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Register a new userInsight into bias in time-stratified case-crossover studies
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Xiaoming Wang
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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The use of case-crossover designs has become widespread in epidemiological and medical investigations of transient associations. However, the most popular reference-select strategy, the time-stratified schema, is not a suitable solution for controlling bias in case-crossover studies. To prove this, we conducted a time series decomposition for daily ozone (O3) records; scrutinized the ability of the time-stratified schema on controlling the yearly, monthly and weekly time trends; and found it failed on controlling the weekly time trend. Based on this finding, we proposed a new logistic regression approach in which we did adjustment for the weekly time trend. A comparison between the traditional model and the proposed method was done by simulation. An empirical study was conducted to explore potential associations between air pollutants and AMI hospitalizations. In summary, time-stratified schema provide effective control on yearly and monthly time trends but not on weekly time trend. Therefore, the estimation from the traditional logistical regression basically reveals the effect of weekly time trend, instead of the transient effect. In contrast, the proposed logistic regression with adjustment for weekly time trend can effectively eliminate system bias in case-crossover studies.
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Typically, case-control studies to estimate odds-ratios associating risk factors with disease incidence from logistic regression only include cases with newly diagnosed disease. Recently proposed methods allow incorporating information on prevalent cases, individuals who survived from disease diagnosis to sampling, into cross-sectionally sampled case-control studies under parametric assumptions for the survival time after diagnosis. Here we propose and study methods to additionally use prospectively observed survival times from prevalent and incident cases to adjust logistic models for the time between disease diagnosis and sampling, the backward time, for prevalent cases. This adjustment yields unbiased odds-ratio estimates from case-control studies that include prevalent cases. We propose a computationally simple two-step generalized method-of-moments estimation procedure. First, we estimate the survival distribution based on a semi-parametric Cox model using an expectation-maximization algorithm that yields fully efficient estimates and accommodates left truncation for the prevalent cases and right censoring. Then, we use the estimated survival distribution in an extension of the logistic model to three groups (controls, incident and prevalent cases), to accommodate the survival bias in prevalent cases. In simulations, when the amount of censoring was modest, odds-ratios from the two-step procedure were equally efficient as those estimated by jointly optimizing the logistic and survival data likelihoods under parametric assumptions. Even with 90% censoring they were as efficient as estimates obtained using only cross-sectionally available information under parametric assumptions. This indicates that utilizing prospective survival data from the cases lessens model dependency and improves precision of association estimates for case-control studies with prevalent cases.
The case-crossover design (Maclure, 1991) is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal interpretation have only been justified under informal conditions. Here, we place the design in a formal counterfactual framework for the first time. Doing so helps to clarify its assumptions and interpretation. In particular, when the treatment effect is non-null, we identify a previously unnoticed bias arising from common causes of the outcome at different person-times. We analytically characterize the direction and size of this bias and demonstrate its potential importance with a simulation. We also use our derivation of the limit of the case-crossover estimator to analyze its sensitivity to treatment effect heterogeneity, a violation of one of the informal criteria for validity. The upshot of this work for practitioners is that, while the case-crossover design can be useful for testing the causal null hypothesis in the presence of baseline confounders, extra caution is warranted when using the case-crossover design for point estimation of causal effects.
Panel studies typically suffer from attrition, which reduces sample size and can result in biased inferences. It is impossible to know whether or not the attrition causes bias from the observed panel data alone. Refreshment samples - new, randomly sampled respondents given the questionnaire at the same time as a subsequent wave of the panel - offer information that can be used to diagnose and adjust for bias due to attrition. We review and bolster the case for the use of refreshment samples in panel studies. We include examples of both a fully Bayesian approach for analyzing the concatenated panel and refreshment data, and a multiple imputation approach for analyzing only the original panel. For the latter, we document a positive bias in the usual multiple imputation variance estimator. We present models appropriate for three waves and two refreshment samples, including nonterminal attrition. We illustrate the three-wave analysis using the 2007-2008 Associated Press-Yahoo! News Election Poll.
Can two separate case-control studies, one about Hepatitis disease and the other about Fibrosis, for example, be combined together? It would be hugely beneficial if two or more separately conducted case-control studies, even for entirely irrelevant purposes, can be merged together with a unified analysis that produces better statistical properties, e.g., more accurate estimation of parameters. In this paper, we show that, when using the popular logistic regression model, the combined/integrative analysis produces a more accurate estimation of the slope parameters than the single case-control study. It is known that, in a single logistic case-control study, the intercept is not identifiable, contrary to prospective studies. In combined case-control studies, however, the intercepts are proved to be identifiable under mild conditions. The resulting maximum likelihood estimates of the intercepts and slopes are proved to be consistent and asymptotically normal, with asymptotic variances achieving the semiparametric efficiency lower bound.
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