Generalized case–cohort sampling

A class of cohort sampling designs, including nested case–control, case–cohort and classical case–control designs involving survival data, is studied through a unified approach using Cox's proportional hazards model. By finding an optimal sample reuse method via local averaging, a closed form estimating function is obtained, leading directly to the estimators of the regression parameters that are relatively easy to compute and are more efficient than some commonly used estimators in case–cohort and nested case–control studies. A semiparametric efficient estimator can also be found with some further computation. In addition, the class of sampling designs in this study provides a variety of sampling options and relaxes the restrictions of sampling schemes that are currently available.     

Weighted analyses for cohort sampling designs

Weighted analysis methods are considered for cohort sampling designs that allow subsampling of both cases and non-cases, but with cases generally sampled more intensively. The methods fit into the general framework for the analysis of survey sampling designs considered by Lin (Biometrika 87:37–47, 2000). Details are given for applying the general methodology in this setting. In addition to considering proportional hazards regression, methods for evaluating the representativeness of the sample and for estimating event-free probabilities are given. In a small simulation study, the one-sample cumulative hazard estimator and its variance estimator were found to be nearly unbiased, but the true coverage probabilities of confidence intervals computed from these sometimes deviated significantly from the nominal levels. Methods for cross-validation and for bootstrap resampling, which take into account the dependencies in the sample, are also considered. An erratum to this article can be found at     

Efficient estimation for case‐cohort studies

The author considers time‐to‐event data from case‐cohort designs. As existing methods are either inefficient or based on restrictive assumptions concerning the censoring mechanism, he proposes a semi‐parametrically efficient estimator under the usual assumptions for Cox regression models. The estimator in question is obtained by a one‐step Newton‐Raphson approximation that solves the efficient score equations with initial value obtained from an existing method. The author proves that the estimator is consistent, asymptotically efficient and normally distributed in the limit. He also resorts to simulations to show that the proposed estimator performs well in finite samples and that it considerably improves the efficiency of existing pseudo‐likelihood estimators when a correlate of the missing covariate is available. Although he focuses on the situation where covariates are discrete, the author also explores how the method can be applied to models with continuous covariates.     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies, individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from human immunodeficiency virus (HIV) infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared with the healthy subjects. So far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore, simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu-Asia Aging Study to estimate the dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from HIV infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared to the healthy subjects. By far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu Asia Aging Study to estimate dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

Cox regression in cohort studies with validation sampling

An estimation procedure is proposed for the Cox model in cohort studies with validation sampling, where crude covariate information is observed for the full cohort and true covariate information is collected on a validation set sampled randomly from the full cohort. The method proposed makes use of the partial information from data that are available on the entire cohort by fitting a working Cox model relating crude covariates to the failure time. The resulting estimator is consistent regardless of the specification of the working model and is asymptotically more efficient than the validation-set-only estimator. Approximate asymptotic relative efficiencies with respect to some alternative methods are derived under a simple scenario and further studied numerically. The finite sample performance is investigated and compared with alternative methods via simulation studies. A similar procedure also works for the case where the validation set is a stratified random sample from the cohort.     

The distribution by age of the frequency of first marriage in a female cohort

The authors present 2 methods for the approximation of a representative schedule recording first marriage frequencies by age. Both treatments are mathematically complex. One method achieves a very close approximation with a simple closed form frequency function, which is the limiting distribution of the convolution of an infinite number of exponentially distributed components. The other method achieves an equal approximation by the convolution of a normal distribution of age of entry into a marriageable state and as few as 3 exponentially distributed delays. This latter convolution provides a feasible model of nuptiality, a model receiving surprising empirical support.     

Analysis of the bovine spongiform encephalopathy maternal cohort study, revisited

The bovine spongiform encephalopathy (BSE) maternal cohort study provided robust evidence of an enhanced risk of developing BSE for offspring of BSE-affected dams. We present for the first time, but in retrospect, an interim analysis of the BSE maternal cohort study and set it in historical context, some of which has only been revealed through the BSE inquiry. We also consider the implications for design of extending the BSE maternal cohort study once an enhanced risk to exposed calves had been established, to assess the risk to calves born further from the clinical onset of BSE in the dam than those in the original study. We demonstrate that, if a data monitoring committee had been established, conclusions similar to those based on the final results could have been drawn several years before the completion of the BSE maternal cohort study. Further, we conclude that an extension of the cohort study is unlikely to have been commissioned because of the substantial financial investment required, yet low power, and practical difficulties associated with implementation of any worthwhile extension.     

Statistical inference for the accelerated failure time model under two-stage generalized case–cohort design

Abstract

In this article, we propose a two-stage generalized case–cohort design and develop an efficient inference procedure for the data collected with this design. In the first-stage, we observe the failure time, censoring indicator and covariates which are easy or cheap to measure, and in the second-stage, select a subcohort by simple random sampling and a subset of failures in remaining subjects from the first-stage subjects to observe their exposures which are different or expensive to measure. We derive estimators for regression parameters in the accelerated failure time model under the two-stage generalized case–cohort design through the estimated augmented estimating equation and the kernel function method. The resulting estimators are shown to be consistent and asymptotically normal. The finite sample performance of the proposed method is evaluated through the simulation studies. The proposed method is applied to a real data set from the National Wilm’s Tumor Study Group.     

Cumulative cohort design for dose-finding

We introduce a new design for dose-finding in the context of toxicity studies for which it is assumed that toxicity increases with dose. The goal is to identify the maximum tolerated dose, which is taken to be the dose associated with a prespecified “target” toxicity rate. The decision to decrease, increase or repeat a dose for the next subject depends on how far an estimated toxicity rate at the current dose is from the target. The size of the window within which the current dose will be repeated is obtained based on the theory of Markov chains as applied to group up-and-down designs. But whereas the treatment allocation rule in Markovian group up-and-down designs is only based on information from the current cohort of subjects, the treatment allocation rule for the proposed design is based on the cumulative information at the current dose. We then consider an extension of this new design for clinical trials in which the subject's outcome is not known immediately. The new design is compared to the continual reassessment method.     

Bayesian Inference from Case–cohort Data with Multiple End-points

Abstract.  In a case–cohort design a random sample from the study cohort, referred as a subcohort, and all the cases outside the subcohort are selected for collecting extra covariate data. The union of the selected subcohort and all cases are referred as the case–cohort set. Such a design is generally employed when the collection of information on an extra covariate for the study cohort is expensive. An advantage of the case–cohort design over more traditional case–control and the nested case–control designs is that it provides a set of controls which can be used for multiple end-points, in which case there is information on some covariates and event follow-up for the whole study cohort. Here, we propose a Bayesian approach to analyse such a case–cohort design as a cohort design with incomplete data on the extra covariate. We construct likelihood expressions when multiple end-points are of interest simultaneously and propose a Bayesian data augmentation method to estimate the model parameters. A simulation study is carried out to illustrate the method and the results are compared with the complete cohort analysis.     

A note on the greenwood variance estimator in cohort life tables: Isolating the effect of one source of bias

A modification of the Greenwood variance estimator is defined and shown to be free of bias whenever its constitu­ent interval estimators are conditionally unbiased, given the sample size at the start of the interval. Using the modified estimator as a standard of comparison, the original Greenwood estimator is seen to have an intrinsic positive bias.Under­estimation of variances through the use of Greenwood's formula must be due to bias in the constituent interval estimators and/or, with fixed interval bounds, due to disregarding the random character of the total number of life table intervals to exhaustion of ttje sample. Some easy to prove properties of the modified and the original Greenwood estimators are stated that apply in the absence of censoring. A suggest­ion is made for reducing the bias of the interval variance estimators.     

Forecasting cohort fertility rates by using an exponential function

"Population forecasts based on cross sectional data do not allow for the variations in cohort fertility. In this paper methods are developed to fit cohort fertility rates by an exponential function. Out of a number of selected functions the Weibull-function shows the best fit. For predicting cohort fertility pattern the parameter values can be derived from the forecasts of a small number of demographic statistics." (summary in ENG)     

Marriage or cohabitation: a competing risks analysis of first-partnership formation among the 1958 British birth cohort

A discrete time competing risks hazards model is used to analyse entry into first partnership among men and women born in Britain in 1958. Using a life-course approach we identify family background and current life experiences which affect the timing and type of first-partnership formation. Education is a key factor influencing the age of entry into first partnership and whether or not the respondent will experience pregnancy before forming the partnership. Religiosity, experience of parental separation and the geographical region of residence are more important in affecting the decision to cohabit rather than to marry directly. The analyses highlight the importance of transitions in other domains such as leaving the parental home in encouraging cohabitation.     

Feature screening for case‐cohort studies with failure time outcome

Case‐cohort design has been demonstrated to be an economical and efficient approach in large cohort studies when the measurement of some covariates on all individuals is expensive. Various methods have been proposed for case‐cohort data when the dimension of covariates is smaller than sample size. However, limited work has been done for high‐dimensional case‐cohort data which are frequently collected in large epidemiological studies. In this paper, we propose a variable screening method for ultrahigh‐dimensional case‐cohort data under the framework of proportional model, which allows the covariate dimension increases with sample size at exponential rate. Our procedure enjoys the sure screening property and the ranking consistency under some mild regularity conditions. We further extend this method to an iterative version to handle the scenarios where some covariates are jointly important but are marginally unrelated or weakly correlated to the response. The finite sample performance of the proposed procedure is evaluated via both simulation studies and an application to a real data from the breast cancer study.     

Prevalent cohort studies and unobserved heterogeneity

Lifetime Data Analysis - Consider lifetimes originating at a series of calendar times $$ t_{1} ,t_{2} , \ldots $$ . At a certain time $$ t_{0} $$ a cross-sectional sample is taken, generating a...     

Approximate variance formulas and asymptotic joint sampling distributions of standardized risk ratios in the presence of competing risks in cohort studies

The present paper is concerned with some results in cohort studies, in which the individuals in two study population are exposed simultaneously to several risks of death, which compete for their lives.

The morality experience of individuals in the two study populations is compared with respect to the morality experience of individuals in a well-defined and fixed population called the standard population.

Under some reasonable assumptions, not only simple variance formulas are-developed for the standardized risk ratio statistics (S[Rcirc]R_i) but also their joint asymptotic sampling distribution. It is demonstrated that these SRcirc;R_i's have asymptotically a multivariate normal distribtion corresponding to any given number of competing risks of death, These results are utilized to construct Scheffé-type and Sidak-type simultaneous confidence intervals for the SRR_i parameters which hold regardless of any covariance structure among the competing risks of death. The corresponding results for the cause-specific SMR and the externally standardized risk ratio parameters follow as special cases.

The present paper generalizes the available results in the literature in two directions, namely, to obtain simple variance formulas for the S[Rcirc]R_i, statistics and to treat the situation in the presence of competing risks to which individuals in a study are simultaneously exposed.

An empirical evaluation of these results is discussed in the last section utilizing some real cohort data from two recent occupational epidemiologic cohort studies.     

Left-censored dementia incidences in estimating cohort effects

Lifetime Data Analysis - We estimate the dementia incidence hazard in Germany for the birth cohorts 1900 until 1954 from a simple sample of Germany’s largest health insurance company....     

Parametric modelling of prevalent cohort data with uncertainty in the measurement of the initial onset date

In prevalent cohort studies with follow-up, if disease duration is the focus, the date of onset must be obtained retrospectively. For some diseases, such as Alzheimer’s disease, the very notion of a date of onset is unclear, and it can be assumed that the reported date of onset acts only as a proxy for the unknown true date of onset. When adjusting for onset dates reported with error, the features of left-truncation and potential right-censoring of the failure times must be modeled appropriately. Under the assumptions of a classical measurement error model for the onset times and an underlying parametric failure time model, we propose a maximum likelihood estimator for the failure time distribution parameters which requires only the observed backward recurrence times. Costly and time-consuming follow-up may therefore be avoided. We validate the maximum likelihood estimator on simulated datasets under varying parameter combinations and apply the proposed method to the Canadian Study of Health and Aging dataset.