Inverse Probability Weighting Enhances Absolute Risk Estimation in Three Common Study Designs of Nosocomial Infections

Purpose

When studying nosocomial infections, resource-efficient sampling designs such as nested case-control, case-cohort, and point prevalence studies are preferred. However, standard analyses of these study designs can introduce selection bias, especially when interested in absolute rates and risks. Moreover, nosocomial infection studies are often subject to competing risks. We aim to demonstrate in this tutorial how to address these challenges for all three study designs using simple weighting techniques.

Patients and Methods

We discuss the study designs and explain how inverse probability weights (IPW) are applied to obtain unbiased hazard ratios (HR), odds ratios and cumulative incidences. We illustrate these methods in a multi-state framework using a dataset from a nosocomial infections study (n = 2286) in Moscow, Russia.

Results

Including IPW in the analysis corrects the unweighted naïve analyses and enables the estimation of absolute risks. Resulting estimates are close to the full cohort estimates using substantially smaller numbers of patients.

Conclusion

IPW is a powerful tool to account for the unequal selection of controls in case-cohort, nested case-control and point prevalence studies. Findings can be generalized to the full population and absolute risks can be estimated. When applied to a multi-state model, competing risks are also taken into account.

Nonparametric estimation of transition probabilities for a general progressive multi-state model under cross-sectional sampling

Nonparametric estimation of the transition probability matrix of a progressive multi-state model is considered under cross-sectional sampling. Two different estimators adapted to possibly right-censored and left-truncated data are proposed. The estimators require full retrospective information before the truncation time, which, when exploited, increases efficiency. They are obtained as differences between two survival functions constructed for sub-samples of subjects occupying specific states at a certain time point. Both estimators correct the oversampling of relatively large survival times by using the left-truncation times associated with the cross-sectional observation. Asymptotic results are established, and finite sample performance is investigated through simulations. One of the proposed estimators performs better when there is no censoring, while the second one is strongly recommended with censored data. The new estimators are applied to data on patients in intensive care units (ICUs).

Nonparametric estimation in the illness-death model using prevalent data

We study nonparametric estimation of the illness-death model using left-truncated and right-censored data. The general aim is to estimate the multivariate distribution of a progressive multi-state process. Maximum likelihood estimation under censoring suffers from problems of uniqueness and consistency, so instead we review and extend methods that are based on inverse probability weighting. For univariate left-truncated and right-censored data, nonparametric maximum likelihood estimation can be considerably improved when exploiting knowledge on the truncation distribution. We aim to examine the gain in using such knowledge for inverse probability weighting estimators in the illness-death framework. Additionally, we compare the weights that use truncation variables with the weights that integrate them out, showing, by simulation, that the latter performs more stably and efficiently. We apply the methods to intensive care units data collected in a cross-sectional design, and discuss how the estimators can be easily modified to more general multi-state models.

Comparing estimation approaches for the illness-death model under left truncation and right censoring

Left-truncated data arise when lifetimes are observed only if they are larger than independent truncation times. For example, in a cross-sectional sampling, only individuals who live long enough to be present on the sampling day are observed. There are several ways to perform statistical inference under this setting. One can do the following: (i) use an unconditional approach, (ii) condition on the value of the truncation variable, or (iii) condition on all the history up to the time of truncation. The latter two approaches are equivalent when analyzing univariate survival outcomes but differ under the multi-state framework. In this paper, we consider the illness-death model and compare between the three estimation approaches in a parametric regression framework. We show that approach (ii) is more efficient than the standard approach (iii), although it requires more computational effort. Approach (i) is the most efficient approach, but it requires knowledge on the distribution of the truncation variable and hence is less robust. The methods are compared using a theoretical example and simulations and are applied to intensive care units data collected in a cross-sectional design, where the illness state corresponds to a bloodstream infection.

Semiparametric modeling of grouped current duration data with preferential reporting

Current duration data arise in cross-sectional studies from questions on the length of time from an initiating event to the time of interview. For example, in the National Survey on Family Growth, women who were considered at risk for pregnancy were asked (i) 'Are you currently attempting pregnancy?' and (ii) 'If yes, how many months have you been attempting to get pregnant?' The responses to (ii), referred to as the current durations, are length-biased because women with longer durations are more likely to answer yes to question (i) and therefore be included in the sample. Previous methods to analyze such data include continuous time nonparametric and parametric approaches. In this article, we propose a semiparametric Cox model and a piecewise constant baseline model (used to account for digit preference) to analyze grouped current duration data. We discuss and investigate through simulation studies, the robustness properties of the proposed methods when digit preference is present. Lastly, we present an analysis of the current duration data resulting from the 2002 National Survey on Family Growth. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Bayesian gamma frailty models for survival data with semi-competing risks and treatment switching

Motivated from a colorectal cancer study, we propose a class of frailty semi-competing risks survival models to account for the dependence between disease progression time, survival time, and treatment switching. Properties of the proposed models are examined and an efficient Gibbs sampling algorithm using the collapsed Gibbs technique is developed. A Bayesian procedure for assessing the treatment effect is also proposed. The deviance information criterion (DIC) with an appropriate deviance function and Logarithm of the pseudomarginal likelihood (LPML) are constructed for model comparison. A simulation study is conducted to examine the empirical performance of DIC and LPML and as well as the posterior estimates. The proposed method is further applied to analyze data from a colorectal cancer study.

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.