Small Number Of Clusters Research Articles

A Quality Improvement Intervention to Enhance Access to Kidney Transplantation and Living Kidney Donation (EnAKT LKD) in Patients With Chronic Kidney Disease: Clinical Research Protocol of a Cluster-Randomized Clinical Trial.

Background:Many patients with kidney failure will live longer and healthier lives if they receive a kidney transplant rather than dialysis. However, multiple barriers prevent patients from accessing this treatment option.Objective:To determine if a quality improvement intervention provided in chronic kidney disease (CKD) programs (vs. usual care) enables more patients with no recorded contraindications to kidney transplant to complete more steps toward receiving a kidney transplant.Design:This protocol describes a pragmatic 2-arm, parallel-group, open-label, registry-based, cluster-randomized clinical trial—the Enhance Access to Kidney Transplantation and Living Kidney Donation (EnAKT LKD) trial.Setting:All 26 CKD programs in Ontario, Canada, with a trial start date of November 1, 2017. The original end date of March 31, 2021 (3.4 years) has been extended to December 31, 2021 (4.1 years) due to the COVID-19 pandemic.Participants:During the trial, the 26 CKD programs are expected to care for more than 10 000 adult patients with CKD (including patients approaching the need for dialysis and patients receiving dialysis) with no recorded contraindications to a kidney transplant.Intervention:Programs were randomly allocated to provide a quality improvement intervention or usual care. The intervention has 4 main components: (1) local quality improvement teams and administrative support; (2) tailored education and resources for staff, patients, and living kidney donor candidates; (3) support from kidney transplant recipients and living kidney donors; and (4) program-level performance reports and oversight by program leaders.Primary Outcome:The primary outcome is the number of key steps completed toward receiving a kidney transplant analyzed at the cluster level (CKD program). The following 4 unique steps per patient will be counted: (1) patient referred to a transplant center for evaluation, (2) at least one living kidney donor candidate contacts a transplant center for an intended recipient and completes a health history questionnaire to begin their evaluation, (3) patient added to the deceased donor transplant wait list, and (4) patient receives a kidney transplant from a living or deceased donor.Planned Primary Analysis:Study data will be obtained from Ontario’s linked administrative healthcare databases. An intent-to-treat analysis will be conducted comparing the primary outcome between randomized groups using a 2-stage approach. First stage: residuals are obtained from fitting a regression model to individual-level variables ignoring intervention and clustering effects. Second stage: residuals from the first stage are aggregated at the cluster level as the outcome.Limitations:It may not be possible to isolate independent effects of each intervention component, the usual care group could adopt intervention components leading to contamination bias, and the relatively small number of clusters could mean the 2 arms are not balanced on all baseline prognostic factors.Conclusions:The EnAKT LKD trial will provide high-quality evidence on whether a multi-component quality improvement intervention helps patients complete more steps toward receiving a kidney transplant.Trial registration:Clinicaltrials.gov; identifier: NCT03329521.

A survey of nature-inspired algorithm for partitional data clustering

The aim of the clustering is representing the huge amount of data objects by a smaller number of clusters or groups based on similarity. It is a task of good data analysis tool that required a rapid and precise partitioning the vast amount of data sets. The clustering problem is bring simplicity in modelling data and plays major role in the process of data mining and knowledge discovery. In the early stage, there are many conventional algorithm are used to solve the problem of data clustering. But, those conventional algorithms do not meet the requirement of clustering problem. Hence, the nature-inspired based approaches have been applied to fulfil the requirements data clustering problem and it can manage the shortcoming of conventional data clustering algorithm. This present paper is conducting a comprehensive review about the data clustering problem, discussed some of the machine learning datasets and performance metrics. This survey paper can helps to researcher in to the next steps in future.

Design and analysis of three-arm parallel cluster randomized trials with small numbers of clusters.

In this article, we review and evaluate a number of methods used in the design and analysis of small three-arm parallel cluster randomized trials. We conduct a simulation-based study to evaluate restricted randomization methods including covariate-constrained randomization and a novel method for matched-group cluster randomization. We also evaluate the appropriate modelling of the data and small sample inferential methods for a variety of treatment effects relevant to three-arm trials. Our results indicate that small-sample corrections are required for high (0.05) but not low (0.001) values of the intraclass correlation coefficient and their performance can depend on trial design, number of clusters, and the nature of the hypothesis being tested. The Satterthwaite correction generally performed best at an ICC of 0.05 with a nominal type I error rate for single-period trials, and in trials with repeated measures type I error rates were between 0.04 and 0.06. Restricted randomization methods produce little benefit in trials with repeated measures but in trials with single post-intervention design can provide relatively large gains in power when compared to the most unbalanced possible allocations. Matched-group randomization improves power but is not as effective as covariate-constrained randomization. For model-based analysis, adjusting for fewer covariates than were used in a restricted randomization process under any design can produce non-nominal type I error rates and reductions in power. Where comparisons to two-arm cluster trials are possible, the performance of the methods is qualitatively very similar.

A Bayesian approach to restricted latent class models for scientifically structured clustering of multivariate binary outcomes.

This paper presents a model-based method for clustering multivariate binary observations that incorporates constraints consistent with the scientific context. The approach is motivated by the precision medicine problem of identifying autoimmune disease patient subsets or classes who may require different treatments. We start with a family of restricted latent class models or RLCMs. However, in the motivating example and many others like it, the unknown number of classes and the definition of classes using binary states are among the targets of inference. We use a Bayesian approach to RLCMs in order to use informative prior assumptions on the number and definitions of latent classes to be consistent with scientific knowledge so that the posterior distribution tends to concentrate on smaller numbers of clusters and sparser binary patterns. The paper derives a posterior sampling algorithm based on Markov chain Monte Carlo with split-merge updates to efficiently explore the space of clustering allocations. Through simulations under the assumed model and realistic deviations from it, we demonstrate greater interpretability of results and superior finite-sample clustering performance for our method compared to common alternatives. The methods are illustrated with an analysis of protein data to detect clusters representing autoantibody classes among sclerodermapatients.

A Source Clustering Approach for Efficient Inundation Modeling and Regional Scale Probabilistic Tsunami Hazard Assessment

For coastal regions on the margin of a subduction zone, near-field megathrust earthquakes are the source of the most extreme tsunami hazards, and are important to handle properly as one aspect of any Probabilistic Tsunami Hazard Assessment (PTHA). Typically, great variability in inundation depth at any point is possible due to the extreme variation in extent and pattern of slip over the fault surface. In this context, we present an approach to estimating inundation depth probabilities (in the form of hazard curves at a set of coastal locations) that consists of two components. The first component uses a Karhunen-Loeve expansion to express the probability density function (PDF) for all possible events, with PDF parameters that are geophysically reasonable for the Cascadia Subduction Zone (CSZ). It is then easy and computationally cheap to generate a large $N$ number of samples from this PDF; doing so and performing a full tsunami inundation simulation for each provides a brute force approach to estimating probabilities of inundation. However, to obtain reasonable results, particularly for extreme flooding due to rare events, $N$ would have to be so large as to make the tsunami simulations prohibitively expensive. The second component tackles this difficulty by using importance sampling techniques to adequately sample the tails of the distribution and properly re-weight the probability assigned to the resulting realizations, and by grouping the realizations into a small number of clusters that we believe will give similar inundation patterns in the region of interest. In this approach, only one fine-grid tsunami simulation need be computed from a representative member of each cluster. We discuss clustering based on proxy quantities that are cheap to compute over a large number of realizations, but that can identify a smaller number of clusters of realizations that will have similar inundation depths. The fine-grid simulations for each cluster representative can also be used to develop an improved strategy, in which these are combined with cheaper coarse-grid simulations of other members of the cluster. We illustrate the methodology by considering two coastal locations: Crescent City, CA and Westport, WA.

Relative efficiency of equal versus unequal cluster sizes in cluster randomized trials with a small number of clusters

ABSTRACT To calculate sample sizes in cluster randomized trials (CRTs), the cluster sizes are usually assumed to be identical across all clusters for simplicity. However, equal cluster sizes are not guaranteed in practice, especially when the number of clusters is limited. Therefore, it is important to understand the relative efficiency (RE) of equal versus unequal cluster sizes when designing CRTs with a limited number of clusters. In this paper, we are interested in the RE of two bias-corrected sandwich estimators of the treatment effect in the Generalized Estimating Equation (GEE) models for CRTs with a small number of clusters. Specifically, we derive the RE of two bias-corrected sandwich estimators for binary, continuous, or count data in CRTs under the assumption of an exchangeable working correlation structure. We consider different scenarios of cluster size distributions and investigate RE performance through simulation studies. We conclude that the number of clusters could be increased by as much as 42% to compensate for efficiency loss due to unequal cluster sizes. Finally, we propose an algorithm of increasing the number of clusters when the coefficient of variation of cluster sizes is known and unknown.

Comparison of small-sample standard-error corrections for generalised estimating equations in stepped wedge cluster randomised trials with a binary outcome: A simulation study.

Generalised estimating equations with the sandwich standard-error estimator provide a promising method of analysis for stepped wedge cluster randomised trials. However, they have inflated type-one error when used with a small number of clusters, which is common for stepped wedge cluster randomised trials. We present a large simulation study of binary outcomes comparing bias-corrected standard errors from Fay and Graubard; Mancl and DeRouen; Kauermann and Carroll; Morel, Bokossa, and Neerchal; and Mackinnon and White with an independent and exchangeable working correlation matrix. We constructed 95% confidence intervals using a t-distribution with degrees of freedom including clusters minus parameters (DFC-P), cluster periods minus parameters, and estimators from Fay and Graubard (DFFG), and Pan and Wall. Fay and Graubard and an approximation to Kauermann and Carroll (with simpler matrix inversion) were unbiased in a wide range of scenarios with an independent working correlation matrix and more than 12 clusters. They gave confidence intervals with close to 95% coverage with DFFG with 12 or more clusters, and DFC-P with 18 or more clusters. Both standard errors were conservative with fewer clusters. With an exchangeable working correlation matrix, approximated Kauermann and Carroll and Fay and Graubard had a small degree of under-coverage.

Participation in adherence clubs and on-time drug pickup among HIV-infected adults in Zambia: A matched-pair cluster randomized trial.

BackgroundCurrent models of HIV service delivery, with frequent facility visits, have led to facility congestion, patient and healthcare provider dissatisfaction, and suboptimal quality of services and retention in care. The Zambian urban adherence club (AC) is a health service innovation designed to improve on-time drug pickup and retention in HIV care through off-hours facility access and pharmacist-led group drug distribution. Similar models of differentiated service delivery (DSD) have shown promise in South Africa, but observational analyses of these models are prone to bias and confounding. We sought to evaluate the effectiveness and implementation of ACs in Zambia using a more rigorous study design.Methods and findingsUsing a matched-pair cluster randomized study design (ClinicalTrials.gov: NCT02776254), 10 clinics were randomized to intervention (5 clinics) or control (5 clinics). At each clinic, between May 19 and October 27, 2016, a systematic random sample was assessed for eligibility (HIV+, age ≥ 14 years, on ART >6 months, not acutely ill, CD4 count not <200 cells/mm3) and willingness to participate in an AC. Clinical and antiretroviral drug pickup data were obtained through the existing electronic medical record. AC meeting attendance data were collected at intervention facilities prospectively through October 28, 2017. The primary outcome was time to first late drug pickup (>7 days late). Intervention effect was estimated using unadjusted Kaplan–Meier survival curves and a Cox proportional hazards model to derive an adjusted hazard ratio (aHR). Medication possession ratio (MPR) and implementation outcomes (adoption, acceptability, appropriateness, feasibility, and fidelity) were additionally evaluated as secondary outcomes. Baseline characteristics were similar between 571 intervention and 489 control participants with respect to median age (42 versus 41 years), sex (62% versus 66% female), median time since ART initiation (4.8 versus 5.0 years), median CD4 count at study enrollment (506 versus 533 cells/mm3), and baseline retention (53% versus 55% with at least 1 late drug pickup in previous 12 months). The rate of late drug pickup was lower in intervention participants compared to control participants (aHR 0.26, 95% CI 0.15–0.45, p < 0.001). Median MPR was 100% in intervention participants compared to 96% in control participants (p < 0.001). Although 18% (683/3,734) of AC group meeting visits were missed, on-time drug pickup (within 7 days) still occurred in 51% (350/683) of these missed visits through alternate means (use of buddy pickup or early return to the facility). Qualitative evaluation suggests that the intervention was acceptable to both patients and providers. While patients embraced the convenience and patient-centeredness of the model, preference for traditional adherence counseling and need for greater human resources influenced intervention appropriateness and feasibility from the provider perspective. The main limitations of this study were the small number of clusters, lack of viral load data, and relatively short follow-up period.ConclusionsACs were found to be an effective model of service delivery for reducing late ART drug pickup among HIV-infected adults in Zambia. Drug pickup outside of group meetings was relatively common and underscores the need for DSD models to be flexible and patient-centered if they are to be effective.Trial registrationClinicalTrials.gov NCT02776254.

Ejecta distribution and transport property of fused silica under the laser shock loading

Laser-induced particle ejection on the exit surface of fused silica serves as an important contaminant source in a high-power laser system. The transport process of molten silica particles in a gas environment or vacuum is important in understanding the change in size and temperature of silica particles, which influence the ultra-clean manufacturing of optical components. In this paper, the ejection process of fused silica is investigated using molecular dynamics simulation. The results show that the geometry of a surface scratch influences the mass of the microjet. With shallower groove depth and a smaller vortex angle, the mass of the microjet is less under shock loading. The size of ejected particles tends to decrease gradually and does not change any more eventually. Besides, these particles become dispersed during the transport process in a vacuum. On the other hand, background gas suppresses the particle flow and slows down the particle flow. As the ejected particles compress gas, vapor and small clusters (N &amp;lt; 50) are stripped from the microjet continuously. Eventually, the number of nanoparticles that exceed the free surface decreases to zero. The stripped small clusters behind the head of the microjet recombine with other clusters, which change the volume density of ejected particles near the free surface. The higher velocity of ejected particles induces a stronger gas stripping effect, which makes an increase in the number of small clusters (N &amp;lt; 50). The results can help understand the behavior of particle ejection and the transport process of silica particles in a gas environment or vacuum, especially in the field of laser-induced particle ejection on the exit surface or the laser ablation of fused silica producing aerosol.

Clustering in Hypergraphs to Minimize Average Edge Service Time

We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications, such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together, and the optimization criteria that we use can be interpreted as the average delay (or cost) to serve the items of a typical edge. We describe and analyze algorithms for this problem for the case in which the clusters have to be disjoint and for the case where clusters can overlap. The analysis is often subtle and reveals interesting structure and invariants that one can utilize.

A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container

This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, we concentrate on mathematical modeling in such an application, where using the “bee” tetrahex is chosen for the new Compact Muon Solenoid (CMS) design upgrade, which is one of four detectors used in Large Hadron Collider (LHC) experiment at European Laboratory for Particle Physics (CERN). We start from the existing hexagonal containers with hexagonal cells packed inside, and uniform clustering applied. We compare the center-aligned (CA) and vertex-aligned (VA) models, analyzing cluster rotations providing the increased packing efficiency. We formally describe the geometrical properties of clustering approaches and show that cluster sharing is inevitable at the container border with uniform clustering. In addition, we propose a new vertex-aligned model decreasing the number of shared clusters in the uniform scenario, but with a smaller number of clusters contained inside the container. Also, we describe a non-uniform tetrahex cluster packing scheme in the proposed container model. With the proposed cluster packing solution, it is accomplished that all clusters are contained inside the container region. Since cluster-sharing is completely avoided at the container border, the maximal packing efficiency is obtained compared to the existing models.

Peer Prediction with Heterogeneous Users

Peer prediction mechanisms incentivize agents to truthfully report their signals, in the absence of a verification mechanism, by comparing their reports with those of their peers. Prior work in this area is essentially restricted to the case of homogeneous agents, whose signal distributions are identical. This is limiting in many domains, where we would expect agents to differ in taste, judgment, and reliability. Although the Correlated Agreement (CA) mechanism [Shnayder et al. 2016a] can be extended to handle heterogeneous agents, there is a new challenge of efficiently estimating agent signal types. We solve this problem by clustering agents based on their reporting behavior, proposing a mechanism that works with clusters of agents, and designing algorithms that learn such a clustering. In this way, we also connect peer prediction with the Dawid and Skene [1979] literature on latent types. We retain the robustness against coordinated misreports of the CA mechanism, achieving an approximate incentive guarantee of ε -informed truthfulness. We show on real data that this incentive approximation is reasonable in practice, even with a small number of clusters.

Specialization, Market Access and Real Income

This paper estimates the impact of external demand shocks on real income. Our empirical strategy is based on a first order approximation to a wide class of small open economy models that feature sector-level gravity in trade flows. The framework allows us to measure foreign shocks and characterize their impact on income in terms of reduced-form elasticities. We use machine learning techniques to group 4-digit manufacturing sectors into a smaller number of clusters, and show that the cluster-level elasticities of income with respect to foreign shocks can be estimated using high-dimensional statistical techniques. We find clear evidence of heterogeneity in the income responses to different foreign shocks. Foreign demand shocks in complex intermediate and capital goods have large positive impacts on real income, whereas impacts in other sectors are negligible. The estimates imply that the pattern of sectoral specialization plays a quantitatively large role in how foreign shocks affect real income, while geographic position plays a smaller role. Finally, a calibrated multi-sector production and trade model can rationalize both the average and the heterogeneity in real income elasticities to foreign shocks under reasonable values of structural parameters.

Local Peaks-Based Clustering Algorithm in Symmetric Neighborhood Graph

Density-based clustering methods have achieved many applications in data mining, whereas most of them still likely suffer poor performances on data sets with extremely uneven distributions, like the manifold or ring data. The paper proposes a novel method for clustering with local peaks in the symmetric neighborhood. Local peaks are points with maximum densities at the local level. During the searching of local peaks, all data, except those outliers, can be easily divided into a number of small clusters in accordance with the local peaks in each point's neighborhood. Especially, a graph-based scheme is adopted here to merge similar clusters based on their similarity in the symmetric neighborhood graph, followed by assigning each outlier to the closest cluster. A variety of artificial, real data sets and a real building data set have been tested for clustering by the proposed method and compared against other popular density-based methods and other algorithms.

Similarity-based clusters are representational units of visual working memory.

We investigated whether clustering based on feature similarity improves the representational quality of visual working memory (VWM). We hypothesized that similar items are organized into clusters, and their recall precision increases with fewer clusters because of reduced memory load. In a series of 6 experiments, participants remembered orientations or colors of several stimuli and estimated the orientation (color) of cued item(s). We measured recall bias to identify whether items formed cluster(s) and measured recall precision to determine the effect of clustering on the representational quality of VWM. In Experiments 1 and 2, orientation similarity was manipulated to partition stimuli into 1, 2, or 3 clusters. In Experiment 3, we varied both the number of stimuli and their similarities such that 5 items were summarized into a smaller number of clusters than 3 items. We consistently found that similar items formed a cluster, and that the precision of the individual items increased with fewer clusters regardless of the number of items. We also observed the same clustering effects using color stimuli when participants were to remember items' colors (Experiment 4). However, a task-irrelevant feature was not potent enough to cluster items and did not increase the precision (Experiment 5). In Experiment 6, we varied item similarity and found that response errors were correlated within the same cluster but not across different clusters. Taken together, these results suggest that clusters formed by similar items can impact the representation of VWM; thus, acting as one of representational units of VWM. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Geomorphometric relief classification with the k-median method in the Silesian Upland, southern Poland

The aim of this study is geomorphometric relief classification of a temperate latitude upland area in Central Europe. The Silesian Upland represents diversified structural relief which contains a fan-shaped configuration of long thresholds and wide erosion depressions. A 20 m × 20 m digital elevation model (DEM) provided input data for the analysis. The k-median method was applied to examine morphometric variables of the relief. The aim of these activities was to identify clusters with objects of similar mathematical characteristics. These clusters were the basis of landform classification. Smaller numbers of clusters 4 transparently show hypsometric relationships. Key elements of the morphology of the area were clearly visible. The division into 6 clusters gives the best results—a detailed but clear image of the morphological diversity by distinguishing characteristic landform elements. The results for 8 clusters show significant background noise and are ambiguous, which makes them difficult to identify. Our research has confirmed that the k-median method is a useful tool for landform classifications. We determined optimal parameters of this method (filtering window size, DEM resolution, number of clusters, aspect influence).

Learning Structured Sparse Representations for Voice Conversion

Sparse-coding techniques for voice conversion assume that an utterance can be decomposed into a sparse code that only carries linguistic contents, and a dictionary of atoms that captures the speakers’ characteristics. However, conventional dictionary-construction and sparse-coding algorithms rarely meet this assumption. The result is that the sparse code is no longer speaker-independent, which leads to lower voice-conversion performance. In this paper, we propose a Cluster-Structured Sparse Representation (CSSR) that improves the speaker independence of the representations. CSSR consists of two complementary components: a Cluster-Structured Dictionary Learning module that groups atoms in the dictionary into clusters, and a Cluster-Selective Objective Function that encourages each speech frame to be represented by atoms from a small number of clusters. We conducted four experiments on the CMU ARCTIC corpus to evaluate the proposed method. In a first ablation study, results show that each of the two CSSR components enhances speaker independence, and that combining both components leads to further improvements. In a second experiment, we find that CSSR uses increasingly larger dictionaries more efficiently than phoneme-based representations by allowing finer-grained decompositions of speech sounds. In a third experiment, results from objective and subjective measurements show that CSSR outperforms prior voice-conversion methods, improving the acoustic quality of the synthesized speech while retaining the target speaker's voice identity. Finally, we show that the CSSR captures latent (i.e., phonetic) information in the speech signal.

Cluster tendency assessment in neuronal spike data.

Sorting spikes from extracellular recording into clusters associated with distinct single units (putative neurons) is a fundamental step in analyzing neuronal populations. Such spike sorting is intrinsically unsupervised, as the number of neurons are not known a priori. Therefor, any spike sorting is an unsupervised learning problem that requires either of the two approaches: specification of a fixed value k for the number of clusters to seek, or generation of candidate partitions for several possible values of c, followed by selection of a best candidate based on various post-clustering validation criteria. In this paper, we investigate the first approach and evaluate the utility of several methods for providing lower dimensional visualization of the cluster structure and on subsequent spike clustering. We also introduce a visualization technique called improved visual assessment of cluster tendency (iVAT) to estimate possible cluster structures in data without the need for dimensionality reduction. Experimental results are conducted on two datasets with ground truth labels. In data with a relatively small number of clusters, iVAT is beneficial in estimating the number of clusters to inform the initialization of clustering algorithms. With larger numbers of clusters, iVAT gives a useful estimate of the coarse cluster structure but sometimes fails to indicate the presumptive number of clusters. We show that noise associated with recording extracellular neuronal potentials can disrupt computational clustering schemes, highlighting the benefit of probabilistic clustering models. Our results show that t-Distributed Stochastic Neighbor Embedding (t-SNE) provides representations of the data that yield more accurate visualization of potential cluster structure to inform the clustering stage. Moreover, The clusters obtained using t-SNE features were more reliable than the clusters obtained using the other methods, which indicates that t-SNE can potentially be used for both visualization and to extract features to be used by any clustering algorithm.

A simulation study of statistical approaches to data analysis in the stepped wedge design.

This paper studies model-based and design-based approaches for the analysis of data arising from a stepped wedge randomized design. Specifically, for different scenarios we compare robustness, efficiency, Type I error rate under the null hypothesis, and power under the alternative hypothesis for the leading analytical options including generalized estimating equations (GEE) and linear mixed model (LMM) based approaches. We find that GEE models with exchangeable correlation structures are more efficient than GEE models with independent correlation structures under all scenarios considered. The model-based GEE Type I error rate can be inflated when applied with a small number of clusters, but this problem can be solved using a design-based approach. As expected, correct model specification is more important for LMM (compared to GEE) since the model is assumed correct when standard errors are calculated. However, in contrast to the model-based results, the design-based Type I error rates for LMM models under scenarios with a random treatment effect show type I error inflation even though the fitted models perfectly match the corresponding data generating scenarios. Therefore, greater robustness can be realized by combining GEE and permutation testing strategies.

Corrected Standard Errors with Clustered Data

The use of cluster robust standard errors (CRSE) is common as data are often collected from units, such as cities, states or countries, with multiple observations per unit. There is considerable discussion of how best to estimate standard errors and confidence intervals when using CRSE (Harden 2011; Imbens and Kolesár 2016; MacKinnon and Webb 2017; Esarey and Menger 2019). Extensive simulations in this literature and here show that CRSE seriously underestimate coefficient standard errors and their associated confidence intervals, particularly with a small number of clusters and when there is little within cluster variation in the explanatory variables. These same simulations show that a method developed here provides more reliable estimates of coefficient standard errors. They underestimate confidence intervals for tests of individual and sets of coefficients in extreme conditions, but by far less than do CRSE. Simulations also show that this method produces more accurate standard error and confidence interval estimates than bootstrapping, which is often recommended as an alternative to CRSE.