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

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

Asymptotic properties of the two one-sided t-tests - new insights and the Schuirmann-constant.

The two one-sided t-tests (TOST) method is the most popular statistical equivalence test with many areas of application, i.e., in the pharmaceutical industry. Proper sample size calculation is needed in order to show equivalence with a certain power. Here, the crucial problem of choosing a suitable mean-difference in TOST sample size calculations is addressed. As an alternative concept, it is assumed that the mean-difference follows an a-priori distribution. Special interest is given to the uniform and some centered triangle a-priori distributions. Using a newly developed asymptotical theory a helpful analogy principle is found: every a-priori distribution corresponds to a point mean-difference, which we call its Schuirmann-constant. This constant does not depend on the standard deviation and aims to support the investigator in finding a well-considered mean-difference for proper sample size calculations in complex data situations. In addition to the proposed concept, we demonstrate that well-known sample size approximation formulas in the literature are in fact biased and state their unbiased corrections as well. Moreover, an R package is provided for a right away application of our newly developed concepts.

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.

Pregnancy outcome after first-trimester exposure to fosfomycin for the treatment of urinary tract infection: an observational cohort study.

PURPOSE: The primary aim of our study was to assess pregnancy outcome after first-trimester exposure to fosfomycin. METHODS: We performed an observational cohort study analysing prospectively ascertained pregnancies including 152 women exposed to fosfomycin in the first trimester of pregnancy in comparison with a randomly selected cohort comprising 456 pregnancies not exposed to fosfomycin. All pregnancies were identified through risk consultations using structured questionnaires between January 2000 and December 2016 by the German Embryotox pharmacovigilance institute in Berlin. Primary objectives were the risks of major birth defects and spontaneous abortion. RESULTS: Only 1 out of 146 exposed infants was affected by a major birth defect (0.7%, 95% CI 0.04-4.33%) in comparison to 15/399 in the non-exposed cohort (3.8%, 95% CI 2.2-6.26%). Spontaneous abortions were observed in 5/152 cases in the fosfomycin cohort vs. 53/456 cases in the comparison cohort (cumulative incidence 6.2% vs. 23.1%; HR adjusted 0.35, 95% CI 0.14-0.90). CONCLUSION: This is the first study specifically examining the teratogenic risk of fosfomycin. The study results do not indicate an increased risk of adverse pregnancy outcome after fosfomycin exposure during early pregnancy. However, larger studies are needed to confirm the safety of fosfomycin during the first trimester.

Impact of mechanical ventilation on the daily costs of ICU care: a systematic review and meta regression.

The impact of mechanical ventilation on the daily costs of intensive care unit (ICU) care is largely unknown. We thus conducted a systematic search for studies measuring the daily costs of ICU stays for general populations of adults (age ≥18 years) and the added costs of mechanical ventilation. The relative increase in the daily costs was estimated using random effects meta regression. The results of the analyses were applied to a recent study calculating the excess length-of-stay associated with ICU-acquired (ventilator-associated) pneumonia, a major complication of mechanical ventilation. The search identified five eligible studies including a total of 54 766 patients and ~238 037 patient days in the ICU. Overall, mechanical ventilation was associated with a 25.8% (95% CI 4.7%-51.2%) increase in the daily costs of ICU care. A combination of these estimates with standardised unit costs results in approximate daily costs of a single ventilated ICU day of €1654 and €1580 in France and Germany, respectively. Mechanical ventilation is a major driver of ICU costs and should be taken into account when measuring the financial burden of adverse events in ICU settings.

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.

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.

The wild bootstrap for multivariate Nelson-Aalen estimators.

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.

Estimation of adjusted expected excess length-of-stay associated with ventilation-acquired pneumonia in intensive care: A multistate approach accounting for time-dependent mechanical ventilation.

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.

A wild bootstrap approach for the Aalen-Johansen estimator.

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.

Assessing Noninferiority in Treatment Trials for Severe Infectious Diseases: an Extension to the Entire Follow-Up Period Using a Cure-Death Multistate Model.

In current and former clinical trials for the development of antibacterial drugs, various primary endpoints have been used, and treatment effects are evaluated mostly in noninferiority analyses at the end of follow-up, which varies between studies. A more convincing and highly patient-relevant statement would be a noninferiority assessment over the entire follow-up period with cure and death as coprimary endpoints, while preserving the desired alpha level for statistical testing. To account for the time-dynamic pattern of cure and death, we apply a cure-death multistate model. The endpoint of interest is "get cured and stay alive over time." Noninferiority between treatments over the entire follow-up period is studied by means of one-sided confidence bands provided by a flexible resampling technique. We illustrate the technique by applying it to a recently published study and establish noninferiority in being cured and alive over a time frame of interest for the entire population, patients with hospital-acquired pneumonia, but not for the subset of patients with ventilator-associated pneumonia. Our analysis improves the original results in the sense that our endpoint is more patient benefiting, a stronger noninferiority statement is demonstrated, and the time dependency of cure and death, competing events, and different follow-up times is captured. Multistate methodology combined with confidence bands adds a valuable statistical tool for clinical trials in the context of infection control. The framework is not restricted to the cure-death model but can be adapted to more complex multistate endpoints and equivalence or superiority analyses.

Determinants of weight change in patients on basal insulin treatment: an analysis of the DIVE registry.

OBJECTIVE: We aimed to describe patterns of weight change in insulin-naive patients with type 2 diabetes mellitus (T2DM) starting basal insulin (BI) treatment. RESEARCH DESIGN AND METHODS: Diabetes Versorgungs-Evaluation (DIVE) is an observational, multicenter, prospective registry in patients with T2DM. Patients were divided into those initiating BI therapy for the first time (with optional oral antidiabetic drugs (OADs)) and those initiating OADs only (OADo). RESULTS: 521 patients were included in the analysis, 113 in the BI arm and 408 in the OADo arm. Relative to baseline, the BI group gained an average of 0.98±7.1 kg at 1 year, compared with a loss of 1.52±11.8 kg in the OADo group (p<0.001). This difference remained statistically significant when expressed as a proportional change from baseline (+0.014±0.08 vs -0.015±0.12, respectively (p<0.001)). Baseline weight (regression coefficient (RC) 0.89; 95% CI 0.81 to 0.97; p<0.001) and diabetes duration (RC 2.52; 95% CI 0.53 to 4.52; p=0.01) were the only factors identified as significant predictors of weight gain between baseline and 1 year follow-up in BI patients. CONCLUSIONS: Though BI therapy leads to modest weight gain over the subsequent year, this may be limited by BI initiation at an early stage of the disease. As such, delaying the start of insulin therapy based on fears of weight gain appears counter-productive, and should be reconsidered.

Time-to-event methodology improved statistical evaluation in register-based health services research.

OBJECTIVES: Complex longitudinal sampling and the observational structure of patient registers in health services research are associated with methodological challenges regarding data management and statistical evaluation. We exemplify common pitfalls and want to stimulate discussions on the design, development, and deployment of future longitudinal patient registers and register-based studies. STUDY DESIGN AND SETTING: For illustrative purposes, we use data from the prospective, observational, German DIabetes Versorgungs-Evaluation register. One aim was to explore predictors for the initiation of a basal insulin supported therapy in patients with type 2 diabetes initially prescribed to glucose-lowering drugs alone. RESULTS: Major challenges are missing mortality information, time-dependent outcomes, delayed study entries, different follow-up times, and competing events. We show that time-to-event methodology is a valuable tool for improved statistical evaluation of register data and should be preferred to simple case-control approaches. CONCLUSION: Patient registers provide rich data sources for health services research. Analyses are accompanied with the trade-off between data availability, clinical plausibility, and statistical feasibility. Cox' proportional hazards model allows for the evaluation of the outcome-specific hazards, but prediction of outcome probabilities is compromised by missing mortality information.

Understanding Mortality of Femoral Fractures Following Low-Impact Trauma in Persons With and Without Care Need.

OBJECTIVES: Persons with osteoporotic fracture history are subject to an increased risk for subsequent fractures and mortality. The aim of this retrospective study was to investigate the impact of a previous osteoporotic low-impact (fragility) index fracture (eg, forearm, lower leg) on mortality of a subsequent femoral fracture. DESIGN: Retrospective cohort study. PARTICIPANTS/MEASUREMENTS: Claims data of a German health insurance agency including >1.2 million insurants aged 65 years or older and observed between 2004 and 2009. METHODS: A multistate model was developed handling index fractures and care need as time-dependent exposures, while age was chosen as the underlying time scale. Excess risks were expressed as differences in cause-specific hazards. Nelson-Aalen estimates were used for their nonparametric estimation. Time-simultaneous statistical inference was based on confidence bands provided by wild bootstrap resampling. RESULTS: Excess femoral fracture risk increased with progressive age and was highest in persons with care need. It was observed starting from an age of 79 years in women and 85 years in men onward. A prior index fracture increased mortality after a femoral fracture by increasing femoral fracture risk, while leaving the hazard of death after a subsequent femoral fracture unchanged. CONCLUSIONS: The results indicated that increased mortality of a subsequent femoral fracture is not triggered by an intrinsically increased mortality hazard but an increased femoral fracture incidence.

Identifying patients with type 2 diabetes in which basal supported oral therapy may not be the optimal treatment strategy.

BACKGROUND: Basal insulin supported oral therapy (BOT) can greatly improve glycaemic control; however, it may not be an optimal treatment for every patient. The identification of patient-related characteristics that may predict a switch of the treatment strategy away from BOT after originally initiating it, would be useful when deciding on treatment strategies clinically. METHODS: Data from the German DIabetes Versorgungs-Evaluation (DIVE) registry were analysed for patients treated with BOT for at least 3months. BOT discontinuation was defined as the cessation of oral therapy, of insulin therapy, or the addition of short-acting insulin. Risk quantification for demographics, glycaemic control, and treatment characteristics of patients were based on Cox proportional hazards regression. RESULTS: BOT discontinuation occurred in 2021 patients (35.7%) of the 5663 that fulfilled the inclusion criteria for the study. Of these, 46.7% discontinued oral therapy, 32.7% discontinued insulin, and 20.6% had short-acting insulin added to their treatment. Multivariate analysis revealed that higher body mass index (BMI; hazard ratio, HR: 1.012; 95% CI: 1.001-1.023; p=0.029), shorter diabetes duration (HR: 0.982; 95% CI: 0.976-0.989; p<0.001), and higher HbA1c level (HR: 1.102; 95% CI: 1.022-1.188; p=0.011) were associated with BOT discontinuation. CONCLUSIONS: Identification of factors that may be predictive of a discontinuation of BOT could be highly useful in a clinical setting when assessing the most appropriate treatment strategy for type 2 diabetes patients.

Treatment intensification using long-acting insulin -predictors of future basal insulin supported oral therapy in the DIVE registry.

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.