Bivariate survival models for analysis of genetic and environmental effects in twins

Estimating Twin Pair Concordance for Age of Onset

Twin and family data provide a key source for evaluating inheritance of specific diseases. A standard analysis of such data typically involves the computation of prevalences and different concordance measures such as the casewise concordance, that is the probability that one twin has the disease given that the co-twin has the disease. Most diseases have a varying age-of-onset that will lead to age-specific prevalence. Typically, this aspect is not considered, and this may lead to severe bias as well as make it very unclear exactly what population quantities that we are estimating. In addition, one will typically need to deal with censoring in the data, that is the fact that we for some subjects only know that they are alive at a specific age without having the disease. These subjects needs to be considered age specifically, and clearly if they are young there is still a risk that they will develop the disease. The aim of this contribution is to show that the standard casewise concordance and standard prevalence estimators do not work in general for age-of-onset data. We show how one can in fact do something easy and simple even with censored data. The key is to take age into account when analysing such data.

Comparison of methods for analyzing recurrent events data: application to the Emergency Department Visits of Pediatric Firearm Victims

In many medical conditions subjects can experience recurrent incidents. A common feature for the recurrent events data and multi-stage failure time observations is that the events are naturally ordered and occur in a certain sequence over time. To analyze such data, conventional methods based on either the frequency of events or the time to the first event or overall survival time is often inefficient and unsophisticated. If data have repeated events over a period with censored failure time in longitudinal studies, more complex analytic approaches are needed to obtain accurate estimates and efficient inferences, because adjustment is necessary for existing correlation between recurrent failure times within a subject. For analyzing different kinds of recurrent event data we review the existing models-multiple failure time models and frailty models, which allow use of all the available information to accurately estimate the relative risks of recurrences in a given dataset. Using the Pediatric Firearm Victim's Emergency Department Visit Study, the results from the proposed models are compared, and applicability and appropriateness of each model are discussed.

The search for cancer risk factors: when can we stop looking?

In recent decades, countless cohort, case-control, and ecologic studies have been conducted in the search for cancer risk factors. On the basis of knowledge gained from these studies, various influential commentaries have endeavored to classify the extent to which the total cancer burden is attributable to general categories of risk, such as diet, tobacco, sun exposure, and others. These commentaries have led to the conventional wisdom that most of the cancer burden is caused by environmental factors and relatively little is directly attributable to genetic susceptibility. In the face of the apparent knowledge that the cancer burden is essentially fully "explainable" on the basis of known environmental risks, this article addresses the conceptual and empirical basis of the continued search for new risk factors. It proposes that the extent of the aggregation of cancer within individuals in the population--that is, the occurrence of second primary cancers--is a crucial statistic in this context. A study of the incidence of second primary melanoma suggests that the bulk of the risk variation in this disease cannot be explained by known risk factors. The implications of these ideas for research strategy and for public health policy are discussed.

Genetic analysis of the age at menopause by using estimating equations and Bayesian random effects models

Multi-wave self-report data on age at menopause in 2182 female twin pairs (1355 monozygotic and 827 dizygotic pairs), were analysed to estimate the genetic, common and unique environmental contribution to variation in age at menopause. Two complementary approaches for analysing correlated time-to-onset twin data are considered: the generalized estimating equations (GEE) method in which one can estimate zygosity-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modelled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the freeware package BUGS.

Risks of breast and testicular cancers in young adult twins in England and Wales: evidence on prenatal and genetic aetiology

BACKGROUND

Aetiology of breast and testicular cancers may have prenatal factors, possibly exposure of the fetus to high concentrations of maternal oestrogen. Dizygotic twinning probably involves high hormone concentrations, and therefore, dizygotic twins might be at raised risk of these cancers. The aetiologies of breast and testicular cancers have genetic components, for breast cancer, especially at younger ages. Twins of these probands may, therefore, be at high risk. We investigated risk in twins of patients with breast cancer at young ages or with testicular cancer.

METHODS

We identified twins with breast cancer incident at ages younger than 45 years and with incident testicular cancer in England and Wales during 1971-89 by cross-matching national cancer-registration and births records. We determined zygosity by questionnaires to the patients. The twins of probands were followed up for cancer incidence and death. We analysed risks of breast and testicular cancer in dizygotic twins compared with monozygotic twins, and in monozygotic and dizygotic twins of probands.

FINDINGS

We identified 500 twins with breast cancer and 194 with testicular cancer. We found a non-significantly raised risk of breast cancer in dizygotic compared with monozygotic twins younger than 30 years (odds ratio 2.3 [95% CI 0.9-5.9]) but not older. The overall risk of testicular cancer was significantly higher in dizygotic twins than in monozygotic twins (1.5 [1.1-2.2]) consequent on a risk for seminomas was high (3.2 [1.6-6.5]; p = 0.001). Risk of breast cancer was significantly raised in female twins of probands (standardised incidence ratio 7.7 [4.9-12.2], p < 0.001). The relative risk of breast cancer was 34.7 (9.5-126.5) in monozygotic twins of women in whom breast cancer had occurred before age 35 years. The cumulative risk of breast cancer for these twins by age 40 years was 29% (13-56). The relative risk of testicular cancer was 37.5 (12.3-115.6) in twins of men with testicular cancer. The cumulative risk by age 40 years in monozygotic twins of men with testicular cancer was 14% (4-46).

INTERPRETATION

The higher risks of these cancers in dizygotic than in monozygotic twins support a prenatal aetiology, and are compatible with aetiology related to raised maternal concentrations of free, unbound oestrogens. The results for twins of probands have implications for genetic aetiology; appropriate clinical action for monozygotic twins needs consideration.

Cancer in twins: genetic and nongenetic familial risk factors

BACKGROUND

Familial clustering has been observed for cancers that occur at specific sites. Most findings, which leave little doubt about the involvement of a heritable (i.e., genetic) component in the development of some cancers, are based on data from "cancer-prone" families or interviews with subjects who have cancer. The study of twins should be of value in cancer epidemiology because twins either are genetically identical or share half of their segregating genes.

PURPOSE

We linked the Swedish Twin Registry to the Swedish Cancer Registry, thereby identifying cases of cancer diagnosed from 1959 through 1992 in twins born in the period from 1886 through 1958, to assess the importance of both genetic and nongenetic (i.e., environmental) familial factors in determining cancer risk.

METHODS

Same-sex twin pairs with both individuals alive and living in Sweden in 1959-1961 or 1970-1972 were identified in the old cohort (born from 1886 through 1925) or the young cohort (born from 1926 through 1958), respectively, of the Swedish Twin Registry; pairs for whom zygosity (i.e., the number of eggs that gave rise to the twins) could be determined were considered further. The association of cancer with combined genetic and nongenetic familial factors was tested by comparing all twin pairs (regardless of zygosity) in which at least one member of the pair had been diagnosed with cancer at one of several specific sites with pairs in which neither twin had that cancer. Heritable effects alone were tested by comparing monozygotic (one egg) and dizygotic (two eggs) twin pairs. Statistical methods used in quantitative genetics and standard methods for epidemiologic research were used in parallel to analyze the data.

RESULTS AND CONCLUSIONS

In the 10503 twin pairs from the old cohort, 361.7 cases of malignant cancer were identified; 918 malignant cancers were identified in the 12883 twin pairs from the young cohort. When cancer sites with a total number of at least 200 cases and at least one twin pair concordant (i.e., both twins affected) for the site were evaluated, namely, cancers of the stomach, colon and rectum, lung, female breast, and prostate, as well as total cancer, profound genetic and/or nongenetic familial effects were identified in twins from the old cohort. Similar findings were obtained for twins in the young cohort for cancers of the prostate and female breast, as well as for total cancer. Genetic and nongenetic familial effects were also identified in twins from both cohorts for in situ cancer of the cervix. The increase in risk of colon and rectum, breast, cervical, and especially prostate cancer, but not stomach or lung cancer, tended to be greater if a monozygotic rather than a dizygotic twin were affected.

IMPLICATIONS

The identification of familial effects for total cancer in this study is consistent with the idea that individuals may possess a genetic susceptibility to cancer in general.

How frailty models can be used for evaluating longevity limits: Taking advantage of an interdisciplinary approach

In this paper we discuss an approach to the analysis of mortality and longevity limits when survival data on related individuals with and without observed covariates are available. The approach combines the ideas of demography and survival analysis with methods of quantitative genetics and genetic epidemiology. It allows us to analyze the genetic structure of frailty in the Cox-type hazard model with random effects. We demonstrate the implementation of this strategy to survival data on Danish twins. We then evaluate the resulting lower bounds for biological limits of human longevity. Finally, we discuss the limitations of this approach and directions of further research.

Use of twins in search for tumor suppressor genes

A new approach is applied in the mapping of tumor suppressor genes: analysis of loss of heterozygosity (LOH) in concordant tumors of monozygotic and dizygotic twins. The method relies on recognition of genome locations undergoing loss in both twins in a high proportion of the set of all twin pairs examined. The method effectively pinpoints, and excludes, the loci of potential tumor suppressor genes. With the help of a high density linkage map any such candidates can be placed within a narrow region of a chromosome arm and perhaps matched with known genes. The analysis of the Swedish Twin Registry has shown a clear genetic component for breast cancer. We have identified mono- and dizygotic twins concordant for breast cancer and collected the pathology specimens. Tumor and normal tissue was microdissected and microsatellite analysis carried out to test for allelic loss (LOH) in entirely new and putative chromosomal loci in this cancer. It can be calculated that using only six pairs of informative monozygotic twins, a locus can be incriminated with a high probability. Using increasingly dense markers and search for homozygous deletions, it should be possible to map one or more candidates for breast cancer.

Bipolar disorder: evidence for a major locus

Complex segregation analyses were conducted on families of bipolar I and bipolar II probands to delineate the mode of inheritance. The probands were ascertained from consecutive referrals to the Mood Disorder Service, University Hospital, University of British Columbia and diagnosed by DSM-III-R and Research Diagnostic Criteria. Data were available on over 1,500 first-degree relatives of the 186 Caucasian probands. The purpose of the analyses was to determine if, after correcting for age and birth cohort, there was evidence for a single major locus. Five models were fit to the data using the statistical package SAGE: i) dominant, ii) recessive, iii) arbitrary mendelian inheritance, iv) environmental, and v) no major effects. A single dominant, mendelian major locus was the best fitting of these models for the sample of bipolar I and II probands when only bipolar relatives were defined as affected (polygenic inheritance could not be tested). Adding recurrent major depression to the diagnosis "affected" for relatives reduced the evidence for a major locus effect. Our findings support the undertaking of linkage studies and are consistent with the analyses of the National Institutes of Mental Health (NIMH) Collaborative Study data by Rice et al. (Arch Gen Psychiatry 44: 441-447, 1987) and Blangero and Elston (Genet Epidemiol 6:221-227, 1989).

How long can humans live? Lower bound for biological limit of human longevity calculated from Danish twin data using correlated frailty model

How long can people live? Opinions of the researchers diverge and debates continue. Is there any systematic way to address this question? In this paper, we suggest an approach to the estimation of the biological limit of human longevity using survival data for twins from different zygocity groups. The approach is based on the genetic model of individual frailty. It combines ideas used in demography and survival analysis with methods of quantitative genetics and genetic epidemiology. The association between the life-spans of related individuals is described by the correlated frailty model of bivariate survival. A version of this model is used in order to estimate heritability of the individual frailty and to calculate the lower bound of human longevity. The limitations of this approach and directions of further research are discussed.

Frailty models for survival data

A frailty model is a random effects model for time variables, where the random effect (the frailty) has a multiplicative effect on the hazard. It can be used for univariate (independent) failure times, i.e. to describe the influence of unobserved covariates in a proportional hazards model. More interesting, however, is to consider multivariate (dependent) failure times generated as conditionally independent times given the frailty. This approach can be used both for survival times for individuals, like twins or family members, and for repeated events for the same individual. The standard assumption is to use a gamma distribution for the frailty, but this is a restriction that implies that the dependence is most important for late events. More generally, the distribution can be stable, inverse Gaussian, or follow a power variance function exponential family. Theoretically, large differences are seen between the choices. In practice, using the largest model makes it possible to allow for more general dependence structures, without making the formulas too complicated.

Genetic analysis of durations: correlated frailty model applied to survival of Danish twins

Population studies of changes in human morbidity and mortality require models which take into account the influence of genetic and environmental factors on life-related durations, such as age at onset of the disease or disability, age at death, etc. In this paper we show how a bivariate survival model based on the concept of correlated individual frailty can be used for the genetic analysis of durations. Six genetic models of frailty are considered and applied to Danish twin survival data. The results of statistical analysis allow us to conclude that at least 50% of variability in individual frailty is determined by environmental factors. The approach suggests a method of estimation of the lower bound for the biological limit of human longevity. Directions for further research are discussed.

Correlated individual frailty: an advantageous approach to survival analysis of bivariate data

"We develop a new model of bivariate survival based on the notion of correlated individual frailty. We analyze the properties of this model and suggest a new approach to the analysis of bivariate data that does not require a parametric specification--but permits estimation--of the form of the hazard function for individuals. We empirically demonstrate the advantages of the model in the statistical analysis of bivariate data." (SUMMARY IN FRE)

Studies of genetic factors in prostate cancer in a twin population

It has been suggested that positive family history constitutes a risk factor for the development of prostate cancer. Familial clustering of prostate cancer might suggest that genetic factors are of importance in the etiology of this disease. To elucidate further the relative importance of genetic factors, we studied prostate cancer among an unselected Swedish twin population. Information from the Swedish Twin Registry and the Swedish Cancer Registry was used. In 4,840 male twin pairs 458 prostate cancers were identified between 1959 and 1989. Among these 16 monozygotic and 6 dizygotic twin pairs were concordant for prostate cancer. Proband concordance rates of 0.192 and 0.043, and a correlation of liability of 0.40 and -0.05 were found for monozygotic and dizygotic pairs, respectively. These differences in proband concordance rates and correlations of liability for monozygotic pairs compared to dizygotic pairs are pronounced. The results indicate that genetic factors might be of importance for the development of prostate cancer. The results of this study indicate the need for further investigations of genetic factors in prostate cancer, including large scale epidemiological studies and investigations of molecular genetics of risk families.

Generalizations and applications of frailty models for survival and event data

A variety of survival models with both discrete and continuously distributed frailty is considered within a framework that involves the specification of three sub-models. An intensity sub-model specifies how the intensity is related to values of covariates and frailty; a measurement sub-model specifies how fallible measures of frailty are related to it; and an exposure sub-model specifies how frailty is distributed within the population. The models include those in which frailty is due to omitted covariates and those where it represents a covariate that has been measured subject to error. Multivariate frailty is also considered, with particular emphasis on models suitable for application to genetically related individuals, notably twins. A numerical example illustrates the use of a model with multivariate frailty for data on repeated exercise times.

HLA haplotype sharing in rheumatoid arthritis sibships: risk estimates in siblings

The distribution of the number of parental HLA haplotypes shared by sibs with rheumatoid arthritis (RA) has been used to obtain information on the genetics of the disease. Thirty-four RA sibships (25 sib-pairs, 9 sib-trios) were ascertained, all of which were HLA typed and which satisfied the 1958 American Rheumatism Association criteria for "definite" RA. These were combined with other published but nonoverlapping data from the literature; thus, 143 sib-pairs, 36 sib-trios and 4 sibquads were identified. The affected RA sibs shared two, one and zero parental HLA haplotypes in a ratio of 40: 45: 15 which was significantly different from random expectations (p less than 0.05). Risk estimates for sibs of probands for those sharing two, one and zero parental HLA haplotypes were 6.2%, 3.5% and 2.3% respectively. Risks subdivided by DR genotype of the proband are also calculated, the highest (8.7%) being for sibs sharing two haplotypes with a proband carrying at least one DR4 allele. The manuscript also considers genetic information in relatives other than siblings; an extension of the affected relative pair haplotype sharing method to second and third degree kinships is presented.

Estimating effects of probands' characteristics on familial risk: I. Adjustment for censoring and correlated ages at onset

Family studies with age at onset of the disease as the endpoint face two important problems: censoring and correlation of age at onset among relatives. We present a multivariate survival model for ages at onset of relatives which incorporates the problems cited above. The interpretations of regression coefficients and association parameter in the context of family studies are emphasized. The present paper describes a statistical method for estimating these parameters. In a companion paper [Pulver and Liang, Genet Epidemiol 8:339-350, 1991] this model is applied to a genetic epidemiologic study of schizophrenia.

A time-dependent logistic hazard function for modeling variable age of onset in analysis of familial diseases

The paper presents an extension of the regressive logistic models proposed by Bonney [Biometrics 42:611-625, 1986], to address the problems of variable age-of-onset and time-dependent covariates in analysis of familial diseases. This goal is achieved by using failure time data analysis methods, and partitioning the time of follow up in K mutually exclusive intervals. The conditional probability of being affected within the kth interval (k = 1...K) given not affected before represents the hazard function in this discrete formulation. A logistic model is used to specify a regression relationship between this hazard function and a set of explanatory variables including genotype, phenotypes of ancestors, and other covariates which can be time dependent. The probability that a given person either becomes affected within the kth interval (i.e., interval k includes age of onset of the person) or remains unaffected by the end of the kth interval (i.e., interval k includes age at examination of the person) are derived from the general results of failure time data analysis and used for the likelihood formulation. This proposed approach can be used in any genetic segregation and linkage analysis in which a penetrance function needs to be defined. Application of the method to familial leprosy data leads to results consistent with our previous analysis performed using the unified mixed model [Abel and Demenais, Am J Hum Genet 42:256-266, 1988], i.e., the presence of a recessive major gene controlling susceptibility to leprosy. Furthermore, a simulation study shows the capability of the new model to detect major gene effects and to provide accurate parameter estimates in a situation of complete ascertainment.