Nonparametric estimation of the random effects distribution for the risk or rate ratio in rare events meta-analysis with the arm-based and contrast-based approaches.

Rare events are events which occur with low frequencies. These often arise in clinical trials or cohort studies where the data are arranged in binary contingency tables. In this article, we investigate the estimation of effect heterogeneity for the risk-ratio parameter in meta-analysis of rare events studies through two likelihood-based nonparametric mixture approaches: an arm-based and a contrast-based model. Maximum likelihood estimation is achieved using the EM algorithm. Special attention is given to the choice of initial values. Inspired by the classification likelihood, a strategy is implemented which repeatably uses random allocation of the studies to the mixture components as choice of initial values. The likelihoods under the contrast-based and arm-based approaches are compared and differences are highlighted. We use simulations to assess the performance of these two methods. Under the design of sampling studies with nested treatment groups, the results show that the nonparametric mixture model based on the contrast-based approach is more appropriate in terms of model selection criteria such as AIC and BIC. Under the arm-based design the results from the arm-based model performs well although in some cases it is also outperformed by the contrast-based model. Comparisons of the estimators are provided in terms of bias and mean squared error. Also included in the comparison is the mixed Poisson regression model as well as the classical DerSimonian-Laird model (using the Mantel-Haenszel estimator for the common effect). Using simulation, estimating effect heterogeneity in the case of the contrast-based method appears to behave better than the compared methods although differences become negligible for large within-study sample sizes. We illustrate the methodologies using several meta-analytic data sets in medicine.

Comprehensive ABA-based interventions in the treatment of children with autism spectrum disorder - a meta-analysis.

BACKGROUND: Many studies display promising results for interventions that are based on Applied Behavior Analysis (ABA) in the treatment of autism spectrum disorder (ASD). METHODS: This meta-analysis assessed the effects of such treatments on developmental outcomes in children with ASD and on parental stress based on 11 studies with 632 participants. RESULTS: Compared to treatment as usual, minimal or no treatment, comprehensive ABA-based interventions showed medium effects for intellectual functioning (standardized mean difference SMD = 0.51, 95% CI [0.09; 0.92]) and adaptive behavior (SMD = 0.37, 95% CI [0.03; 0.70]). Language abilities, symptom severity or parental stress did not improve beyond the improvement in control groups. Moderator analyses indicate that language abilities at intake could influence the effect sizes and the influence of treatment intensity might decrease with older age. CONCLUSIONS: Practical implications and limitations are discussed.

Random-effects meta-analysis models for the odds ratio in the case of rare events under different data-generating models: A simulation study.

Meta-analysis of binary data is challenging when the event under investigation is rare, and standard models for random-effects meta-analysis perform poorly in such settings. In this simulation study, we investigate the performance of different random-effects meta-analysis models in terms of point and interval estimation of the pooled log odds ratio in rare events meta-analysis. First and foremost, we evaluate the performance of a hypergeometric-normal model from the family of generalized linear mixed models (GLMMs), which has been recommended, but has not yet been thoroughly investigated for rare events meta-analysis. Performance of this model is compared to performance of the beta-binomial model, which yielded favorable results in previous simulation studies, and to the performance of models that are frequently used in rare events meta-analysis, such as the inverse variance model and the Mantel-Haenszel method. In addition to considering a large number of simulation parameters inspired by real-world data settings, we study the comparative performance of the meta-analytic models under two different data-generating models (DGMs) that have been used in past simulation studies. The results of this study show that the hypergeometric-normal GLMM is useful for meta-analysis of rare events when moderate to large heterogeneity is present. In addition, our study reveals important insights with regard to the performance of the beta-binomial model under different DGMs from the binomial-normal family. In particular, we demonstrate that although misalignment of the beta-binomial model with the DGM affects its performance, it shows more robustness to the DGM than its competitors.

The relationship of trauma-related guilt with PTSD symptoms in adult trauma survivors: a meta-analysis.

Posttraumatic stress disorder (PTSD) is a severe condition that is associated with trauma-related guilt. We aimed at providing a comprehensive quantitative systematic review on the relationship between trauma-related guilt and adult PTSD. Database searches in Medline, PsycINFO, PTSDpubs and Web of Knowledge resulted in the inclusion of 163 eligible studies with a total of 35 020 trauma survivors. The studies reported on 157 cross-sectional and 19 longitudinal data points. Overall, we included 135 studies not included in previous meta-analyses. Random-effect models yielded a moderate cross-sectional correlation (r = 0.38, 95% CI 0.35-0.42, p < 0.001, I2 = 90.3%) and a small to moderate predictive correlation (r = 0.21, 95% CI 0.13-0.29, p < 0.001, I2 = 66.7%). The association appeared to be stable over time and was robust to sensitivity analyses. All symptom clusters significantly correlated with guilt. No effects were found for military v. civilian populations or clinical v. non-clinical samples. Effects were smaller for high-quality studies and larger for instruments based on DSM-5. Further significant moderators were type of guilt measure and trauma type. The largest association was found among participants reporting war-related trauma (r = 0.44, 95% CI 0.36-0.51) and the smallest among survivors of motor-vehicle accidents (r = 0.18, 95% CI 0.02-0.33). The results underpin the role of trauma-related guilt in the onset and maintenance of PTSD symptoms, which have important clinical implications. Future studies should further explore the change interactions of guilt and PTSD symptoms.

Neurology and neuropsychiatry of COVID-19: a systematic review and meta-analysis of the early literature reveals frequent CNS manifestations and key emerging narratives.

There is accumulating evidence of the neurological and neuropsychiatric features of infection with SARS-CoV-2. In this systematic review and meta-analysis, we aimed to describe the characteristics of the early literature and estimate point prevalences for neurological and neuropsychiatric manifestations.We searched MEDLINE, Embase, PsycINFO and CINAHL up to 18 July 2020 for randomised controlled trials, cohort studies, case-control studies, cross-sectional studies and case series. Studies reporting prevalences of neurological or neuropsychiatric symptoms were synthesised into meta-analyses to estimate pooled prevalence.13 292 records were screened by at least two authors to identify 215 included studies, of which there were 37 cohort studies, 15 case-control studies, 80 cross-sectional studies and 83 case series from 30 countries. 147 studies were included in the meta-analysis. The symptoms with the highest prevalence were anosmia (43.1% (95% CI 35.2% to 51.3%), n=15 975, 63 studies), weakness (40.0% (95% CI 27.9% to 53.5%), n=221, 3 studies), fatigue (37.8% (95% CI 31.6% to 44.4%), n=21 101, 67 studies), dysgeusia (37.2% (95% CI 29.8% to 45.3%), n=13 686, 52 studies), myalgia (25.1% (95% CI 19.8% to 31.3%), n=66 268, 76 studies), depression (23.0% (95% CI 11.8% to 40.2%), n=43 128, 10 studies), headache (20.7% (95% CI 16.1% to 26.1%), n=64 613, 84 studies), anxiety (15.9% (5.6% to 37.7%), n=42 566, 9 studies) and altered mental status (8.2% (95% CI 4.4% to 14.8%), n=49 326, 19 studies). Heterogeneity for most clinical manifestations was high.Neurological and neuropsychiatric symptoms of COVID-19 in the pandemic's early phase are varied and common. The neurological and psychiatric academic communities should develop systems to facilitate high-quality methodologies, including more rapid examination of the longitudinal course of neuropsychiatric complications of newly emerging diseases and their relationship to neuroimaging and inflammatory biomarkers.

Comparison of random-effects meta-analysis models for the relative risk in the case of rare events: A simulation study.

Pooling the relative risk (RR) across studies investigating rare events, for example, adverse events, via meta-analytical methods still presents a challenge to researchers. The main reason for this is the high probability of observing no events in treatment or control group or both, resulting in an undefined log RR (the basis of standard meta-analysis). Other technical challenges ensue, for example, the violation of normality assumptions, or bias due to exclusion of studies and application of continuity corrections, leading to poor performance of standard approaches. In the present simulation study, we compared three recently proposed alternative models (random-effects [RE] Poisson regression, RE zero-inflated Poisson [ZIP] regression, binomial regression) to the standard methods in conjunction with different continuity corrections and to different versions of beta-binomial regression. Based on our investigation of the models' performance in 162 different simulation settings informed by meta-analyses from the Cochrane database and distinguished by different underlying true effects, degrees of between-study heterogeneity, numbers of primary studies, group size ratios, and baseline risks, we recommend the use of the RE Poisson regression model. The beta-binomial model recommended by Kuss (2015) also performed well. Decent performance was also exhibited by the ZIP models, but they also had considerable convergence issues. We stress that these recommendations are only valid for meta-analyses with larger numbers of primary studies. All models are applied to data from two Cochrane reviews to illustrate differences between and issues of the models. Limitations as well as practical implications and recommendations are discussed; a flowchart summarizing recommendations is provided.

Psychological interventions for posttraumatic stress disorder and depression in refugees: A meta-analysis of randomized controlled trials.

Millions of refugees around the globe suffer from posttraumatic stress disorder (PTSD) and/or depression. We conducted a meta-analysis of randomized controlled trials (RCTs) to determine the efficacy of psychological interventions for PTSD and/or depression in refugees. The meta-analysis was registered on the PROSPERO database (CRD42017071384). A search using the Medline, PsycINFO, and PILOTS databases was conducted in January 2019, resulting in 17 RCTs, of which 14 were conducted with adult refugees (1,108 participants) and 3 with young refugees (<18 years; 151 participants). Further inclusion criteria were at least 10 participants completing an active psychological intervention for PTSD, depression, or both and less than 50% of participants receiving concurrent psychotropic drugs. Random effects models showed that active interventions for adult PTSD yielded a medium to large aggregated effect size (g = 0.77; 95% confidence interval [CI] [0.26, 1.28]) at posttreatment when compared with passive and active control conditions. Active interventions for adult depression also produced large controlled effect sizes at posttreatment (g = 0.82; 95% CI [0.24, 1.40]). The effects appeared to persist over the average follow-up period of 6 months. The findings suggest that psychological interventions can effectively reduce symptoms of both PTSD and depression in adult refugees. However, the considerable heterogeneity between studies indicates that the efficacy may vary significantly. Future studies should aim to explore the substantial heterogeneity in effect sizes between studies with adult refugees. Additionally, more trials with young refugees suffering from PTSD or depression are needed to determine treatment efficacy for this population.

Statistical methodology for estimating the mean difference in a meta-analysis without study-specific variance information.

Statistical inference for analyzing the results from several independent studies on the same quantity of interest has been investigated frequently in recent decades. Typically, any meta-analytic inference requires that the quantity of interest is available from each study together with an estimate of its variability. The current work is motivated by a meta-analysis on comparing two treatments (thoracoscopic and open) of congenital lung malformations in young children. Quantities of interest include continuous end-points such as length of operation or number of chest tube days. As studies only report mean values (and no standard errors or confidence intervals), the question arises how meta-analytic inference can be developed. We suggest two methods to estimate study-specific variances in such a meta-analysis, where only sample means and sample sizes are available in the treatment arms. A general likelihood ratio test is derived for testing equality of variances in two groups. By means of simulation studies, the bias and estimated standard error of the overall mean difference from both methodologies are evaluated and compared with two existing approaches: complete study analysis only and partial variance information. The performance of the test is evaluated in terms of type I error. Additionally, we illustrate these methods in the meta-analysis on comparing thoracoscopic and open surgery for congenital lung malformations and in a meta-analysis on the change in renal function after kidney donation. Copyright © 2017 John Wiley & Sons, Ltd.

Optimal design of the Wilcoxon-Mann-Whitney-test.

In scientific research, many hypotheses relate to the comparison of two independent groups. Usually, it is of interest to use a design (i.e., the allocation of sample sizes m and n for fixed N=m+n) that maximizes the power of the applied statistical test. It is known that the two-sample t-tests for homogeneous and heterogeneous variances may lose substantial power when variances are unequal but equally large samples are used. We demonstrate that this is not the case for the nonparametric Wilcoxon-Mann-Whitney-test, whose application in biometrical research fields is motivated by two examples from cancer research. We prove the optimality of the design m=n in case of symmetric and identically shaped distributions using normal approximations and show that this design generally offers power only negligibly lower than the optimal design for a wide range of distributions.

ENHANCEMENT OF LEARNING ON SAMPLE SIZE CALCULATION WITH A SMARTPHONE APPLICATION: A CLUSTER-RANDOMIZED CONTROLLED TRIAL.

Sample size determination usually is taught based on theory and is difficult to understand. Using a smartphone application to teach sample size calculation ought to be more attractive to students than using lectures only. This study compared levels of understanding of sample size calculations for research studies between participants attending a lecture only versus lecture combined with using a smartphone application to calculate sample sizes, to explore factors affecting level of post-test score after training sample size calculation, and to investigate participants' attitude toward a sample size application. A cluster-randomized controlled trial involving a number of health institutes in Thailand was carried out from October 2014 to March 2015. A total of 673 professional participants were enrolled and randomly allocated to one of two groups, namely, 341 participants in 10 workshops to control group and 332 participants in 9 workshops to intervention group. Lectures on sample size calculation were given in the control group, while lectures using a smartphone application were supplied to the test group. Participants in the intervention group had better learning of sample size calculation (2.7 points out of maximnum 10 points, 95% CI: 24 - 2.9) than the participants in the control group (1.6 points, 95% CI: 1.4 - 1.8). Participants doing research projects had a higher post-test score than those who did not have a plan to conduct research projects (0.9 point, 95% CI: 0.5 - 1.4). The majority of the participants had a positive attitude towards the use of smartphone application for learning sample size calculation.

A flexible ratio regression approach for zero-truncated capture-recapture counts.

Capture-recapture methods are used to estimate the size of a population of interest which is only partially observed. In such studies, each member of the population carries a count of the number of times it has been identified during the observational period. In real-life applications, only positive counts are recorded, and we get a truncated at zero-observed distribution. We need to use the truncated count distribution to estimate the number of unobserved units. We consider ratios of neighboring count probabilities, estimated by ratios of observed frequencies, regardless of whether we have a zero-truncated or an untruncated distribution. Rocchetti et al. (2011) have shown that, for densities in the Katz family, these ratios can be modeled by a regression approach, and Rocchetti et al. (2014) have specialized the approach to the beta-binomial distribution. Once the regression model has been estimated, the unobserved frequency of zero counts can be simply derived. The guiding principle is that it is often easier to find an appropriate regression model than a proper model for the count distribution. However, a full analysis of the connection between the regression model and the associated count distribution has been missing. In this manuscript, we fill the gap and show that the regression model approach leads, under general conditions, to a valid count distribution; we also consider a wider class of regression models, based on fractional polynomials. The proposed approach is illustrated by analyzing various empirical applications, and by means of a simulation study.

Clinical trial on tonal tinnitus with tailor-made notched music training.

BACKGROUND: Tinnitus is a result of hyper-activity/hyper-synchrony of auditory neurons coding the tinnitus frequency, which has developed due to synchronous mass activity owing to the lack of inhibition. We assume that removal of exactly these frequencies from a complex auditory stimulus will cause the brain to reorganize around tonotopic regions coding the tinnitus frequency through inhibition-induced plasticity. Based on this assumption, a novel treatment for tonal tinnitus--tailor-made notched music training (TMNMT)--has been introduced and was tested in this clinical trial. METHODS: A randomized controlled trial in parallel group design was performed in a double-blinded manner. We included 100 participants with chronic, tonal tinnitus who listened to tailor-made notched music for two hours a day for three consecutive months. Our primary outcome measures were the Tinnitus Handicap Questionnaire and Visual Analog Scales measuring perceived tinnitus loudness, awareness, distress and handicap. Participants rated their tinnitus before and after the training as well as one month after cessation of the training. RESULTS: While no effect was found for the primary outcome measures, tinnitus distress, as measured by the Tinnitus Questionnaire, a secondary outcome measure, developed differently in the two groups. The treatment group showed higher distress scores while the placebo group revealed lower distress scores after the training. However, this effect did not reach significance in post-hoc analysis and disappeared at follow-up measurements. At follow-up, tinnitus loudness in the treatment group was significantly reduced as compared to the control group. Post hoc analysis, accounting for low reliability scores in the Visual Analog Scales, showed a significant reduction of the overall Visual Analog Scale mean score in the treatment group even at the post measurement. CONCLUSION: This is the first study on TMNMT that was planned and conducted following the CONSORT statement standards for clinical trials. The current work is one more step towards a final evaluation of TMNMT. Already after three months the effect of training with tailor-made notched music is observable in the most direct rating of tinnitus perception - the tinnitus loudness, while more global measures of tinnitus distress do not show relevant changes. TRIAL REGISTRATION: Current Controlled Trials ISRCTN04840953; Trial registration date: 17.07.2013.

Is functional integration of resting state brain networks an unspecific biomarker for working memory performance?

Is there one optimal topology of functional brain networks at rest from which our cognitive performance would profit? Previous studies suggest that functional integration of resting state brain networks is an important biomarker for cognitive performance. However, it is still unknown whether higher network integration is an unspecific predictor for good cognitive performance or, alternatively, whether specific network organization during rest predicts only specific cognitive abilities. Here, we investigated the relationship between network integration at rest and cognitive performance using two tasks that measured different aspects of working memory; one task assessed visual-spatial and the other numerical working memory. Network clustering, modularity and efficiency were computed to capture network integration on different levels of network organization, and to statistically compare their correlations with the performance in each working memory test. The results revealed that each working memory aspect profits from a different resting state topology, and the tests showed significantly different correlations with each of the measures of network integration. While higher global network integration and modularity predicted significantly better performance in visual-spatial working memory, both measures showed no significant correlation with numerical working memory performance. In contrast, numerical working memory was superior in subjects with highly clustered brain networks, predominantly in the intraparietal sulcus, a core brain region of the working memory network. Our findings suggest that a specific balance between local and global functional integration of resting state brain networks facilitates special aspects of cognitive performance. In the context of working memory, while visual-spatial performance is facilitated by globally integrated functional resting state brain networks, numerical working memory profits from increased capacities for local processing, especially in brain regions involved in working memory performance.

Meta-analysis and meta-modelling for diagnostic problems.

BACKGROUND: A proportional hazards measure is suggested in the context of analyzing SROC curves that arise in the meta-analysis of diagnostic studies. The measure can be motivated as a special model: the Lehmann model for ROC curves. The Lehmann model involves study-specific sensitivities and specificities and a diagnostic accuracy parameter which connects the two. METHODS: A study-specific model is estimated for each study, and the resulting study-specific estimate of diagnostic accuracy is taken as an outcome measure for a mixed model with a random study effect and other study-level covariates as fixed effects. The variance component model becomes estimable by deriving within-study variances, depending on the outcome measure of choice. In contrast to existing approaches - usually of bivariate nature for the outcome measures - the suggested approach is univariate and, hence, allows easily the application of conventional mixed modelling. RESULTS: Some simple modifications in the SAS procedure proc mixed allow the fitting of mixed models for meta-analytic data from diagnostic studies. The methodology is illustrated with several meta-analytic diagnostic data sets, including a meta-analysis of the Mini-Mental State Examination as a diagnostic device for dementia and mild cognitive impairment. CONCLUSIONS: The proposed methodology allows us to embed the meta-analysis of diagnostic studies into the well-developed area of mixed modelling. Different outcome measures, specifically from the perspective of whether a local or a global measure of diagnostic accuracy should be applied, are discussed as well. In particular, variation in cut-off value is discussed together with recommendations on choosing the best cut-off value. We also show how this problem can be addressed with the proposed methodology.

Rare events meta-analysis using the Bayesian beta-binomial model.

In meta-analyses of rare events, it can be challenging to obtain a reliable estimate of the pooled effect, in particular when the meta-analysis is based on a small number of studies. Recent simulation studies have shown that the beta-binomial model is a promising candidate in this situation, but have thus far only investigated its performance in a frequentist framework. In this study, we aim to make the beta-binomial model for meta-analysis of rare events amenable to Bayesian inference by proposing prior distributions for the effect parameter and investigating the models' robustness to different specifications of priors for the scale parameter. To evaluate the performance of Bayesian beta-binomial models with different priors, we conducted a simulation study with two different data generating models in which we varied the size of the pooled effect, the degree of heterogeneity, the baseline probability, and the sample size. Our results show that while some caution must be exercised when using the Bayesian beta-binomial in meta-analyses with extremely sparse data, the use of a weakly informative prior for the effect parameter is beneficial in terms of mean bias, mean squared error, and coverage. For the scale parameter, half-normal and exponential distributions are identified as candidate priors in meta-analysis of rare events using the Bayesian beta-binomial model.

Estimating risk and rate ratio in rare events meta-analysis with the Mantel-Haenszel estimator and assessing heterogeneity.

Meta-analysis of binary outcome data faces often a situation where studies with a rare event are part of the set of studies to be considered. These studies have low occurrence of event counts to the extreme that no events occur in one or both groups to be compared. This raises issues how to estimate validly the summary risk or rate ratio across studies. A preferred choice is the Mantel-Haenszel estimator, which is still defined in the situation of zero studies unless all studies have zeros in one of the groups to be compared. For this situation, a modified Mantel-Haenszel estimator is suggested and shown to perform well by means of simulation work. Also, confidence interval estimation is discussed and evaluated in a simulation study. In a second part, heterogeneity of relative risk across studies is investigated with a new chi-square type statistic which is based on a conditional binomial distribution where the conditioning is on the event margin for each study. This is necessary as the conventional Q-statistic is undefined in the occurrence of zero studies. The null-distribution of the proposed Q-statistic is obtained by means of a parametric bootstrap as a chi-square approximation is not valid for rare events meta-analysis, as bootstrapping of the null-distribution shows. In addition, for the effect heterogeneity situation, confidence interval estimation is considered using a nonparametric bootstrap procedure. The proposed techniques are illustrated at hand of three meta-analytic data sets.

The Manic Idea Creator? A Review and Meta-Analysis of the Relationship between Bipolar Disorder and Creative Cognitive Potential.

Even though a relationship between psychopathology and creativity has been postulated since the time of ancient Greece, systematic meta-analyses on this topic are still scarce. Thus, the meta-analysis described here can be considered the first to date that specifically focuses on the relationship between creative potential, as measured by divergent thinking, and bipolar disorder, as opposed to psychopathology in general. An extensive literature search of 4670 screened hits identified 13 suitable studies, including a total of 42 effect sizes and 1857 participants. The random-effects model showed an overall significant, positive, yet diminutively small effect (d = 0.11, 95% CI: [0.002, 0.209], p = 0.045) between divergent thinking and bipolar disorder. A handful of moderators were examined, which revealed a significant moderating effect for bipolar status, as either euthymic (d = 0.14, p = 0.043), subclinical (d = 0.17, p = 0.001), manic (d = 0.25, p = 0.097), or depressed (d = -0.51, p < 0.001). However, moderator analyses should be treated with caution because of the observed confounding of moderators. Finally, none of the employed methods for publication-bias detection revealed any evidence for publication bias. We discuss further results, especially regarding the differences between subclinical and clinical samples.

The efficacy and acceptability of psychological interventions for adult PTSD: A network and pairwise meta-analysis of randomized controlled trials.

OBJECTIVE: A comprehensive quantitative summary of the efficacy and acceptability of psychological interventions (PIs) for adult posttraumatic stress disorder (PTSD) is lacking. METHOD: We conducted a systematic literature search to identify randomized controlled trials (RCTs) examining the efficacy and acceptability (all-cause dropout) of psychological interventions (i.e., trauma-focused cognitive behavior therapy [TF-CBT], eye movement desensitization and reprocessing [EMDR], other trauma-focused interventions and non-trauma-focused interventions). RESULTS: One hundred fifty-seven RCTs were included comprising 11,565 patients. Most research (64% of RCTs) accumulated for TF-CBT. In network meta-analyses, all therapies were effective when compared to control conditions. Interventions did not differ significantly in their efficacy. Yet, TF-CBT yielded higher short- (g = 0.17, 95% CI [0.03-0.31], number of comparisons kes = 190), mid- (i.e., ≤5 months posttreatment, g = 0.23, 95% CI [0.06-0.40], kes = 73) and long-term efficacy (i.e., >5 months posttreatment, g = 0.20, 95% CI [0.04-0.35], kes = 41) than non-trauma-focused interventions. There was some evidence of network inconsistencies, and heterogeneity in outcomes was large. In pairwise meta-analysis, slightly more patients dropped out from TF-CBT than non-trauma-focused interventions (RR = 1.36; 95% CI [1.08-1.70], kes = 22). Other than that, interventions did not differ in their acceptability. CONCLUSIONS: Interventions with and without trauma focus are effective and acceptable in the treatment of PTSD. While TF-CBT yields the highest efficacy, slightly more patients discontinued TF-CBT than non-trauma-focused interventions. Altogether, the present results align with results of most previous quantitative reviews. Yet, results need to be interpreted with caution in light of some network inconsistencies and high heterogeneity in outcomes. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

ICAOD: An R Package for Finding Optimal designs for Nonlinear Statistical Models by Imperialist Competitive Algorithm.

Optimal design ideas are increasingly used in different disciplines to rein in experimental costs. Given a nonlinear statistical model and a design criterion, optimal designs determine the number of experimental points to observe the responses, the design points and the number of replications at each design point. Currently, there are very few free and effective computing tools for finding different types of optimal designs for a general nonlinear model, especially when the criterion is not differentiable. We introduce an R package ICAOD to find various types of optimal designs and they include locally, minimax and Bayesian optimal designs for different nonlinear statistical models. Our main computational tool is a novel metaheuristic algorithm called imperialist competitive algorithm (ICA) and inspired by socio-political behavior of humans and colonialism. We demonstrate its capability and effectiveness using several applications. The package also includes several theory-based tools to assess optimality of a generated design when the criterion is a convex function of the design.