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Register a new userHandling Attrition in Longitudinal Studies: The Case for Refreshment Samples
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Added by
Yiting Deng
Publication date
2013
fields
Mathematical Statistics
and research's language is
English
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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.
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Many panel studies collect refreshment samples---new, randomly sampled respondents who complete the questionnaire at the same time as a subsequent wave of the panel. With appropriate modeling, these samples can be leveraged to correct inferences for biases caused by non-ignorable attrition. We present such a model when the panel includes many categorical survey variables. The model relies on a Bayesian latent pattern mixture model, in which an indicator for attrition and the survey variables are modeled jointly via a latent class model. We allow the multinomial probabilities within classes to depend on the attrition indicator, which offers additional flexibility over standard applications of latent class models. We present results of simulation studies that illustrate the benefits of this flexibility. We apply the model to correct attrition bias in an analysis of data from the 2007-2008 Associated Press/Yahoo News election panel study.
A standard assumption for causal inference about the joint effects of time-varying treatment is that one has measured sufficient covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values, also known as sequential randomization assumption (SRA). SRA is often criticized as it requires one to accurately measure all confounders. Realistically, measured covariates can rarely capture all confounders with certainty. Often covariate measurements are at best proxies of confounders, thus invalidating inferences under SRA. In this paper, we extend the proximal causal inference (PCI) framework of Miao et al. (2018) to the longitudinal setting under a semiparametric marginal structural mean model (MSMM). PCI offers an opportunity to learn about joint causal effects in settings where SRA based on measured time-varying covariates fails, by formally accounting for the covariate measurements as imperfect proxies of underlying confounding mechanisms. We establish nonparametric identification with a pair of time-varying proxies and provide a corresponding characterization of regular and asymptotically linear estimators of the parameter indexing the MSMM, including a rich class of doubly robust estimators, and establish the corresponding semiparametric efficiency bound for the MSMM. Extensive simulation studies and a data application illustrate the finite sample behavior of proposed methods.
Causal effect sizes may vary among individuals and they can even be of opposite directions. When there exists serious effect heterogeneity, the population average causal effect (ACE) is not very informative. It is well-known that individual causal effects (ICEs) cannot be determined in cross-sectional studies, but we will show that ICEs can be retrieved from longitudinal data under certain conditions. We will present a general framework for individual causality where we will view effect heterogeneity as an individual-specific effect modification that can be parameterized with a latent variable, the receptiveness factor. The distribution of the receptiveness factor can be retrieved, and it will enable us to study the contrast of the potential outcomes of an individual under stationarity assumptions. Within the framework, we will study the joint distribution of the individuals potential outcomes conditioned on all individuals factual data and subsequently the distribution of the cross-world causal effect (CWCE). We discuss conditions such that the latter converges to a degenerated distribution, in which case the ICE can be estimated consistently. To demonstrate the use of this general framework, we present examples in which the outcome process can be parameterized as a (generalized) linear mixed model.
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.
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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