Small-sample Adjustments Research Articles

Small sample adjustment for inference without assuming orthogonality in a mixed model for repeated measures analysis

ABSTRACT The mixed model for repeated measures (MMRM) analysis is sometimes used as a primary statistical analysis for a longitudinal randomized clinical trial. When the MMRM analysis is implemented in ordinary statistical software, the standard error of the treatment effect is estimated by assuming orthogonality between the fixed effects and covariance parameters, based on the characteristics of the normal distribution. However, orthogonality does not hold unless the normality assumption of the error distribution holds, and/or the missing data are derived from the missing completely at random structure. Therefore, assuming orthogonality in the MMRM analysis is not preferable. However, without the assumption of orthogonality, the small-sample bias in the standard error of the treatment effect is significant. Nonetheless, there is no method to improve small-sample performance. Furthermore, there is no software that can easily implement inferences on treatment effects without assuming orthogonality. Hence, we propose two small-sample adjustment methods inflating standard errors that are reasonable in ideal situations and achieve empirical conservatism even in general situations. We also provide an R package to implement these inference processes. The simulation results show that one of the proposed small-sample adjustment methods performs particularly well in terms of underestimation bias of standard errors; consequently, the proposed method is recommended. When using the MMRM analysis, our proposed method is recommended if the sample size is not large and between-group heteroscedasticity is expected.

Regression Approaches to Assess Effect of Treatments That Arrest Progression of Symptoms.

Motivated by a small sample example in neonatal onset multisystem inflammatory disease (NOMID), we propose a method that can be used when the interest is testing for an association between a changes in disease progression with start of treatment compared to historical disease progression prior to treatment. Our method estimates the longitudinal trajectory of the outcome variable and adds an interaction term between an intervention indicator variable and the time since initiation of the intervention. This method is appropriate for a situation in which the intervention slows or arrests the effect of the disease on the outcome, as is the case in our motivating example. By simulation in small samples and restricted sets of treatment initiation times, we show that the generalized estimating equations (GEE) formulation with small sample adjustments can bound the Type I error rate better than GEE and linear mixed models without small sample adjustments. Permutation tests (permuting the time of treatment initiation) is another valid approach that can also be useful. We illustrate the methodology through an application to a prospective cohort of NOMID patients enrolled at the NIH clinical center.

Anti-inflamatórios não esteroides afetam as respostas ao treinamento resistido em indivíduos idosos e de meia-idade?

Introdução: Os anti-inflamatórios não esteroides (AINEs) estão entre os medicamentos mais populares do mundo para o tratamento da dor e inflamação. Embora o uso a longo prazo de AINEs esteja associado a efeitos adversos renais, cardiovasculares, hepáticos e outros, também foi sugerido que ele pode causar comprometimento nas adaptações neuromuscular promovida pelo exercício. Objetivo: O objetivo desta revisão sistemática foi comparar os efeitos do uso de AINEs nas adaptações neuromusculares, como hipertrofia e força muscular em pessoas de meia-idade e idosos praticantes de treinamento resistido. Métodos: As bases de dados pesquisadas incluíram Bireme, Pubmed e Science Direct. As meta-análises foram conduzidas usando o método de estimativa de variância robusta de efeitos correlacionados com ajustes de pequenas amostras. Resultados: Seis estudos foram incluídos para análise meta-analítica, nenhuma diferença estatística foi encontrada para hipertrofia (ES: 0,000531 ± 0,0424, IC 95%: -0,123 - 0,124; P = 0,991) e força muscular (ES: 0,323 ± 0,213, 95% CI: -0,417 - 1,06; P = 0,258). Conclusão: Os achados desta revisão não sustentam a hipótese de que o uso de AINEs combinado com exercícios resistidos, influencie negativamente a hipertrofia e a força muscular.

Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors

Abstract Johansen’s (2000. “A Bartlett Correction Factor for Tests of on the Cointegrating Relations.” Econometric Theory 16: 740–78) Bartlett correction factor for the LR test of linear restrictions on cointegrated vectors is derived under the i.i.d. Gaussian assumption for the innovation terms. However, the distribution of most data relating to financial variables is fat-tailed and often skewed; there is therefore a need to examine small sample inference procedures that require weaker assumptions for the innovation term. This paper suggests that using the non-parametric bootstrap to approximate a Bartlett-type correction provides a statistic that does not require specification of the innovation distribution and can be used by applied econometricians to perform a small sample inference procedure that is less computationally demanding than it’s analytical counterpart. The procedure involves calculating a number of bootstrap values of the LR test statistic and estimating the expected value of the test statistic by the average value of the bootstrapped LR statistic. Simulation results suggest that the inference procedure has good finite sample property and is less dependent on the parameter space of the data generating process.

Variant-set association test for generalized linear mixed model.

Advances in high-throughput biotechnologies have culminated in a wide range of omics (such as genomics, epigenomics, transcriptomics, metabolomics, and metagenomics) studies, and increasing evidence in these studies indicates that the biological architecture of complex traits involves a large number of omics variants each with minor effects but collectively accounting for the full phenotypic variability. Thus, a major challenge in many "ome-wide" association analyses is to achieve adequate statistical power to identify multiple variants of small effect sizes, which is notoriously difficult for studies with relatively small-sample sizes. A small-sample adjustment incorporated in the kernel machine regression framework was proposed to solve this for association studies under various settings. However, such an adjustment in the generalized linear mixed model (GLMM) framework, which accounts for both sample relatedness and non-Gaussian outcomes, has not yet been attempted. In this study, we fill this gap by extending small-sample adjustment in kernel machine association test to GLMM. We propose a new Variant-Set Association Test (VSAT), a powerful and efficient analysis tool in GLMM, to examine the association between a set of omics variants and correlated phenotypes. The usefulness of VSAT is demonstrated using both numerical simulation studies and applications to data collected from multiple association studies. The software for implementing the proposed method in R is available at https://www.github.com/jchen1981/SSKAT.

Maintaining the validity of inference in small-sample stepped wedge cluster randomized trials with binary outcomes when using generalized estimating equations.

Stepped wedge cluster trials are an increasingly popular alternative to traditional parallel cluster randomized trials. Such trials often utilize a small number of clusters and numerous time intervals, and these components must be considered when choosing an analysis method. A generalized linear mixed model containing a random intercept and fixed time and intervention covariates is the most common analysis approach. However, the sole use of a random intercept applies a constant intraclass correlation coefficient structure, which is an assumption that is likely to be violated given stepped wedge trials (SWTs) have multiple time intervals. Alternatively, generalized estimating equations (GEE) are robust to the misspecification of the working correlation structure, although it has been shown that small-sample adjustments to standard error estimates and the use of appropriate degrees of freedom are required to maintain the validity of inference when the number of clusters is small. In this article, we show, using an extensive simulation study based on a motivating example and a more general design, the use of GEE can maintain the validity of inference in small-sample SWTs with binary outcomes. Furthermore, we show which combinations of bias corrections to standard error estimates and degrees of freedom work best in terms of attaining nominal type I error rates.

Extrapolating sparse gold standard cause of death designations to characterize broader catchment areas

Abstract Objectives The Child Health and Mortality Prevention Surveillance (CHAMPS) Network is designed to elucidate and track causes of under-5 child mortality and stillbirth in multiple sites in sub-Saharan Africa and South Asia using advanced surveillance, laboratory and pathology methods. Expert panels provide an arguable gold standard determination of underlying cause of death (CoD) on a subset of child deaths, in part through examining tissue obtained via minimally invasive tissue sampling (MITS) procedures. We consider estimating a population-level distribution of CoDs based on this sparse but precise data, in conjunction with data on subgrouping characteristics that are measured on the broader population of cases and are potentially associated with selection for MITS and with cause-specific mortality. Methods We illustrate how estimation of each underlying CoD proportion using all available data can be addressed equivalently in terms of a Horvitz-Thompson adjustment or a direct standardization, uncovering insights relevant to the designation of appropriate subgroups to adjust for non-representative sampling. Taking advantage of the functional form of the result when expressed as a multinomial distribution-based maximum likelihood estimator, we propose small-sample adjustments to Bayesian credible intervals based on Jeffreys or related weakly informative Dirichlet prior distributions. Results Our analyses of early data from CHAMPS sites in Kenya and Mozambique and accompanying simulation studies demonstrate the validity of the adjustment approach under attendant assumptions, together with marked performance improvements associated with the proposed adjusted Bayesian credible intervals. Conclusions Adjustment for non-representative sampling of those validated via gold standard diagnostic methods is a critical endeavor for epidemiologic studies like CHAMPS that seek extrapolation of CoD proportion estimates.

Correlating multidimensional short-term empirical protein properties to long-term protein physical stability data via empirical phase diagrams

Identification of long-term stable biopharmaceutical formulations is essential for biopharmaceutical product development. Reduction of the number of long-term storage experiments and a well-defined formulation search space requires knowledge-based formulation screenings and a detailed protein phase behavior understanding. To achieve this, short-term analytical techniques can serve as predictors for long-term protein phase behavior. Protein phase behavior studies that investigate this concept commonly display shortcomings such as limited and small datasets, sample adjustments, or simplistic data analysis. To overcome these shortcomings, 150 unique lysozyme solutions were analyzed using six different short-term analytical techniques. Lysozyme’s structural properties, conformational stability, colloidal stability, surface charge, and surface hydrophobicity were obtained directly after formulation preparation. Employing the empirical phase diagram method, this short-term data was correlated to long-term physical stability data obtained during 40 days of storage. Short-term protein properties showed partial correlation to long-term phase behavior. Structural differences, changing surface properties, colloidal stability, and conformation stability as a function of formulation conditions were observed. This study contributes to long-term protein phase behavior research by presenting a systematic, data-dependent, and multidimensional data evaluation workflow to create a comprehensive overview of short-term protein analytics in relation to long-term protein phase behavior.

A readily available improvement over method of moments for intra-cluster correlation estimation in the context of cluster randomized trials and fitting a GEE-type marginal model for binary outcomes.

Cluster randomized trials are popular in health-related research due to the need or desire to randomize clusters of subjects to different trial arms as opposed to randomizing each subject individually. As outcomes from subjects within the same cluster tend to be more alike than outcomes from subjects within other clusters, an exchangeable correlation arises that is measured via the intra-cluster correlation coefficient. Intra-cluster correlation coefficient estimation is especially important due to the increasing awareness of the need to publish such values from studies in order to help guide the design of future cluster randomized trials. Therefore, numerous methods have been proposed to accurately estimate the intra-cluster correlation coefficient, with much attention given to binary outcomes. As marginal models are often of interest, we focus on intra-cluster correlation coefficient estimation in the context of fitting such a model with binary outcomes using generalized estimating equations. Traditionally, intra-cluster correlation coefficient estimation with generalized estimating equations has been based on the method of moments, although such estimators can be negatively biased. Furthermore, alternative estimators that work well, such as the analysis of variance estimator, are not as readily applicable in the context of practical data analyses with generalized estimating equations. Therefore, in this article we assess, in terms of bias, the readily available residual pseudo-likelihood approach to intra-cluster correlation coefficient estimation with the GLIMMIX procedure of SAS (SAS Institute, Cary, NC). Furthermore, we study a possible corresponding approach to confidence interval construction for the intra-cluster correlation coefficient. We utilize a simulation study and application example to assess bias in intra-cluster correlation coefficient estimates obtained from GLIMMIX using residual pseudo-likelihood. This estimator is contrasted with method of moments and analysis of variance estimators which are standards of comparison. The approach to confidence interval construction is assessed by examining coverage probabilities. Overall, the residual pseudo-likelihood estimator performs very well. It has considerably less bias than moment estimators, which are its competitor for general generalized estimating equation-based analyses, and therefore, it is a major improvement in practice. Furthermore, it works almost as well as analysis of variance estimators when they are applicable. Confidence intervals have near-nominal coverage when the intra-cluster correlation coefficient estimate has negligible bias. Our results show that the residual pseudo-likelihood estimator is a good option for intra-cluster correlation coefficient estimation when conducting a generalized estimating equation-based analysis of binary outcome data arising from cluster randomized trials. The estimator is practical in that it is simply a result from fitting a marginal model with GLIMMIX, and a confidence interval can be easily obtained. An additional advantage is that, unlike most other options for performing generalized estimating equation-based analyses, GLIMMIX provides analysts the option to utilize small-sample adjustments that ensure valid inference.

Utilizing Whole-Exome Sequencing to Characterize the Phenotypic Variability of Sickle Cell Disease.

Sickle cell disease (SCD) is a monogenic disease that has wide variety of phenotypes with both and environmental factors contributing to its severity. We performed whole-exome sequencing (WES) in 22 Saudi SCD patients to identify variants that could explain differences in disease phenotypes. All variants, except those that were benign and likely benign, described in the ClinVar database, were considered in our analysis. Gene-based association testing using sequence kernel association optimal unified test (SKAT-O) with small sample adjustment was performed to evaluate the effect of multiple variants in genes on SCD phenotypes. The mean age of participants was 28 (range, 10-48 years). All patients were homozygous for the sickle cell mutation. The Benin haplotype was present in 15 patients and the Arab-Indian haplotype in 7 patients. One patient who had both SCD and CHARGE association was heterozygous for pathogenic mutation p.Arg987Ter in the CHD7 gene. One SCD individual who had a stroke was a carrier of the pathogenic variant p.Asp36Tyr in the VKORC1 gene which is, associated with warfarin resistance. Two patients with steady hemoglobin levels of 7.5 and 7.1 g/dL were carriers of the pathogenic mutation p.Gly140Ser in the RPL5 gene that is associated with Diamond-Blackfan anemia. None of the patients were transfusion dependent. A heterozygous pathogenic mutation in the LDLR gene associated with autosomal dominant familial hypercholesterolemia was present in one patient with deep venous thrombosis, although their cholesterol level was normal. One individual with stroke was a carrier for the p.Arg284Ter variant in the NLRP12 gene, which is associated with familial cold autoinflammatory syndrome 2. Another patient with stroke and a pulmonary embolism was heterozygous for the p.Pro106Leu variant of the MPL gene, which has been associated with thrombocytosis. Coding variants in the GOLGB1, ENPP1, and PON1 genes showed no association with stroke in our study. SKAT-O analysis did not explain SCD heterogeneity. WES provided limited information to explain the severity of SCD. Whole genome sequencing, epigenetic studies, and assessment of environmental factors might expand our knowledge of SCD heterogeneity.

PROTOCOL: Voluntary work for the physical and mental health of older volunteers.

PROTOCOL: Voluntary work for the physical and mental health of older volunteers.

Assessing meta-regression methods for examining moderator relationships with dependent effect sizes: A Monte Carlo simulation.

Dependent effect sizes are ubiquitous in meta-analysis. Using Monte Carlo simulation, we compared the performance of 2 methods for meta-regression with dependent effect sizes-robust variance estimation (RVE) and 3-level modeling-with the standard meta-analytic method for independent effect sizes. We further compared bias-reduced linearization and jackknife estimators as small-sample adjustments for RVE and Wald-type and likelihood ratio tests for 3-level models. The bias in the slope estimates, width of the confidence intervals around those estimates, and empirical type I error and statistical power rates of the hypothesis tests from these different methods were compared for mixed-effects meta-regression analysis with one moderator either at the study or at the effect size level. All methods yielded nearly unbiased slope estimates under most scenarios, but as expected, the standard method ignoring dependency provided inflated type I error rates when testing the significance of the moderators. Robust variance estimation methods yielded not only the best results in terms of type I error rate but also the widest confidence intervals and the lowest power rates, especially when using the jackknife adjustments. Three-level models showed a promising performance with a moderate to large number of studies, especially with the likelihood ratio test, and yielded narrower confidence intervals around the slope and higher power rates than those obtained with the RVE approach. All methods performed better when the moderator was at the effect size level, the number of studies was moderate to large, and the between-studies variance was small. Our results can help meta-analysts deal with dependency in their data.

Identification of Rare Variants in ATP8B4 as a Risk Factor for Systemic Sclerosis by Whole-Exome Sequencing.

To determine the contribution of rare variants as genetic modifiers of the expressivity, penetrance, and severity of systemic sclerosis (SSc). We performed whole-exome sequencing of 78 European American patients with SSc, including 35 patients without pulmonary arterial hypertension (PAH) and 43 patients with PAH. Association testing of case-control probability for rare variants was performed using the unified sequence kernel association test with optimal kernel weighting and small sample adjustment by comparing all SSc patients with a reference population of 3,179 controls from the Exome Sequencing Project 5,500 exome data set. Replication genotyping was performed in an independent sample of 3,263 patients (415 patients with SSc and 2,848 controls). We conducted expression profiling of messenger RNA from 61 SSc patients (19 without PAH and 42 with PAH) and 41 corresponding controls. The ATP8B4 gene was associated with a significant increase in the risk of SSc (P = 2.77 × 10(-7)). Among the 64 ATP8B4 variants tested, a single missense variant, c.1308C>G (F436L, rs55687265), provided the most compelling evidence of association (P = 9.35 × 10(-10), odds ratio [OR] 6.11), which was confirmed in the replication cohort (P = 0.012, OR 1.86) and meta-analysis (P = 1.92 × 10(-7), OR 2.5). Genes involved in E3 ubiquitin-protein ligase complex (ASB10) and cyclic nucleotide gated channelopathies (CNGB3) as well as HLA-DRB5 and HSPB2 (heat-shock protein 27) provided additional evidence of association (P < 10(-5)). Differential ATP8B4 expression was observed among the SSc patients compared to the controls (P = 0.0005). ATP8B4 may represent a putative genetic risk factor for SSc and pulmonary vascular complications.

Small Sample Kernel Association Tests for Human Genetic and Microbiome Association Studies.

Kernel machine based association tests (KAT) have been increasingly used in testing the association between an outcome and a set of biological measurements due to its power to combine multiple weak signals of complex relationship with the outcome through the specification of a relevant kernel. Human genetic and microbiome association studies are two important applications of KAT. However, the classic KAT framework relies on large sample theory, and conservativeness has been observed for small sample studies, especially for microbiome association studies. The common approach for addressing the small sample problem relies on computationally intensive resampling methods. Here, we derive an exact test for KAT with continuous traits, which resolve the small sample conservatism of KAT without the need for resampling. The exact test has significantly improved power to detect association for microbiome studies. For binary traits, we propose a similar approximate test, and we show that the approximate test is very powerful for a wide range of kernels including common variant- and microbiome-based kernels, and the approximate test controls the type I error well for these kernels. In contrast, the sequence kernel association tests have slightly inflated genomic inflation factors after small sample adjustment. Extensive simulations and application to a real microbiome association study are used to demonstrate the utility of our method.

Small-Sample Adjustments for Tests of Moderators and Model Fit Using Robust Variance Estimation in Meta-Regression

Meta-analyses often include studies that report multiple effect sizes based on a common pool of subjects or that report effect sizes from several samples that were treated with very similar research protocols. The inclusion of such studies introduces dependence among the effect size estimates. When the number of studies is large, robust variance estimation (RVE) provides a method for pooling dependent effects, even when information on the exact dependence structure is not available. When the number of studies is small or moderate, however, test statistics and confidence intervals based on RVE can have inflated Type I error. This article describes and investigates several small-sample adjustments to F-statistics based on RVE. Simulation results demonstrate that one such test, which approximates the test statistic using Hotelling’s T2 distribution, is level-α and uniformly more powerful than the others. An empirical application demonstrates how results based on this test compare to the large-sample F-test.

Commodity Prices, Growth, and Civil War Revisited

Bruckner and Ciccone (2010) find that there is a higher probability of the outbreak of civil war in Sub-Sahara Africa following downturns in the international commodity prices of the countries’ main traded commodities. I use R to replicate their results which yields identical estimates but slight discrepancies in the standard errors due to a small sample adjustment, although this doesn’t affect the level of statistical significance. Re-estimating the model using the latest data for 1981-2013 I am unable to find a strong link between commodity price shocks and civil war but do find that economic growth in OECD export countries negatively affects civil war onset.

Small sample adjustments for robust variance estimation with meta-regression.

Although primary studies often report multiple outcomes, the covariances between these outcomes are rarely reported. This leads to difficulties when combining studies in a meta-analysis. This problem was recently addressed with the introduction of robust variance estimation. This new method enables the estimation of meta-regression models with dependent effect sizes, even when the dependence structure is unknown. Although robust variance estimation has been shown to perform well when the number of studies in the meta-analysis is large, previous simulation studies suggest that the associated tests often have Type I error rates that are much larger than nominal. In this article, I introduce 6 estimators with better small sample properties and study the effectiveness of these estimators via 2 simulation studies. The results of these simulations suggest that the best estimator involves correcting both the residuals and degrees of freedom used in the robust variance estimator. These studies also suggest that the degrees of freedom depend on not only the number of studies but also the type of covariates in the meta-regression. The fact that the degrees of freedom can be small, even when the number of studies is large, suggests that these small-sample corrections should be used more generally. I conclude with an example comparing the results of a meta-regression with robust variance estimation with the results from the corrected estimator.

A generalized genetic random field method for the genetic association analysis of sequencing data.

With the advance of high-throughput sequencing technologies, it has become feasible to investigate the influence of the entire spectrum of sequencing variations on complex human diseases. Although association studies utilizing the new sequencing technologies hold great promise to unravel novel genetic variants, especially rare genetic variants that contribute to human diseases, the statistical analysis of high-dimensional sequencing data remains a challenge. Advanced analytical methods are in great need to facilitate high-dimensional sequencing data analyses. In this article, we propose a generalized genetic random field (GGRF) method for association analyses of sequencing data. Like other similarity-based methods (e.g., SIMreg and SKAT), the new method has the advantages of avoiding the need to specify thresholds for rare variants and allowing for testing multiple variants acting in different directions and magnitude of effects. The method is built on the generalized estimating equation framework and thus accommodates a variety of disease phenotypes (e.g., quantitative and binary phenotypes). Moreover, it has a nice asymptotic property, and can be applied to small-scale sequencing data without need for small-sample adjustment. Through simulations, we demonstrate that the proposed GGRF attains an improved or comparable power over a commonly used method, SKAT, under various disease scenarios, especially when rare variants play a significant role in disease etiology. We further illustrate GGRF with an application to a real dataset from the Dallas Heart Study. By using GGRF, we were able to detect the association of two candidate genes, ANGPTL3 and ANGPTL4, with serum triglyceride.

Abstract P4-01-03: HDACi (vorinostat) in metastatic breast cancer to restore sensitivity to ER-directed (AI) therapy: A phase II clinical trial with FES imaging correlates

Abstract Background: Histone deacetylase inhibitors (HDACi) have shown pre-clinical promise in estrogen receptor(ER)-modulation and restoring sensitivity to endocrine manipulation, suggesting potential clinical benefit (Sabnis 2011) (Huang 2000) in ER+ breast cancer. Vorinostat is an FDA-approved HDACi for CTCL, and could have a beneficial role in restoring ER-signaling in endocrine-resistant tumors (Munster 2011) (Yardley 2011). [F-18]fluoroestradiol (FES) PET imaging may be used to monitor regional tumor ER expression in patients with breast cancer (Linden 2011). Methods: Patients with metastatic breast cancer with prior clinical benefit from endocrine manipulation who progressed on an AI therapy are eligible for this ongoing trial. In part A, patients were given vorinostat for 2 weeks, then resumed AI for 6 W. In part B (reflecting results of prior HDACi trials) patients are given vorinostat 400mg po daily 5/7 days 3/4 weeks while AI is given continuously. Paired FES and FDG PET are performed at baseline, week 2 and 8; clinical/radiologic assessment of disease is also performed at week 8. Patients with clinical benefit (response or stable disease) may continue on treatment until progressive disease or study withdrawal. Lesion-level analysis of the association between baseline FES uptake (logged) and FES/FDG ratio used generalized estimating equations (GEE) with small-sample adjustments to standard errors. Results: 12/ 20 planned patients have accrued, and the treatment is well tolerated. Enrolled women were postmenopausal, the majority with primary infiltrating ductal tumors, bone/soft tissue dominant with longstanding metastatic disease, exposed to multiple endocrine and chemotherapy regimens. Five patients have had clinical benefit (2/4 on part B with greater HDACi exposure). One patient withdrew from the study due to toxicity. FES and FDG uptake was analyzed in 42 lesions in 11 patients. Average FES uptake was 2.0 (SULmean) for patients with clinical benefit, and 1.2 in patients with progressive disease by 8 weeks (p = 0.09). FES/FDG ratio at baseline was also associated with response (p = 0.04). Conclusions: HDACi therapy is promising in relapsed ER+ breast cancer. Imaging of metabolic pathways in parallel with clinical trials may accelerate understanding of the underlying tumor biology and refine treatment selection. Citation Information: Cancer Res 2013;73(24 Suppl): Abstract nr P4-01-03.

Modified likelihood ratio statistics for inflated beta regressions

The class of inflated beta regression models generalizes that of beta regressions [S.L.P. Ferrari and F. Cribari-Neto, Beta regression for modelling rates and proportions, J. Appl. Stat. 31 (2004), pp. 799–815] by incorporating a discrete component that allows practitioners to model data on rates and proportions with observations that equal an interval limit. For instance, one can model responses that assume values in (0, 1]. The likelihood ratio test tends to be quite oversized (liberal, anticonservative) in inflated beta regressions estimated with a small number of observations. Indeed, our numerical results show that its null rejection rate can be almost twice the nominal level. It is thus important to develop alternative testing strategies. This paper develops small-sample adjustments to the likelihood ratio and signed likelihood ratio test statistics in inflated beta regression models. The adjustments do not require orthogonality between the parameters of interest and the nuisance parameters and are fairly simple since they only require first- and second-order log-likelihood cumulants. Simulation results show that the modified likelihood ratio tests deliver much accurate inference in small samples. An empirical application is presented and discussed.