Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

/pdf/fitting-linear-mixed-effects-models-using-lme4-4zzrpoy9lh.pdf

Fitting Linear Mixed-Effects Models Using lme4

Meta-Analysis in Clinical Trials*

Systematic review and meta-analysis

Systematic reviews and meta-analyses are essential to summarize evidence relating to efficacy and safety of health care interventions accurately and reliably. The clarity and transparency of these reports, however, is not optimal. Poor reporting of systematic reviews diminishes their value to clinicians, policy makers, and other users.

Since the development of the QUOROM (QUality Of Reporting Of Meta-analysis) Statement—a reporting guideline published in 1999—there have been several conceptual, methodological, and practical advances regarding the conduct and reporting of systematic reviews and meta-analyses. Also, reviews of published systematic reviews have found that key information about these studies is often poorly reported. Realizing these issues, an international group that included experienced authors and methodologists developed PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analyses) as an evolution of the original QUOROM guideline for systematic reviews and meta-analyses of evaluations of health care interventions.

The PRISMA Statement consists of a 27-item checklist and a four-phase flow diagram. The checklist includes items deemed essential for transparent reporting of a systematic review. In this Explanation and Elaboration document, we explain the meaning and rationale for each checklist item. For each item, we include an example of good reporting and, where possible, references to relevant empirical studies and methodological literature. The PRISMA Statement, this document, and the associated Web site (http://www.prisma-statement.org/) should be helpful resources to improve reporting of systematic reviews and meta-analyses.

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The PRISMA Statement for Reporting Systematic Reviews and Meta-Analyses of Studies That Evaluate Health Care Interventions: Explanation and Elaboration

The extent of heterogeneity in a meta-analysis partly determines the difficulty in drawing overall conclusions. This extent may be measured by estimating a between-study variance, but interpretation is then specific to a particular treatment effect metric. A test for the existence of heterogeneity exists, but depends on the number of studies in the meta-analysis. We develop measures of the impact of heterogeneity on a meta-analysis, from mathematical criteria, that are independent of the number of studies and the treatment effect metric. We derive and propose three suitable statistics: H is the square root of the chi2 heterogeneity statistic divided by its degrees of freedom; R is the ratio of the standard error of the underlying mean from a random effects meta-analysis to the standard error of a fixed effect meta-analytic estimate, and I2 is a transformation of (H) that describes the proportion of total variation in study estimates that is due to heterogeneity. We discuss interpretation, interval estimates and other properties of these measures and examine them in five example data sets showing different amounts of heterogeneity. We conclude that H and I2, which can usually be calculated for published meta-analyses, are particularly useful summaries of the impact of heterogeneity. One or both should be presented in published meta-analyses in preference to the test for heterogeneity.

Quantifying heterogeneity in a meta‐analysis

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1977.tb01600.x

Maximum likelihood from incomplete data via the EM algorithm

Models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit. Multivariate models with general covariance structure are often difficult to apply to highly unbalanced data, whereas two-stage random-effects models can be used easily. In two-stage models, the probability distributions for the response vectors of different individuals belong to a single family, but some random-effects parameters vary across individuals, with a distribution specified at the second stage. A general family of models is discussed, which includes both growth models and repeated-measures models as special cases. A unified approach to fitting these models, based on a combination of empirical Bayes and maximum likelihood estimation of model parameters and using the EM algorithm, is discussed. Two examples are taken from a current epidemiological study of the health effects of air pollution.

Random-effects models for longitudinal data

Background As part of an interdisciplinary study of medical injury and malpractice litigation, we estimated the incidence of adverse events, defined as injuries caused by medical management, and of the subgroup of such injuries that resulted from negligent or substandard care. Methods We reviewed 30,121 randomly selected records from 51 randomly selected acute care, nonpsychiatric hospitals in New York State in 1984. We then developed population estimates of injuries and computed rates according to the age and sex of the patients as well as the specialties of the physicians. Results Adverse events occurred in 3.7 percent of the hospitalizations (95 percent confidence interval, 3.2 to 4.2), and 27.6 percent of the adverse events were due to negligence (95 percent confidence interval, 22.5 to 32.6). Although 70.5 percent of the adverse events gave rise to disability lasting less than six months, 2.6 percent caused permanently disabling injuries and 13.6 percent led to death. The percentage of adverse events...

Incidence of adverse events and negligence in hospitalized patients. Results of the Harvard Medical Practice Study I.

Background In a sample of 30,195 randomly selected hospital records, we identified 1133 patients (3.7 percent) with disabling injuries caused by medical treatment. We report here an analysis of these adverse events and their relation to error, negligence, and disability. Methods Two physician-reviewers independently identified the adverse events and evaluated them with respect to negligence, errors in management, and extent of disability. One of the authors classified each event according to type of injury. We tested the significance of differences in rates of negligence and disability among categories with at least 30 adverse events. Results Drug complications were the most common type of adverse event (19 percent), followed by wound infections (14 percent) and technical complications (13 percent). Nearly half the adverse events (48 percent) were associated with an operation. Adverse events during surgery were less likely to be caused by negligence (17 percent) than nonsurgical ones (37 percent). The proportion of adverse events due to negligence was highest for diagnostic mishaps (75 percent), noninvasive therapeutic mishaps ("errors of omission") (77 percent), and events occurring in the emergency room (70 percent). Errors in management were identified for 58 percent of the adverse events, among which nearly half were attributed to negligence. Conclusions Although the prevention of many adverse events must await improvements in medical knowledge, the high proportion that are due to management errors suggests that many others are potentially preventable now. Reducing the incidence of these events will require identifying their causes and developing methods to prevent error or reduce its effects.

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Nan M. Laird

Papers

Maximum likelihood from incomplete data via the EM algorithm

Meta-Analysis in Clinical Trials*

Random-effects models for longitudinal data

Incidence of adverse events and negligence in hospitalized patients. Results of the Harvard Medical Practice Study I.

The nature of adverse events in hospitalized patients. Results of the Harvard Medical Practice Study II