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Semi-competing risks data involve a non-terminal event time, such as time to disease progression, and a terminal event time such as time to death. Existing methods for handling semi-competing risks data often assume that the underlying association between the two event times follows a pre-specified copula with unknown association parameters, which often correspond to the strength of association. In this article we propose a flexible association model that does not require pre-specifying a copula. Therefore our methods facilitate a convenient and robust evaluation of the underlying association pattern, as well as the association strength. Furthermore the proposed association model leads to a robust estimator for the conditional survival probability of the terminal event given the non-terminal event. The methods were also extended to handle left-truncation. Both the association and survival estimators were shown to feature desirable asymptotic properties and satisfactory numerical performance. Our methods were successfully applied to a diabetes data set to study the association between time to diabetic nephropathy and time to death, and to predict the mortality rate given the onset time of nephropathy. The Canadian Journal of Statistics 44: 361-374; 2016 © 2016 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

To shed light on the etiology of metabolic syndrome development, it is important to understand whether its 5 component disorders follow certain onset sequences. To explore disease progression of the syndrome, we studied the ages at onset of 5 cardiometabolic diseases: abdominal obesity, diabetes, hypertension, hypertriglyceridemia, and hypo-α-lipoproteinemia. In analyzing longitudinal data from the Cardiovascular Disease Risk Factors Two-Township Study (1989-2002) in Taiwan, we adjusted for nonsusceptibility, utilizing the logistic-accelerated failure time location-scale mixture regression models for left-truncated and interval-censored data to simultaneously estimate the associations of township and sex with the susceptibility probability and the age-at-onset distribution of susceptible individuals for each disease. We then validated the onset sequences of 5 cardiometabolic diseases by comparing the overall probability density curves across township-sex strata. Visualization of these curves indicates that women tended to have onsets of abdominal obesity and hypo-α-lipoproteinemia in young adulthood, hypertension and hypertriglyceridemia in middle age, and diabetes later; men tended to have onsets of abdominal obesity, hypo-α-lipoproteinemia, and hypertriglyceridemia in young adulthood, hypertension in middle age, and diabetes later. Different onset patterns of abdominal obesity, hypo-α-lipoproteinemia, and male hypertension were identified between townships. Our proposed method provides a novel strategy for investigating both pathogenesis and preventive measures of complex syndromes. [ABSTRACT FROM AUTHOR]

We develop time-varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left-truncated by ages of entry and competing-risk censored by deaths. Two types of association estimators are proposed based on conditional cause-specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections. [ABSTRACT FROM AUTHOR]

A now common goal in medical research is to investigate the inter-relationships between a repeatedly measured biomarker, measured with error, and the time to an event of interest. This form of question can be tackled with a joint longitudinal-survival model, with the most common approach combining a longitudinal mixed effects model with a proportional hazards survival model, where the models are linked through shared random effects. In this article, we look at incorporating delayed entry (left truncation), which has received relatively little attention. The extension to delayed entry requires a second set of numerical integration, beyond that required in a standard joint model. We therefore implement two sets of fully adaptive Gauss-Hermite quadrature with nested Gauss-Kronrod quadrature (to allow time-dependent association structures), conducted simultaneously, to evaluate the likelihood. We evaluate fully adaptive quadrature compared with previously proposed non-adaptive quadrature through a simulation study, showing substantial improvements, both in terms of minimising bias and reducing computation time. We further investigate, through simulation, the consequences of misspecifying the longitudinal trajectory and its impact on estimates of association. Our scenarios showed the current value association structure to be very robust, compared with the rate of change that we found to be highly sensitive showing that assuming a simpler trend when the truth is more complex can lead to substantial bias. With emphasis on flexible parametric approaches, we generalise previous models by proposing the use of polynomials or splines to capture the longitudinal trend and restricted cubic splines to model the baseline log hazard function. The methods are illustrated on a dataset of breast cancer patients, modelling mammographic density jointly with survival, where we show how to incorporate density measurements prior to the at-risk period, to make use of all the available information. User-friendly Stata software is provided. [ABSTRACT FROM AUTHOR]

Left-truncated and right-censored (LTRC) data are encountered frequently due to a prevalent cohort sampling in follow-up studies. Because of the skewness of the distribution of survival time, quantile regression is a useful alternative to the Cox's proportional hazards model and the accelerated failure time model for survival analysis. In this paper, we apply the quantile regression model to LTRC data and develops an unbiased estimating equation for regression coefficients. The proposed estimation methods use the inverse probabilities of truncation and censoring weighting technique. The resulting estimator is uniformly consistent and asymptotically normal. The finite-sample performance of the proposed estimation methods is also evaluated using extensive simulation studies. Finally, analysis of real data is presented to illustrate our proposed estimation methods. [ABSTRACT FROM PUBLISHER]

Traditional analysis with truncated survival data has been developed under the assumption that the lifetime variable of interest is statistically independent of the truncation variable. However, empirical evidence has shown that the truncation variable may depend on the lifetime of interest in many real-world examples. The lack of independence can lead to seriously biased analysis. In this article, we revisit an existing estimation procedure for survival under a copula-based dependent truncation model. Here, the same estimating equation is adopted but a different algorithm to solve the equation is proposed. We compare the new algorithm with the existing one and discuss its theoretical and practical usefulness. Real data examples are analyzed for illustration. We implemented the proposed algorithm in an R 'depend.truncation' package, available from CRAN. [ABSTRACT FROM AUTHOR]

The idea that epidemiologic studies should start from first exposure onward has been advocated in the past few years. The study of incident exposures is contrasted with studies of prevalent exposures in which follow-up may commence after first exposure. The former approach is seen as a hallmark of a good study and necessary for causal inference. We argue that studying incident exposures may be necessary in some situations, but it is not always necessary and is not the preferred option in many instances. Conducting a study involves decisions as to which person-time experience should be included. Although studies of prevalent exposures involve left truncation (missingness on the left), studies of incident exposures may involve right censoring (missingness on the right) and therefore may not be able to assess the long-term effects of exposure. These considerations have consequences for studies of dynamic (open) populations that involve a mixture of prevalent and incident exposures. We argue that studies with prevalent exposures will remain a necessity for epidemiology. The purpose of this paper is to restore the balance between the emphasis on first exposure cohorts and the richness of epidemiologic information obtained when studying prevalent exposures. [ABSTRACT FROM AUTHOR]

Analyses of observational data aimed at supporting decision-making are ideally framed as a contrast between well-defined treatment strategies. These analyses compare individuals' outcomes from the start of the treatment strategies under consideration. Exceptions to this synchronizing of the start of follow-up and the treatment strategies may be justified on a case-by-case basis. [ABSTRACT FROM AUTHOR]

For the regression parameter β in the Cox model, there have been several estimates based on different types of approximated likelihood. For right-censored data, Ren and Zhou [Full likelihood inferences in the Cox model: an empirical approach. Ann Inst Statist Math. 2011;63:1005–1018] derive the full likelihood function for (β,F0), whereF0is the baseline distribution function in the Cox model. In this article, we extend their results to left-truncated and right-censored data with discrete covariates. Using the empirical likelihood parameterization, we obtain the full-profile likelihood function for β when covariates are discrete. Simulation results indicate that the maximum likelihood estimator outperforms Cox's partial likelihood estimator in finite samples. [ABSTRACT FROM AUTHOR]

Interval censoring refers to a situation in which, T i ∗ , the time to occurrence of an event of interest is only known to lie in an interval [ L i ∗ , R i ∗ ] . In some cases, the variable T i ∗ also suffers left-truncation. The nonparametric maximum likelihood estimator (NPMLE) of the survival function of T i ∗ can be obtained by using an EM algorithm of Turnbull (1976). One disadvantage of the NPMLE is that it is not uniquely defined in the innermost intervals. In this article, we propose a self-consistent estimator (SCE), which does not require interpolation. Furthermore, we show that the NPMLE is also an SCE. We establish the consistency of the SCE under certain conditions, which implies that the NPMLE is also a consistent estimator. A simulation study is conducted to compare the performance between the SCE and the NPMLE. [ABSTRACT FROM AUTHOR]

This paper considers two-sample nonparametric comparison of survival function when data are subject to left truncation and interval censoring. We propose a class of rank-based tests, which are generalization of weighted log-rank tests for right-censored data. Simulation studies indicate that the proposed tests are appropriate for practical use. [ABSTRACT FROM AUTHOR]

For a linear regression model subject to left-truncation and right-censoring where the truncation and censoring points are known constants (or always observed if random), Karlsson and Laitila (Stat Probab Lett 78:2567-2571, ) proposed a semiparametric estimator which deals with left-truncation by trimming and right-censoring by 'winsorizing'. The estimator was motivated by a zero moment condition where a transformed error term appears with trimmed and winsorized tails. This paper takes the semiparametric estimator further by deriving the asymptotic distribution that was not shown in Karlsson and Laitila (Stat Probab Lett 78:2567-2571, ) and discusses its implementation aspects in practice, albeit brief. [ABSTRACT FROM AUTHOR]

Purpose This study aims to explore the influence of gestational age at enrollment, and enrollment before or after prenatal screening, on the estimation of drug effects in pregnancy exposure registries. Methods We assessed the associations between first trimester antiepileptic drug (AED) exposure and risk of spontaneous abortion and major congenital malformations in the North American AED Registry (1996-2013). We performed logistic regression analyses, conditional or unconditional on gestational age at enrollment, to estimate relative risk (RR) for first trimester AED users compared with non-users. We also compared first trimester users of valproic acid and lamotrigine. Analyses were repeated in women who enrolled before prenatal screening. Results Enrollment occurred earlier among 7029 AED users than among 581 non-users; it was similar among AEDs. Comparing AED users with non-users, RR (95% confidence interval) of spontaneous abortion ( n = 359) decreased from 5.1 (2.3-14.1) to 2.0 (0.9-5.6) after conditioning on gestational week at enrollment and to 1.9 (0.8-5.4) upon further restriction to before-screening enrollees. RR of congenital malformations ( n = 216) changed from 3.1 (1.4-8.5) to 3.2 (1.4-9.0) after conditioning on gestational week at enrollment and to 2.0 (0.7-10.1) upon further restriction to before-screening enrollees. When comparing valproic acid users and lamotrigine users, the RR of congenital malformations was not substantially changed by conditioning or restricting. Conclusions Spontaneous abortion rates were sensitive to gestational age at enrollment. Estimates of congenital malformation risks for AED users relative to non-users were sensitive to before/after-screening enrollment. This difference was not apparent between active drugs, likely due to similar gestational age at enrollment. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Semi-competing risks data frequently arise in biomedical studies when time to a disease landmark event is subject to dependent censoring by death, the observation of which however is not precluded by the occurrence of the landmark event. In observational studies, the analysis of such data can be further complicated by left truncation. In this work, we study a varying coefficient subdistribution regression model for left-truncated semi-competing risks data. Our method appropriately accounts for the specifical truncation and censoring features of the data, and moreover has the flexibility to accommodate potentially varying covariate effects. The proposed method can be easily implemented and the resulting estimators are shown to have nice asymptotic properties. We also present inference, such as Kolmogorov–Smirnov type and Cramér–Von-Mises type hypothesis testing procedures for the covariate effects. Simulation studies and an application to the Denmark diabetes registry demonstrate good finite-sample performance and practical utility of the proposed method. [ABSTRACT FROM AUTHOR]

We analyze left-truncated and right-censored (LTRC) data using Aalen’s linear models. The integrated square error (ISE) is used to select an optimal bandwidth of the weighted least-squared estimator. We also consider a semiparametric approach for the case when the distribution of the left-truncated variable is parameterized. A simulation study is conducted to investigate the performance of the proposed estimators. The approaches are illustrated with the data of Stanford heart transplant. [ABSTRACT FROM AUTHOR]

Concentration curve is the inverse Lorenz curve. Together, they form the basis for most measures of distributional inequality. In this paper, we consider the empirical estimator of the concentration curve when the data are subjected to random left truncation and/or right censorship. Simultaneous strong Gaussian approximations for the associated Lorenz and normed concentration processes are established under appropriate assumptions. Functional laws of the iterated logarithm for the two processes are established as easy consequences. The construction provides a solid foundation for the study of functional statistics based on the two processes. [ABSTRACT FROM AUTHOR]

There has been considerable interest in studying the magnitude and type of inheritance of specific diseases. This is typically derived from family or twin studies, where the basic idea is to compare the correlation for different pairs that share different amount of genes. We here consider data from the Danish twin registry and discuss how to define heritability for cancer occurrence. The key point is that this should be done taking censoring as well as competing risks due to e.g. death into account. We describe the dependence between twins on the probability scale and show that various models can be used to achieve sensible estimates of the dependence within monozygotic and dizygotic twin pairs that may vary over time. These dependence measures can subsequently be decomposed into a genetic and environmental component using random effects models. We here present several novel models that in essence describe the association in terms of the concordance probability, i.e., the probability that both twins experience the event, in the competing risks setting. We also discuss how to deal with the left truncation present in the Nordic twin registries, due to sampling only of twin pairs where both twins are alive at the initiation of the registries. [ABSTRACT FROM AUTHOR]

Quantile regression methods have been used to estimate upper and lower quantile reference curves as the function of several covariates. In this article, it is demonstrated that the estimating equation of Zhou [A weighted quantile regression for randomly truncated data, Comput. Stat. Data Anal. 55 (2011), pp. 554–566.] can be extended to analyse left-truncated and right-censored data. We evaluate the finite sample performance of the proposed estimators through simulation studies. The proposed estimator βˆ(q) is applied to the Veteran's Administration lung cancer data reported by Prentice [Exponential survival with censoring and explanatory variables, Biometrika 60 (1973), pp. 279–288]. [ABSTRACT FROM AUTHOR]

Information on the distribution and bloom scale of the giant jellyfish Nemopilema nomurai is necessary to understand the impact on fisheries. In October 2009, we had an opportunity for visual counting of N. nomurai around Japan from a research/training vessel. To take into account possibly severe missed detection of N. nomurai in the close vicinity of the vessel, detection functions were modified by introducing an additional parameter δ expressing the proportion of detectable N. nomurai within a threshold perpendicular distance. Some covariate effects in the detection process were also investigated. The δ-modified hazard-rate detection function with δ variation parameter of jellyfish body size was chosen as the best-fit one by AIC model selection. The results suggested that a higher proportion (>30 % or more) of N. nomurai were undetected in the vicinity of vessel. The δ-modified model had an advantage of no loss of left-truncated data and provided better estimation of density with the smaller coefficient of variation than the conventional left truncation approach. It is applicable to other line transect surveys, e.g. aerial surveys. High densities of N. nomurai were found in the central part of the Sea of Japan and off Iwate Prefecture. [ABSTRACT FROM AUTHOR]

ABSTRACT In multistate survival analysis, the sojourn of a patient through various clinical states is shown to correspond to the diffusion of 1 C of electrical charge through an electrical network. The essential comparison has differentials of probability for the patient to correspond to differentials of charge, and it equates clinical states to electrical nodes. Indeed, if the death state of the patient corresponds to the sink node of the circuit, then the transient current that would be seen on an oscilloscope as the sink output is a plot of the probability density for the survival time of the patient. This electrical circuit analogy is further explored by considering the simplest possible survival model with two clinical states, alive and dead (sink), that incorporates censoring and truncation. The sink output seen on an oscilloscope is a plot of the Kaplan-Meier mass function. Thus, the Kaplan-Meier estimator finds motivation from the dynamics of current flow, as a fundamental physical law, rather than as a nonparametric maximum likelihood estimate (MLE). Generalization to competing risks settings with multiple death states (sinks) leads to cause-specific Kaplan-Meier submass functions as outputs at sink nodes. With covariates present, the electrical analogy provides for an intuitive understanding of partial likelihood and various baseline hazard estimates often used with the proportional hazards model. [ABSTRACT FROM AUTHOR]

Dementia is one of the world’s major public health challenges. The lifetime risk of dementia is the proportion of individuals who ever develop dementia during their lifetime. Despite its importance to epidemiologists and policy-makers, this measure does not seem to have been estimated in the Canadian population. Data from a birth cohort study of dementia are not available. Instead, we must rely on data from the Canadian Study of Health and Aging, a large cross-sectional study of dementia with follow-up for survival. These data present challenges because they include substantial loss to follow-up and are not representatively drawn from the target population because of structural sampling biases. A first bias is imparted by the cross-sectional sampling scheme, while a second bias is a result of stratified sampling. Estimation of the lifetime risk and related quantities in the presence of these biases has not been previously addressed in the literature. We develop and study nonparametric estimators of the lifetime risk, the remaining lifetime risk, and cumulative risk at specific ages, accounting for these complexities. In particular, we reveal the fact that estimation of the lifetime risk is invariant to stratification by current age at sampling. We present simulation results validating our methodology, and provide novel facts about the epidemiology of dementia in Canada using data from the Canadian Study of Health and Aging. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This paper considers the estimation of the regression coefficients in the Cox proportional hazards model with left-truncated and interval-censored data. Using the approaches of Pan [A multiple imputation approach to Cox regression with interval-censored data, Biometrics 56 (2000), pp. 199–203] and Heller [Proportional hazards regression with interval censored data using an inverse probability weight, Lifetime Data Anal. 17 (2011), pp. 373–385], we propose two estimates of the regression coefficients. The first estimate is based on a multiple imputation methodology. The second estimate uses an inverse probability weight to select event time pairs where the ordering is unambiguous. A simulation study is conducted to investigate the performance of the proposed estimators. The proposed methods are illustrated using the Centers for Disease Control and Prevention (CDC) acquired immunodeficiency syndrome (AIDS) Blood Transfusion Data. [ABSTRACT FROM PUBLISHER]

The maximum likelihood estimates (MLEs) of the parameters of a two-parameter lognormal distribution with left truncation and right censoring are developed through the Expectation Maximization (EM) algorithm. For comparative purpose, the MLEs are also obtained by the Newton–Raphson method. The asymptotic variance-covariance matrix of the MLEs is obtained by using the missing information principle, under the EM framework. Then, using asymptotic normality of the MLEs, asymptotic confidence intervals for the parameters are constructed. Asymptotic confidence intervals are also obtained using the estimated variance of the MLEs by the observed information matrix, and by using parametric bootstrap technique. Different confidence intervals are then compared in terms of coverage probabilities, through a Monte Carlo simulation study. A prediction problem concerning the future lifetime of a right censored unit is also considered. A numerical example is given to illustrate all the inferential methods developed here. [ABSTRACT FROM PUBLISHER]

The cross-ratio is an important local measure that characterizes the dependence between bivariate failure times. To estimate the cross-ratio in follow-up studies where delayed entry is present, estimation procedures need to account for left truncation. Ignoring left truncation yields biased estimates of the cross-ratio. We extend the method of Hu et al., Biometrika 98:341-354 () by modifying the risk sets and relevant indicators to handle left-truncated bivariate failure times, which yields the cross-ratio estimate with desirable asymptotic properties that can be shown by the same techniques used in Hu et al., Biometrika 98:341-354 (). Numerical studies are conducted. [ABSTRACT FROM AUTHOR]

Abstract: We consider the problem of fitting a heteroscedastic median regression model from left-truncated and interval-censored data. It is demonstrated that the adapted Efron’s self-consistency equation of McKeague, Subramanian, and Sun (2001) can be extended to analyze left-truncated and interval-censored data. The asymptotic property of the proposed estimator is established. We evaluate the finite sample performance of the proposed estimators through simulation studies. [Copyright &y& Elsevier]

The gamma distribution is used as a lifetime distribution widely in reliability analysis. Lifetime data are often left truncated, and right censored. The EM algorithm is developed here for the estimation of the scale and shape parameters of the gamma distribution based on left truncated and right censored data. The Newton-Raphson method is also used for the same purpose, and then these two methods of estimation are compared through an extensive Monte Carlo simulation study. The asymptotic variance-covariance matrix of the MLEs under the EM framework is obtained by using the missing information principle (Louis, 1982). Then, the asymptotic confidence intervals for the parameters are constructed. The confidence intervals based on the EM algorithm and the Newton-Raphson method are then compared empirically in terms of coverage probabilities. Finally, all the methods of inference discussed here are illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

In longitudinal studies, the additive hazard model is often used to analyze covariate effects on the duration time, defined as the elapsed time between the first and the second event. In this article, we consider the situation when the first event suffers partly interval censoring and the second event suffers left truncation and right-censoring. We proposed a two-step estimation procedure for estimating the regression coefficients of the additive hazards model. A simulation study is conducted to investigate the performance of the proposed estimator. The proposed method is applied to the Centers for Disease Control acquired immune deficiency syndrome blood transfusion data. [ABSTRACT FROM PUBLISHER]

Studies of chronic diseases routinely sample individuals subject to conditions on an event time of interest. In epidemiology, for example, prevalent cohort studies aiming to evaluate risk factors for survival following onset of dementia require subjects to have survived to the point of screening. In clinical trials designed to assess the effect of experimental cancer treatments on survival, patients are required to survive from the time of cancer diagnosis to recruitment. Such conditions yield samples featuring left-truncated event time distributions. Incomplete covariate data often arise in such settings, but standard methods do not deal with the fact that individuals' covariate distributions are also affected by left truncation. We describe an expectation-maximization algorithm for dealing with incomplete covariate data in such settings, which uses the covariate distribution conditional on the selection criterion. We describe an extension to deal with subgroup analyses in clinical trials for the case in which the stratification variable is incompletely observed. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Numerous methods for joint analysis of longitudinal measures of a continuous outcome y and a time to event outcome T have recently been developed either to focus on the longitudinal data y while correcting for nonignorable dropout, to predict the survival outcome T using the longitudinal data y, or to examine the relationship between y and T. The motivating problem for our work is in joint modeling of the serial measurements of pulmonary function (FEV1% predicted) and survival in cystic fibrosis (CF) patients using registry data. Within the CF registry data, an additional complexity is that not all patients have been followed from birth; therefore, some patients have delayed entry into the study while others may have been missed completely, giving rise to a left truncated distribution. This paper shows in joint modeling situations where y and T are not independent, that it is necessary to account for this left truncation to obtain valid parameter estimates related to both survival and the longitudinal marker. We assume a linear random effects model for FEV1% predicted, where the random intercept and slope of FEV1% predicted, along with a specified transformation of the age at death follow a trivariate normal distribution. We develop an expectation-maximization algorithm for maximum likelihood estimation of parameters, which takes left truncation and right censoring of survival times into account. The methods are illustrated using simulation studies and using data from CF patients in a registry followed at Rainbow Babies and Children's Hospital, Cleveland, OH. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The Cox proportional hazards model is widely used in time-to-event analysis. Two time scales are used in practice: time-on-study and chronological age. The former is the most frequently used time scale in clinical studies and longitudinal observation studies. However, there is no general consensus about which time scale is the best. It has been asserted that if the cumulative baseline hazard is exponential or if the age-at-entry is independent of the covariate, then the two models are equivalent. We show that neither of these conditions leads to equivalency. Variability in the age-at-entry of individuals in the study causes the models to differ significantly. This is shown both analytically and through a simulation study. Additionally, we show that the time-on-study model is more robust to changes in age-at-entry than the chronological age model. [ABSTRACT FROM AUTHOR]

Traditional actuarial techniques for mortality analysis are being supplanted by statistical models. Chief amongst these are survival models, which model mortality continuously at the level of the individual. An assumption of a mathematical form for the hazard function or, equivalently, the assumption of a continuous distribution for an individual's lifetime, leads automatically to smooth fitted mortality rates. This note gives an overview of the survival models commonly found in statistical packages and compares their suitability for actuarial work with the mortality ‘laws’ proposed by actuaries over the past two centuries. We find that the actuarial laws provide substantially better fits at post-retirement ages. We also give a common structure of parameterisation which gives consistent behaviour and interpretation of risk factors across all 16 survival models listed here. Finally, we consider the benefits of working directly with the log-likelihood function, including making allowance for the left truncation which is common for the data with which actuaries work. [ABSTRACT FROM AUTHOR]

ABSTRACT Purpose In studying the safety of vaccine for influenza A (H1N1) given during pregnancy, spontaneous abortion (SAB) is one of the important points to consider. Because women may receive the vaccine any time during their pregnancy, evaluation of the effect of the vaccine on SAB should only take place after vaccination and in the risk window for SAB, that is, the first 20 weeks of gestation. In addition, when such studies are conducted through pregnancy registries where recruitment occurs after pregnancy recognition, the accrued subjects are left truncated in the sense that they are not followed from the start of pregnancy. Methods As previously reported, left truncation needs to be properly handled using survival analysis methods to avoid bias. In the context of time-dependent vaccine exposure, a time-dependent covariate Cox model can be used to simultaneously take into account the left truncation and the vaccine exposure timing. Results In this communication, we illustrate the approach using the Vaccine and Medication in Pregnancy Surveillance System data. We explain in details how the model is fitted using different software. Conclusions We recommend survival analysis methods together with collection of necessary data to study the effects of vaccine on SAB. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: We study the problem of fitting a heteroscedastic median regression model from left-truncated and right-censored data. It is demonstrated that the adapted Efron''s self-consistency equation of can be extended to analyze left-truncated and right-censored data. We evaluate the finite sample performance of the proposed estimators through simulation studies. [Copyright &y& Elsevier]