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Background: The SAVVY project aims to improve the analyses of adverse events (AEs) in clinical trials through the use of survival techniques appropriately dealing with varying follow-up times and competing events (CEs). This paper summarizes key features and conclusions from the various SAVVY papers. Methods: Summarizing several papers reporting theoretical investigations using simulations and an empirical study including randomized clinical trials from several sponsor organizations, biases from ignoring varying follow-up times or CEs are investigated. The bias of commonly used estimators of the absolute (incidence proportion and one minus Kaplan-Meier) and relative (risk and hazard ratio) AE risk is quantified. Furthermore, we provide a cursory assessment of how pertinent guidelines for the analysis of safety data deal with the features of varying follow-up time and CEs. Results: SAVVY finds that for both, avoiding bias and categorization of evidence with respect to treatment effect on AE risk into categories, the choice of the estimator is key and more important than features of the underlying data such as percentage of censoring, CEs, amount of follow-up, or value of the gold-standard. Conclusions: The choice of the estimator of the cumulative AE probability and the definition of CEs are crucial. Whenever varying follow-up times and/or CEs are present in the assessment of AEs, SAVVY recommends using the Aalen-Johansen estimator (AJE) with an appropriate definition of CEs to quantify AE risk. There is an urgent need to improve pertinent clinical trial reporting guidelines for reporting AEs so that incidence proportions or one minus Kaplan-Meier estimators are finally replaced by the AJE with appropriate definition of CEs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Randomized clinical trials with time‐to‐event endpoints are frequently stopped after a prespecified number of events has been observed. This practice leads to dependent data and nonrandom censoring, which can in general not be solved by conditioning on the underlying baseline information. In case of staggered study entry, matters are complicated substantially. The present paper demonstrates that the study design at hand entails general independent censoring in the counting process sense, provided that the analysis is based on study time information only. To illustrate that the filtrations must not use abundant information, we simulated data of event‐driven trials and evaluated them by means of Cox regression models with covariates for the calendar times. The Breslow curves of the cumulative baseline hazard showed considerable deviations, which implies that the analysis is disturbed by conditioning on the calendar time variables. A second simulation study further revealed that Efron's classical bootstrap, unlike the (martingale‐based) wild bootstrap, may lead to biased results in the given setting, as the assumption of random censoring is violated. This is exemplified by an analysis of data on immunotherapy in patients with advanced, previously treated nonsmall cell lung cancer. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Objective: To investigate whether osteoarthritis (OA)‐specific assessment values (i.e., Western Ontario and McMaster Universities Osteoarthritis Index [WOMAC]) and generic pain and function (visual analog scale, Hanover Functionality Status Questionnaire) measured before and 12 months after arthroplasty are associated with the risk of long‐term mortality in a cohort of patients with advanced OA of the hip or knee. Methods: The Ulm Osteoarthritis Study was a prospective cohort study of OA patients with unilateral total hip or knee replacement between January 1995 and December 1996. Correlation coefficients were calculated to describe the agreement between the different assessments. Mortality was assessed during the follow‐up period (last update July 2019). Cox proportional regression models were used to estimate hazard ratios (HRs) for mortality after adjusting for covariates. Results: Arthroplasty was accompanied by a clear reduction in pain and improved function throughout all assessments in the 706 included patients. The results of the adjusted Cox models showed no relationship between baseline and follow‐up joint‐specific WOMAC assessments and long‐term mortality. However, an independent increased risk of mortality was found with generic function assessments. In the final adjusted model, the HR for the 12‐month follow‐up value was 1.79 (95% confidence interval 1.24–2.60) in the group with clinically relevant impairment versus the reference group. Conclusion: Poor function based on the generic assessment was associated with increased long‐term mortality, suggesting that functional impairments in daily life activities may be more important for long‐term survival than OA‐specific impairments in this patient group. [ABSTRACT FROM AUTHOR]

Recently, treatment interruptions such as a clinical hold in randomized clinical trials have been investigated by using a multistate model approach. The phase III clinical trial START (Stimulating Targeted Antigenic Response To non-small-cell cancer) with primary endpoint overall survival was temporarily placed on hold for enrollment and treatment by the US Food and Drug Administration (FDA). Multistate models provide a flexible framework to account for treatment interruptions induced by a time-dependent external covariate. Extending previous work, we propose a censoring and a filtering approach both aimed at estimating the initial treatment effect on overall survival in the hypothetical situation of no clinical hold. A special focus is on creating a link to causal inference. We show that calculating the matrix of transition probabilities in the multistate model after application of censoring (or filtering) yields the desired causal interpretation. Assumptions in support of the identification of a causal effect by censoring (or filtering) are discussed. Thus, we provide the basis to apply causal censoring (or filtering) in more general settings such as the COVID-19 pandemic. A simulation study demonstrates that both causal censoring and filtering perform favorably compared to a naïve method ignoring the external impact. [ABSTRACT FROM AUTHOR]

Background: The current standard endpoint to assess disability accumulation in multiple sclerosis (MS) clinical trials is the time to the first confirmed disability progression, which excludes subsequent progression events. Including recurrent progression events may permit a more comprehensive assessment of treatment effects on disability progression. Objective: To propose a definition of recurrent disability progression events and to compare time-to-first and recurrent event analysis. Methods: Recurrent disability progression events were defined by expanding the recommended first event definition. Marginal recurrent event methods (negative binomial model, Lin–Wei–Yang–Ying model) were compared with Cox regression in data from three randomized controlled trials in relapsing multiple sclerosis (RMS) and primary progressive multiple sclerosis (PPMS), and in simulated randomized controlled trial data. Results: The recurrent event analyses included a substantially larger number of progression events compared with the time-to-first-event analyses (+7.5% and +9.9% in the RMS trials and +22.7% in the PPMS trial). The increase in the number of events resulted in more precise treatment effect estimates and a corresponding gain in statistical power. Conclusion: Our results support the use of recurrent event data analysis, especially in progressive MS trials, to improve estimates of treatment effects, increase statistical power, and better capture the clinically meaningful long-term disability progression experience. [ABSTRACT FROM AUTHOR]

As a reaction to the pandemic of the severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2), a multitude of clinical trials for the treatment of SARS‐CoV‐2 or the resulting corona disease 2019 (COVID‐19) are globally at various stages from planning to completion. Although some attempts were made to standardize study designs, this was hindered by the ferocity of the pandemic and the need to set up clinical trials quickly. We take the view that a successful treatment of COVID‐19 patients (i) increases the probability of a recovery or improvement within a certain time interval, say 28 days; (ii) aims to expedite favorable events within this time frame; and (iii) does not increase mortality over this time period. On this background, we discuss the choice of endpoint and its analysis. Furthermore, we consider consequences of this choice for other design aspects including sample size and power and provide some guidance on the application of adaptive designs in this particular context. [ABSTRACT FROM AUTHOR]

Objective: The aim was to study the evolution of disability in spinocerebellar ataxias (SCAs) type 1, 2, 3, and 6 (SCA1, 2, 3, 6). Methods: We analyzed data of two longitudinal cohorts (RISCA, EUROSCA) which recruited ataxic and non‐ataxic SCA1, SCA2, SCA3, and SCA6 mutation carriers. To study disability, we used a five‐stage system for ataxia defined by walking ability (stages 0–3) and death (stage 4). Transitions were analyzed using a multi‐state model with proportional transition hazards. Based on the hazard estimates, transition probabilities and the expected lengths of stay in each stage were calculated. We further studied the effect of sex and CAG repeat length on progression. Results: Data of 3138 visits in 677 participants were analyzed. Median SARA scores for SCA1, SCA2, SCA3, and SCA6 ranged from 1.5 (interquartile range [IQR] = 0.0–3.5) to 3.5 (IQR = 1.4–6.1) in stage 0, 11.5 (IQR = 9.6–14.0) to 13.8 (IQR = 11.0–16.0) in stage 1, 19.0 (IQR = 17.0–21.0) to 23.8 (IQR = 19.5–27.0) in stage 2, and 28.5 (IQR = 26.0–32.5) to 34.0 (IQR = 32.6–37.1) in stage 3. Modeling allowed to calculate the subtype‐specific probability to be in a certain stage at a given age and duration of each stage. CAG repeat length was associated with faster progression in SCA1 (HR, 95% CI: 1.1, 1.1–1.2), SCA2 (1.2, 1.1–1.3), and SCA3 (1.1, 1.0–1.2). In SCA6, female sex was associated with faster progression (1.7, 1.1–2.6). Interpretation: Our data are important for counselling of patients, assessment of the relevance of outcome markers, and design of clinical trials. [ABSTRACT FROM AUTHOR]

Objectives: To three-dimensionally evaluate deviations of full-arch intraoral (IO) scans from reference desktop scans in terms of translations and rotations of individual teeth and different types of (mal)occlusion. Materials and methods: Three resin model pairs reflecting different tooth (mal)positions were mounted in the phantom head of a dental simulation unit and scanned by three dentists and three non-graduate investigators using a confocal laser IO scanner (Trios 3®). The tooth-crown surfaces of the IO scans and reference scans were superimposed by means of best-fit alignment. A novel method comprising the measurement of individual tooth positions was used to determine the deviations of each tooth in the six degrees of freedom, i.e., in terms of 3D translation and rotation. Deviations between IO and reference scans, among tooth-(mal)position models, and between dentists and non-graduate investigators were analyzed using linear mixed-effects models. Results: The overall translational deviations of individual teeth on the IO scans were 76, 32, and 58 µm in the lingual, mesial, and intrusive directions, respectively, resulting in a total displacement of 114 µm. Corresponding rotational deviations were 0.58° buccal tipping, 0.04° mesial tipping, and 0.14° distorotation leading to a combined rotation of 0.78°. These deviations were the smallest for the dental arches with anterior crowding, followed by those with spacing and those with good alignment (p < 0.05). Results were independent of the operator's level of education. Conclusions: Compared to reference desktop scans, individual teeth on full-arch IO scans showed high trueness with total translational and rotational deviations < 115 µm and < 0.80°, respectively. Clinical relevance: Available confocal laser IO scanners appear sufficiently accurate for diagnostic and therapeutic orthodontic applications. Results indicate that full-arch IO scanning can be delegated to non-graduate dental staff members. [ABSTRACT FROM AUTHOR]

Safety analyses of adverse events (AEs) are important in assessing benefit–risk of therapies but are often rather simplistic compared to efficacy analyses. AE probabilities are typically estimated by incidence proportions, sometimes incidence densities or Kaplan–Meier estimation are proposed. These analyses either do not account for censoring, rely on a too restrictive parametric model, or ignore competing events. With the non‐parametric Aalen‐Johansen estimator as the "gold standard", that is, reference estimator, potential sources of bias are investigated in an example from oncology and in simulations, for both one‐sample and two‐sample scenarios. The Aalen‐Johansen estimator serves as a reference, because it is the proper non‐parametric generalization of the Kaplan–Meier estimator to multiple outcomes. Because of potential large variances at the end of follow‐up, comparisons also consider further quantiles of the observed times. To date, consequences for safety comparisons have hardly been investigated, the impact of using different estimators for group comparisons being unclear. For example, the ratio of two both underestimating or overestimating estimators may not be comparable to the ratio of the reference, and our investigation also considers the ratio of AE probabilities. We find that ignoring competing events is more of a problem than falsely assuming constant hazards by the use of the incidence density and that the choice of the AE probability estimator is crucial for group comparisons. [ABSTRACT FROM AUTHOR]

Background: Passive mandibular advancement with functional appliances is commonly used to treat juvenile patients with mandibular retrognathism. Objective: The aim of this study was to investigate whether active repetitive training of the mandible into an anterior position would result in a shift of the habitual mandibular position (HMP). Methods: Twenty adult healthy subjects were randomly assigned to one of two groups: a training group receiving six supervised functional training sessions of 10 min each and a control group without training. Bonded lateral biteplates disengaged occlusion among both groups throughout the 15‐day experiment. Customised registration‐training appliances consisted of a maxillary component with an anterior plane and a mandibular component with an attached metal sphere. Training sessions consisted of repeated mouth‐opening/closing cycles (frequency: 30/min) to hit an anteriorly positioned hemispherical target notch with this metal sphere. The HMP was registered at defined times during the experiment. Results: The HMP in the training group showed a statistically significant anterior shift of 1.6 mm (interquartile range [IQR]: 1.2 mm), compared with a significant posterior shift of −0.8 mm (IQR: 2.8 mm) in the control group (p <.05). Although the anterior shift among the training group showed a partial relapse 4 days after the first training block, it then advanced slightly in the 4‐day interval after the second training block, which might indicate neuroplasticity of the masticatory motor system. Conclusions: Motor learning by repetitive training of the mandible into an anterior position might help to improve the results of functional appliance therapy among patients with mandibular retrognathism. [ABSTRACT FROM AUTHOR]

Background: The SAVVY project aims to improve the analyses of adverse events (AEs), whether prespecified or emerging, in clinical trials through the use of survival techniques appropriately dealing with varying follow-up times and competing events (CEs). Although statistical methodologies have advanced, in AE analyses, often the incidence proportion, the incidence density, or a non-parametric Kaplan-Meier estimator are used, which ignore either censoring or CEs. In an empirical study including randomized clinical trials from several sponsor organizations, these potential sources of bias are investigated. The main purpose is to compare the estimators that are typically used to quantify AE risk within trial arms to the non-parametric Aalen-Johansen estimator as the gold-standard for estimating cumulative AE probabilities. A follow-up paper will consider consequences when comparing safety between treatment groups.Methods: Estimators are compared with descriptive statistics, graphical displays, and a more formal assessment using a random effects meta-analysis. The influence of different factors on the size of deviations from the gold-standard is investigated in a meta-regression. Comparisons are conducted at the maximum follow-up time and at earlier evaluation times. CEs definition does not only include death before AE but also end of follow-up for AEs due to events related to the disease course or safety of the treatment.Results: Ten sponsor organizations provided 17 clinical trials including 186 types of investigated AEs. The one minus Kaplan-Meier estimator was on average about 1.2-fold larger than the Aalen-Johansen estimator and the probability transform of the incidence density ignoring CEs was even 2-fold larger. The average bias using the incidence proportion was less than 5%. Assuming constant hazards using incidence densities was hardly an issue provided that CEs were accounted for. The meta-regression showed that the bias depended mainly on the amount of censoring and on the amount of CEs.Conclusions: The choice of the estimator of the cumulative AE probability and the definition of CEs are crucial. We recommend using the Aalen-Johansen estimator with an appropriate definition of CEs whenever the risk for AEs is to be quantified and to change the guidelines accordingly. [ABSTRACT FROM AUTHOR]

The assessment of safety is an important aspect of the evaluation of new therapies in clinical trials, with analyses of adverse events being an essential part of this. Standard methods for the analysis of adverse events such as the incidence proportion, that is the number of patients with a specific adverse event out of all patients in the treatment groups, do not account for both varying follow‐up times and competing risks. Alternative approaches such as the Aalen–Johansen estimator of the cumulative incidence function have been suggested. Theoretical arguments and numerical evaluations support the application of these more advanced methodology, but as yet there is to our knowledge only insufficient empirical evidence whether these methods would lead to different conclusions in safety evaluations. The Survival analysis for AdVerse events with VarYing follow‐up times (SAVVY) project strives to close this gap in evidence by conducting a meta‐analytical study to assess the impact of the methodology on the conclusion of the safety assessment empirically. Here we present the rationale and statistical concept of the empirical study conducted as part of the SAVVY project. The statistical methods are presented in unified notation, and examples of their implementation in R and SAS are provided. [ABSTRACT FROM AUTHOR]

A popular modeling approach for competing risks analysis in longitudinal studies is the proportional subdistribution hazards model by Fine and Gray (1999. A proportional hazards model for the subdistribution of a competing risk. Journal of the American Statistical Association94, 496-509). This model is widely used for the analysis of continuous event times in clinical and epidemiological studies. However, it does not apply when event times are measured on a discrete time scale, which is a likely scenario when events occur between pairs of consecutive points in time (e.g., between two follow-up visits of an epidemiological study) and when the exact lengths of the continuous time spans are not known. To adapt the Fine and Gray approach to this situation, we propose a technique for modeling subdistribution hazards in discrete time. Our method, which results in consistent and asymptotically normal estimators of the model parameters, is based on a weighted ML estimation scheme for binary regression. We illustrate the modeling approach by an analysis of nosocomial pneumonia in patients treated in hospitals. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

For large cohort studies with rare outcomes, the nested case-control design only requires data collection of small subsets of the individuals at risk. These are typically randomly sampled at the observed event times and a weighted, stratified analysis takes over the role of the full cohort analysis. Motivated by observational studies on the impact of hospital-acquired infection on hospital stay outcome, we are interested in situations, where not necessarily the outcome is rare, but time-dependent exposure such as the occurrence of an adverse event or disease progression is. Using the counting process formulation of general nested case-control designs, we propose three sampling schemes where not all commonly observed outcomes need to be included in the analysis. Rather, inclusion probabilities may be time-dependent and may even depend on the past sampling and exposure history. A bootstrap analysis of a full cohort data set from hospital epidemiology allows us to investigate the practical utility of the proposed sampling schemes in comparison to a full cohort analysis and a too simple application of the nested case-control design, if the outcome is not rare. [ABSTRACT FROM AUTHOR]

In this paper, we derive the joint distribution of progression-free and overall survival as a function of transition probabilities in a multistate model. No assumptions on copulae or latent event times are needed and the model is allowed to be non-Markov. From the joint distribution, statistics of interest can then be computed. As an example, we provide closed formulas and statistical inference for Pearson's correlation coefficient between progression-free and overall survival in a parametric framework. The example is inspired by recent approaches to quantify the dependence between progression-free survival, a common primary outcome in Phase 3 trials in oncology and overall survival. We complement these approaches by providing methods of statistical inference while at the same time working within a much more parsimonious modeling framework. Our approach is completely general and can be applied to other measures of dependence. We also discuss extensions to nonparametric inference. Our analytical results are illustrated using a large randomized clinical trial in breast cancer. [ABSTRACT FROM AUTHOR]

Estimating the potential risk associated with an exposure occurring over time requires complex statistical techniques, since ignoring the time from study entry until the exposure leads to potentially seriously biased effect estimates. A prominent example is estimating the effect of hospital-acquired infections on adverse outcomes in patients admitted to the intensive care unit. Exposure density sampling has been proposed as an approach to dynamic matching with respect to a time-dependent exposure. Firstly, exposure density sampling can be useful to reduce the workload of study follow up, as it includes all exposed but only a subset of the not yet exposed individuals. Secondly, it can help to obtain a comparable control group by including propensity score matching. In the present article, we provide the theoretical justification that data obtained by exposure density sampling can be analyzed as a left-truncated cohort. It is shown that exposure density sampling allows estimation of the effect of a time-dependent exposure as well as further baseline covariates on a subsequent event, with only minor loss in precision as compared with a full cohort analysis. The sampling is applied to a real data example (hospital-acquired infections in intensive care units) and in a simulation study. We also provide an estimate of the loss in precision in terms of an increased standard error in the reduced data set after exposure density sampling as compared with the full cohort. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Purpose Observational cohort studies are essential to evaluate the risk of adverse pregnancy outcomes associated with drug intake. Besides left truncation and competing events, it is crucial to account for the time‐dynamic pattern of drug exposure. In fact, potentially harmful medications are often discontinued, which might affect the outcome. Ignoring these challenges may lead to biased estimation of drug‐related risks highlighting the need for adequate statistical techniques. Methods: We reanalyze updated data of a recently published study provided by the German Embryotox pharmacovigilance institute. The aim of the study was to quantify the effect of discontinuation of vitamin K antagonist phenprocoumon on the risk of spontaneous abortion. Results: We outline multistate methodology as a powerful method removing bias in probability estimation inherent to commonly used crude proportions. We incorporate time‐dependent discontinuation and competing pregnancy outcomes as separate states in a multistate model, which enables the formulation of hazard‐based Cox proportional hazard models and the application of so‐called landmark techniques. Results show that early discontinuation of phenprocoumon substantially reduces the risk of spontaneous abortion, which is of great importance for both pregnant women and treating physicians. Conclusions: An adequate handling of discontinuation times is essential when analyzing the risk of spontaneous abortion. The proposed concepts are not restricted to pregnancy outcome studies but have broad usage in other fields of epidemiology. Our nontechnical report may provide guidance for the design and analysis of future studies. Example code is provided. [ABSTRACT FROM AUTHOR]

After exploratory drug development, companies face the decision whether to initiate confirmatory trials based on limited efficacy information. This proof-of-concept decision is typically performed after a Phase II trial studying a novel treatment versus either placebo or an active comparator. The article aims to optimize the design of such a proof-of-concept trial with respect to decision making. We incorporate historical information and develop pre-specified decision criteria accounting for the uncertainty of the observed treatment effect. We optimize these criteria based on sensitivity and specificity, given the historical information. Specifically, time-to-event data are considered in a randomized 2-arm trial with additional prior information on the control treatment. The proof-of-concept criterion uses treatment effect size, rather than significance. Criteria are defined on the posterior distribution of the hazard ratio given the Phase II data and the historical control information. Event times are exponentially modeled within groups, allowing for group-specific conjugate prior-to-posterior calculation. While a non-informative prior is placed on the investigational treatment, the control prior is constructed via the meta-analytic-predictive approach. The design parameters including sample size and allocation ratio are then optimized, maximizing the probability of taking the right decision. The approach is illustrated with an example in lung cancer. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson-Aalen estimator under Aalen's multiplicative intensity model. Aalen's model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of the new procedures are investigated in a simulation study. [ABSTRACT FROM AUTHOR]

Innovations are urgently required for clinical development of antibacterials against multidrug-resistant organisms. Therefore, a European, public-private working group (STAT-Net; part of Combatting Bacterial Resistance in Europe [COMBACTE]), has reviewed and tested several innovative trials designs and analytical methods for randomized clinical trials, which has resulted in 8 recommendations. The first 3 focus on pharmacokinetic and pharmacodynamic modeling, emphasizing the pertinence of population-based pharmacokinetic models, regulatory procedures for the reassessment of old antibiotics, and rigorous quality improvement. Recommendations 4 and 5 address the need for more sensitive primary end points through the use of rank-based or time-dependent composite end points. Recommendation 6 relates to the applicability of hierarchical nested-trial designs, and the last 2 recommendations propose the incorporation of historical or concomitant trial data through Bayesian methods and/or platform trials. Although not all of these recommendations are directly applicable, they provide a solid, evidence-based approach to develop new, and established, antibacterials and address this public health challenge. [ABSTRACT FROM AUTHOR]

The expected excess length‐of‐stay is an established concept to assess the health and economic impact of nosocomial, that is, hospital‐acquired infections such as ventilation‐acquired pneumonia in intensive care. Estimation must account for the timing of infection as in a multistate perspective, because common retrospective comparisons yield inflated estimates due to time‐dependent bias. Since occurrence of ventilation‐acquired pneumonia is closely linked to ventilation status, we suggest a multistate model incorporating time‐dependent mechanical ventilation as additional states. The appeal is that the expected excess length‐of‐stay decomposes into extra days spent under ventilation and not under ventilation. This is not only highly relevant from a patient's perspective regarding quality of life, but also from an economic point of view, because ventilation is a major cost driver. The challenge is that estimation involves complex functionals of the matrix of transition probabilities, which in turn are based on the transition hazards. To address heterogeneity between patients, which is a common phenomenon in observational hospital epidemiology, we apply pseudovalue regression to adjust the ventilation‐specific quantities for baseline confounding. The performance of our proposal is assessed by simulation and the methods are illustrated on data provided by 12 French intensive care units. Preliminary results indicate that the expected excess length‐of‐stay associated with ventilation‐acquired pneumonia is mainly triggered by extra days spent under mechanical ventilation, and that the excess is most pronounced for intensive care patients with fewer comorbidities at baseline. We also find that such a decomposition is challenging for early times. Example code is provided. [ABSTRACT FROM AUTHOR]

Summary: We suggest a wild bootstrap resampling technique for nonparametric inference on transition probabilities in a general time‐inhomogeneous Markov multistate model. We first approximate the limiting distribution of the Nelson–Aalen estimator by repeatedly generating standard normal wild bootstrap variates, while the data is kept fixed. Next, a transformation using a functional delta method argument is applied. The approach is conceptually easier than direct resampling for the transition probabilities. It is used to investigate a non‐standard time‐to‐event outcome, currently being alive without immunosuppressive treatment, with data from a recent study of prophylactic treatment in allogeneic transplanted leukemia patients. Due to non‐monotonic outcome probabilities in time, neither standard survival nor competing risks techniques apply, which highlights the need for the present methodology. Finite sample performance of time‐simultaneous confidence bands for the outcome probabilities is assessed in an extensive simulation study motivated by the clinical trial data. Example code is provided in the web‐based Supplementary Materials. [ABSTRACT FROM AUTHOR]

Abstract: Realistic power calculations for large cohort studies and nested case control studies are essential for successfully answering important and complex research questions in epidemiology and clinical medicine. For this, we provide a methodical framework for general realistic power calculations via simulations that we put into practice by means of an R‐based template. We consider staggered recruitment and individual hazard rates, competing risks, interaction effects, and the misclassification of covariates. The study cohort is assembled with respect to given age‐, gender‐, and community distributions. Nested case‐control analyses with a varying number of controls enable comparisons of power with a full cohort analysis. Time‐to‐event generation under competing risks, including delayed study‐entry times, is realized on the basis of a six‐state Markov model. Incidence rates, prevalence of risk factors and prefixed hazard ratios allow for the assignment of age‐dependent transition rates given in the form of Cox models. These provide the basis for a central simulation‐algorithm, which is used for the generation of sample paths of the underlying time‐inhomogeneous Markov processes. With the inclusion of frailty terms into the Cox models the Markov property is specifically biased. An “individual Markov process given frailty” creates some unobserved heterogeneity between individuals. Different left‐truncation‐ and right‐censoring patterns call for the use of Cox models for data analysis. p‐values are recorded over repeated simulation runs to allow for the desired power calculations. For illustration, we consider scenarios with a “testing” character as well as realistic scenarios. This enables the validation of a correct implementation of theoretical concepts and concrete sample size recommendations against an actual epidemiological background, here given with possible substudy designs within the German National Cohort. [ABSTRACT FROM AUTHOR]

Abstract: We consider modeling competing risks data in high dimensions using a penalized cause‐specific hazards (CSHs) approach. CSHs have conceptual advantages that are useful for analyzing molecular data. First, working on hazards level can further understanding of the underlying biological mechanisms that drive transition hazards. Second, CSH models can be used to extend the multistate framework for high‐dimensional data. The CSH approach is implemented by fitting separate proportional hazards models for each event type (iCS). In the high‐dimensional setting, this might seem too complex and possibly prone to overfitting. Therefore, we consider an extension, namely “linking” the separate models by choosing penalty tuning parameters that in combination yield best prediction of the incidence of the event of interest (penCR). We investigate whether this extension is useful with respect to prediction accuracy and variable selection. The two approaches are compared to the subdistribution hazards (SDH) model, which is an established method that naturally achieves “linking” by working on incidence level, but loses interpretability of the covariate effects. Our simulation studies indicate that in many aspects, iCS is competitive to penCR and the SDH approach. There are some instances that speak in favor of linking the CSH models, for example, in the presence of opposing effects on the CSHs. We conclude that penalized CSH models are a viable solution for competing risks models in high dimensions. Linking the CSHs can be useful in some particular cases; however, simple models using separately penalized CSH are often justified. [ABSTRACT FROM AUTHOR]

Competing risks extend standard survival analysis to considering time-to-first-event and type-of-first-event, where the event types are called competing risks. The competing risks process is completely described by all cause-specific hazards, ie, the hazard marked by the event type. Separate Cox models for each cause-specific hazard are the standard approach to regression modelling, but they come with the interpretational challenge that there are as many regression coefficients as there are competing risks. An alternative approach is to directly model the cumulative event probabilities, but again, there will be as many models as there are competing risks. The aim of this paper is to investigate the usefulness of a third alternative. Proportional odds modelling of all cause-specific hazards summarizes the effect of one covariate on "opposing" competing outcomes in one regression coefficient. For instance, if the competing outcomes are hospital death and alive discharge from hospital, the modelling assumption is that a covariate affects both outcomes in opposing directions, but the effect size is of the same absolute magnitude. We will investigate the interpretational aspects of the approach analysing a data set on intensive care unit patients using parametric methods. [ABSTRACT FROM AUTHOR]

Competing risks consider time to first event and type of first event. This subdiscipline of survival analysis is challenging in that multiple hazards determine the outcome probabilities. The paper demonstrates that Nightingale and Farr were aware of these connections in their co-operative work in hospital epidemiology. At the fourth International Statistical Congress (in London, 1860), they suggested forms for reporting hospital mortality that were conceptually more complete than many reported competing risks analyses today. [ABSTRACT FROM AUTHOR]

Meta-analysis of a survival endpoint is typically based on the pooling of hazard ratios (HRs). If competing risks occur, the HRs may lose translation into changes of survival probability. The cumulative incidence functions (CIFs), the expected proportion of cause-specific events over time, re-connect the cause-specific hazards (CSHs) to the probability of each event type. We use CIF ratios to measure treatment effect on each event type. To retrieve information on aggregated, typically poorly reported, competing risks data, we assume constant CSHs. Next, we develop methods to pool CIF ratios across studies. The procedure computes pooled HRs alongside and checks the influence of follow-up time on the analysis. We apply the method to a medical example, showing that follow-up duration is relevant both for pooled cause-specific HRs and CIF ratios. Moreover, if all-cause hazard and follow-up time are large enough, CIF ratios may reveal additional information about the effect of treatment on the cumulative probability of each event type. Finally, to improve the usefulness of such analysis, better reporting of competing risks data is needed. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the linear model for cross-over trials, with fixed subject effects and normal i.i.d. random errors, the residual variability corresponds to the intraindividual variability. While population variances are in general unknown, an estimate can be derived that follows a gamma distribution, where the scale parameter is based on the true unknown variability. This gamma distribution is often used for the sample size calculation for trial planning with the precision approach, where the aim is to achieve in the next trial a predefined precision with a given probability. But then the imprecision in the estimated residual variability or, from a Bayesian perspective, the uncertainty of the unknown variability is not taken into account. Here, we present the predictive distribution for the residual variability, and we investigate a link to the F distribution. The consequence is that in the precision approach more subjects will be necessary than with the conventional calculation. For values of the intraindividual variability that are typical of human pharmacokinetics, that is a gCV of 17-36%, we would need approximately a sixth more subjects. [ABSTRACT FROM AUTHOR]

The aim of this work is to shed some light on common issues in the statistical analysis of adverse events (AEs) in clinical trials, when the main outcome is a time-to-event endpoint. To begin, we show that AEs are always subject to competing risks. That is, the occurrence of a certain AE may be precluded by occurrence of the main time-to-event outcome or by occurrence of another (fatal) AE. This has raised concerns on 'informative' censoring. We show that, in general, neither simple proportions nor Kaplan-Meier estimates of AE occurrence should be used, but common survival techniques for hazards that censor the competing event are still valid, but incomplete analyses. They must be complemented by an analogous analysis of the competing event for inference on the cumulative AE probability. The commonly used incidence rate (or incidence density) is a valid estimator of the AE hazard assuming it to be time constant. An estimator of the cumulative AE probability can be derived if the incidence rate of AE is combined with an estimator of the competing hazard. We discuss less restrictive analyses using non-parametric and semi-parametric approaches. We first consider time-to-first-AE analyses and then briefly discuss how they can be extended to the analysis of recurrent AEs. We will give a practical presentation with illustration of the methods by a simple example. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Background: In patients with type-2 diabetes receiving oral antidiabetic drugs (OADs), the addition of insulin is frequently required to achieve sufficient control over blood glucose levels. It is, however, difficult to predict if, when and in which patients insulin therapy will be needed. We aimed to identify patient related variables associated with the addition of basal insulin to oral therapy resulting in a basal supported oral therapy (BOT). Methods: DIVE (DIabetes Versorgungs-Evaluation) is a prospective, observational, multi-centre diabetes registry established in Germany in 2011. For the present explorative analysis, 31,008 patients with type-2 diabetes prescribed at least one OAD were included. Patients who had previously received insulin and those over 90 years old were excluded. The event of interest was defined as the initiation of BOT during the observational period. Cause-specific Cox proportional hazards models based on a competing risk framework were applied for risk quantification. Results: Multivariable adjusted hazard ratios demonstrated that longer diabetes duration, higher BMI, poorer glycaemic control, documentation of any micro- or macrovascular comorbidity, the presence of concomitant non-antidiabetic pharmacotherapies, and greater numbers of prescribed OADs increased the likelihood of BOT initiation. On the other hand BOT initiation was less likely in patients with older age and female gender. Analysing the likelihood of OAD termination without initiation of BOT provided supportive evidence for the variables predictive of BOT initiation. Discussion: Analysis of the DIVE registry has resulted in the identification of a number of factors that may be predictive for the initiation of BOT for type-2 diabetes patients initially prescribed one or more OADs. Poor glycaemic control, the presence of vascular comorbidities and concomitant medications, and a greater number of OADs were all detected to increase the risk of a switch to BOT. Female gender and younger age showed protective properties. Conclusions: The close monitoring of patients displaying these characteristics may help to identify individuals who might benefit from early addition of insulin therapy to their oral treatment regimen. [ABSTRACT FROM AUTHOR]

Background: In patients with type-2 diabetes receiving oral antidiabetic drugs (OADs), the addition of insulin is frequently required to achieve sufficient control over blood glucose levels. It is, however, difficult to predict if, when and in which patients insulin therapy will be needed. We aimed to identify patient related variables associated with the addition of basal insulin to oral therapy resulting in a basal supported oral therapy (BOT). Methods: DIVE (DIabetes Versorgungs-Evaluation) is a prospective, observational, multi-centre diabetes registry established in Germany in 2011. For the present explorative analysis, 31,008 patients with type-2 diabetes prescribed at least one OAD were included. Patients who had previously received insulin and those over 90 years old were excluded. The event of interest was defined as the initiation of BOT during the observational period. Cause-specific Cox proportional hazards models based on a competing risk framework were applied for risk quantification. Results: Multivariable adjusted hazard ratios demonstrated that longer diabetes duration, higher BMI, poorer glycaemic control, documentation of any micro- or macrovascular comorbidity, the presence of concomitant non-antidiabetic pharmacotherapies, and greater numbers of prescribed OADs increased the likelihood of BOT initiation. On the other hand BOT initiation was less likely in patients with older age and female gender. Analysing the likelihood of OAD termination without initiation of BOT provided supportive evidence for the variables predictive of BOT initiation. Discussion: Analysis of the DIVE registry has resulted in the identification of a number of factors that may be predictive for the initiation of BOT for type-2 diabetes patients initially prescribed one or more OADs. Poor glycaemic control, the presence of vascular comorbidities and concomitant medications, and a greater number of OADs were all detected to increase the risk of a switch to BOT. Female gender and younger age showed protective properties. Conclusions: The close monitoring of patients displaying these characteristics may help to identify individuals who might benefit from early addition of insulin therapy to their oral treatment regimen. [ABSTRACT FROM AUTHOR]

Competing risks model time to first event and type of first event. An example from hospital epidemiology is the incidence of hospital-acquired infection, which has to account for hospital discharge of non-infected patients as a competing risk. An illness-death model would allow to further study hospital outcomes of infected patients. Such a model typically relies on a Markov assumption. However, it is conceivable that the future course of an infected patient does not only depend on the time since hospital admission and current infection status but also on the time since infection. We demonstrate how a modified competing risks model can be used for nonparametric estimation of transition probabilities when the Markov assumption is violated. [ABSTRACT FROM AUTHOR]