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.

Comparison of nonparametric estimators of the expected number of recurrent events.

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.

Recurrent disability progression endpoints in multiple sclerosis clinical trials.

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.

General independent censoring in event-driven trials with staggered entry.

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.

Trueness of full-arch IO scans estimated based on 3D translational and rotational deviations of single teeth-an in vitro study.

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.

Design aspects of COVID-19 treatment trials: Improving probability and time of favorable events.

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.

Subdistribution hazard models for competing risks in discrete time.

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.

Estimating and comparing adverse event probabilities in the presence of varying follow-up times and competing events.

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.

Survival analysis for AdVerse events with VarYing follow-up times (SAVVY): Rationale and statistical concept of a meta-analytic study.

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.

Motor learning might contribute to a therapeutic anterior shift of the habitual mandibular position-An exploratory study.

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.

Relapse- and Immunosuppression-Free Survival after Hematopoietic Stem Cell Transplantation: How Can We Assess Treatment Success for Complex Time-to-Event Endpoints?

In most clinical oncology trials, time-to-first-event analyses are used for efficacy assessment, which often do not capture the entire disease process. Instead, the focus may be on more complex time-to-event endpoints, such as the course of disease after the first event or endpoints occurring after randomization. We propose "relapse- and immunosuppression-free survival" (RIFS) as an innovative and clinically relevant outcome measure for assessing treatment success after hematopoietic stem cell transplant (SCT). To capture the time-dynamic relationship of multiple episodes of immunosuppressive therapy during follow-up, relapse, and nonrelapse mortality, a multistate model was developed. The statistical complexity is that the probability of RIFS is nonmonotonic over time; thus, standard time-to-first-event methodology is inappropriate for formal treatment comparisons. Instead, a generalization of the Kaplan-Meier method was used for probability estimation, and simulation-based resampling was suggested as a strategy for statistical inference. We reanalyzed data from a recently published phase III trial in 201 leukemia patients after SCT. The study evaluated long-term treatment success of standard graft-versus-host disease prophylaxis plus a pretransplant antihuman T-lymphocyte immunoglobulin compared with standard prophylaxis alone. Results suggested that treatment increased the long-term probability of RIFS by approximately 30% during the entire follow-up period, which complements the original findings. This article highlights the importance of complex endpoints in oncology, which provide deeper insight into the treatment and disease process over time. Multistate models combined with resampling are highlighted as a promising tool to evaluate treatment success beyond standard endpoints. An example code is provided in the Supplementary Materials.

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.

Association of acute kidney injury and bleeding events with mortality after radial or femoral access in patients with acute coronary syndrome undergoing invasive management: secondary analysis of a randomized clinical trial.

AIMS: In the Minimizing Adverse Haemorrhagic Events by TRansradial Access Site and Systemic Implementation of angioX (MATRIX) trial, adults with acute coronary syndrome undergoing coronary intervention who were allocated to radial access had a lower risk of bleeding, acute kidney injury (AKI), and all-cause mortality, as compared with those allocated to femoral access. The mechanism of the mortality benefit of radial access remained unclear. METHODS AND RESULTS: We used multistate and competing risk models to determine the effects of radial and femoral access on bleeding, AKI and all-cause mortality in the MATRIX trial and to disentangle the relationship between these different types of events. There were large relative risk reductions in mortality for radial compared with femoral access for the transition from AKI to death [hazard ratio (HR) 0.55, 95% confidence interval (CI) 0.31-0.97] and for the pathway from coronary intervention to AKI to death (HR 0.49, 95% CI 0.26-0.92). Conversely, there was little evidence for a difference between radial and femoral groups for the transition from bleeding to death (HR 1.05, 95% CI 0.42-2.64) and the pathway from coronary intervention to bleeding to death (HR 0.84, 95% CI 0.28-2.49). CONCLUSION: The prevention of AKI appeared predominantly responsible for the mortality benefit of radial as compared with femoral access in the MATRIX trial. There was little evidence for an equally important, independent role of bleeding.

Multistate modeling of clinical hold in randomized clinical trials.

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.

Nested exposure case-control sampling: a sampling scheme to analyze rare time-dependent exposures.

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.

Exposure density sampling: Dynamic matching with respect to a time-dependent exposure.

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.

Joint modeling of progression-free and overall survival and computation of correlation measures.

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.

Bootstrapping complex time-to-event data without individual patient data, with a view toward time-dependent exposures.

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.

Estimands to quantify prolonged hospital stay associated with nosocomial infections.

BACKGROUND: Length of stay evaluations are very common to determine the burden of nosocomial infections. However, there exist fundamentally different methods to quantify the prolonged length of stay associated with nosocomial infections. Previous methodological studies emphasized the need to account for the timing of infection in order to differentiate the length of stay before and after the infection. METHODS: We derive four different approaches in a simple multi-state framework, display their mathematical relationships in a multiplicative as well as additive way and apply them to a real cohort study (n=756 German intensive-care unit patients of whom 124 patients acquired a nosocomial infection). RESULTS: The first approach ignores the timing of infection and quantifies the difference of eventually infected and eventually uninfected; it is 12.31 days in the real data. The second approach compares the average sojourn time with infection with the average sojourn time of being hypothetically uninfected; it is 2.12 days. The third one compares the average length of stay of a population in a world with nosocomial infections with a population in a hypothetical world without nosocomial infections; it is 0.35 days. Finally, approach four compares the mean residual length of stay between currently infected and uninfected patients on a daily basis; the difference is 1.77 days per infected patient. CONCLUSIONS: The first approach should be avoided because it compares the eventually infected with the eventually uninfected, but has no prospective interpretation. The other approaches differ in their interpretation but are suitable because they explicitly distinguish between the pre- and post-time of the nosocomial infection.

Multistate methodology improves risk assessment under time-varying drug intake-a new view on pregnancy outcomes following coumarin exposure.

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.