ELIMINATING BIAS IN CANCER RISK ESTIMATES A SIMULATION STUDY

Transcription

1 ELIMINATING BIAS IN CANCER RISK ESTIMATES A SIMULATION STUDY by SARADHA RAJAMANI A Project submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Master of Statistics Department of Mathematics The University of Utah October 2016

2 Copyright c SARADHA RAJAMANI 2016 All Rights Reserved

3 The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL THIS PAGE IS A PLACE HOLDER ONLY Please use the updated form on the Thesis Office website The dissertation of SARADHA RAJAMANI has been approved by the following supervisory committee members: BRAXTON OSTING, Chair(s) 17 Aug 2016 Date Approved ELISHA HUGHES, Member 17 Aug 2016 Date Approved TOM ALBERTS, Member 17 Aug 2016 Date Approved

4 ABSTRACT Hereditary breast cancer is aggressive and known to affect women at early age. The lifetime and age-specific cancer risk should be accurate as the management of disease depends on these estimates. The recommended action for high risk individual ranges from frequent screening to prophylactic surgeries, having huge consequences on patient quality of life. Case-control studies estimate the relative risk of cancer harboring genetic mutations that predisposes the patients to disease. The prevalence of the gene mutations that are highly penetrant is less than 1%. For studying rare mutations, population based random sampling would yield an underpowered study. Hence, most of the studies are done in high risk families which create bias in risk estimates. In this project, we simulated the sampling condition in hereditary genetic testing laboratories like Myriad Genetics Inc., and the factors that contribute to bias in this type of study. We have shown that the bias is due to ascertainment on family history and personal cancer condition. We were able to prove that no matter the severity, bias can be eliminated by properly accounting for it in the logistic regression model that predicts cancer risk based on mutation status. We also investigated non-hereditary factors, such as environmental exposure and age confounding the relationship between genetic variant status and the occurrence of cancer.

5 To my beloved parents. No amount of experimentation can ever prove me right; a single experiment can prove me wrong. Albert Einstein

6 CONTENTS ABSTRACT LIST OF TABLES iii vii LIST OF FIGURES viii ACKNOWLEDGMENTS ix CHAPTERS INTRODUCTION Breast Cancer Types Genes Associated With Hereditary Breast Cancer Risks Associated With Hereditary Breast Cancer Relative and Absolute Risk Calculating Risk Familial Risk Risk Due To Rare Allele Risk For High-Risk Cases Bias in Risk Estimation Berkson Bias Adjustment For Bias Risk Bias Due To Study Design Population-Based Case-Control Study Family-Based Case-Control Study Kin Cohort Study Clinic Based Study Segregation Study Prospective Cohort Study Volunteer Study Bias in Myriad Genetics data Causal Pathway Project Assumptions and Design BIAS DUE TO FAMILY HISTORY OF CANCER Family History (FH) Of Breast Cancer High Risk Familial Criteria Simulation Model Bias and Increased Cancer Risk in Carriers

7 3. BIAS DUE TO ENVIRONMENTAL EXPOSURE AND FAMILY HISTORY OF CANCER Environmental Exposure and Breast Cancer Risk Environmental Factors and Breast Cancer Simulation BIAS DUE TO AGE AND FAMILY HISTORY OF CANCER Age Calculating Cumulative Lifetime Risk of breast cancer for carriers and non-carriers Pedigree Simulation SUMMARY OF FINDINGS Discussion Conclusion APPENDICES A. R CODE Bibliography vi

8 LIST OF TABLES 1.1 Observed proportion in population and Myriad data Breast Cancer (BC) incidence in ascertained data Mutation Status and BC in whole data data Cumulative Lifetime Risk Distribution (%) by Age and Mutation Status Number of cancer incidence in first degree relatives

9 LIST OF FIGURES 1.1 Proportion of familial hereditary risk of breast cancer [18] Causal Diagram showing ascertainment bias Elimination of bias in ascertained set Bias and relation to personal mutation risk Bias in cancer risk estimate due to family history and exposure Breast cancer incidence and mortality risk by age [22] BRCA genes cancer risk by age [7] Cumulative risk estimates of relatives Cumulative risk estimates of proband Bias in ascertained set due to family history and age

10 ACKNOWLEDGMENTS Many thanks are due for making this project possible. First, I would like to thank my project advisor BRAXTON OSTING Ph.D., of Deparment of Mathematics at University of Utah. He is always eager to help and available whenever I needed some expertise. He guided me in to right direction, giving a sense of broader view on the project. He also gave me the opportunity to make this project my own. I would also like to express my profound gratitude to ELISHA HUGHES Ph.D., Myriad Genetics Labs, for her constant support throughout this project. Without her passionate participation and input, the project could not have been successfully completed. Our inspiring conversations often led me to think more clearly about this project. My appreciation extends to TOM ALBERTS Ph.D., of Department of Mathematics at University of Utah, for being member of my committee and provide valuable comments. I wish to thank DARL FLAKE Ph.D., Myriad Genetics Labs, for helping me with basic understanding of simulations and samplings. His thoughts gave this projects a more structure and cohesiveness. I would like to acknowledge ALEXANDER GUTIN Ph.D., Myriad Genetics Labs, for the conception of this project. His valuable comments proved to be corner stone of this project. Lastly, I would like to thank my parents for their unwavering support throughout these years of my work and professional goals.

11 CHAPTER 1 INTRODUCTION Breast cancer remains the most common form of cancer diagnosed worldwide. The incidence of breast cancer is also reported to be rapidly rising in a number of developing countries, possibly owing to the congruence of a number of factors, including changes in lifestyle, behavioral patterns, and improved diagnostics, all results of economic growth. Despite enormous research in understanding of breast cancer risk, the clinical validity and utility of such studies are often questioned. Recently, advances have been made to provide an accurate estimate of cancer risk by eliminating the bias and conducting a well-powered study [19]. In this chapter, basic concepts like breast cancer types, associated genes, cancer risk due to gene mutation and how to estimate risk and bias in cancer risk are introduced. [24]. 1.1 Breast Cancer Types There are three main categories of breast cancer depending on the type of risk factors Hereditary Breast Cancer - Hereditary breast cancer is caused by gene variants that predisposes the patient to cancer. The onset of cancer is younger for these patients and first degree relatives are at 50% risk of having the same variant. Sporadic Breast Cancer - Nearly 70-80% of the breast cancer are of sporadic type where the factors that predisposes the patient to breast cancer are unknown. Familial Breast Cancer - Familial clustering results from chance clustering of sporadic cases in families. There is no specific pattern of inheritance. This type of breast cancer can be caused by unknown genetic, environmental and/or lifestyle factors.

12 2 Figure 1.1. Proportion of familial hereditary risk of breast cancer [18]. Sporadic cancer is the most common type of breast cancer whose risk factors are unknown. Familial cancer risk factors are unknown genetic, environmental or lifestyle factors. Hereditary cancer risk is due to genetic variants that predisposes to breast cancer. fig1 1.2 Genes Associated With Hereditary Breast Cancer Most inherited cases of breast cancer are associated with abnormal changes or mutations in one of two genes, BRCA1 (BReast CAncer gene 1) and BRCA2 (BReast CAncer gene 2). The class of BRCA proteins, tumor suppressor proteins help repair cell DNA damage. Certain mutations in BRCA genes either causes the protein to not function properly or the protein is not produced at all. BRCA deficient cells accumulates DNA damage leading to cancer. The carriers of these mutations where the BRCA protein is affected has increased risk of female breast and ovarian cancers. Abnormal BRCA genes may account for up to 10% of all breast cancers [3]. The measure of the effect of a mutation in a cancer gene is defined as penetrance or absolute risk of cancer in carriers. 1.3 Risks Associated With Hereditary Breast Cancer The risk for breast cancer varies with age, presence of breast cancer associated gene variants, hormonal status, familial breast cancer, etc. The risk also varies from one study to another depending on the selection of control and cases for the case-control studies. A woman living in the US has a 12.3%, or a 1 in 8, lifetime risk of being diagnosed

13 3 with breast cancer [3]. The cumulative lifetime risk (CLTR) for developing a disease also known as penetrance, is frequently reported as the probability of cancer by the age of 70 years. CLTR is used in genetic counseling where options for cancer prevention include prophylactic removal of both breasts. In most of the studies, penetrance is estimated from the degree of familial aggregation of cancer. Early penetrance is calculated to be 71-85% [Easton2002, 6]. The validity of these studies have been questioned due to the ascertainment bias. For clinic-based population of mutation carriers, female breast cancer risk was 72.8% (95% CI = 68-78%) by age 70 and ovarian cancer risk is 40.7% (95% CI = 36-46%). There is an increased risk of colon cancer (two-fold), pancreas (threefold), stomach (three fold) and fallopian tube (120-fold) in BRCA1 mutation carriers compared to population-based estimates from Surveillance, Epidemiology, and End Results (SEER) database. Familial risk estimate is 85% for breast cancer and 60% for ovarian cancer [4]. The population based risk estimate range from 35-50% for breast cancer and 15% for ovarian cancer [11, 9]. The age adjusted risk of breast cancer in the clinic-based population is 77% and 56% risk for Ashkenazi Jewish volunteers [11]. The estimate is 85% for breast cancer studies in high risk family cohort. Risk is lower in clinic-based population since there are fewer families of increased and early breast cancer cases compared to familial studies Relative and Absolute Risk The relative risk or odds ratio is not an estimate of absolute risk without making adjustments for all known and unknown risk factors. The estimates of epidemiological studies are presented as average relative risk or odds ratio. For the purpose of counseling, relative risk has to be converted to absolute risk which gives the risk over lifetime or 10-years etc. Absolute risk are strongly influenced by risk factors for breast cancer such as familial history of breast cancer, age at menopause and breast density on mammography. In case of a rare variant, a relative risk of 2 or 4 translates to 18% and 32% absolute risk in absence of other risk factors. A relative risk higher than 4 is categorized as high-risk category. If the patient has a variant that confers a relative risk of 2 to 4, the patient will be in high-risk only if other factors are present [5].

14 4 1.4 Calculating Risk Familial Risk Assume that a mother is a carrier, denoted by A* on one allele and A w, the wild type allele. The father s genotype is unknown and denoted by A 1 A 2. The child genotype will be A A 1, A A 2, A w A 1 or A w A 2, each with probability of For autosomal dominant inheritance, the probability of being a carrier are equal to 1, 1, p or p respectively where p is the prevalence of the mutation in population. The probability that the mother is a carrier conditional on offspring being an mutant is P(Mother = carrier o f f spring = mutant) = p P(mother = carrier o f f spring = non mutant) = p. (1.1) We assume Mendelian inheritance, that an individual inherits two BRCA1 or BRCA2 alleles, one from each parent independently [8]. The mutations are inherited in autosomal dominant mode where mutation in one allele causes loss of protein function even though the other copy is intact. At each gene locus, an individual has zero, one or two mutations. Suppose the frequency of mutations for BRCA1 is indicated by p, then the probabilities that an individual inherits mutation in both alleles is P(BRCA1=2) is p 2. For individual with one or no mutation, P(BRCA1=1) = p(1-p) and P(BRCA1=0) = (1 p) 2. The distribution of BRCA1 genetic status given her family history is P[BRCA1 Fam.Hist] = P[BRCA1]P[Fam.Hist BRCA1]/P[Fam.Hist] Hardy-Weinberg equilibrium states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. For two alleles A and a with frequencies p(a) = p and p(a) = q respectively, the expected genotype frequencies of homozygotes are p(aa) = p 2 and p(aa) = q 2. The expected value in heterozygotes p(aa) = 2pq. The above expected values are called Hardy-Weinberg proportions. Hence, p 2 + 2pq + q 2 = Risk Due To Rare Allele If A denotes the event that an individual has at least one copy of a rare allele and D denotes the individual has disease, then the probability of observing the rare allele can be expressed using Baye s law,

15 P(A D) = γ P(A)when γ = P(D A) P(D). (1.2) is a measure of the relative risk. The relative risk can also be expressed as γ = P(D A) P(D A c ), where A c is the event that an individual does not have the allele of inquiry. γ and γ are the same for rare alleles with modest rate difference in risk (attributable risk) between exposed and unexposed. 5 (1.3) Risk For High-Risk Cases Cases are at higher risk than controls due to non-genetic factors and hence the risk is overestimated. Such estimate of cancer risk is meaningful only for carrier women who do not have breast cancer yet. The distribution of risk in the population is different than the distribution of risk in incident cases [2]. The distribution of risks in carriers identified from an incident series of breast cancer represent higher risk than the carrier population. Let r denote the risk of a randomly selected carrier who is at risk in the population. Let p(r) be the probability density of the risks in carriers with mean risk µ. The distribution of breast cancer risk for carriers with breast cancer is not p(r) but q(r) where, q(r) = If the mean risk of this distribution is µ c, then rp(r) rp(r)dx. (1.4) µ c µ = 1 + v2 µ 2 (1.5) where v 2 is the variance of risk in the population. This shows that the mean risk in carriers identified through breast cancer is greater than mean risk of the carriers. This size-based sampling is the basis of cancer research. For a binary exposure with a prevalence, p and relative risk ψ, the cases and controls should be sampled in proportion to pψ and (1-p). The prevalence of exposure among cases is q = pψ (µ 2 )(1 p + pψ). (1.6) The odds ratio is calculated from case-control along with exposure status, OR = q(1 p) = ψ. (1.7) p(1 q)

16 The above paradigm enable us to calculate the relative risk but not absolute risk with additional information about the cancer incidence data [2] Bias in Risk Estimation Bias is the lack of internal validity of a study where the association between exposure and disease is measured incorrectly. A study without internal validity will also lack external validity where the study results are applied to everyone in that population. Bias occurs in a study due to selection bias, information bias or confounding. Ascertainment bias is a kind of selection or sampling bias resulting in non-random sample. Depending on the severity of the bias, the odds ratio which estimates the cancer risk due to exposure varies from study to study. Accurate assessment of cancer risk is important for clinical management of the cancer, ranging from more frequent MRI screening to preventive surgeries, with substantial consequences on the patient s life. Prophylactic oophorectomy decreases the BC risk in BRCA1 mutation carriers by 50%. Wide variation in risk estimates makes counseling in risk evaluation program difficult Berkson Bias When both exposure and outcome both affect the sample selection process, the type of bias is called Berkson bias. This causes a downward bias of the estimate even when the dependence of selection on disease and exposure is not perfect or intermediates are present [12]. Berkson s bias can arise in prospective or retrospective studies, and in randomized or observational settings Adjustment For Bias Two most common methods of controlling for confounding are adjusting using multivariable regression models and stratified analysis after matching for confounder [13]. For example, if gender is a confounder, then the cases and controls are matched based on gender followed by calculation of disease risk for each strata. These methods work only if all confounders are accurately measured [12]. Ascertainment-adjusted likelihood approaches calculating retrospective likelihood allow unbiased estimation and use all the information available on individual in the family; members who are not genotypes are useful for risk analysis through their probability of

17 7 being a carrier, whatever their phenotype [17]. 1.6 Risk Bias Due To Study Design Population-Based Case-Control Study In population-based studies, cases are randomly selected by their breast cancer diagnosis and controls are population-matched. This study design provide direct estimate of relative risk or odds ratio which is not biased by familial genetic predisposition or exposure that increase the cancer risk. Most common mutations in BRCA1 and BRCA2 occur at a frequency of 1% or less in the general population. To study this mutation and estimate the cancer risk, a large number of samples would have to be collected otherwise the study would be under-powered. Population based risk estimates underestimate the risk, especially if the disease is rare and hence the mutation carriers are represented at low frequency. Population-based studies are not practical especially for founder mutations, like the ones in Ashkenazi Jewish families [5] Family-Based Case-Control Study For family-based case-control studies, the samples are selected based on personal and familial cancer history. For rare mutations, this study design enriches the cases thereby improving the power of the study. The patients are restricted to the ones who meet the eligibility criteria for genetic testing. Also, patients with severe breast cancer family history are more likely to seek genetic concealing or testing. Early penetrance studies of BRCA1 and BRCA2 mutations used high-risk families with multiple cases of breast cancer [2]. This leads to ascertainment bias that may contribute to the difficulty in replicating the genetic study finding. Also, additional assumptions about the modifying effects of other familial factors has to be made for bias correction [5] Kin Cohort Study The kin-cohort study design has widespread acceptance for studying rare mutations that are autosomal dominant [23]. The risks are estimated using maximum-likelihood methods [26]. The advantages of this study design is that it requires smaller sample size compared to cohort or case-control study and enables the investigator to study several disease outcomes.

18 8 The disadvantages being proband s decision to volunteer in the study and information recall bias by proband. Patients who volunteer for such studies are inherently different from people who don t in the same population. The patients decision could be due to disease severity, cancer at young age, strong family history or all of the above. Also, patients with disease are more likely to recall information about family cancer than one who doesn t. Risks may also be overestimated if all familial factors are not accounted for Clinic Based Study Patients who are diagnosed with breast cancer at clinics are enrolled in this study. The information about the relatives are obtained from the participants. Studies comparing cases ascertained for clinical genetic testing to general population controls upwardly bias estimates of penetrance [5] Segregation Study Segregation studies are conducted on families that have strong familial occurrence of cancer. For this type of study, controls are not required. This study requires a large number of individuals from the same family to participate in the study. Segregation studies are usually under powered Prospective Cohort Study Individuals with and without the exposure of interest, like genetic abnormalities are observed over a long period of time for the incidence of cancer. This study provides direct estimate of absolute risk. Key disadvantages are long-term commitment required by both participants and investigator, expensive and risk estimates are confounded if other familial factors are not accounted for. Also, failure to report preventive surgeries would lead to underestimation of risk since preventive surgeries would reduce the incidence of breast cancer Volunteer Study The penetrance of breast cancer in 5318 volunteer Jewish population is 56% with 120 patient identified to have familial cancer history which is lower than familial breast cancer studies. In these types of studies, the cases are still different from controls, i.e, they don t

19 9 have the same risk for breast cancer. 1.7 Bias in Myriad Genetics data Myriad patients are ascertained directly on breast cancer and for breast cancer variants through family history of cancer. Both personal and familial cancer histories motivate participants to seek genetic testing and cancer management. As the variables that explaining differential baseline risk were captured for all patients before testing, ascertainment bias can be controlled using standard methods like multivariate regression models and matched case-control analysis. The analysis would provide adjusted ORs that estimate the relative risk conferred by mutations after accounting for confounders like family history of cancer, age and ancestry. If all the confounders are measured accurately and adjusted, then the resultant estimate should be reproducible in population-based studies. The odds ratio for breast cancer risk Table 1.1. Observed proportion in population and Myriad data Carrier Breast Cancer General Population P(Myriad testing) Observed in Myriad Yes Affected A S 1 AS 1 Yes Unaffected B S 2 BS 2 No Affected C S 3 CS 3 No Unaffected D S 4 DS 4 due to genetic variants is AD/BC in the general population. In Myriad data, the bias is S 1 S 4 S 2 S 3. We expect the bias to arise mainly from S2 > S4 since, among unaffected patients in the general population, carriers will have family history that motivate myrisk testing which is Myriad s hereditary multigene cancer test. We could also have (opposite effect) S1 > S3 if breast cancer cases with family history are more often referred to myrisk testing (and have more variants) than breast cancer cases without family history. This seems to contradict the statement above regarding downward bias. However, S2 > S4 should be stronger than S1 > S3 since unaffected patients require family history for myrisk testing, where affected patients do not.

20 Causal Pathway Causal diagrams can be used to illustrate and quantify ascertainment bias in Myriad data. Pathogenic variants are synonymous with mutations. The figure shows our assump- Figure 1.2. Causal Diagram showing ascertainment bias. fig2 tions regarding causal dependence in Myriad myrisk test population. Direct causal associations of mutation on breast cancer and family history. Conditional on Myriad ascertainment, PV>FH>mT>BC is a biasing path. This will bias PV>BC associations. Conditioning on FH blocks the biasing path PV>FH>mT>BC, but opens a new biasing path PV>FH>Other>BC. There will be some bias from PV>FH>Other>BC in any study that estimates the effect of PV on BC after accounting for FH. 1.8 Project Assumptions and Design In this project, I am exploring the bias due to family history, family history in relation with exposure and family history along with age. For this project, the following assumptions were made. Autosomal dominant mode of inheritance - a fact well established in the literature.

21 mother is carrier and father is wild-type - this assumption helps simplify the family tree. 11 Hereditary gene mutation are the only cause of familial breast cancer - limiting the scope of hereditary breast cancer type. Risk is same in every generation - also a fact well established in the literature.

22 CHAPTER 2 BIAS DUE TO FAMILY HISTORY OF CANCER 2.1 Family History (FH) Of Breast Cancer High Risk Familial Criteria Having two or more of the following criteria defines the family as high-risk, Breast cancer diagnosed at age 50 or younger Breast and Ovarian cancer on the same side of the family or in a single individual More than one cancer occurrence for the patient or relatives Two or more relatives with breast or ovarian cancer A known mutation in cancer susceptibility gene within the family Ashkenazi Jewish descent with familial breast or ovarian cancer The bias in cancer risk estimate due to familial cancer occurrence has been well documented and thoroughly discussed in previous chapter. In this chapter, family history is simulated to show how Odds Ratio (OR) estimates varies from the true estimate. Also shown here are relation between bias and personal cancer risk. With increasing risk, there is more downward shift in OR. A logistic regression model is used to eliminate the bias when the dataset is ascertained on family history and personal cancer status. 2.2 Simulation Model The population frequency of a genetic mutation is set at 1% with a sample size of 50,000.

23 13 P(MUT) = 0.01 (2.1) For the first degree (FD) relative, the probability of being a carrier depends on the proband mutation status. If the proband has genetic variants that predisposes to breast cancer, then the probabilty follows mendelian inheritance and the relative has a 50% chance of being a carrier. For non-carrier proband, the probability of relative is half of the 1% general population risk since one shared allele between the relative and proband is known to be wild-type. The probability of cancer risk for first degree relative dependent on carrier is P(FD.MUT = 1 MUT = 1) = 0.50 P(FD.MUT = 1 MUT = 0) = (2.2) The outcome, cancer status for the proband is coded as a function of β 0, the population prevalence of breast cancer (10%), β 1, the coefficient for mutation status of the proband and β 2, the coefficient of first degree mutation status. All coefficients are in log scale since logistic regression model is used. Probability, p for proband and first degree relative is calculated from the above models. The model can be written as Cancer = β 0 + β 1 MUT + β 2 FH (2.3) A uniform random variable (N=50000), Y is created with values between 0 and 1. If the Y <= p, then the individual s cancer status is classified as affected and unaffected otherwise. The first degree relative being a carrier doubles the risk of patient. Hence β 2 is set at log(2). For patient mutation status β 1, the risk is fixed at six-fold difference between carrier and non-carrier (log(6)). A biased set ascertained on first degree cancer status and proband cancer status is created by eliminating 36,749 patients who do not have breast cancer or family history. The distribution of cancer in relative and proband in the remaining set (N = 13251) is listed in the table 2.1. Logistic regression models are used to calculate crude OR in the whole sample set of and ascertained set, where cancer status is a function of mutation status of the proband. The adjusted OR is obtained after adjusting for family history.

24 14 Table 2.1. Breast Cancer (BC) incidence in ascertained data Patient BC Status Kin has BC Kin unaffected A 1000 replicate of the above simulation is performed to obtain the distribution of OR. Figure 3 shows the distribution of OR with and without adjustments for the unascertained and ascertained set. Unascertained Ascertained Odds Ratio crude adjusted FH crude adjusted FH Figure 2.1. Elimination of bias in ascertained set. fig3 The orange boxplot shows the crude and adjusted OR where family history (FH) did not cause any bias in unascertained set. The crude OR is downward biased due to family history in ascertained set whereas the bias is eliminated after adjusting.

25 15 The distribution of OR (orange) with and without adjusting is the same in the unascertained set since family history of cancer is not a confounder. The distribution of OR (blue) in ascertained data before adjusting is lower than the true estimate. This downward bias occurs when the independent variable of interest is correlated with a confounder and the confounder is not accounted for. After adjusting with family history, the bias is eliminated. 2.3 Bias and Increased Cancer Risk in Carriers The patient mutation status β 1 is varied from two to ten-fold (log(2) - log(10)). The correlation of proband and first degree mutation status are recorded for each value of β 1. Bias in ascertained sample log2 log4 log6 log8 log10 Beta for Patient Mutation Status Figure 2.2. Bias and relation to personal mutation risk. The figure shows that the bias in estimate increases with the increase in cancer risk due to mutation. fig4

26 16 The bias increases as the risk increases for carrier. Since the ascertainment is on first degree cancer status and proband cancer status, which in turn depends on the proband mutation stutus, the bias increases as the prevalence of cancer increases. Table 2.2. Mutation Status and BC in whole data data Beta for MUT Dataset MUT status % of BC log(2) unascertained log(2) unascertained log(2) ascertained log(2) ascertained log(10) unascertained log(10) unascertained log(10) ascertained log(10) ascertained In the table 2.2, breast cancer remains constant for non-mutant at 10% and 53% in unascertained and ascertained simulated data set. But the proportion of breast cancer cases increases for carriers in both datasets as β 1 increases. As β 1 increases, the risk increases by three to seven-fold for mutants compared to non-mutants. On the other hand, as β 1 increases, the relative risk (the % of breast cancer in mutant over the % of breast cancer in non-mutant for ascertained set) increases but only marginally. Since the non-carriers or controls are becoming enriched for breast cancer, the relative risk decreases which explains the downward shift of OR.

27 CHAPTER 3 BIAS DUE TO ENVIRONMENTAL EXPOSURE AND FAMILY HISTORY OF CANCER 3.1 Environmental Exposure and Breast Cancer Risk Only up to 30% of the familial occurrence of breast cancer is explained by known genetic markers [20, 15]. Rare varients in genes like BRCA1, BRCA2, PALB2, ATM and CHEK2 genes with moderate to high penetrance along with over 90 common mutations explain 37% of the excess familial risk [14]. Hereditary, genetic, lifestyle and environmental factors are responsible for breast cancer development [21]. Heterogeneity of risks caused by unknown genetic or environmental factors within families also leads to overestimate of risks. If additional factors are likely to increase the breast cancer risk in BC families in addition to genetic predisposition, then carrier women with strong family history of breast cancer are likely to have much higher risk than a woman with gene mutation alone. Some of the environment and lifestyle factors that increase cancer risk are age at menarche Age at first birth and number of live births Age at menopause using hormone replacement therapy drinking alcohol smoking cigarettes lack of exercise

28 18 BMI 3.2 Environmental Factors and Breast Cancer Women with genetic mutations are at higher risk for breast cancer if certain environmental factors are present. Gene-environment interaction is assumed if the odds ratios of the genetic and the environmental factors is significantly different from the expected value obtained by multiplying the relative risks for genetic and environment alone. The above is true only if all genetic and environmental factors are accounted for. Interaction studies for rare variants with higher penetrance are often underpowered. A small meta-analysis study found an 35% (95% CI ) decreased breast cancer risk for women with BRCA1 mutation when they had first birth at 30 years of age or older [25]. This is contradictory to the finding in general population where older age at first birth is associated with increased breast cancer risk [10]. However, this gene-environmental interaction could be due to ascertainment bias. This study has a small sample size. In this project, we assume that there is no gene-environmental interaction since no well-powered study was able to establish the relatioship scientifically. 3.3 Simulation Our goal of simulating environmental exposure is to find the bias in our estimate when not all the factors are accounted for. The population frequency of a genetic mutation is set at 1% with a sample size of 50,000 and the frequency of exposure is 10 as shown in the equation below.%. P(MUT) = 0.01P(EXP) = 0.10 (3.1) Among individuals without mutations or exposure, the prevalence of cancer is 10%. The probability of breast cancer is 1 if the patient is a carrier and also exposed. For patients with either exposure or hereditary gene variants, the probabilites are 0.20 for individuals with exposure and without mutation. It increases to 0.60 if the individuals are not exposed and if they have mutation.

29 19 P(BC = 1 MUT = 0, EXP = 0) = 0.10 P(BC = 1 MUT = 0, EXP = 1) = 0.20 P(BC = 1 MUT = 1, EXP = 0) = 0.60 (3.2) P(BC = 1 Mut = 1, EXP = 1) = 1.00 For the first degree relative, the probability of being a carrier depends on the proband mutation status. If the proband has genetic variants that predisposes to breast cancer, then the probabilty follows mendelian inheritance and the relative has 50% chance of being a carrier. For non-carrier proband, the probability of relative is half of the 1% general population risk since one shared allele between the relative and proband is known to be wild-type. The breast cancer status follow the same paradigm as the proband cancer assignment. For the first degree relative exposure status also depends on the proband status. If the proband is not exposed, then by Baye s theorem, the total possible probability is 0.09 and if the proband is exposed then the FD exposure status is given twice that of proband exposure cancer risk. P(FD.MUT = 1 MUT = 1) = 0.50 P(FD.MUT = 1 MUT = 0) = P(FD.EXP = 1 EXP = 1) = 0.20 (3.3) P(FD.EXP = 1 EXP = 0) = 0.09 The ascertainment bias set is created with all patients who have family history or personal breast cancer. Logistic regression is used to estimate the cancer risk with cancer as outcome and proband mutation status as the predictor. Odds ratio is calculated without adjusting is the crude OR in ascertained set. The model is then adjusted for first degree relative cancer status in the unascertained and ascertained data. Finally, in both datasets, OR adjusted for first degree relative cancer status and exposure status is estimated. A 100 replicate of the above simulation is performed to get the median OR. The cancer risk of exposure is varied from 10% to 50% to assess the magnitude of bias. In the unascertained set, the bias between crude and adjusted OR increases with increase in cancer risk due to exposure. With the prevalence of exposure at 10% and high cancer risk makes the exposure a confounder in the population. Hence the crude OR does not reflect the true measure of association between mutation status and cancer risk.

30 OR Ascertainment No Yes adj FH 2.adj FH 2.adj FH,exp 1.adj FH,Exp 1.crude 2.crude 1.adj FH 2.adj FH 2.adj FH,exp 1.adj FH,Exp 1.crude 2.crude Figure 3.1. Bias in cancer risk estimate due to family history and exposure. The bias due to exposure is seen in the crude and family history adjusted OR. The bias increases as the cancer risk due to exposure increases. The plot facet title indicates the probability of cancer due to exposure. The bias is eliminated only after adjusting for exposure in addition to family history. fig5 Since exposure is a confounder, adjusting for family history alone is not enough to correct the bias due to family history and exposure. The crude OR in ascertained set is same across different exposure conditions since the mutation prevalence and its cancer risk did not vary. Just like in unascertained set, adjusting for family history alone is not enough to correct the bias due to family history and exposure. The bias is corrected after adjusting for family history and exposure. But the variance increases in the ascertained estimate after adjusting for biases. This might be due to smaller number of samples in the ascertained set. The variance of the estimate in the ascertained set increases, probably due to small sample size.

31 CHAPTER 4 BIAS DUE TO AGE AND FAMILY HISTORY OF CANCER 4.1 Age Age is the strongest risk factor for breast cancer. The older a woman is, the more likely she is to get breast cancer. The decrease in incidence rates that occurs in women 80 years of age and older may reflect lower rates of screening, the detection of cancers by mammography before 80 years of age, and/or incomplete detection. During , the median age at the time of breast cancer diagnosis was 61 [1]. Inherited changes in BRCA genes and age further increase the risk of breast cancer than either of the component risk. The average age of female breast cancer diagnosis is 42 years (95% CI= years) in clinical population [16]. The ages are 20 and 10 years younger, compared to population averages. Also, women who are carrier and has breast cancer at a younger age is more likely to have aggressive cancer type increasing the mortality risk [1] Calculating Cumulative Lifetime Risk of breast cancer for carriers and non-carriers The relatives of the volunteers who carry pathogenic variants are referred to as carrier kin and non-carrier kin if they have wild-type allele. The cumulative risk of both carrier and non-carrier kin are weighted averages of the risks in carriers and non-carriers, conditional on risk factors. The weighted averages are further stratified by age to provide age-specific penetrance of a mutation. The weights depends on prevalence, p of the mutation and mode of inheritance [23]. According to Mendelian autosomal dominant inheritance, the probability of a kin being a carrier is p/2. In case of BRCA genes where the prevalence p is 1%, the probability

32 22 Figure 4.1. Breast cancer incidence and mortality risk by age [22]. The breast cancer risk increases with age. After 70, the risk decreases due to lower screening or incomplete detection of cancer. fig6 of the risk is (0.01/2) = The probability of non-carrier kin is p. Let R + and R are proportion of individuals who develop disease before age t in carrier and non-carrier kin respectively. R + and R are weighted averages of S + and S, the cumulative risk of individuals developing disease before age t [23]. R = ps + + (1 p)s R + = ( p 2 + l 2 )S + + ( l 2 p 2 )S (4.1) Solving the above, S = 1 + p 1 p R p 2 1 p R + (4.2) S + = 2R + R R + and R are obtained using Kaplan-Meier methods. To calculate CLTR for carriers, prevalence is not required. For low prevalence, the CLTR difference between carriers and non-carriers can be approximated by

33 23 Figure 4.2. BRCA genes cancer risk by age [7] The risk for breast cancer increases due to BRCA1 or BRCA2 gene mutation and age. fig7 S + S = 2 R + R 1 p 2(R + R ) (4.3) The figure 4.3 shows the cumulative risk of occurrence of breast or ovarian cancer in firstdegree relatives of carriers of any of the three founder mutations and that of non-carriers among Ashkenazi Jewish volunteers study [23]. The figure 4.4 shows the cumulative risk of breast or ovarian cancer of the carrier with any of the three founder mutations and that of non-carriers among Ashkenazi Jewish volunteers study Pedigree Simulation The pedigree is created with 50,000 proband being a carrier at the frequency of 1%. The probabilities of mother and offspring being an carrier depends on the proband and follows the same paradigm as the first degree relative simulation. The prevalence of mutation in sister depends on the mother. If the mother is mutant, then the probability of her being an mutant is 50%. If the mother is not a carrier, the probability of cancer is half that of general population which is 0.5%.

34 24 Figure 4.3. Cumulative risk estimates of relatives. Figure 4.3 shows the age-dependent cumulative breast cancer risk of first degree relatives who are carriers along with non-carrier relatives who are R + and R in equation 4.1 fig8. fig8 Figure 4.4. Cumulative risk estimates of proband. Figure 4.4 shows the age-dependent cumulative breast cancer risk of mutant and nonmutant carriers who are S + and S in equation 4.1 fig8 fig9 The age range for mutant in the simulation is 35 to 62 years of age and that of nonmutant is years of age. Mothers age range is , sister and that of daughter is Both mother and proband are assumed to have given birth between 15 to 30 years of age. The age-specific cumulative risk varies with mutation status. The risk decreases after 80 years of age in the population. For simulation purpose, the risk after eighty years of age is set at same level as 70. Based on the cancer risk each individual in the pedigree is given cancer status. The first degree cancer status is the sum of

35 25 Table 4.1. Cumulative Lifetime Risk Distribution (%) by Age and Mutation Status Status non-carrier carrier mother, sister and daughter cancer status, cancer being a binary variable with 1 indicating cancer and 0 for no disease. The table below shows the first degree cancer status in a sample of Table 4.2. Number of cancer incidence in first degree relatives The simulation is repeated 1000 times to get the median OR. In the fig 4.5, the orange boxplot are distribution of OR in unascertained group where as the blue group represent the ascertained set. In the simulation, age distribution is different for carriers and non-carriers in the whole population. Hence age is a confounder in the unascertained set, the OR bias between the crude and adjusted with age and FH. When adjusted for family history alone, the distribution matches the crude OR of the unascertained set. When the ascertained set is adjusted for both family history and age, then the distribution matches that of adjusted OR in the unascertained set which is the true OR.

36 26 Unascertained Ascertained Odds Ratio crude adjusted FH adjusted FH,Age crude adjusted FH adjusted FH,Age Figure 4.5. Bias in ascertained set due to family history and age. fig

37 CHAPTER 5 SUMMARY OF FINDINGS 5.1 Discussion Active management of hereditary breast cancer risk plays a major role in preventing the incidence of cancer. The family history of breast cancer predisposes the individual to high risk for the disease. The risk estimates vary with the selection of cases and controls. Family-based studies provide higher risk estimates due to the enrichment of cases. The population-based studies, on the other hand, have fewer cases of breast cancer since the prevalence of these genetic variants are rare in the population. This leads to lower risk estimates. In hereditary cancer testing labs like Myriad Genetics Inc., the ascertainment is on personal cancer status and family history of cancer. In this study, I simulated a model to understand and eliminate ascertainment bias in risk estimates when the study is done in laboratory setting. In the first model, I have studied the bias caused due to family history. After controlling for the family history of cancer, the bias is eliminated and the odds ratio reflect the true strength between the personal mutation status and cancer status. I have also shown the bias in relation to increase in relationship between personal mutation status and cancer status. Strengthening this relationship also leads to increased correlation between the mutation status and family history of cancer. In the second model, I have simulated exposure as another variable that alters the relation between mutation and cancer status. Here exposure acts as a confounder and it is accounted for in unascertained as well as ascertained set to get the true odds ratio. The magnitude of confounding increases as the cancer risk due to exposure also increases. This causes a increased downward bias, similar to what is shown in case of family history.

38 28 In the third model, age is simulated to be a confounder. Here the age distribution of cancer onset is different for mutants and non-mutants. Mutants have early onset of cancer and also higher risk of cancer. This causes a downward bias of the odds ratio as well. Again, as in the case of family history and exposure, accounting for age eliminates the bias. The strength of this study is that mutation prevalence and cancer risks are based on literature figures and hence the odds ratio reflect the true study scenario. This study also shows what unaccounting for other confounders, like exposure and age can do the estimates. The bias relationship to predictor as well as confounders are defined. A common method of adjusting, logistic regression is used to show that the bias can be eliminated. The study does not reflect the odds ratio in every study types. The prevalence of alleles of moderate penetrance are not studied here since their prevalence tend to higher. Another limitation of the study is that only one predictor is considered and interaction between two predictor variables are not addressed. 5.2 Conclusion An underestimate of cancer risk has huge implication in patient clinical management of the cancer. Eliminating the bias allows the risk estimate to be applied to the general population. This simulation project studies in detail about confounders and its relation to predictor and outcome variables. The magnitude of bias is shown for varying condition and how it can be eliminated. Three major risk factors are considered, like family history which addresses the hereditary component, environmental exposures and age-specific risks. This project model can be further extended to multiple predictors and various other types of cancer.

39 APPENDIX A R CODE # I n i t i a l i z e d a t a s e t data < data.frame ( seq ( 1, ) ) colnames ( data ) < sample f o r ( i in data $sample ){ # u n a s c e r t a i n e d s e t N = df < data.frame ( seq ( 1, ) ) colnames ( df ) < sample # Proband mutation s t a t u s df $ mut.status < rbinom ( n=50000, s i z e =1, prob= ) df $ e x p. s t a t u s < rbinom ( n=50000, s i z e =1, prob= ) # B r e a s t c a n c e r s t a t u s f o r probands df $ c a n. s t a t u s [ df $ mut.status ==0] < rbinom ( nrow ( df [ df $ mut.status = = 0, ] ), s i z e =1, 0. 1 ) df $ c a n. s t a t u s [ df $ mut.status ==1] < rbinom ( nrow ( df [ df $ mut.status = = 1, ] ), s i z e =1, 0. 6 ) # a s s i g n f a m i l y h i s t o r y mutation s t a t u s df $ FD.mut.status [ df $ mut.status ==0] < rbinom ( nrow ( df [ df $ mut.status = = 0, ] ), s i z e =1, ) df $ FD.mut.status [ df $ mut.status ==1] < rbinom ( nrow ( df [ df $ mut.status = = 1, ] ), s i z e =1, 0. 5 ) # a s s i g n f a m i l y h i s t o r y c a n c e r s t a t u s df $ F D. c a n. s t a t u s [ df $ FD.mut.status ==0] < rbinom ( nrow ( df [ df $ FD.mut.status = = 0, ] ), s i z e =1, 0. 1 ) df $ F D. c a n. s t a t u s [ df $ FD.mut.status ==1] < rbinom ( nrow ( df [ df $ FD.mut.status = = 1, ] ), s i z e =1, 0. 6 )