Simple Random Effects Research Articles

Surrogate endpoint metaregression: useful statistics for regulators and trialists

ObjectivesThe main purpose of using a surrogate endpoint is to estimate the treatment effect on the true endpoint sooner than with a true endpoint. Based on a metaregression of historical randomized trials with surrogate and true endpoints, we discuss statistics for applying and evaluating surrogate endpoints. MethodsWe computed statistics from 2 types of linear metaregressions for trial-level data: simple random effects and novel random effects with correlations among estimated treatment effects in trials with more than 2 arms. A key statistic is the estimated intercept of the metaregression line. An intercept that is small or not statistically significant increases confidence when extrapolating to a new treatment because of consistency with a single causal pathway and invariance to labeling of treatments as controls. For a regulator applying the metaregression to a new treatment, a useful statistic is the 95% prediction interval. For a clinical trialist planning a trial of a new treatment, useful statistics are the surrogate threshold effect proportion, the sample size multiplier adjusted for dropouts, and the novel true endpoint advantage. ResultsWe illustrate these statistics with surrogate endpoint metaregressions involving antihypertension treatment, breast cancer screening, and colorectal cancer treatment. ConclusionRegulators and trialists should consider using these statistics when applying and evaluating surrogate endpoints.

Likelihood function derivatives for a linear mixed model with compound symmetry assumption

The paper explores the properties of linear mixed models with simple random effects of the form: yi = Xiβ + ZiYi + εi, i = 1, . . . ,M, Yi ∼ N(0, Ψ), εi ∼ Т(0, σ2I), where M is the number of distinct groups, each consisting of ni observations. Random effects Yi and within-group errors εi are independent across different groups and within the same group. β is a p-dimensional vector of fixed effects, Yi is a q-dimensional vector of random effects, and Xi and Zi are known design matrices of dimensions nixp and nixq, of fixed and random effects respectively. Vectors εi represent within-group errors with a spherically Gaussian distribution.Assuming a compound symmetry in the correlation structure of the matrix Ψ governing the dependence among within-group errors, analytical formulas for the first two partial derivatives of the profile restricted maximum likelihood function with respect to the correlation parameters of the model are derived. The analytical representation of derivatives facilitates the effective utilization of numerical algorithms like Newton-Raphson or Levenberg-Marquardt.The restricted maximum likelihood (REML) estimation is a statistical technique employed to estimate the parameters within a mixed-effects model, particularly in the realm of linear mixed models. It serves as an extension of the maximum likelihood estimation method, aiming to furnish unbiased and efficient parameter estimates, especially in scenarios involving correlated data. Within the framework of the REML approach, the likelihood function undergoes adjustments to remove the nuisance parameters linked to fixed effects. This modification contributes to enhancing the efficiency of parameter estimation, particularly in situations where the primary focus is on estimating variance components or when the model encompasses both fixed and random effects.

The Prevalence of Thyroid Cancer in Iran: a Systematic Review and Meta-analysis.

Cancer is the most common malignant tumor of the endocrine glands and comprises 1% of all malignant cancers and its incidence is still increasing. No comprehensive study summarizing the results of these studies was found. Therefore, this study aimed to determine the prevalence of thyroid cancer in Iran in a systematic review and meta-analysis. In this review, studies were extracted by searching the national and international databases of SID, MagIran, IranMedex, IranDoc, and Google Scholar, Cochrane, Embase, ScienceDirect, Scopus, PubMed, and Web of Science (WoS) from 1997 to September 2019. Simple random effects model was used for data analysis and heterogeneity of studies was investigated with I 2 index. Data were analyzed using Comprehensive Meta-Analysis (version 2) software. In 28 reviewed articles, the prevalence of thyroid cancer in Iran was reported to be 3.5% with a sample size of 100,869 (95% CI: 2.7-4.4%). Regarding heterogeneity on the basis of meta-regression, there was no significant difference between the effect of the year of study (P = 0.531) and sample size (P = 0.864) and the prevalence of thyroid cancer in Iran. The results of this study indicated that the prevalence of thyroid cancer is high in Iran. Therefore, appropriate strategies should be put in place by providing feedback to hospitals in order to improve the aforementioned situation, and troubleshoot and monitor at all levels.

Power and sample size calculation for stepped-wedge designs with discrete outcomes

BackgroundStepped-wedge designs (SWD) are increasingly used to evaluate the impact of changes to the process of care within health care systems. However, to generate definitive evidence, a correct sample size calculation is crucial to ensure such studies are properly powered. The seminal work of Hussey and Hughes (Contemp Clin Trials 28(2):182–91, 2004) provides an analytical formula for power calculations with normal outcomes using a linear model and simple random effects. However, minimal development and evaluation have been done for power calculation with non-normal outcomes on their natural scale (e.g., logit, log). For example, binary endpoints are common, and logistic regression is the natural multilevel model for such clustered data.MethodsWe propose a power calculation formula for SWD with either normal or non-normal outcomes in the context of generalized linear mixed models by adopting the Laplace approximation detailed in Breslow and Clayton (J Am Stat Assoc 88(421):9–25, 1993) to obtain the covariance matrix of the estimated parameters.ResultsWe compare the performance of our proposed method with simulation-based sample size calculation and demonstrate its use on a study of patient-delivered partner therapy for STI treatment and a study that assesses the impact of providing additional benchmark prevalence information in a radiologic imaging report. To facilitate adoption of our methods we also provide a function embedded in the R package “swCRTdesign” for sample size and power calculation for multilevel stepped-wedge designs.ConclusionsOur method requires minimal computational power. Therefore, the proposed procedure facilitates rapid dynamic updates of sample size calculations and can be used to explore a wide range of design options or assumptions.

Assessment of treatment outcomes for facial prostheses in patients with craniofacial defects: A pilot retrospective study

Statement of problemThe longevity of silicone facial prostheses is short, and published data concerning this type of rehabilitation are limited. PurposeThe purpose of this retrospective study was to identify predictive variables for prosthetic failure and to highlight the results that can be expected after treatment with silicone facial prostheses. Material and methodsAfter institutional approval, patient records from a single Brazilian institution for the time period 2004 to 2015 were assessed. A standardized form was used to collect patient data. Frailty survival modeling (simple random effects survival model) was used to test whether age, sex, type of prosthesis, source of defect, number of implants, and type of retention have a direct impact on the prosthetic failure rate (α=.05). ResultsAuricular prostheses were the most frequently fabricated prostheses. Eighty-four prostheses were fabricated during the follow-up period. The overall survival rate for facial prostheses was 34.5%. Color alteration was the most common reason for new prostheses (27.38%). The implant success rate was 98.18%. The number of implants approached statistical significance (P=.06) with a reduced risk of failure when the patient had 2 implants compared with patients with zero implants and patients with more than 2 implants. ConclusionsPatients should be recalled frequently so that retouches can be performed, avoiding the repeated fabrication of new prostheses. Well-designed studies are necessary to identify more relevant complications and factors that lead to prosthetic failure.

From Randomized Controlled Trials of Antidepressant Drugs to the Meta-Analytic Synthesis of Evidence: Methodological Aspects Lead to Discrepant Findings.

During the last decade, several meta-analytic studies employing different methodological approaches have had inconsistent conclusions regarding antidepressant efficacy. Herein, we aim to comment on methodological aspects that may have contributed to disparate findings. We initially discuss methodological inconsistencies and limitations related to the conduct of individual antidepressant randomized controlled trials (RCTs), including differences in allocated samples, limitations of psychometric scales, possible explanations for the heightened placebo response rates in antidepressant RCTs across the past two decades as well as the reporting of conflicts of interest. In the second part of this article, we briefly describe the various meta-analyses techniques (e.g., simple random effects meta-analysis and network meta-analysis) and the application of these methods to synthesize evidence related to antidepressant efficacy. Recently published antidepressant metaanalyses often provide discrepant results and similar results often lead to different interpretations. Finally, we propose strategies to improve methodology considering real-world clinical scenarios.

Analysis and reporting of stepped wedge randomised controlled trials: synthesis and critical appraisal of published studies, 2010 to 2014.

BackgroundStepped wedge cluster randomised trials introduce interventions to groups of clusters in a random order and have been used to evaluate interventions for health and wellbeing. Standardised guidance for reporting stepped wedge trials is currently absent, and a range of potential analytic approaches have been described.MethodsWe systematically identified and reviewed recently published (2010 to 2014) analyses of stepped wedge trials. We extracted data and described the range of reporting and analysis approaches taken across all studies. We critically appraised the strategy described by three trials chosen to reflect a range of design characteristics.ResultsTen reports of completed analyses were identified. Reporting varied: seven of the studies included a CONSORT diagram, and only five also included a diagram of the intervention rollout. Seven assessed the balance achieved by randomisation, and there was considerable heterogeneity among the approaches used. Only six reported the trend in the outcome over time. All used both ‘horizontal’ and ‘vertical’ information to estimate the intervention effect: eight adjusted for time with a fixed effect, one used time as a condition using a Cox proportional hazards model, and one did not account for time trends. The majority used simple random effects to account for clustering and repeat measures, assuming a common intervention effect across clusters. Outcome data from before and after the rollout period were often included in the primary analysis. Potential lags in the outcome response to the intervention were rarely investigated. We use three case studies to illustrate different approaches to analysis and reporting.ConclusionsThere is considerable heterogeneity in the reporting of stepped wedge cluster randomised trials. Correct specification of the time-trend underlies the validity of the analytical approaches. The possibility that intervention effects vary by cluster or over time should be considered. Further work should be done to standardise the reporting of the design, attrition, balance, and time-trends in stepped wedge trials.

SSN: AnRPackage for Spatial Statistical Modeling on Stream Networks

The SSN package for R provides a set of functions for modeling stream network data. The package can import geographic information systems data or simulate new data as a ‘SpatialStreamNetwork’, a new object class that builds on the spatial sp classes. Functions are provided that fit spatial linear models (SLMs) for the ‘SpatialStreamNetwork’ object. The covariance matrix of the SLMs use distance metrics and geostatistical models that are unique to stream networks; these models account for the distances and topological configuration of stream networks, including the volume and direction of flowing water. In addition, traditional models that use Euclidean distance and simple random effects are included, along with Poisson and binomial families, for a generalized linear mixed model framework. Plotting and diagnostic functions are provided. Prediction (kriging) can be performed for missing data or for a separate set of unobserved locations, or block prediction (block kriging) can be used over sets of stream segments. This article summarizes the SSN package for importing, simulating, and modeling of stream network data, including diagnostics and prediction.

A Generalized Spatial Panel Data Model with Random Effects

This paper proposes a generalized panel data model with random effects and first-order spatially autocorrelated residuals that encompasses two previously suggested specifications. The first one is described in Anselin's (1988) book and the second one by Kapoor et al. (2007). Our encompassing specification allows us to test for these models as restricted specifications. In particular, we derive three Lagrange multiplier (LM) and likelihood ration (LR) tests that restrict our generalized model to obtain (i) the Anselin model, (ii) the Kapoor, Kelejian, and Prucha model, and (iii) the simple random effects model that ignores the spatial correlation in the residuals. For two of these three tests, we obtain closed form solutions and we derive their large sample distributions. Our Monte Carlo results show that the suggested tests are powerful in testing for these restricted specifications even in small and medium sized samples.

Estimating common mean and heterogeneity variance in two study case meta-analysis

The relative behavior of estimators of the common mean and of the heterogeneity variance in the simple random effects model of meta-analysis is explored. A new risk function relating these estimation problems is introduced. Bayes estimators for each of the parameters are derived.

Accounting for regression‐to‐the‐mean in tests for recent changes in institutional performance: Analysis and power

Recent changes in individual units are often of interest when monitoring and assessing the performance of healthcare providers. We consider three high profile examples: (a) annual teenage pregnancy rates in English local authorities, (b) quarterly rates of the hospital-acquired infection Clostridium difficile in National Health Service (NHS) Trusts and (c) annual mortality rates following heart surgery in New York State hospitals. Increasingly, government targets call for continual improvements, in each individual provider as well as overall.Owing to the well-known statistical phenomenon of regression-to-the-mean, observed changes between just two measurements are potentially misleading. This problem has received much attention in other areas, but there is a need for guidelines within performance monitoring.In this paper we show theoretically and with worked examples that a simple random effects predictive distribution can be used to 'correct' for the potentially undesirable consequences of regression-to-the-mean on a test for individual change. We discuss connections to the literature in other fields, and build upon this, in particular by examining the effect of the correction on the power to detect genuine changes. It is demonstrated that a gain in average power can be expected, but that this gain is only very slight if the providers are very different from one another, for example due to poor risk adjustment. Further, the power of the corrected test depends on the provider's baseline rate and, although large gains can be expected for some providers, this is at the cost of some power to detect real changes in others.

A Generalized Spatial Panel Data Model with Random Effects

This paper proposes a generalized panel data model with random effects and first-order spatially autocorrelated residuals that encompasses two previously suggested specifications. The first one is described in Anselin's (1988) book and the second one by Kapoor, Kelejian, and Prucha (2007). Our encompassing specification allows us to test for these models as restricted specifications. In particular, we derive three LM and LR tests that restrict our generalized model to obtain (i) the Anselin model, (ii) the Kapoor, Kelejian, and Prucha model, and (iii) the simple random effects model that ignores the spatial correlation in the residuals. For two of these three tests, we obtain closed form solutions and we derive their large sample distributions. Our Monte Carlo results show that the suggested tests are powerful in testing for these restricted specifications even in small and medium sized samples.

Estimation in a simple random effects model with nonnormal distributions

SUMMARY A simple structural model is considered involving the addition of two random variables representing between- and within-group variation. Methods for estimating the cumulants of the two components of variation are proposed, based on homogeneous polynomials in the data. Emphasis is placed on situations in which the number of observations per group is quite small. In some cases an essentially unique estimator is available, whereas in others there is a family of possible consistent estimators. The choice of the polynomial is considered.

Evaluation of some random effects methodology applicable to bird ringing data

Existing models for ring recovery and recapture data analysis treat temporal variations in annual survival probability (S) as fixed effects. Often there is no explainable structure to the temporal variation in S 1 , … , S k ; random effects can then be a useful model: Si = E(S) + k i . Here, the temporal variation in survival probability is treated as random with average value E( k 2 ) = σ 2 . This random effects model can now be fit in program MARK. Resultant inferences include point and interval estimation for process variation, σ 2 , estimation of E(S) and var(Ê(S)) where the latter includes a component for σ 2 as well as the traditional component for v ar(S|S). Furthermore, the random effects model leads to shrinkage estimates, S i , as improved (in mean square error) estimators of Si compared to the MLE, S i , from the unrestricted time-effects model. Appropriate confidence intervals based on the S i are also provided. In addition, AIC has been generalized to random effects models. This paper presents results of a Monte Carlo evaluation of inference performance under the simple random effects model. Examined by simulation, under the simple one group Cormack-Jolly-Seber (CJS) model, are issues such as bias of σ 2 , confidence interval coverage on σ 2 , coverage and mean square error comparisons for inference about Si based on shrinkage versus maximum likelihood estimators, and performance of AIC model selection over three models: S i = S (no effects), Si = E(S) + k i (random effects), and S 1 , … , S k (fixed effects). For the cases simulated, the random effects methods performed well and were uniformly better than fixed effects MLE for the S i .

Spectral Analysis of Replicated Biomedical Time Series

SUMMARY Standard methods of spectral analysis are adapted to the interpretation of biomedical time series data with replication across subjects. The methodology is applied to two sets of data consisting of concentrations of luteinizing hormone in serial blood samples. For such data, the between-subject variability in periodogram ordinates at a given frequency is typically larger than would be implied by the usual asymptotic distribution theory for single series. We interpret this to mean that the underlying spectrum of the stochastic process representing the time variation in hormone concentration varies randomly between subjects. We describe simple random effects models to account for this extra variability and develop likelihood-based methods of inference, using a Monte Carlo integration method to evaluate the likelihood function. For our first data set, which comprises hormone concentrations in blood samples taken from eight subjects at 1 min intervals for 1 h, our model captures the qualitative behaviour of the between-subject variation in the spectrum. We conclude that there is a genuine high frequency component of variation in hormone concentrations and that the amplitude and frequency of this high frequency component vary between subjects. Our second data set relates to a similar sampling protocol, except that each subject is sampled before and after hormone replacement therapy. We conclude that this intervention has a significant effect on the spectrum.

A Computationally Practical Simulation Estimator for Panel Data

In this paper I develop a practical extension of McFadden's method of simulated moments estimator for limited dependent variable models to the panel data case. The method is based on a factorization of the MSM first order condition into transition probabilities, along with the development of a new highly accurate method for similating these transition probabilities. A series of Monte-Carlo tests show that this MSM estimator performs quite well relative to quadrature-based ML estimators, even when large numbers of quadrature points are employed. The estimator also performs well relative to simulated ML, even when a highly accurate method is used to simulate the choice probabilities. In terms of computational speed, complex panel data models involving random effects and ARMA errors may be estimated via MSM in times similar to those necessary for estimation of simple random effects models via ML-quadrature.

Tracking of markers and onset of disease among HIV-1 seroconverters.

Repeated measurements on persons infected with HIV-1 indicate that infection has a dynamic impact on several markers of immune suppression and activation. The objectives of this report are: (a) to provide a statistical model for the correlation structure of serial measurements of immunological markers, and (b) to identify features of marker profiles associated with the timing of AIDS diagnoses. We analyse data obtained from 328 seroconverters participating in the Multicenter AIDS Cohort Study on whom the date of HIV-1 seroconversion is known within +/- 4.5 months. Immunological markers considered here are CD4 cell counts, serum beta 2-microglobulin and serum neopterin. The statistical model for HIV-related changes in markers consists of (1) a piecewise linear regression model for the trajectories of markers over time and (2) a two-parameter autocorrelation function that generalizes Markovian and simple random effects autocorrelation structures. Application of this model for marker measurements revealed a high degree of tracking, as the estimated autocorrelation function exhibited sub-exponential decay over time. Though current marker levels are most informative on future values, there is substantial information (memory) in previous measurements. A feature suggested by the analysis of groups formed according to the length of the AIDS-free period, is the sequential divergence of the CD4 trajectories where steeper declines occurred with a two-year lag prior to AIDS onset. For AIDS cases diagnosed 3-5 and 5-7 years after seroconversion, the rates of decline compared with those free of AIDS for at least 4 years were steeper by 95 and 46 per cent respectively at two years prior to AIDS.

Censored observations, repeated measures and mixed effects models: An approach using the EM algorithm and normal errors

SUMMARY Maximum likelihood estimation of a vector regression parameter and variance com- ponents is considered for the mixed effects model when observations are right censored. A general scheme of estimation is given using the EM algorithm and detailed results found for the model with between and within block variation. This model is applied to the logarithms of survival times from a repeated measures design. In this paper we consider the estimation of the parameters when some of the observa- tions are right-censored. This can occur with repeated measurements on subjects where the response is a waiting time and the variability in log times is modelled by a normal distribution. Alternative models for this situation are given by Clayton & Cuzick (1985) and their methods involve partially parametric techniques using ranks and are based on models involving extreme value, log gamma and logistic distributions. We are concerned with use of the EM algorithm (Dempster, Laird & Rubin, 1977) to estimate the parameters of the mixed model. For uncensored data, Hartley & Rao (1967) have considered this solution. The analysis leads to a method which is straightforward to implement for the repeated measures model. Dempster et al. (1984) give an account of the method with uncensored observations. In ? 2 we consider a general implementation of the EM algorithm for the pure random effects model with censored data and then, in ? 3, we give explicit results for the simple random effects model. Section 4 uses these results for the analysis of repeated measures and ? 5 discusses some miscellaneous points arising. Finally, in ? 6, we give an example involving skin graft data, where there has been extensive analysis using matched pairs techniques.