Flagging unusual clusters based on linear mixed models using weighted and self-calibrated predictors.

Statistical models incorporating cluster-specific intercepts are commonly used in hierarchical settings, for example, observations clustered within patients or patients clustered within hospitals. Predicted values of these intercepts are often used to identify or "flag" extreme or outlying clusters, such as poorly performing hospitals or patients with rapid declines in their health. We consider a variety of flagging rules, assessing different predictors, and using different accuracy measures. Using theoretical calculations and comprehensive numerical evaluation, we show that previously proposed rules based on the 2 most commonly used predictors, the usual best linear unbiased predictor and fixed effects predictor, perform extremely poorly: the incorrect flagging rates are either unacceptably high (approaching 0.5 in the limit) or overly conservative (eg, much <0.05 for reasonable parameter values, leading to very low correct flagging rates). We develop novel methods for flagging extreme clusters that can control the incorrect flagging rates, including very simple-to-use versions that we call "self-calibrated." The new methods have substantially higher correct flagging rates than previously proposed methods for flagging extreme values, while controlling the incorrect flagging rates. We illustrate their application using data on length of stay in pediatric hospitals for children admitted for asthma diagnoses.

Analysis of longitudinal data from outcome-dependent visit processes: Failure of proposed methods in realistic settings and potential improvements.

The timing and frequency of the measurement of longitudinal outcomes in databases may be associated with the value of the outcome. Such visit processes are termed outcome dependent, and previous work showed that conducting standard analyses that ignore outcome-dependent visit times can produce highly biased estimates of the associations of covariates with outcomes. The literature contains several classes of approaches to analyze longitudinal data subject to outcome-dependent visit times, and all of these are based on simplifying assumptions about the visit process. Based on extensive discussions with subject matter investigators, we identified common characteristics of outcome-dependent visit processes that allowed us to evaluate the performance of existing methods in settings with more realistic visit processes than have been previously investigated. This paper uses the analysis of data from a study of kidney function, theory, and simulation studies to examine a range of settings that vary from those where all visits have a low degree of missingness and outcome dependence (which we call "regular" visits) to those where all visits have a high degree of missingness and outcome dependence (which we call "irregular" visits). Our results show that while all the approaches we studied can yield biased estimates of some covariate effects, other covariate effects can be estimated with little bias. In particular, mixed effects models fit by maximum likelihood yielded little bias in estimates of the effects of covariates not associated with the random effects and small bias in estimates of the effects of covariates associated with the random effects. Other approaches produced estimates with greater bias. Our results also show that the presence of some regular visits in the data set protects mixed model analyses from bias but not other methods.

Non-Markov multistate modeling using time-varying covariates, with application to progression of liver fibrosis due to hepatitis C following liver transplant.

Multistate modeling methods are well-suited for analysis of some chronic diseases that move through distinct stages. The memoryless or Markov assumptions typically made, however, may be suspect for some diseases, such as hepatitis C, where there is interest in whether prognosis depends on history. This paper describes methods for multistate modeling where transition risk can depend on any property of past progression history, including time spent in the current stage and the time taken to reach the current stage. Analysis of 901 measurements of fibrosis in 401 patients following liver transplantation found decreasing risk of progression as time in the current stage increased, even when controlled for several fixed covariates. Longer time to reach the current stage did not appear associated with lower progression risk. Analysis of simulation scenarios based on the transplant study showed that greater misclassification of fibrosis produced more technical difficulties in fitting the models and poorer estimation of covariate effects than did less misclassification or error-free fibrosis measurement. The higher risk of progression when less time has been spent in the current stage could be due to varying disease activity over time, with recent progression indicating an "active" period and consequent higher risk of further progression.