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We compare the performance of nonparametric estimators for the mean number of recurrent events and provide a systematic overview for different recurrent event settings. The mean number of recurrent events is an easily interpreted marginal feature often used for treatment comparisons in clinical trials. Incomplete observations, dependencies between successive events, terminating events acting as competing risk, or gaps between at risk periods complicate the estimation. We use survival multistate models to represent different complex recurrent event situations, profiting from recent advances in nonparametric estimation for non-Markov multistate models, and explain several estimators by using multistate intensity processes, including the common Nelson-Aalen-type estimators with and without competing mortality. In addition to building on estimation of state occupation probabilities in non-Markov models, we consider a simple extension of the Nelson-Aalen estimator by allowing for dependence on the number of prior recurrent events. We pay particular attention to the assumptions required for the censoring mechanism, one issue being that some settings require the censoring process to be entirely unrelated while others allow for state-dependent or event-driven censoring. We conducted extensive simulation studies to compare the estimators in various complex situations with recurrent events. Our practical example deals with recurrent chronic obstructive pulmonary disease exacerbations in a clinical study, which will also be used to illustrate two-sample-inference using resampling., (© 2023 The Authors. Pharmaceutical Statistics published by John Wiley & Sons Ltd.)

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., (© 2023 The Authors. Pharmacoepidemiology and Drug Safety published by John Wiley & Sons Ltd.)

A clinical hold order by the Food and Drug Administration (FDA) to the sponsor of a clinical trial is a measure to delay a proposed or to suspend an ongoing clinical investigation. The phase III clinical trial START serves as motivating data example to explore implications and potential statistical approaches for a trial continuing after a clinical hold is lifted. In spite of a modified intention-to-treat (ITT) analysis introduced to account for the clinical hold by excluding patients potentially affected most by the clinical hold, results of the trial did not show a significant improvement of overall survival duration, and the question remains whether the negative result was an effect of the clinical hold. In this paper, we propose a multistate model incorporating the clinical hold as well as disease progression as intermediate events to investigate the impact of the clinical hold on the treatment effect. Moreover, we consider a simple counterfactual censoring approach as alternative strategy to the modified ITT analysis to deal with a clinical hold. Using a realistic simulation study informed by the START data and with a design based on our multistate model, we show that the modified ITT analysis used in the START trial was reasonable. However, the censoring approach will be shown to have some benefits in terms of power and flexibility., (© 2019 The Authors. Pharmaceutical Statistics published by John Wiley & Sons Ltd.)

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., (© 2019 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

We consider nonparametric and semiparametric resampling of multistate event histories by simulating multistate trajectories from an empirical multivariate hazard measure. One advantage of our approach is that it does not necessarily require individual patient data, but may be based on published information. This is also attractive for both study planning and simulating realistic real-world event history data in general. The concept extends to left-truncation and right-censoring mechanisms, nondegenerate initial distributions, and nonproportional as well as non-Markov settings. A special focus is on its connection to simulating survival data with time-dependent covariates. For the case of qualitative time-dependent exposures, we demonstrate that our proposal gives a more natural interpretation of how such data evolve over the course of time than many of the competing approaches. The multistate perspective avoids any latent failure time structure and sampling spaces impossible in real life, whereas its parsimony follows the principle of Occam's razor. We also suggest empirical simulation as a novel bootstrap procedure to assess estimation uncertainty in the absence of individual patient data. This is not possible for established procedures such as Efron's bootstrap. A simulation study investigating the effect of liver functionality on survival in patients with liver cirrhosis serves as a proof of concept. Example code is provided., (© 2019 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

The analysis of adverse events (AEs) is a key component in the assessment of a drug's safety profile. Inappropriate analysis methods may result in misleading conclusions about a therapy's safety and consequently its benefit-risk ratio. The statistical analysis of AEs is complicated by the fact that the follow-up times can vary between the patients included in a clinical trial. This paper takes as its focus the analysis of AE data in the presence of varying follow-up times within the benefit assessment of therapeutic interventions. Instead of approaching this issue directly and solely from an analysis point of view, we first discuss what should be estimated in the context of safety data, leading to the concept of estimands. Although the current discussion on estimands is mainly related to efficacy evaluation, the concept is applicable to safety endpoints as well. Within the framework of estimands, we present statistical methods for analysing AEs with the focus being on the time to the occurrence of the first AE of a specific type. We give recommendations which estimators should be used for the estimands described. Furthermore, we state practical implications of the analysis of AEs in clinical trials and give an overview of examples across different indications. We also provide a review of current practices of health technology assessment (HTA) agencies with respect to the evaluation of safety data. Finally, we describe problems with meta-analyses of AE data and sketch possible solutions., (© 2018 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.)