Sampling designs for rare time-dependent exposures: a comparison of the nested exposure case-control design and exposure density sampling.

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 case-control 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.

Analysis of Clinical Cohort Data Using Nested Case-control and Case-cohort Sampling Designs. A Powerful and Economical Tool.

BACKGROUND: Sampling from a large cohort in order to derive a subsample that would be sufficient for statistical analysis is a frequently used method for handling large data sets in epidemiological studies with limited resources for exposure measurement. For clinical studies however, when interest is in the influence of a potential risk factor, cohort studies are often the first choice with all individuals entering the analysis. OBJECTIVES: Our aim is to close the gap between epidemiological and clinical studies with respect to design and power considerations. Schoenfeld's formula for the number of events required for a Cox' proportional hazards model is fundamental. Our objective is to compare the power of analyzing the full cohort and the power of a nested case-control and a case-cohort design. METHODS: We compare formulas for power for sampling designs and cohort studies. In our data example we simultaneously apply a nested case-control design with a varying number of controls matched to each case, a case cohort design with varying subcohort size, a random subsample and a full cohort analysis. For each design we calculate the standard error for estimated regression coefficients and the mean number of distinct persons, for whom covariate information is required. RESULTS: The formula for the power of a nested case-control design and the power of a case-cohort design is directly connected to the power of a cohort study using the well known Schoenfeld formula. The loss in precision of parameter estimates is relatively small compared to the saving in resources. CONCLUSIONS: Nested case-control and case-cohort studies, but not random subsamples yield an attractive alternative for analyzing clinical studies in the situation of a low event rate. Power calculations can be conducted straightforwardly to quantify the loss of power compared to the savings in the num-ber of patients using a sampling design instead of analyzing the full cohort.

Risk of osteoporotic fractures following stroke in older persons.

UNLABELLED: The aim of this study was to explore the increased risk of stroke survivors to different sustained osteoporotic fractures. We used hospital data and data on functional impairment. We found a higher risk in stroke survivors without functional impairment with the risk higher for lower than for upper extremity fractures. INTRODUCTION: Stroke survivors are at high risk of osteoporotic fractures due to frequent falls and an increased risk to develop osteoporosis. Data on their relative risk to sustain other than hip fractures is limited. Furthermore, the role of severe functional impairment on their fracture risk has not been considered yet. The aim of this study was to determine the relative risk of stroke survivors to sustain different osteoporotic fractures with regard to the presence of severe functional impairment. METHODS: Data from 2004 to 2009 of more than 1.2 million individuals aged 65 years or older and insured at a large German health insurance company were used for the analyses. Incident stroke and fractures were obtained from hospital diagnoses. Analyses were stratified by gender and information on severe functional impairment. Persons without preceding incident stroke were used as the reference group. Multistate models were used to estimate hazard ratios. RESULTS: Stroke survivors had a higher risk for fractures. However, a strong effect modification by functional impairment was apparent. Stroke survivors with functional impairment had no significantly increased risk for any fractures site compared to the corresponding reference group with functional impairment. In contrast, stroke survivors without functional impairment had a clearly and significantly increased fracture risk for most fracture sites. In these persons, the relative fracture risk for fractures of the lower extremities was higher than for fractures of the upper extremities. CONCLUSION: To evaluate the relative risk of stroke survivors for osteoporotic fractures, functional status appears to be a relevant parameter.

Planning and evaluating clinical trials with composite time-to-first-event endpoints in a competing risk framework.

Composite endpoints combine several events of interest within a single variable. These are often time-to-first-event data, which are analyzed via survival analysis techniques. To demonstrate the significance of an overall clinical benefit, it is sufficient to assess the test problem formulated for the composite. However, the effect observed for the composite does not necessarily reflect the effects for the components. Therefore, it would be desirable that the sample size for clinical trials using composite endpoints provides enough power not only to detect a clinically relevant superiority for the composite but also to address the components in an adequate way. The single components of a composite endpoint assessed as time-to-first-event define competing risks. We consider multiple test problems based on the cause-specific hazards of competing events to address the problem of analyzing both a composite endpoint and its components. Thereby, we use sequentially rejective test procedures to reduce the power loss to a minimum. We show how to calculate the sample size for the given multiple test problem by using a simply applicable simulation tool in SAS. Our ideas are illustrated by two clinical study examples.

Initially fewer bloodstream infections for allogeneic vs. autologous stem-cell transplants in neutropenic patients.

Chemotherapy and/or radiotherapy used as conditioning regimens before autologous or allogeneic haematopoietic cell transplantations (HCTs) cause neutropenia, which is the main reason for bloodstream infections. Autologous HCTs are considered to be superior to allogeneic HCTs in terms of infection outcome. A previous analysis suggested that patients with allogeneic HCTs are exposed to a reduced infection hazard and that an unfavourable infection outcome of allogeneic HCTs may be mediated through prolonged neutropenia. Therefore, we investigated whether allogeneic HCTs initially lead to fewer infections. We evaluated data from a prospective non-randomized multi-centre cohort study, with a total of 1616 patients. Of these, 703 patients received autologous and 913 patients received allogeneic HCTs from January 2000 to June 2004. The retrospective analysis used simultaneous confidence bands for the cumulative infection probability in the presence of competing risks. Patients with allogeneic HCTs experienced fewer infections during the early phase of neutropenia. As patients with autologous HCTs are not necessarily subject to antibiotic prophylaxis, a future study should investigate this policy. A limitation of the analysis is that it did not find the effect of crossing cumulative infection probabilities to be significant.

Multistate modelling to estimate the excess length of stay associated with meticillin-resistant Staphylococcus aureus colonisation and infection in surgical patients.

Currently available evidence on the excess length of stay (LOS) associated with nosocomial infections is limited by methodology, including time-dependent bias. To determine the excess LOS associated with nosocomial meticillin-resistant Staphylococcus aureus (MRSA) infection and colonisation, 797 MRSA-colonised, 167 MRSA-infected and 13,640 MRSA-negative surgical patients were included in a multistate model. The occurrence of MRSA infection or colonisation was the time-dependent exposure, and discharge or death was the study endpoint. The excess LOS was extracted by computing the Aalen-Johansen estimator of the matrix of transition probabilities. Multivariate Cox regression analysis was used to assess the independent effect of MRSA on excess LOS. MRSA infection prolonged LOS by 14.5 [95% confidence interval (CI): 7.8, 21.3] days compared to uninfected patients, and by 5.9 (95% CI: 0.1, 11.7) days compared to patients only colonised by MRSA. The hazard of discharge was reduced by nosocomial MRSA infection both with respect to MRSA-free patients and MRSA carriers [adjusted hazard ratio (HR): 0.69; 95% CI: 0.59, 0.81; and HR: 0.79; 95% CI: 0.65, 0.95, respectively]. MRSA carriage alone did not decrease the hazard of discharge after adjustment for confounding (HR: 1.00; 95% CI: 0.93, 1.07). Multistate modelling is a promising statistical method to evaluate the health-economic impact of nosocomial antibiotic-resistant infections.

Estimating the impact of healthcare-associated infections on length of stay and costs.

Healthcare-associated infections (HAIs) unquestionably have substantial effects on morbidity and mortality. However, quantifying the exact economic burden attributable to HAIs still remains a challenging issue. Inaccurate estimations may arise from two major sources of bias. First, factors other than infection may affect patients' length of stay (LOS) and healthcare utilization. Second, HAI is a time-varying exposure, as the infection can impact on LOS and costs only after the infection has started. The most frequent mistake in previously published evidence is the introduction of time-dependent information as time-fixed, on the assumption that the impact of such exposure on the outcome was already present on admission. Longitudinal and multistate models avoid time-dependent bias and address the time-dependent complexity of the data. Appropriate statistical methods are important in analysis of excess costs and LOS associated with HAI, because informed decisions and policy developments may depend on them.

Efficient risk set sampling when a time-dependent exposure is present: matching for time to exposure versus exposure density sampling.

OBJECTIVES: The impact of time-dependent exposures on the time until study endpoint may correctly be analyzed with data of a full cohort. Ignoring the time-dependent nature of these exposures leads to time-dependent bias. Matching for time to exposure is often applied to take the time-dependency into account, but prefixed sets of exposed and unexposed may still create bias. This approach is attractive since a subcohort would also save resources, especially when exposure and outcome data are only available in the full cohort but further covariate information is required. The first objective is to show to which extent matching for time to exposure yields biased results. Secondly, exposure density sampling is introduced and explored. METHODS: To evaluate how both sampling methods perform, they are compared to the correct method as well as to the approach in which the time-dependent nature of the exposure is ignored. Real data of the SIR-3 study (Germany, 2000-2001) and a simulation study are used. RESULTS: Simulations show that matching may reduce the time-dependent bias but still there is a bias. The matching bias decreases if fewer patients are exposed. Exposure density sampling yields unbiased results. CONCLUSIONS: Results from studies in which matching for time to exposure was applied are only tolerable for rare exposures. Whenever subcohorting is the intention in order to save resources, exposure density sampling should be preferred instead.

Attributable mortality due to nosocomial infections. A simple and useful application of multistate models.

OBJECTIVES: Nosocomial infections constitute a major medical problem leading to increased morbidity and mortality of patients. Besides prolongation of length of hospital stay, hospital mortality attributable to those infections is often the quantity of interest when describing their impact and consequences. Since occurrence of nosocomial infections is a time-dynamic process, estimation of this quantity might be hampered by that fact. A general framework shall be developed for defining and estimating attributable mortality that in addition is taking discharge of patients as competing risk and potential censoring of observation time into account. METHODS: Since the term "attributable mortality" is used in a variety of meanings we first review basic definitions; the quantities of interest are then derived in terms of transition probabilities arising in a suitably defined multistate model that allows straightforward estimation and interpretation. Bootstrap resampling is used to calculate corresponding standard errors and confidence intervals. RESULTS: The methodology is applied to the data of the SIR-3 study, a prospective cohort study on the incidence of nosocomial infections in intensive care unit patients. Occurrence of nosocomial pneumonia is shown to be associated with increased mortality; the population-attributable fraction is estimated as 7.7% (95% confidence interval: 2.6-12.8%) for an observation period of 120 days. CONCLUSION: Attributable mortality is an important risk measure in epidemiology. If risk exposure is time dependent, multistate models provide an easily understandable framework to define and estimate attributable mortality. The approach is capable of handling competing events, which are omnipresent in clinical research and censoring.

Risk factor analysis of blood stream infection and pneumonia in neutropenic patients after peripheral blood stem-cell transplantation.

The purpose of this study was to analyse risk factors for blood stream infection (BSI) and pneumonia in neutropenic patients who have undergone peripheral blood stem-cell transplantation (PBSCT). Data were taken from the ONKO-KISS multicenter surveillance project. Infections were identified using CDC definitions (laboratory-confirmed BSI) and modified criteria for pneumonia in neutropenic patients. The multivariate analysis was performed using the Fine-Gray regression model for the cumulative incidences of the competing events 'infection', 'death' and 'end of neutropenia'. The risk factors investigated were: sex, age, underlying disease and type of transplant. From January 2000 to June 2004, a total of 1699 patients in 20 hospitals were investigated. In the multivariate analysis, male patients had a significantly higher risk of acquiring BSI than female patients (P=0.002). The risk of acquiring BSI is highest in patients with advanced acute myeloid leukaemia (AML). In the univariate and multivariate analysis, unrelated donor allogeneic transplantation constituted a risk factor for pneumonia (P=0.012). ONKO-KISS provides reference data on the incidence of pneumonia and BSI. The increased risk for BSI in males and patients with advanced AML, and the increased risk for pneumonia in unrelated donor allogeneic PBSCT patients should be targeted to prevent infections in these higher risk groups.

Are KISS data representative of German intensive care units? Statistical issues.

OBJECTIVES: Data collected within the German nosocomial infection surveillance system KISS are recommended as reference data for judging nosocomial infection rates in German intensive care units (ICUs). It is unknown whether the KISS data tend to under- or overestimate the true infection incidence rates. In this article, methodological aspects of the SIR1 study on the incidence of nosocomial infections are discussed, with the aim of estimating unbiased incidence rates of nosocomial infections in interdisciplinary German ICUs and examining whether the KISS data are representative. METHODS: We discuss the following methodological issues: 1) Sample size estimation. 2) Stratified random sampling of German ICUs. 3) Investigation of seasonal effects. 4) Statistical modeling of incidence rates using a negative binomial regression model. 5) Comparison of weighted incidence rates with the standardized rate ratio (SRR). RESULTS: Random sampling proved difficult to realize in practice since many ICUs refused to participate, particularly those in small hospitals. Analysis was adjusted for hospital size. No seasonal trends were found in the KISS data. Due to marked differences between ICUs, the number of infections is over-dispersed compared to a Poisson model, so negative binomial regression was used. Fifty ICUs were observed for two consecutive months each, corresponding to 21,832 patient days, during which 262 infections occurred. Infections were more frequent in large hospitals. The incidence rates provided by the SIR study are on average (SRR) 1.89 (1.63-2.20) times as large as those estimated by the KISS system. CONCLUSION: For estimating nosocomial infection incidence rates, random sampling and statistical modeling of over-dispersion were successfully performed. The study provides evidence that the KISS surveillance system tends to underestimate the true incidence rates of nosocomial infections in German ICUs.

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.