Regulation of insurers' use of genetic information means actuaries are interested in age-at-onset of genetic disorders. Arjas & Haara (1984) suggested marked point processes (MPPs) as useful models for life history data with complex covariates. Age-at-onset distributions (or equivalently, hazard rates) in respect of inherited disorders are often estimated from pedigrees, which are life histories with unusually complex covariates, as well as strong dependencies induced by shared genes. Since Elston (1973) parametric models have often been used, conditioning the likelihood on known genotypes. However, a genotype identii ed by a presymptomatic genetic test is a form of internal covariate (Kalbfleisch & Prentice, 2002). We propose a very general MPP model of a pedigree, including presymptomatic genetic testing, (‘the full model’) and show under what circumstances the partial model leading to Elston's likelihood is valid. In practice, pedigrees are often ascertained retrospectively. Many such events can be modelled by augmenting the natural filtration of the MPP. We show that, except in simple special cases, the partial model is no longer valid, and the resulting likelihoods appear to be intractable. In particular, ascertainment interacts even with independent censoring so that likelihoods no longer factorize. For one simple special case — studies of sibships — we generalise a classical result to age-at-onset data. We conclude that the study of genetic conditions with variable age at onset gains insights from the underlying principles of survival analysis in their modern form, but that great care is needed in translating epidemiological studies into actuarial models.

Recording of smoking status in general practice was compared according to the presence or absence of four diseases in which smoking cessation is important (asthma, hypertension, ischaemic heart disease and diabetes). Five of seven practices in one locality of Leicester took part. Our aims were to discover whether patients with these diseases were more likely to have a record of smoking status in their general practice notes than patients without them, and to examine the accuracy of this record compared with results from a patient questionnaire. For all diseases included, the proportion of records containing data on smoking status was higher if the disease was present than if it was not. When adjusted for age and sex, differences in recording reached statistical significance for asthma, diabetes and ischaemic heart disease, but not for hypertension. Smoking rates, as estimated from both the GP record and the postal questionnaire, were lower for all disease groups, but for asthma this did not reach statistical significance. In all disease groups GP data overestimated smoking prevalence compared with the postal questionnaire. We conclude that practices targeted their recording of smoking to those with smoking-related conditions, but achieving higher and more accurate rates of recording in those with smoking-related diseases remains a priority.

This report examines the impact of two major kinds of unequal ascertainment on the estimation of true probandwise concordance (Cpbt ) in twin studies: 1) concordance-dependent – where the ascertainment rate differs in affected members of concordant vs discordant pairs, and 2) non-independent – where ascertainment rates differ in affected members of concordant pairs where the cotwin has vs has not been ascertained. Concordance-dependent ascertainment is easily modeled algebraically; non-independent ascertainment is more complex and we here propose a model based on survival analysis. Overall, concordance-dependent ascertainment produces greater bias in estimates of probandwise concordance than does non-independent ascertainment. The bias introduced by concordance-dependent ascertainment is greatest when Cpbt is low and/or when the ascertainment rate for twins in concordant pairs is low. The bias introduced by non-independent ascertainment is greatest when Cpbt is high and/or when the ascertainment probability for an affected twin in a concordant pair where the cotwin has already been ascertained approaches unity. The impact of concordance-dependent and non-independent ascertainment on estimates of heritability and common environment is examined. Correction terms to estimate Cpbt in the presence of concordance-dependent and/or non-independent ascertainment are presented.

In a large population-based study in Northern Ireland during the period 1974-1979, the rate of anencephalus in twins (9.1/10,000) was found to be less than that in singletons (24.3/10,000). This finding is in contrast with most other studies and the possibility of underascertainment of twin cases is considered, but it is concluded that chance is the likeliest explanation. The rate of spina bifida in twins (36.4/10,000) was similar to that in singletons (31.9/10,000). All of the twins with anencephalus were female and from pairs of like sex. Rates of spina bifida in twins from pairs of the two sex types were similar but, unusually, there was a male preponderance. As in previous studies, the great majority of twins with NTDs had unaffected cotwins.

Rates of congenital anomalies of the cardiovascular system were compared between twins and singletons in a population-based study in Northern Ireland during the period 1974-1978. Multiple sources of ascertainment were used. As in previous studies, the rate of anomalies of the cardiovascular system in twins (91.0/10,000) was higher than the rate in singletons (66.4/10,000). The excess was confined to twins from pairs of like sex and, in the main, anomalies of the circulatory system other than of the heart itself were involved. Problems in the interpretation of this excess are discussed. No twins were concordant for congenital cardiovascular anomalies of any type.

Data are presented from a large-scale population-based study in Northern Ireland, in which multiple sources of ascertainment were used. As found in other studies, the overall prevalence at birth of congenital anomalies amogst twins (285.4/10,000) was somewhat higher than the rate amongst singletons (241.8/10,000). Unlike in other studies, however, the rate amongst twins of like sex (287.8/10,000) was not markedly higher than that amongst twins of unlike sex (252.3/10,000). Problems of comparison between series are discussed.

Problems of ascertainment bedevil the investigation of the etiology of congenital anomalies in singletons and in multiple births by epidemiological methods. It is shown that the definition of the population of affected births is ambiguous and that the problem of tracing etiology is complicated by the systematic way in which anomalies may be missed at birth. The available methods of dealing with problems of ascertainment are reviewed. Methods of adjusting for possible bias of ascertainment of affected births, by fitting statistical models to data from several sources, have been employed in some previous studies. In these methods, it is assumed that there are no errors of diagnosis or of recording. However, it is shown that there may be discrepancies in recorded diagnoses between sources, rendering this assumption untenable. In these methods, it is also assumed that the model which is the best fit to the data on the ascertained cases in also the best model for the cases which were not ascertained. This assumption is tested indirectly in a retrospective analysis of data from Aberdeen and Belfast collected concurrently through routine recording systems. It is demonstrated that there was a social process in ascertainment which renders the methods of adjusting for bias of ascertainment at best very complicated and at worst inapplicable.

During 1967-79 the population-based Medical Birth Registry of Norway registered 7,660 twin pairs (1% of births) born to 7,596 mothers, who gave birth to 6,608 additional infants (twin siblings). The total rate of malformations among twins (278.1/10,000) was not significantly different than among singletons (302.1/10,000), nor among twin siblings (314.8/10,000). By specific type of defect, twins had significantly higher rates than singletons of central nervous system (CNS) defects (Rate Ratio = 1.8) and cardiovascular defects (RR = 1.5). The twins also had a significantly low rate of congenital hip dislocation (RR = 0.4), which may explain the relatively low incidence of malformations in twins. Like-sex (LS) twins had a slightly higher rate of malformations than unlike-sex (US) twins (RR = 1.1), as well as a higher rate of CNS defects (RR = 3.0). The siblings also had a significantly increased rate of CNS defects compared to singletons (RR = 1.9), but not of cardiovascular defects (RR = 0.9). The results indicate that twins have elevated rates of at least some congenital malformations. The observations about CNS defects suggest common factors that can lead to either like-sex twinning, CNS defects, or both. The increased frequency of cardiovascular defects in twins appears to be associated with the biologic conditions of twinning.

In their general model of twin concordance Allen and Hrubec recently introduced the concept of secondary ascertainment rate to consider partial ascertainment of secondary cases. This concept is found to be of limited interest because only pairs where valid information can be obtained from both twins should be included in genetic analyses. It is furthermore shown that the validity of the proband method and the Allen/Hrubec model depends on the equivalence of ascertainment in twins from concordant and discordant pairs. However, if this condition is fulfilled, it has been shown how the ascertainment probability in cotwins of probands is related to the overall ascertainment probability in the total twin population.

Estimation of the twin concordance rate for a disease often requires two stages. First, the disease is ascertained in a population or in a population sample, and such twins as are found with the disease become probands. Second, twin pairs with only one proband are further investigated and additional concordant pairs are thus discovered. A mathematical model is presented that allows for continuous variation in completeness of ascertainment in both stages, for correlation within pairs in the primary ascertainment process, and for correlation within pairs in occurrence of the disease. The concordance rate can be estimated by the proband method if secondary ascertainment is complete; other measures of concordance are accurate only if primary ascertainment is complete. A parameter analogous to the concordance rate but related to correlation in primary ascertainment can be estimated from the same data.