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International audience; 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.

When planning an oncology clinical trial, the usual approach is to assume an exponential distribution for the time-to-event endpoints. Often, besides the gold-standard endpoint overall survival, progression-free survival is considered as a second confirmatory endpoint. We use a survival multistate model to jointly model these two endpoints and find that neither exponential distribution nor proportional hazards will typically hold for both endpoints simultaneously. The multistate model approach allows us to consider the joint distribution of the two endpoints and to derive quantities of interest as the correlation between overall survival and progression-free survival. In this paper, we use the multistate model framework to simulate clinical trials with endpoints OS and PFS and show how design planning questions can be answered using this approach. In addition to the major advantage that we can model non-proportional hazards quite naturally with this approach, the correlation between the two endpoints can be exploited to determine sample size and type-I-error. We consider an oncology trial on non-small-cell lung cancer as a motivating example from which we derive relevant trial design questions. We then illustrate how clinical trial design can be based on simulations from a multistate model. Key applications are co-primary endpoints and group-sequential designs. Simulations for these applications show that the standard simplifying approach often leads to underpowered or overpowered clinical trials. Our approach is quite general and can be extended to more complex trial designs, further endpoints, and other therapeutic areas., 27 pages, 3 tables, 12 figures

To describe the 5 years��� trajectories in functionality and pain of patients with hip or knee osteoarthritis and arthroplasty and analyze the association of these with long-term patients survival. Patients with OA receiving total hip or knee arthroplasty were recruited and completed two sets of standardized questionnaires for functionality and pain 6, 12, and 60 months postoperatively. Multivariate mixed models were conducted to assess trajectories over time and the resulting improvement per month during the last time period was included in a landmark-model to estimate adjusted hazard ratios for mortality. In total 809 patients with joint replacement were included (mean age 65.0 years, 62.2% female), 407 patients died (median follow-up 18.4 years). Both instruments of functionality and pain showed extensive improvement during the first 6 months. Baseline and change in functionality (both p, publishedVersion

Supplemental material, sj-docx-1-msj-10.1177_13524585221125382 for Recurrent disability progression endpoints in multiple sclerosis clinical trials by Alexandra Bühler, Marcel Wolbers, Fabian Model, Qing Wang, Shibeshih Belachew, Marianna Manfrini, Johannes Lorscheider, Ludwig Kappos and Jan Beyersmann in Multiple Sclerosis Journal

Supplemental material, sj-pdf-1-smm-10.1177_09622802221133551 for A connection between survival multistate models and causal inference for external treatment interruptions by Alexandra Erdmann, Anja Loos and Jan Beyersmann in Statistical Methods in Medical Research

Supplemental material, sj-pdf-1-smm-10.1177_09622802221133551 for A connection between survival multistate models and causal inference for external treatment interruptions by Alexandra Erdmann, Anja Loos and Jan Beyersmann in Statistical Methods in Medical Research

Supplemental material, sj-docx-1-msj-10.1177_13524585221125382 for Recurrent disability progression endpoints in multiple sclerosis clinical trials by Alexandra Bühler, Marcel Wolbers, Fabian Model, Qing Wang, Shibeshih Belachew, Marianna Manfrini, Johannes Lorscheider, Ludwig Kappos and Jan Beyersmann in Multiple Sclerosis Journal

The choice of endpoints is important for clinical trials. Due to the development of more and more effective drugs patients live longer, which often results in longer follow-up times until the clinical endpoint can be measured. In order to shorten studies as well as reduce costs and sample sizes we often[for full text, please go to the a.m. URL], 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

Within the area of oncology dose-finding several model-based methods for the determination of the maximum tolerated dose (MTD) have been developed. A prominent and widely used approach implements a Bayesian logistic regression model based on the patient-level information of dose-limiting toxicities.[for full text, please go to the a.m. URL], 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

In extensive cohort studies, the ascertainment of covariate information on all individuals can be challenging. In hospital epidemiology, an additional issue is often the time-dependency of the exposure of interest. We revisit and compare two sampling designs constructed for rare time-dependent exposures and possibly common outcomes ��� the nested exposure casecontrol design and exposure density sampling. Both designs enable efficient hazard ratio estimation by sampling all exposed individuals but only a small fraction of the unexposed ones. Moreover, they account for time-dependent exposure to avoid immortal time bias. We evaluate and compare their performance using data of patients hospitalised in the neuro-intensive care unit at the Burdenko Neurosurgery Institute in Moscow, Russia. Three different types of hospital-acquired infections with different prevalence are considered. Additionally, inflation factors, a primary performance measure, are discussed. We enhance both designs to allow for a competitive analysis of combined and competing endpoints compared to the full cohort approach while substantially reducing the amount of necessary information. Nonetheless, exposure density sampling outperforms the nested exposure case-control design concerning efficiency and accuracy in most considered settings., publishedVersion

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 (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 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 favourable 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.

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.

Analyses of adverse events (AEs) are an important aspect of the evaluation of experimental therapies. The SAVVY (Survival analysis for AdVerse events with Varying follow-up times) project aims to improve the analyses of AE data in clinical trials through the use of survival techniques appropriately dealing with varying follow-up times, censoring, and competing events (CE). In an empirical study including seventeen randomized clinical trials the effect of varying follow-up times, censoring, and competing events on comparisons of two treatment arms with respect to AE risks is investigated. The comparisons of relative risks (RR) of standard probability-based estimators to the gold-standard Aalen-Johansen estimator or hazard-based estimators to an estimated hazard ratio (HR) from Cox regression are done descriptively, with graphical displays, and using a random effects meta-analysis on AE level. The influence of different factors on the size of the bias is investigated in a meta-regression. We find 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 RR. There is an urgent need to improve the guidelines of reporting AEs so that incidence proportions are finally replaced by the Aalen-Johansen estimator - rather than by Kaplan-Meier - with appropriate definition of CEs. For RRs based on hazards, the HR based on Cox regression has better properties than the ratio of incidence densities.

The Aalen-Johansen estimator generalizes the Kaplan-Meier estimator for independently left-truncated and right-censored survival data to estimating the transition probability matrix of a time-inhomogeneous Markov model with finite state space. Such multi-state models have a wide range of applications for modelling complex courses of a disease over the course of time, but the Markov assumption may often be in doubt. If censoring is entirely unrelated to the multi-state data, it has been noted that the Aalen-Johansen estimator, standardized by the initial empirical distribution of the multi-state model, still consistently estimates the state occupation probabilities. Recently, this result has been extended to transition probabilities using landmarking, which is, inter alia, useful for dynamic prediction. We complement these results in three ways. Firstly, delayed study entry is a common phenomenon in observational studies, and we extend the earlier results to multi-state data also subject to left-truncation. Secondly, we present a rigorous proof of consistency of the Aalen-Johansen estimator for state occupation probabilities, on which also correctness of the landmarking approach hinges, correcting, simplifying and extending the earlier result. Thirdly, our rigorous proof motivates wild bootstrap resampling. Our developments for left-truncation are motivated by a prospective observational study on the occurrence and the impact of a multi-resistant infectious organism in patients undergoing surgery. Both the real data example and simulation studies are presented. Studying wild bootstrap is motivated by the fact that, unlike drawing with replacement from the data, it is desirable to have a technique that works both with non-Markov models subject to random left-truncation and right-censoring and with Markov models where left-truncation and right-censoring need not be entirely random., Comment: 21 pages with 3 figures

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 III 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 modelling 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.

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.

Monetary valuations of the economic cost of health care-associated infections (HAIs) are important for decision making and should be estimated accurately. Erroneously high estimates of costs, designed to jolt decision makers into action, may do more harm than good in the struggle to attract funding for infection control. Expectations among policy makers might be raised, and then they are disappointed when the reduction in the number of HAIs does not yield the anticipated cost saving. For this article, we critically review the field and discuss 3 questions. Why measure the cost of an HAI? What outcome should be used to measure the cost of an HAI? What is the best method for making this measurement? The aim is to encourage researchers to collect and then disseminate information that accurately guides decisions about the economic value of expanding or changing current infection control activities

Supplemental Material for Bayesian Phase II optimization for time-to-event data based on historical information by Anja Bertsche, Frank Fleischer, Jan Beyersmann and Gerhard Nehmiz in Statistical Methods in Medical Research

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., publishedVersion

International audience; We performed a multicentre retrospective cohort study including 606,649 acute inpatient episodes at 10 European hospitals in 2010 and 2011 to estimate the impact of antimicrobial resistance on hospital mortality, excess length of stay (LOS) and cost. Bloodstream infections (BSI) caused by third-generation cephalosporin-resistant Enterobacteriaceae (3GCRE), meticillin-susceptible (MSSA) and -resistant Staphylococcus aureus (MRSA) increased the daily risk of hospital death (adjusted hazard ratio (HR) = 1.80; 95% confidence interval (CI): 1.34-2.42, HR = 1.81; 95% CI: 1.49-2.20 and HR = 2.42; 95% CI: 1.66-3.51, respectively) and prolonged LOS (9.3 days; 95% CI: 9.2-9.4, 11.5 days; 95% CI: 11.5-11.6 and 13.3 days; 95% CI: 13.2-13.4, respectively). BSI with third-generation cephalosporin-susceptible Enterobacteriaceae (3GCSE) significantly increased LOS (5.9 days; 95% CI: 5.8-5.9) but not hazard of death (1.16; 95% CI: 0.98-1.36). 3GCRE significantly increased the hazard of death (1.63; 95% CI: 1.13-2.35), excess LOS (4.9 days; 95% CI: 1.1-8.7) and cost compared with susceptible strains, whereas meticillin resistance did not. The annual cost of 3GCRE BSI was higher than of MRSA BSI. While BSI with S. aureus had greater impact on mortality, excess LOS and cost than Enterobacteriaceae per infection, the impact of antimicrobial resistance was greater for Enterobacteriaceae.

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., Comment: Tobias Bluhmki and Dennis Dobler are authors with equal contribution, 3 figures, 3 tables

Introduction: The German DIVE (Diabetes Versorgung-Evaluation) registry is a prospective, observational, multi-centre database established in 2011. It contains information on antidiabetic treatment prescription, concomitant therapies, and other covariate values of patients diagnosed with type 2 diabetes[for full text, please go to the a.m. URL], GMDS 2015; 60. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (GMDS)

Concomitant pharmacotherapy: ATC indices*. Legend: DDP-4, dipeptidyl peptidase-4. *World Health Organisation Collaborating Centre for Drugs Statistics Methodology. (DOCX 14 kb)

Absolute Number of Missing Values and Relative Proportion w.r.t. total study population. (DOCX 14 kb)

Predictors of switch to BOT: Multivariate HRs and corresponding lower and upper bounds of the 95Â % CIs including only patients with complete covariate information. (DOCX 16 kb)

Absolute Number of Missing Values and Relative Proportion w.r.t. total study population. (DOCX 14 kb)

Predictors of switch to BOT: Multivariate HRs and corresponding lower and upper bounds of the 95Â % CIs including only patients with complete covariate information. (DOCX 16 kb)

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.

Background: The incidence density is an attractive measure in epidemiological applications, e.g., for infectious disease data. However, incidence densities may be misleading, if the constant hazard assumption fails [ref:1]. Another difficulty arises, if competing events are present, e.g., [for full text, please go to the a.m. URL], 54. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie (gmds)