A modification of the Hartung-Knapp confidence interval on the variance component in two-variance-component models

summary:We consider a construction of approximate confidence intervals on the variance component $\sigma ^2_1$ in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large $\sigma ^2_1/\sigma ^2,$ was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when $\sigma ^2_1/\sigma ^2\rightarrow \infty$ suggests a modification of this interval that preserves some nice properties of the original and that is, in addition, exact when $\sigma ^2_1/\sigma ^2\rightarrow \infty .$ It turns out that this modification is an interval suggested by El-Bassiouni in [eb]. We comment on its properties that were not emphasized in the original paper [eb], but which support use of the procedure. Also a small simulation study is provided

Extensions and applications of generalized linear mixed models for network meta-analysis of randomized controlled trials

Network meta-analyses of published clinical trials has received increased attention over the past years with some meta-analytic publications having had a big impact on the cost-benefit assessment of important drugs. Much of the research has been based on Bayesian analysis using so called base-line contrast model. The research in network meta-analysis methodology has in parts been isolated from other fields of mathematical statistics and is lacking an integrative framework clearly separating statistical models and assumptions, inferential principles, and computational algorithms. The very extensive past research on ANOVA and MANOVA of un- balanced designs, variance component models, generalised linear models with fixed and/or random effects, provides a wealth of useful approaches and insights. These models are especially common in agricultural statistics and this thesis extended the use of the general statistical methods mainly applied in agricultural statistics to applications of network meta-analysis of clinical trials. The methods were applied to four different research problems in separate manuscripts. The first manuscript was based on a simulated case (based on real example) where some of the trials provided individual patient data and some only aggregated data. The outcome type considered was continuous normally distributed data. This manuscript provides models for jointly model the individual patient data and aggregated data. It was also explored how much information is lost if data is aggregated and how to quantify the amount of lost information. The second manuscript was based a real life dataset with pain medications used in acute postoperative pain. The outcome of interest was binomial, whether a subject experienced pain relief or not. The dataset used for NMA included 261 trials with 52 different treatment and dose combinations, making it extraordinarily rich and large network. The third manuscript developed methods for a case of time-to-event-outcome extracted from published Kaplan-Meier curves of survival analyses. This re-generated individual patient data was then used to model and compare the Kaplan-Meier curves and hazards of different treatments. The fourth manuscript of the thesis was tackling the problem of between-trial variance estimation for a specific method of Hartung-Knapp in classical two-treatment meta-analysis. The main finding of the paper was that in some cases random effect meta-analysis using Hartung-Knapp method may yield shorter confidence intervals for combined treatment effect than fixed effect meta-analysis and therefore the recommendation is to always compare results from Hartung-Knapp method with fixed effect meta-analysis. This thesis explored and developed the use of generalized linear mixed models in a setting of network meta-analysis of randomized clinical trials. In practice the most popular analysis method in the field of network meta-analysis has been the baseline contrast model which is usually fitted in a Bayesian framework. The baseline contrast model and Bayesian estimation provides great flexibility, but also come with some unnecessary complications for certain types of analyses. This thesis showed how methods originally developed and extensively used in agricultural research can be used in other field providing efficient calculation, estimation, and inference. Some of the examples used in this thesis arose from analyses needed for real applications in drug development and were directly used in medical research.  In den letzten Jahren haben Netzwerk-Meta-Analysen von publizierten Ergebnissen klinischer Studien viel Aufmerksamkeit erhalten und die Kosten-Nutzen-Einschätzung wichtiger pharmazeutischer Präparate in erheblichem Umfang beeinflusst. Ein Großteil der methodischen Forschung zur Meta-Analyse konzentrierte sich dabei auf Bayessche Methoden im sogenannten Baseline-Contrast-Modell. Diese methodischen Untersuchungen haben z.T. losgelöst von anderen Bereichen der mathematischen Statistik stattgefunden. Daher fehlte ein integrativer Rahmen, welcher mathematische Modelle und Annahmen, Prinzipien der Inferenz und Algorithmen zur Ermittlung von Effektschätzungen klar voneinander trennte. Die sehr umfangreichen Erkenntnisse zur Varianzanalyse (ANOVA und MANOVA) unbalanzierter Versuchsanordnungen, Varianzkomponentenmodellen sowie generalisierten linearen Modellen mit festen und zufälligen Effekten, welche in der Vergangenheit, nicht zuletzt im Bereich der Agrarwissenschaften, erlangt wurden, sind auch für die Methodik der Meta-Analyse sehr nützlich. Diese Arbeit erweitert die Nutzung solcher Methoden auf die Netzwerk-Meta-Analyse klinischer Studien. Die Anwendung dieser Methoden wird in vier Manuskripten dieser kumulativen Thesis dargestellt. Im ersten Manuskript wird eine Situation untersucht, bei der für einen Teil der untersuchten klinischen Studien individuelle Patientendaten (IPD) vorliegen, für einen anderen Teil indes nur aggregierte Daten (AD). Das Manuskript stellt Modelle vor, welche sich für die gemeinsame Analyse solcher Daten eignen. Es wird angenommen, dass die Daten Normalverteilungen entstammen. Die Daten wurden basierend auf realen Studiendaten simuliert. Das Manuskript untersucht, wieviel Information durch die Datenaggregation verloren geht und wie dieser Informationsverlust quantifiziert werden kann. Das zweite Manuskript untersucht einen Datensatz aus 261 klinischen Studien, in denen insgesamt 52 verschiedene Behandlungen gegen akute postoperative Schmerzen geprüft wurden. Die Zielgröße ist binär und hält fest, ob Schmerzlinderung erzielt wurde oder nicht. Aufgrund der vielen Studien und Behandlungen liegt hier ein aussergewöhnlich umfangreiches und komplexes Netzwerk vor. Im dritten Manuskript werden Methoden zur Analyse von Überlebenszeitdaten vorgestellt. Die Daten wurden mithilfe von Softwaretools aus publizierten Kaplan-Meier-Kurven extrahiert. Die so gewonnenen individuellen Patientendaten wurden benutzt, um die Überlebenskurven zu modellieren und die Hazardraten verschiedener Behandlungen zu vergleichen. Das vierte Manuskript betrachtet einen speziellen Aspekt der Inter-Studien-Varianzschätzung in der klassischen Meta-Analyse mit zwei Behandlungsarmen. Das Hauptergebnis dieser Untersuchung ist, dass die sogenannte Hartung-Knapp-Methode in Modellen mit zufälligen Effekten in bestimmten Fällen zu kürzeren Konfidenzintervallen für die kombinierte Behandlungseffektschätzung führen kann als die entsprechende Schätzung in einem Modell mit festen Effekten. Daher wird empfohlen, in konkreten Analysen beide Methoden zu verwenden und die Ergebnisse zu vergleichen. Übergreifendes Thema dieser Thesis ist die Untersuchung generalisierter linearer gemischter Modelle für Netzwerk-Meta-Analysen klinischer Studien. In der Praxis ist in diesem Bereich das Baseline-Kontrast-Modell mit Bayesschen Effektschätzungen das populärste Modell. Dieses Modell und die Methode der Bayes-Schätzung erlauben hohe Flexibilität, aber in manchen Fällen verkomplizieren sie die Analyse auf unnötige Weise. Diese Arbeit zeigt, wie Methoden, die ursprünglich in den Agrarwissenschaften entwickelt wurden und ausgiebig genutzt werden, auch für die Meta-Analyse klinischer Studien effiziente Schätz- und Inferenzmethoden zur Verfügung stellen. Einige der Beispiele in dieser Arbeit sind durch Anwendungen in der Medikamentenentwicklung motiviert und wurden bereits in konkreten medizinischen Forschungsvorhaben eingesetzt

Methods to calculate uncertainty in the estimated overall effect size from a random-effects meta-analysis

Meta-analyses are an important tool within systematic reviews to estimate the overall effect size and its confidence interval for an outcome of interest. If heterogeneity between the results of the relevant studies is anticipated, then a random-effects model is often preferred for analysis. In this model, a prediction interval for the true effect in a new study also provides additional useful information. However, the DerSimonian and Laird method - frequently used as the default method for meta-analyses with random effects - has been long challenged due to its unfavourable statistical properties. Several alternative methods have been proposed that may have better statistical properties in specific scenarios. In this paper, we aim to provide a comprehensive overview of available methods for calculating point estimates, confidence intervals and prediction intervals for the overall effect size under the random-effects model. We indicate whether some methods are preferable than others by considering the results of comparative simulation and real-life data studies

Meta-analysis and meta-regression: application and discussion in case of small sample size

Nel presente lavoro si affronta il tema delle correzioni per piccoli campioni o piccolo numero di studi applicate ai modelli di metanalisi. Le metodologie riportate si basano sulle approssimazioni asintotiche di secondo ordine e sulla teoria della verosimiglianza integrata. Si propone uno studio di simulazione per confrontare l'efficacia dei diversi approcci in un contesto controllato e infine un'applicazione a un caso reale.This work addresses the issue of corrections for small samples or small number of studies applied to meta-analysis models. The reported methodologies are based on second-order asymptotic approximations and integrated likelihood theory. A simulation study is proposed to compare the effectiveness of the different approaches in a controlled setting and finally an application to a real case

Confidence intervals for the between-study variance in random-effects meta-analysis using generalised heterogeneity statistics: should we use unequal tails?

BACKGROUND: Confidence intervals for the between study variance are useful in random-effects meta-analyses because they quantify the uncertainty in the corresponding point estimates. Methods for calculating these confidence intervals have been developed that are based on inverting hypothesis tests using generalised heterogeneity statistics. Whilst, under the random effects model, these new methods furnish confidence intervals with the correct coverage, the resulting intervals are usually very wide, making them uninformative. METHODS: We discuss a simple strategy for obtaining 95 % confidence intervals for the between-study variance with a markedly reduced width, whilst retaining the nominal coverage probability. Specifically, we consider the possibility of using methods based on generalised heterogeneity statistics with unequal tail probabilities, where the tail probability used to compute the upper bound is greater than 2.5 %. This idea is assessed using four real examples and a variety of simulation studies. Supporting analytical results are also obtained. RESULTS: Our results provide evidence that using unequal tail probabilities can result in shorter 95 % confidence intervals for the between-study variance. We also show some further results for a real example that illustrates how shorter confidence intervals for the between-study variance can be useful when performing sensitivity analyses for the average effect, which is usually the parameter of primary interest. CONCLUSIONS: We conclude that using unequal tail probabilities when computing 95 % confidence intervals for the between-study variance, when using methods based on generalised heterogeneity statistics, can result in shorter confidence intervals. We suggest that those who find the case for using unequal tail probabilities convincing should use the '1-4 % split', where greater tail probability is allocated to the upper confidence bound. The 'width-optimal' interval that we present deserves further investigation

The Hartung-Knapp modification for random-effects meta-analysis: A useful refinement but are there any residual concerns?

The modified method for random-effects meta-analysis, usually attributed to Hartung andKnapp and also proposed by Sidik and Jonkman, is easy to implement and is becoming advocated for general use. Here, we examine a range of potential concerns about the widespread adoption of this method. Motivated by these issues, a variety of different conventions can be adopted when using the modified method in practice. We describe and investigate the use of a variety of these conventions using a new taxonomy ofmeta-analysis datasets.We conclude that the Hartung and Knapp modificationmay be a suitable replacement for the standard method. Despite this, analysts who advocate the modified method should be ready to defend its use against the possible objections to it that we present. We further recommend that the results from more conventional approaches should be used as sensitivity analyses when using the modified method. It has previously been suggested that a common-effect analysis should be used for this purpose but we suggest amending this recommendation and argue that a standard random-effects analysis should be used instead.UK Medical Research Council, Grant/Award Number: U105260558 ; NIHR, Grant/Award Number: RP-PG-0109-10056 ; Deutsche Forschungsgemeinschaft, Grant/Award Number: RU1747/1-

Effects of psychological and psychosocial interventions on sport performance:a meta-analysis

Background: Psychologists are increasingly supporting the quest for performance enhancement in sport and there is a need to evaluate the evidence base underpinning their work. Objectives: To synthesize the most rigorous available research that has evaluated psychological, social, and psychosocial interventions with sport performers on variables relating to their athletic performance, and to address some of the perplexing issues in the sport psychology intervention literature (e.g., do interventions have a lasting effect on sport performance?). Methods: Randomized controlled trials were identified through electronic databases, hand-searching volumes of pertinent journals, scrutinizing reference lists of previous reviews, and contacting experts in the evaluation of interventions in this field. Included studies were required to evaluate the effects of psychological, social, or psychosocial interventions on sport performance in athletes when compared to a no-treatment or placebo-controlled treatment comparison group. A random effects meta-analysis calculating the standardized mean difference (Hedges’ g), meta-regressions, and trim and fill analyses were conducted. Data were analyzed at post-test and follow-up (ranging from 1 to 4 weeks after the intervention finished) assessments. Results: Psychological and psychosocial interventions were shown to enhance sport performance at post-test (k = 35, n = 997, Hedges’ g = 0.57, 95 % CI = 0.22–0.92) and follow-up assessments (k = 8, n = 189, Hedges’ g = 1.16, 95 % CI = 0.25–2.08); no social interventions were included or evaluated. Larger effects were found for psychosocial interventions and there was some evidence that effects were greatest in coach-delivered interventions and in samples with a greater proportion of male participants. Conclusions: Psychological and psychosocial interventions have a moderate positive effect on sport performance, and this effect may last at least a month following the end of the intervention. Future research would benefit from following guidelines for intervention reporting

A comparison of analytic approaches for individual patient data meta-analyses with binary outcomes

Abstract Background Individual patient data meta-analyses (IPD-MA) are often performed using a one-stage approach-- a form of generalized linear mixed model (GLMM) for binary outcomes. We compare (i) one-stage to two-stage approaches (ii) the performance of two estimation procedures (Penalized Quasi-likelihood-PQL and Adaptive Gaussian Hermite Quadrature-AGHQ) for GLMMs with binary outcomes within the one-stage approach and (iii) using stratified study-effect or random study-effects. Methods We compare the different approaches via a simulation study, in terms of bias, mean-squared error (MSE), coverage and numerical convergence, of the pooled treatment effect (β 1) and between-study heterogeneity of the treatment effect (τ 1 2 ). We varied the prevalence of the outcome, sample size, number of studies and variances and correlation of the random effects. Results The two-stage and one-stage methods produced approximately unbiased β 1 estimates. PQL performed better than AGHQ for estimating τ 1 2 with respect to MSE, but performed comparably with AGHQ in estimating the bias of β 1 and of τ 1 2 . The random study-effects model outperformed the stratified study-effects model in small size MA. Conclusion The one-stage approach is recommended over the two-stage method for small size MA. There was no meaningful difference between the PQL and AGHQ procedures. Though the random-intercept and stratified-intercept approaches can suffer from their underlining assumptions, fitting GLMM with a random-intercept are less prone to misfit and has good convergence rate

Neutrophil to lymphocyte ratio and cancer prognosis: an umbrella review of systematic reviews and meta-analyses of observational studies

Background Although neutrophils have been linked to the progression of cancer, uncertainty exists around their association with cancer outcomes, depending on the site, outcome and treatments considered. We aimed to evaluate the strength and validity of evidence on the association between either the neutrophil to lymphocyte ratio (NLR) or tumour-associated neutrophils (TAN) and cancer prognosis. Methods We searched MEDLINE, Embase and Cochrane Database of Systematic Reviews from inception to 29 May 2020 for systematic reviews and meta-analyses of observational studies on neutrophil counts (here NLR or TAN) and specific cancer outcomes related to disease progression or survival. The available evidence was graded as strong, highly suggestive, suggestive, weak or uncertain through the application of pre-set GRADE criteria. Results A total of 204 meta-analyses from 86 studies investigating the association between either NLR or TAN and cancer outcomes met the criteria for inclusion. All but one meta-analyses found a hazard ratio (HR) which increased risk (HR > 1). We did not find sufficient meta-analyses to evaluate TAN and cancer outcomes (N = 9). When assessed for magnitude of effect, significance and bias related to heterogeneity and small study effects, 18 (9%) associations between NLR and outcomes in composite cancer endpoints (combined analysis), cancers treated with immunotherapy and some site specific cancers (urinary, nasopharyngeal, gastric, breast, endometrial, soft tissue sarcoma and hepatocellular cancers) were supported by strong evidence. Conclusion In total, 60 (29%) meta-analyses presented strong or highly suggestive evidence. Although the NLR and TAN hold clinical promise in their association with poor cancer prognosis, further research is required to provide robust evidence, assess causality and test clinical utility