Survival analysis for AdVerse events with VarYing follow-up times (SAVVY): summary of findings and assessment of existing guidelines.

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.

Assessment of assumptions of statistical analysis methods in randomised clinical trials: the what and how.

When analysing and presenting results of randomised clinical trials, trialists rarely report if or how underlying statistical assumptions were validated. To avoid data-driven biased trial results, it should be common practice to prospectively describe the assessments of underlying assumptions. In existing literature, there is no consensus on how trialists should assess and report underlying assumptions for the analyses of randomised clinical trials. With this study, we developed suggestions on how to test and validate underlying assumptions behind logistic regression, linear regression, and Cox regression when analysing results of randomised clinical trials.Two investigators compiled an initial draftbased on a review of the literature. Experienced statisticians and trialists from eight different research centres and trial units then participated in a anonymised consensus process, where we reached agreement on the suggestions presented in this paper.This paper provides detailed suggestions on 1) which underlying statistical assumptions behind logistic regression, multiple linear regression and Cox regression each should be assessed; 2) how these underlying assumptions may be assessed; and 3) what to do if these assumptions are violated.We believe that the validity of randomised clinical trial results will increase if our recommendations for assessing and dealing with violations of the underlying statistical assumptions are followed.

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.

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.

On estimands and the analysis of adverse events in the presence of varying follow-up times within the benefit assessment of therapies.

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.

A simulation approach for power calculation in large cohort studies based on multistate models.

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.

The health and economic burden of bloodstream infections caused by antimicrobial-susceptible and non-susceptible Enterobacteriaceae and Staphylococcus aureus in European hospitals, 2010 and 2011: a multicentre retrospective cohort study.

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.

A competing risks approach for nonparametric estimation of transition probabilities in a non-Markov illness-death model.

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.

Application of multistate models in hospital epidemiology: advances and challenges.

Survival analysis has established itself as a major statistical technique in medical research. Applications in hospital epidemiology, however, are only beginning to emerge. One reason for this delay is that usually complete follow-up of patients in hospital is feasible. This overview discusses where survival techniques provide additional insight into hospital epidemiology, and where they are, in fact, needed even in the absence of right-censoring.

The time-dependent bias and its effect on extra length of stay due to nosocomial infection.

OBJECTIVES: Many studies disregard the time dependence of nosocomial infection when examining length of hospital stay and the associated financial costs. This leads to the "time-dependent bias," which biases multiplicative hazard ratios. We demonstrate the time-dependent bias on the additive scale of extra length of stay. METHODS: To estimate the extra length of stay due to infection, we used a multistate model that accounted for the time of infection. For comparison we used a generalized linear model assuming a gamma distribution, a commonly used model that ignores the time of infection. We applied these two methods to a large prospective cohort of hospital admissions from Argentina, and compared the methods' performance using a simulation study. RESULTS: For the Argentina data the extra length of stay due to nosocomial infection was 11.23 days when ignoring time dependence and only 1.35 days after accounting for the time of infection. The simulations showed that ignoring time dependence consistently overestimated the extra length of stay. This overestimation was similar for different rates of infection and even when an infection prolonged or shortened stay. We show examples where the time-dependent bias remains unchanged for the true discharge hazard ratios, but the bias for the extra length of stay is doubled because length of stay depends on the infection hazard. CONCLUSIONS: Ignoring the timing of nosocomial infection gives estimates that greatly overestimate its effect on the extra length of hospital stay.

Estimating the cost of health care-associated infections: mind your p's and q's.

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.