Landmarking for Left-Truncated Competing Risk Data

Landmarking is an alternative to complex multistate models when the aim is to calculate dynamic predictions. We develop the concept of landmarking for the case of left truncation and competing risks from the application background of drug safety assessment in pregnancy. The method is illustrated with a cohort study of the German Embryotox Pharmacovigilance Institute in Berlin to assess if the risk or the cumulative incidence of adverse pregnancy outcomes, like spontaneous abortions (SABs), is increased in fluoroquinolone-exposed women. Furthermore, we conduct an extensive simulation study to compare the dynamic predictions and coefficient estimates obtained by landmarking to those from nonparametric multistate models and classical time-dependent covariate Cox regression. The results from the simulation study indicate that attenuation of the effects is present in the landmark estimates, also in the complex setting considered here, but the estimates are still close to those from the multistate models. Regarding the Berlin fluoroquinolone data, the fluoroquinolone exposure of a pregnant woman in the first trimester seems to increase her cumulative incidence of elective termination of pregnancy over women never exposed before, but there is no evidence of a significantly increased risk or cumulative incidence in exposed women for SABs. This supports previous results on the same data, which were driven from an analysis without landmarking methods.

Pitfalls in time-to-event analysis of registry data: a tutorial based on simulated and real cases

Survival analysis (also referred to as time-to-event analysis) is the study of the time elapsed from a starting date to some event of interest. In practice, these analyses can be challenging and, if methodological errors are to be avoided, require the application of appropriate techniques. By using simulations and real-life data based on the French national registry of patients with primary immunodeficiencies (CEREDIH), we sought to highlight the basic elements that need to be handled correctly when performing the initial steps in a survival analysis. We focused on non-parametric methods to deal with right censoring, left truncation, competing risks, and recurrent events. Our simulations show that ignoring these aspects induces a bias in the results; we then explain how to analyze the data correctly in these situations using non-parametric methods. Rare disease registries are extremely valuable in medical research. We discuss the application of appropriate methods for the analysis of time-to-event from the CEREDIH registry. The objective of this tutorial article is to provide clinicians and healthcare professionals with better knowledge of the issues facing them when analyzing time-to-event data.

On the role of benchmarking data sets and simulations in method comparison studies

Method comparisons are essential to provide recommendations and guidance for applied researchers, who often have to choose from a plethora of available approaches. While many comparisons exist in the literature, these are often not neutral but favor a novel method. Apart from the choice of design and a proper reporting of the findings, there are different approaches concerning the underlying data for such method comparison studies. Most manuscripts on statistical methodology rely on simulation studies and provide a single real-world data set as an example to motivate and illustrate the methodology investigated. In the context of supervised learning, in contrast, methods are often evaluated using so-called benchmarking data sets, that is, real-world data that serve as gold standard in the community. Simulation studies, on the other hand, are much less common in this context. The aim of this paper is to investigate differences and similarities between these approaches, to discuss their advantages and disadvantages, and ultimately to develop new approaches to the evaluation of methods picking the best of both worlds. To this aim, we borrow ideas from different contexts such as mixed methods research and Clinical Scenario Evaluation.

How to account for early overly small risk sets in the analysis of pregnancy outcome data?-Comparison of different methods for stabilizing the Aalen-Johansen estimator

PURPOSE

In analyzing pregnancy data concerning drug exposure in the first trimester, the risk of spontaneous abortions is of primary interest. For estimating the cumulative incidence function, the Aalen-Johansen estimator is typically used, and competing risks such as induced abortion and livebirth are considered. However, the delayed study entry can lead to overly small risk sets for the first events. This results in large jumps in the estimated cumulative incidence function of spontaneous abortions or induced abortions using the Aalen-Johansen estimator, and consequently in an overestimation of the probability.

METHODS

Several approaches account for early overly small risk sets. The first approach is conditioning on the event time being greater than the event time causing the large jump. Second, the events can be ignored by censoring them. Third, the events can be postponed until a large enough number is at risk. These three approaches are compared.

RESULTS

All approaches are applied using data of 54 lacosamide-exposed pregnancies. The Aalen-Johansen estimate of the probability of spontaneous abortion is 22.64%, which is relatively large for only three spontaneous abortions in the dataset. The conditional approach and the ignore approach have an estimated probability of 7.17%. In contrast, the estimate of the postpone approach is 16.45%. In this small sample, bootstrapped confidence intervals seem more accurate.

CONCLUSIONS

In the analyses of pregnancy data with rare events, the postpone approach is favorable as no events are excluded. However, the approach that ignores early events has the narrowest confidence interval.

Modeling unmeasured baseline information in observational time-to-event data subject to delayed study entry

Unmeasured baseline information in left-truncated data situations frequently occurs in observational time-to-event analyses. For instance, a typical timescale in trials of antidiabetic treatment is "time since treatment initiation", but individuals may have initiated treatment before the start of longitudinal data collection. When the focus is on baseline effects, one widespread approach is to fit a Cox proportional hazards model incorporating the measurements at delayed study entry. This has been criticized because of the potential time dependency of covariates. We tackle this problem by using a Bayesian joint model that combines a mixed-effects model for the longitudinal trajectory with a proportional hazards model for the event of interest incorporating the baseline covariate, possibly unmeasured in the presence of left truncation. The novelty is that our procedure is not used to account for non-continuously monitored longitudinal covariates in right-censored time-to-event studies, but to utilize these trajectories to make inferences about missing baseline measurements in left-truncated data. Simulating times-to-event depending on baseline covariates we also compared our proposal to a simpler two-stage approach which performed favorably. Our approach is illustrated by investigating the impact of baseline blood glucose levels on antidiabetic treatment failure using data from a German diabetes register.

Integrating relative survival in multi-state models—a non-parametric approach

Multi-state models provide an extension of the usual survival/event-history analysis setting. In the medical domain, multi-state models give the possibility of further investigating intermediate events such as relapse and remission. In this work, a further extension is proposed using relative survival, where mortality due to population causes (i.e. non-disease-related mortality) is evaluated. The objective is to split all mortality in disease and non-disease-related mortality, with and without intermediate events, in datasets where cause of death is not recorded or is uncertain. To this end, population mortality tables are integrated into the estimation process, while using the basic relative survival idea that the overall mortality hazard can be written as a sum of a population and an excess part. Hence, we propose an upgraded non-parametric approach to estimation, where population mortality is taken into account. Precise definitions and suitable estimators are given for both the transition hazards and probabilities. Variance estimating techniques and confidence intervals are introduced and the behaviour of the new method is investigated through simulations. The newly developed methodology is illustrated by the analysis of a cohort of patients followed after an allogeneic hematopoietic stem cell transplantation. The work has been implemented in the R package mstate.

Estimating cumulative incidence functions in competing risks data with dependent left-truncation

Both delayed study entry (left-truncation) and competing risks are common phenomena in observational time-to-event studies. For example, in studies conducted by Teratology Information Services (TIS) on adverse drug reactions during pregnancy, the natural time scale is gestational age, but women enter the study after time origin and upon contact with the service. Competing risks are present, because an elective termination may be precluded by a spontaneous abortion. If left-truncation is entirely random, the Aalen-Johansen estimator is the canonical estimator of the cumulative incidence functions of the competing events. If the assumption of random left-truncation is in doubt, we propose a new semiparametric estimator of the cumulative incidence function. The dependence between entry time and time-to-event is modeled using a cause-specific Cox proportional hazards model and the marginal (unconditional) estimates are derived via inverse probability weighting arguments. We apply the new estimator to data about coumarin usage during pregnancy. Here, the concern is that the cause-specific hazard of experiencing an induced abortion may depend on the time when seeking advice by a TIS, which also is the time of left-truncation or study entry. While the aims of counseling by a TIS are to reduce the rate of elective terminations based on irrational overestimation of drug risks and to lead to better and safer medical treatment of maternal disease, it is conceivable that women considering an induced abortion are more likely to seek counseling. The new estimator is also evaluated in extensive simulation studies and found preferable compared to the Aalen-Johansen estimator in non-misspecified scenarios and to at least provide for a sensitivity analysis otherwise.

Stabilizing cumulative incidence estimation of pregnancy outcome with delayed entries

A pregnancy may end up with (at least) three possible events: live birth, spontaneous abortion, or elective termination, yielding a competing risks issue when studying an association between a risk factor and a pregnancy outcome. Cumulative incidences (probabilities to end up with the different outcomes depending on gestational age) can be estimated via the Aalen-Johansen estimate. Another issue is that women are usually not entering such an observational study from the first day of pregnancy, resulting in delayed entries. As in traditional survival analysis, this can be solved by considering "at risk" at a given gestational age only for those women who entered the study before that age. However, the number of women at risk at an early gestational age might be extremely low, such that the estimates of cumulative incidence may increase exaggeratedly at that age because of a single event. One solution to reduce the problem has been recently proposed in the literature, which is to ignore simply those early events, creating a small mean bias but enhancing stability of estimates. In the present paper, we propose an alternative computationally simple approach to tackle this problem that consists to postpone to later gestational ages (rather than to ignore) those early events. The two approaches are compared with respect to bias, stability, and sensitivity on the smoothing parameter via simulations reproducing realistic pregnancy scenarios, and are illustrated with data from a study on the effects of statins on pregnancy outcomes. We also outline that all three approaches are asymptotically equivalent.