Residual Analysis for Linear Mixed Models

Regression tree-based diagnostics for linear multilevel models

Longitudinal and clustered data, where multiple observations for individuals are observed, require special models that reflect their hierarchical structure. The most commonly used such model is the linear multilevel model, which combines a linear model for the population-level fixed effects, a linear model for normally distributed individual-level random effects and normally distributed observation-level errors with constant variance. It has the advantage of simplicity of interpretation, but if the assumptions of the model do not hold inferences drawn can be misleading. In this paper, we discuss the use of regression trees that are designed for multilevel data to construct goodness-of-fit tests for this model that can be used to test for nonlinearity of the fixed effects or heteroscedasticity of the errors. Simulations show that the resultant tests are slightly conservative as 0.05 level tests, and have good power to identify explainable model violations (that is, ones that are related to available covariate information in the data). Application of the tests is illustrated on two real datasets.

Mechanistic analysis of challenge-response experiments

We present an application of mechanistic modeling and nonlinear longitudinal regression in the context of biomedical response-to-challenge experiments, a field where these methods are underutilized. In this type of experiment, a system is studied by imposing an experimental challenge, and then observing its response. The combination of mechanistic modeling and nonlinear longitudinal regression has brought new insight, and revealed an unexpected opportunity for optimal design. Specifically, the mechanistic aspect of our approach enables the optimal design of experimental challenge characteristics (e.g., intensity, duration). This article lays some groundwork for this approach. We consider a series of experiments wherein an isolated rabbit heart is challenged with intermittent anoxia. The heart responds to the challenge onset, and recovers when the challenge ends. The mean response is modeled by a system of differential equations that describe a candidate mechanism for cardiac response to anoxia challenge. The cardiac system behaves more variably when challenged than when at rest. Hence, observations arising from this experiment exhibit complex heteroscedasticity and sharp changes in central tendency. We present evidence that an asymptotic statistical inference strategy may fail to adequately account for statistical uncertainty. Two alternative methods are critiqued qualitatively (i.e., for utility in the current context), and quantitatively using an innovative Monte-Carlo method. We conclude with a discussion of the exciting opportunities in optimal design of response-to-challenge experiments.

Factors influencing aster leafhopper (Hemiptera: Cicadellidae) abundance and aster yellows phytoplasma infectivity in Wisconsin carrot fields

In Wisconsin, vegetable crops are threatened annually by infection of the aster yellows phytoplasma (AYp), the causal agent of aster yellows (AY) disease, vectored by the aster leafhopper, Macrosteles quadrilineatus Forbes. Aster leafhopper abundance and infectivity are influenced by processes operating across different temporal and spatial scales. We applied a multilevel modeling approach to partition variance in multifield, multiyear, pest scouting data sets containing temporal and spatial covariates associated with aster leafhopper abundance and infectivity. Our intent was to evaluate the relative importance of temporal and spatial covariates to infer the relevant scale at which ecological processes are driving AY epidemics and identify periods of elevated risk for AYp spread. The relative amount of aster leafhopper variability among and within years (39%) exceeded estimates of variation among farm locations and fields (7%). Similarly, time covariates explained the largest amount of variation of aster leafhopper infectivity (50%). Leafhopper abundance has been decreasing since 2001 and reached its minimum in 2010. The average seasonal pattern indicated that periods of above average abundance occurred between 11 June and 1 August. Annual infectivity appears to oscillate around an average value of 2% and seasonal periods of above average infectivity occur between 19 May and 15 July. The coincidence of the expected periods of high leafhopper abundance and infectivity increases our knowledge of when the insect moves into susceptible crop fields and when it spreads the pathogen to susceptible crops, representing a seasonal interval during which management of the insect can be focused.

Does pharmacological conditioning with the volatile anaesthetic sevoflurane offer protection in liver surgery?

BACKGROUND

A recently published randomized control trial (RCT) showed a protection of the remnant liver from ischemia-reperfusion (I/R) injury by pharmacological pre-conditioning with a volatile anaesthetic in patients undergoing hepatic resection. Whether the continuous application of volatile anaesthetics (pharmacological conditioning) also protects against I/R injury is unknown.

METHODS

Consecutive patients undergoing liver resection with inflow occlusion from 2005-2007 were included in the trial. Two groups of anaesthesia regimens with either continuous application of the volatile anaesthetic sevoflurane (pharmacological conditioning) or continuous infusion of the intravenous (i.v.) anaesthetic propofol (control group) were compared. Endpoints were serum-peak-aspartate aminotransferase (AST)/ alanine aminotranferease (ALT) levels, length of stay (LOS) and intensive care unit (ICU) stays, and the occurrence of post-operative complications.

RESULTS

Two hundred and twenty-seven patients were included. Pharmacological conditioning did not protect the remnant liver from IR injury (adjusted difference for peak-AST:61.9 U/l, 95% confidence interval (CI): -151.7-275.4 U/l, P = 0.568; peak-ALT:136.1 U/l, 95% CI: -113.7-385.9 U/l, P = 0.284) nor reduce LOS (adjusted difference 0.9 days, 95% CI: -2.6-4.3 days, P = 0.622) or ICU stay (1.6 days, 95% CI: -0.2-3.3 days, P = 0.079), and was not associated with reduced complication rates (adjusted OR 1.12, 95% CI:0.6-2.3, P = 0.761) compared with the control group.

CONCLUSION

In this retrospective study, continuous volatile anaesthesia in liver resection does not provide protection of the remnant liver from IR injury compared with continuous i.v. anaesthesia.

On the impact of parametric assumptions and robust alternatives for longitudinal data analysis

Models for longitudinal data are employed in a wide range of behavioral, biomedical, psychosocial, and health-care-related research. One popular model for continuous response is the linear mixed-effects model (LMM). Although simulations by recent studies show that LMM provides reliable estimates under departures from the normality assumption for complete data, the invariable occurrence of missing data in practical studies renders such robustness results less useful when applied to real study data. In this paper, we show by simulated studies that in the presence of missing data estimates of the fixed effect of LMM are biased under departures from normality. We discuss two robust alternatives, the weighted generalized estimating equations (WGEE) and the augmented WGEE (AWGEE), and compare their performances with LMM using real as well as simulated data. Our simulation results show that both WGEE and AWGEE provide valid inference for skewed non-normal data when missing data follows the missing at random, the most popular missing data mechanism for real study data.