Jan Beyersmann

Competing Risks and Multistate Models with R

Data examples.- An informal introduction to hazard-based analyses.- Competing risks.- Multistate modelling of competing risks.- Nonparametric estimation.- Proportional hazards models.- Nonparametric hypothesis testing.- Further topics in competing risks.- Multistate models and their connection to competing risks.- Nonparametric estimation.- Proportional transition hazards models.- Time-dependent covariates and multistate models.- Further topics in multistate modeling.

A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions.

Competing risks endpoints are frequently encountered in hematopoietic stem cell transplantation where patients are exposed to relapse and treatment-related mortality. Both cause-specific hazards and direct models for the cumulative incidence functions have been used for analyzing such competing risks endpoints. For both approaches, the popular models are of a proportional hazards type. Such models have been used for studying prognostic factors in acute and chronic leukemias. We argue that a complete understanding of the event dynamics requires that both hazards and cumulative incidence be analyzed side by side, and that this is generally the most rigorous scientific approach to analyzing competing risks data. That is, understanding the effects of covariates on cause-specific hazards and cumulative incidence functions go hand in hand. A case study illustrates our proposal.

Use of multistate models to assess prolongation of intensive care unit stay due to nosocomial infection

BACKGROUND Reliable data on the costs attributable to nosocomial infection (NI) are crucial to demonstrating the real cost-effectiveness of infection control measures. Several studies investigating this issue with regard to intensive care unit (ICU) patients have probably overestimated, as a result of inappropriate study methods, the part played by NIs in prolonging the length of stay. METHODS Data from a prospective study of the incidence of NI in 5 ICUs over a period of 18 months formed the basis of this analysis. For describing the temporal dynamics of the data, a multistate model was used. Thus, ICU patients were counted as case patients as soon as an NI was ascertained on any particular day. All patients were then regarded as control subjects as long as they remained free of NI (time-to-event data analysis technique). RESULTS Admitted patients (n=1,876) were observed for the development of NI over a period of 28,498 patient-days. In total, 431 NIs were ascertained during the study period (incidence density, 15.1 NIs per 1,000 patient-days). The influence of NI as a time-dependent covariate in a proportional hazards model was highly significant (P< .0001, Wald test). NI significantly reduced the discharge hazard (hazard ratio, 0.72 [95% confidence interval, 0.63-0.82])--that is, it prolonged the ICU stay. The mean prolongation of ICU length of stay due to NI (+/- standard error) was estimated to be 5.3+/-1.6 days. CONCLUSIONS Further studies are required to enable comparison of data on prolongation of ICU length of stay with the results of various study methods.

An easy mathematical proof showed that time-dependent bias inevitably leads to biased effect estimation

OBJECTIVE Time-dependent bias occurs when future exposure status is analyzed as being known with start of observation. As this bias is common, we sought to determine whether it always leads to biased effect estimation. We also sought to determine the direction of the effect bias. STUDY DESIGN AND SETTING We derived an easy mathematical proof investigating the nature of time-dependent bias. We applied the general mathematical result to data from a prospective cohort study on the incidence of hospital infection in intensive care: Here, we investigated the effect of time-dependent hospital infection status on intensive care unit stay. The nature of time-dependent bias was also illustrated graphically. RESULTS Biased effect estimation is a mathematically inevitable consequence of time-dependent bias, because the number of individuals at risk of exposure is distorted over the course of time. In case of a time-dependent exposure that prolongs time until the study endpoint, the prolonging effect will be overestimated. CONCLUSION Because time-dependent bias inevitably leads to erroneous findings, it is a major concern that it is common in the clinical literature. Time-dependent bias can be avoided by proper hazard-based analyses.

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.

Risk factors for the development of nosocomial pneumonia and mortality on intensive care units: application of competing risks models

IntroductionPneumonia is a very common nosocomial infection in intensive care units (ICUs). Many studies have investigated risk factors for the development of infection and its consequences. However, the evaluation in most of theses studies disregards the fact that there are additional competing events, such as discharge or death.MethodsA prospective cohort study was conducted over 18 months in five intensive care units at one university hospital. All patients that were admitted for at least 2 days were included, and surveillance of nosocomial pneumonia was conducted. Various potential risk factors (baseline- and time-dependent) were evaluated in two competing risks models: the acquisition of nosocomial pneumonia and discharge (dead or alive; model 1) and for the risk of death in the ICU and discharge alive (model 2).ResultsPatients from 1,876 admissions were included. A total of 158 patients developed nosocomial pneumonia. The main risk factors for nosocomial pneumonia in the multivariate analysis in model 1 were: elective surgery (cause-specific hazard ratio = 1.95; 95% CI 1.33 to 2.85) or emergency surgery (1.59; 95% CI 1.10 to 2.28) prior to ICU admission, usage of a nasogastric tube (3.04; 95% CI 1.25 to 7.37) and mechanical ventilation (5.90; 95% CI 2.47 to 14.09). Nosocomial pneumonia prolonged the length of ICU stay but was not directly associated with a fatal outcome (p = 0.55).ConclusionMore studies using competing risk models, which provide more accurate data compared to naive survival curves or logistic models, should be carried out to verify the impact of risk factors and patient characteristics for the acquisition of nosocomial infections and infection-associated mortality.

The impact of time‐dependent bias in proportional hazards modelling

In the clinical literature, time-dependent exposure status has regularly been analysed as if known at time origin. Although statisticians agree that such an analysis yields biased results when analysing the effect on the time until some endpoint of interest, this paper is the first to study in detail the bias arising in a proportional hazards analysis. We show that the biased hazard ratio estimate will always be less than the unbiased one; this leads to either an inflated or a damped effect of exposure, depending on the sign of the correct log hazard ratio estimate. We find an explicit formula of the asymptotic bias based on generalized rank estimators, and we investigate the role of censoring, which may prevent an individual from being considered as being baseline exposed in the biased analysis. We illustrate our results with data on hospital infection status and different censoring patterns.

Nosocomial infection, length of stay, and time-dependent bias.

Nosocomial pneumonia and its impact on length of stay are major healthcare concerns. From an epidemiological perspective, nosocomial pneumonia is a time-dependent event. Any statistical analysis that does not explicitly model this time dependency will be biased. The bias is not redeemed by adjusting for baseline information.

Time-dependent covariates in the proportional subdistribution hazards model for competing risks

Separate Cox analyses of all cause-specific hazards are the standard technique of choice to study the effect of a covariate in competing risks, but a synopsis of these results in terms of cumulative event probabilities is challenging. This difficulty has led to the development of the proportional subdistribution hazards model. If the covariate is known at baseline, the model allows for a summarizing assessment in terms of the cumulative incidence function. black Mathematically, the model also allows for including random time-dependent covariates, but practical implementation has remained unclear due to a certain risk set peculiarity. We use the intimate relationship of discrete covariates and multistate models to naturally treat time-dependent covariates within the subdistribution hazards framework. The methodology then straightforwardly translates to real-valued time-dependent covariates. As with classical survival analysis, including time-dependent covariates does not result in a model for probability functions anymore. Nevertheless, the proposed methodology provides a useful synthesis of separate cause-specific hazards analyses. We illustrate this with hospital infection data, where time-dependent covariates and competing risks are essential to the subject research question.

Modeling the effect of time-dependent exposure on intensive care unit mortality

PurposeTo illustrate modern survival models with focus on the temporal dynamics of intensive care data. A typical situation is given in which time-dependent exposures and competing events are present.MethodsWe briefly review the following established statistical methods: logistic regression, regression models for event-specific hazards and the subdistribution hazard. These approaches are compared by showing advantages as well as disadvantages. All methods are applied to real data from a study of day-by-day ICU surveillance.ResultsStandard logistic regression ignores the time-dependent nature of the data and is only a crude approach. Cumulative hazards and probability plots add important information and provide a deep insight into the temporal dynamics.ConclusionThis paper might help to encourage researchers working in hospital epidemiology to apply adequate statistical models to complex medical questions.