single- and multi-SNP association studies, as well as haplotype analyses, were performed. All statistical tests were two-sided. Results: Several SNPs in very strong linkage disequilibrium in the KLK 6 region and located within the same haplotype (rs113640578, rs79324425, rs11666929, rs28384475, rs3810287), identified individuals at increased risk of aggressive PCa in both discovery (odds ratio [OR] = 3.51-3.64, 95% confidence interval [CI] = 2.01 to 6.36, P = 1.0x10 -5 -8.4x10 -6 ) and validation (OR = 1.89-1.96, 95% CI = 0.99 to 3.71, P = .04-.05) cohorts. The overall test of haplotype association was highly statistically significant in each cohort ( P = 3.5x10 -4 and .006, respectively) and in the three data sets combined ( P = 2.3x10 -5 ). These germline SNPs independently predicted relapse in the ICGC cohort (hazard ratio = 3.15, 95% CI = 1.57 to 6.34, P = .001). Conclusions: Our fine-mapping study has identified novel loci in the KLK 6 region strongly associated with aggressive PCa.

Modeling of successive cancer risks in Lynch syndrome families in the presence of competing risks using copulas.

In this article, we propose an association model to estimate the penetrance (risk) of successive cancers in the presence of competing risks. The association between the successive events is modeled via a copula and a proportional hazards model is specified for each competing event. This work is motivated by the analysis of successive cancers for people with Lynch Syndrome in the presence of competing risks. The proposed inference procedure is adapted to handle missing genetic covariates and selection bias, induced by the data collection protocol of the data at hand. The performance of the proposed estimation procedure is evaluated by simulations and its use is illustrated with data from the Colon Cancer Family Registry (Colon CFR).

A BAYESIAN GRAPHICAL MODEL FOR GENOME-WIDE ASSOCIATION STUDIES (GWAS).

The analysis of GWAS data has long been restricted to simple models that cannot fully capture the genetic architecture of complex human diseases. As a shift from standard approaches, we propose here a general statistical framework for multi-SNP analysis of GWAS data based on a Bayesian graphical model. Our goal is to develop a general approach applicable to a wide range of genetic association problems, including GWAS and fine-mapping studies, and, more specifically, be able to: (1) Assess the joint effect of multiple SNPs that can be linked or unlinked and interact or not; (2) Explore the multi-SNP model space efficiently using the Mode Oriented Stochastic Search (MOSS) algorithm and determine the best models. We illustrate our new methodology with an application to the CGEM breast cancer GWAS data. Our algorithm selected several SNPs embedded in multi-locus models with high posterior probabilities. Most of the SNPs selected have a biological relevance. Interestingly, several of them have never been detected in standard single-SNP analyses. Finally, our approach has been implemented in the open source R package genMOSS.

Prevalence of germline mutations in cancer predisposition genes in patients with pancreatic cancer.

BACKGROUND & AIMS: We investigated the prevalence of germline mutations in APC, ATM, BRCA1, BRCA2, CDKN2A, MLH1, MSH2, MSH6, PALB2, PMS2, PRSS1, STK11, and TP53 in patients with pancreatic cancer. METHODS: The Ontario Pancreas Cancer Study enrolls consenting participants with pancreatic cancer from a province-wide electronic pathology database; 708 probands were enrolled from April 2003 through August 2012. To improve the precision of BRCA2 prevalence estimates, 290 probands were selected from 3 strata, based on family history of breast and/or ovarian cancer, pancreatic cancer, or neither. Germline DNA was analyzed by next-generation sequencing using a custom multiple-gene panel. Mutation prevalence estimates were calculated from the sample for the entire cohort. RESULTS: Eleven pathogenic mutations were identified: 3 in ATM, 1 in BRCA1, 2 in BRCA2, 1 in MLH1, 2 in MSH2, 1 in MSH6, and 1 in TP53. The prevalence of mutations in all 13 genes was 3.8% (95% confidence interval, 2.1%-5.6%). Carrier status was associated significantly with breast cancer in the proband or first-degree relative (P < .01), and with colorectal cancer in the proband or first-degree relative (P < .01), but not family history of pancreatic cancer, age at diagnosis, or stage at diagnosis. Of patients with a personal or family history of breast and colorectal cancer, 10.7% (95% confidence interval, 4.4%-17.0%) and 11.1% (95% confidence interval, 3.0%-19.1%) carried pathogenic mutations, respectively. CONCLUSIONS: A small but clinically important proportion of pancreatic cancer is associated with mutations in known predisposition genes. The heterogeneity of mutations identified in this study shows the value of using a multiple-gene panel in pancreatic cancer.

Inferring gene network from candidate SNP association studies using a Bayesian graphical model: application to a breast cancer case-control study from ontario.

BACKGROUND/AIMS: Gene network analysis can be a very valuable approach for elucidating complex dependence between functional SNPs in a candidate genetic pathway and for assessing their association with a disease of interest. Even when the number of SNPs evaluated is relatively small (<20), the number of potential gene networks induced by the SNPs can be very large and the contingency tables representing their joint distribution very sparse. METHODS: In this paper, we propose a Bayesian model determination for gene network analysis using decomposable discrete graphical models combined with Reversible Jump Markov chain Monte Carlo. We show the application of this approach in a study of 13 SNPs in the DNA repair pathway and their association with breast cancer from a case-control study conducted in Ontario, Canada. RESULTS: The strength of associations among the SNPs and between the SNPs and the disease status is evaluated by computing the posterior probability of any pair of variables. The corresponding gene network is reconstructed by retaining pair-wise associations with the highest posterior probabilities. In our real data analysis, we found evidence for a particular association between one SNP in the gene POLL and the disease status and also several interesting patterns of association between the SNPs themselves. CONCLUSION: This general statistical framework could serve as a basis for prioritizing genes and SNPs that play a major role in breast cancer etiology and to better understand their complex interactions in a specific genetic pathway.

Estimating successive cancer risks in Lynch Syndrome families using a progressive three-state model.

Lynch Syndrome (LS) families harbor mutated mismatch repair genes,which predispose them to specific types of cancer. Because individuals within LS families can experience multiple cancers over their lifetime, we developed a progressive three-state model to estimate the disease risk from a healthy (state 0) to a first cancer (state 1) and then to a second cancer (state 2). Ascertainment correction of the likelihood was made to adjust for complex sampling designs with carrier probabilities for family members with missing genotype information estimated using their family's observed genotype and phenotype information in a one-step expectation-maximization algorithm. A sandwich variance estimator was employed to overcome possible model misspecification. The main objective of this paper is to estimate the disease risk (penetrance) for age at a second cancer after someone has experienced a first cancer that is also associated with a mutated gene. Simulation study results indicate that our approach generally provides unbiased risk estimates and low root mean squared errors across different family study designs, proportions of missing genotypes, and risk heterogeneities. An application to 12 large LS families from Newfoundland demonstrates that the risk for a second cancer was substantial and that the age at a first colorectal cancer significantly impacted the age at any LS subsequent cancer. This study provides new insights for developing more effective management of mutation carriers in LS families by providing more accurate multiple cancer risk estimates.