Loss Of Statistical Power Research Articles

INFLECT: an R-package for cytometry cluster evaluation using marker modality

BackgroundCurrent methods of high-dimensional unsupervised clustering of mass cytometry data lack means to monitor and evaluate clustering results. Whether unsupervised clustering is correct is typically evaluated by agreement with dimensionality reduction techniques or based on benchmarking with manually classified cells. The ambiguity and lack of reproducibility of sequential gating has been replaced with ambiguity in interpretation of clustering results. On the other hand, spurious overclustering of data leads to loss of statistical power. We have developed INFLECT, an R-package designed to give insight in clustering results and provide an optimal number of clusters. In our approach, a mass cytometry dataset is overclustered intentionally to ensure the smallest phenotypically different subsets are captured using FlowSOM. A range of metacluster number endpoints are generated and evaluated using marker interquartile range and distribution unimodality checks. The fraction of marker distributions that pass these checks is taken as a measure of clustering success. The fraction of unimodal distributions within metaclusters is plotted against the number of generated metaclusters and reaches a plateau of diminishing returns. The inflection point at which this occurs gives an optimal point of capturing cellular heterogeneity versus statistical power.ResultsWe applied INFLECT to four publically available mass cytometry datasets of different size and number of markers. The unimodality score consistently reached a plateau, with an inflection point dependent on dataset size and number of dimensions. We tested both ConsenusClusterPlus metaclustering and hierarchical clustering. While hierarchical clustering is less computationally expensive and thus faster, it achieved similar results to ConsensusClusterPlus. The four datasets consisted of labeled data and we compared INFLECT metaclustering to published results. INFLECT identified a higher optimal number of metaclusters for all datasets. We illustrated the underlying heterogeneity within labels, showing that these labels encompass distinct types of cells.ConclusionINFLECT addresses a knowledge gap in high-dimensional cytometry analysis, namely assessing clustering results. This is done through monitoring marker distributions for interquartile range and unimodality across a range of metacluster numbers. The inflection point is the optimal trade-off between cellular heterogeneity and statistical power, applied in this work for FlowSOM clustering on mass cytometry datasets.

Evaluation of machine learning methods for covariate data imputation in pharmacometrics.

Missing data create challenges in clinical research because they lead to loss of statistical power and potentially to biased results. Missing covariate data must be handled with suitable approaches to prepare datasets for pharmacometric analyses, such as population pharmacokinetic and pharmacodynamic analyses. To this end, various statistical methods have been widely adopted. Here, we introduce two machine-learning (ML) methods capable of imputing missing covariate data in a pharmacometric setting. Based on a previously published pharmacometric analysis, we simulated multiple missing data scenarios. We compared the performance of four established statistical methods, listwise deletion, mean imputation, standard multiple imputation (hereafter "Norm"), and predictive mean matching (PMM) and two ML based methods, random forest (RF) and artificial neural networks (ANNs), to handle missing covariate data in a statistically plausible manner. The investigated ML-based methods can be used to impute missing covariate data in a pharmacometric setting. Both traditional imputation approaches and ML-based methods perform well in the scenarios studied, with some restrictions for individual methods. The three methods exhibiting the best performance in terms of least bias for the investigated scenarios are the statistical method PMM and the two ML-based methods RF and ANN. ML-based approaches had comparable good results to the best performing established method PMM. Furthermore, ML methods provide added flexibility when encountering more complex nonlinear relationships, especially when associated parameters are suitably tuned to enhance predictive performance.

The case against censoring of progression-free survival in cancer clinical trials – A pandemic shutdown as an illustration

BackgroundMissing data may lead to loss of statistical power and introduce bias in clinical trials. The Covid-19 pandemic has had a profound impact on patient health care and on the conduct of cancer clinical trials. Although several endpoints may be affected, progression-free survival (PFS) is of major concern, given its frequent use as primary endpoint in advanced cancer and the fact that missed radiographic assessments are to be expected. The recent introduction of the estimand framework creates an opportunity to define more precisely the target of estimation and ensure alignment between the scientific question and the statistical analysis.MethodsWe used simulations to investigate the impact of two basic approaches for handling missing tumor scans due to the pandemic: a “treatment policy” strategy, which consisted in ascribing events to the time they are observed, and a “hypothetical” approach of censoring patients with events during the shutdown period at the last assessment prior to that period. We computed the power of the logrank test, estimated hazard ratios (HR) using Cox models, and estimated median PFS times without and with a hypothetical 6-month shutdown period with no patient enrollment or tumor scans being performed, varying the shutdown starting times.ResultsCompared with the results in the absence of shutdown, the “treatment policy” strategy slightly overestimated median PFS proportionally to the timing of the shutdown period, but power was not affected. Except for one specific scenario, there was no impact on the estimated HR. In general, the pandemic had a greater impact on the analyses using the “hypothetical” strategy, which led to decreased power and overestimated median PFS times to a greater extent than the “treatment policy” strategy.ConclusionAs a rule, we suggest that the treatment policy approach, which conforms with the intent-to-treat principle, should be the primary analysis to avoid unnecessary loss of power and minimize bias in median PFS estimates.

Exploratory analyses of clinical trial data used for health technology assessments: a retrospective evaluation.

ObjectivesTo examine the validity and statistical limitations of exploratory analyses of clinical trial data commonly requested by agencies responsible for determining which medical products may be financed or reimbursed by a healthcare system.DesignThis was a retrospective review of efficacy and safety analyses conducted for German Health Technology Assessment (HTA) evaluations with a decision date between 2015 and 2020, and an illustrative safety-related exploratory analysis of data from two phase III clinical trials of verubecestat (an anti-amyloid drug whose development was stopped for lack of efficacy) as would be mandated by the German HTA agency.ResultsWe identified 422 HTA evaluations of 404 randomised controlled clinical trials. For 140 trials (34.7%), the evaluation was based on subpopulations of participants in the originating confirmatory trial (175 subpopulations were assessed). In 57% (100 of 175), the subpopulation sample size was 50% or less of the original study population. Detailed analysis of five evaluations based on subpopulations of the original trial is presented. The safety-related exploratory analysis of verubecestat led to 206 statistical analyses for treatments and 812 treatment-by-subgroup interaction tests. Of 31 safety endpoints with an elevated HR (suggesting association with drug treatment), the HR for 81% of these (25 of 31) was not elevated in both trials. Of the 812 treatment-by-subgroup interactions evaluated, 26 had an elevated HR for a subgroup in one trial, but only 1 was elevated in both trials.ConclusionsMany HTA evaluations rely on subpopulation analyses and numerous post hoc statistical hypothesis tests. Subpopulation analysis may lead to loss of statistical power and uncontrolled influences of random imbalances. Multiple testing may introduce spurious findings. Decisions about benefits of medical products should therefore not rely on exploratory analyses of clinical trial data but rather on prospective clinical studies and careful synthesis of all available evidence based on prespecified criteria.

Reclaiming independence in spatial-clustering datasets: A series of data-driven spatial weights matrices.

Most spatial models include a spatial weights matrix (W) derived from the first law of geography to adjust the spatial dependence to fulfill the independence assumption. In various fields such as epidemiological and environmental studies, the spatial dependence often shows clustering (or geographic discontinuity) due to natural or social factors. In such cases, adjustment using the first‐law‐of‐geography‐based W might be inappropriate and leads to inaccuracy estimations and loss of statistical power. In this work, we propose a series of data‐driven Ws (DDWs) built following the spatial pattern identified by the scan statistic, which can be easily carried out using existing tools such as SaTScan software. The DDWs take both the clustering (or discontinuous) and the intuitive first‐law‐of‐geographic‐based spatial dependence into consideration. Aiming at two common purposes in epidemiology studies (ie, estimating the effect value of explanatory variable X and estimating the risk of each spatial unit in disease mapping), the common spatial autoregressive models and the Leroux‐prior‐based conditional autoregressive (CAR) models were selected to evaluate performance of DDWs, respectively. Both simulation and case studies show that our DDWs achieve considerably better performance than the classic W in datasets with clustering (or discontinuous) spatial dependence. Furthermore, the latest published density‐based spatial clustering models, aiming at dealing with such clustering (or discontinuity) spatial dependence in disease mapping, were also compared as references. The DDWs, incorporated into the CAR models, still show considerable advantage, especially in the datasets for common diseases.

Efficacy of a Toothpaste Based on Microcrystalline Hydroxyapatite on Children with Hypersensitivity Caused by MIH: A Randomised Controlled Trial.

Hypersensitivity is a frequent complaint in children with molar incisor hypomineralisation (MIH). This double-blind randomised controlled trial aimed to evaluate non-inferiority in hypersensitivity relief of a toothpaste containing microcrystalline hydroxyapatite compared to amine fluoride in children with MIH. Children were randomised into 2 groups: either hydroxyapatite (intervention) or amine fluoride toothpaste (control). The primary endpoint was pain sensation in response to tactile stimulus (Wong-Baker FACES Pain Rating Scale) 56 days after randomisation and analysed by mixed effects linear regression analysis. Non-inferiority was inferred if the upper limit of the one-sided 95% confidence interval (CI) of the difference between intervention and control group was below the non-inferiority margin of 1 in the ITT (intention-to-treat) and PP (per protocol) population. Twenty-one children were randomised and 14 children finished the study per protocol. In the ITT population, hydroxyapatite was non-inferior to amine fluoride (mean difference: -0.75 95%CI [-∞;0.49]). In the PP population, non-inferiority could not be shown (-0.62 [-∞;1.08]). Overall non-inferiority in hypersensitivity relief of a toothpaste containing hydroxyapatite compared to amine fluoride could not be shown. However, the hydroxyapatite group tended to be less hypersensitive in both populations. Attrition of the PP population due to the COVID-19 pandemic led to loss of statistical power.

Efficient spline regression for neural spiking data.

Point process generalized linear models (GLMs) provide a powerful tool for characterizing the coding properties of neural populations. Spline basis functions are often used in point process GLMs, when the relationship between the spiking and driving signals are nonlinear, but common choices for the structure of these spline bases often lead to loss of statistical power and numerical instability when the signals that influence spiking are bounded above or below. In particular, history dependent spike train models often suffer these issues at times immediately following a previous spike. This can make inferences related to refractoriness and bursting activity more challenging. Here, we propose a modified set of spline basis functions that assumes a flat derivative at the endpoints and show that this limits the uncertainty and numerical issues associated with cardinal splines. We illustrate the application of this modified basis to the problem of simultaneously estimating the place field and history dependent properties of a set of neurons from the CA1 region of rat hippocampus, and compare it with the other commonly used basis functions. We have made code available in MATLAB to implement spike train regression using these modified basis functions.

Widespread and interrelated gray matter reductions in child sexual offenders with and without pedophilia: Evidence from a multivariate structural MRI study.

To further investigate the neuroanatomical correlates of child sexual offending and disentangle them from the neural correlates of pedophilia, using a multivariate analytical approach in order to minimize loss of statistical power. This study presents structural MRI data on gray matter in an incarcerated, male population of 22 pedophilic and 21 non-pedophilic child sexual offenders, and 20 violent non-sexual offender controls, based on a multivariate whole-brain approach using source-based morphometry. We identify a network of several neuroanatomical regions exhibiting interrelated reduced gray matter in both child sexual offender groups relative to controls, comprising extensive clusters in the bilateral cerebellum and frontal lobe, as well as smaller clusters in the bilateral parietal, temporal, and occipital lobes, the bilateral basal ganglia, the medial cingulate and the hippocampus. Our results speak to the interpretation that there are inter- and possibly connectivity-related brain structural abnormalities in child sexual offenders that are not (only) pertaining to pedophilia per se. Interpretations and limitations of the present data are discussed and recommendations for future works are given.

Impact of Tumor Assessment Frequency on Statistical Power in Randomized Cancer Clinical Trials Evaluating Progression-Free Survival.

Progression-free survival (PFS) is frequently used as a primary endpoint in late-phase clinical trials for anti-metastatic cancer agents. Previous studies have indicated that the frequency of tumor assessment affects the statistical power for PFS because progression dates are inaccurate; however, this finding may be difficult to generalize because of its unrealistic assumptions. Therefore, we re-examined this issue under realistic assumptions and various scenarios that approximate actual clinical trials. Randomized clinical trials comparing two interventions against a solid tumor were simulated under conditions where progressive disease (PD)-dominant PFS or a non-negligible number of deaths (death-competitive PFS) contributed to PFS events, which are conditions that resemble clinical trials of first-line therapy and later-line therapy, respectively. We assessed the impact of tumor assessment frequency on the statistical power. Under the PD-dominant PFS condition, even in extreme scenarios, statistical power loss was only approximately 3%. Under the death-competitive PFS condition, tumor assessment frequency affected the statistical power of PFS if the effect of the treatment on overall survival was lower than that on time to progression. In this case, loss of statistical power was often more than 10% in some realistic scenarios. In trials investigating first-line treatments (PD-dominant PFS), tumor assessment frequency has a negligible impact on statistical power, whereas in trials investigating late-line therapies (death-competitive PFS), the potential impact of tumor assessment frequency on statistical power should be carefully evaluated at the design stage.

2dFDR: a new approach to confounder adjustment substantially increases detection power in omics association studies

One challenge facing omics association studies is the loss of statistical power when adjusting for confounders and multiple testing. The traditional statistical procedure involves fitting a confounder-adjusted regression model for each omics feature, followed by multiple testing correction. Here we show that the traditional procedure is not optimal and present a new approach, 2dFDR, a two-dimensional false discovery rate control procedure, for powerful confounder adjustment in multiple testing. Through extensive evaluation, we demonstrate that 2dFDR is more powerful than the traditional procedure, and in the presence of strong confounding and weak signals, the power improvement could be more than 100%.

The impact of left truncation of exposure in environmental case-control studies: evidence from breast cancer risk associated with airborne dioxin.

In epidemiology, left-truncated data may bias exposure effect estimates. We analyzed the bias induced by left truncation in estimating breast cancer risk associated with exposure to airborne dioxins. Simulations were run with exposure estimates from a Geographic Information System(GIS)-based metric and considered two hypotheses for historical exposure, three scenarios for intra-individual correlation of annual exposures, and three exposure-effect models. For each correlation/model combination, 500 nested matched case-control studies were simulated and data fitted using a conditional logistic regression model. Bias magnitude was assessed by estimated odds-ratios (ORs) versus theoretical relative risks (TRRs) comparisons. With strong intra-individual correlation and continuous exposure, left truncation overestimated the Beta parameter associated with cumulative dioxin exposure. Versus a theoretical Beta of 4.17, the estimated mean Beta (5%; 95%) was 73.2 (67.7; 78.8) with left-truncated exposure and 4.37 (4.05; 4.66) with lifetime exposure. With exposure categorized in quintiles, the TRR was 2.0, the estimated ORQ5 vs. Q1 2.19 (2.04; 2.33) with truncated exposure versus 2.17 (2.02; 2.32) with lifetime exposure. However, the difference in exposure between Q5 and Q1 was 18× smaller with truncated data, indicating an important overestimation of the dose effect. No intra-individual correlation resulted in effect dilution and statistical power loss. Left truncation induced substantial bias in estimating breast cancer risk associated with exposure with continuous and categorical models. With strong intra-individual exposure correlation, both models detected associations, but categorical models provided better estimates of effect trends. This calls for careful consideration of left truncation-induced bias in interpreting environmental epidemiological data.

Analytic results for scalar-mediated Higgs boson production in association with two jets

We present compact analytic formulae for all one-loop amplitudes representing the production of a Higgs boson in association with two jets, mediated by a colour triplet scalar particle. Many of the integral coefficients present for scalar mediators are identical to the case when a massive fermion circulates in the loop, reflecting a close relationship between the two theories. The calculation is used to study Higgs boson production in association with two jets in a simplified supersymmetry (SUSY) scenario in which the dominant additional contributions arise from loops of top squarks. The results presented here facilitate an indirect search for top squarks in this channel, by a precision measurement of the corresponding cross section. However, we find that the potential for improved discrimination between the Standard Model and SUSY cases suggested by the pattern of results in the one- and two-jet samples is unlikely to be realized due to the loss in statistical power compared to an inclusive analysis.

Genotype imputation in case-only studies of gene-environment interaction: validity and power

Case-only (CO) studies are a powerful means to uncover gene-environment (G × E) interactions for complex human diseases. Moreover, such studies may in principle also draw upon genotype imputation to increase statistical power even further. However, genotype imputation usually employs healthy controls such as the Haplotype Reference Consortium (HRC) data as an imputation base, which may systematically perturb CO studies in genomic regions with main effects upon disease risk. Using genotype data from 719 German Crohn Disease (CD) patients, we investigated the level of imputation accuracy achievable for single nucleotide polymorphisms (SNPs) with or without a genetic main effect, and with varying minor allele frequency (MAF). Genotypes were imputed from neighbouring SNPs at different levels of linkage disequilibrium (LD) to the target SNP using the HRC data as an imputation base. Comparison of the true and imputed genotypes revealed lower imputation accuracy for SNPs with strong main effects. We also simulated different levels of G × E interaction to evaluate the potential loss of statistical validity and power incurred by the use of imputed genotypes. Simulations under the null hypothesis revealed that genotype imputation does not inflate the type I error rate of CO studies of G × E. However, the statistical power was found to be reduced by imputation, particularly for SNPs with low MAF, and a gradual loss of statistical power resulted when the level of LD to the SNPs driving the imputation decreased. Our study thus highlights that genotype imputation should be employed with great care in CO studies of G × E interaction.

Contour prognostic model for predicting survival after resection of colorectal liver metastases: development and multicentre validation study using largest diameter and number of metastases with RAS mutation status.

Most current models for predicting survival after resection of colorectal liver metastasis include largest diameter and number of colorectal liver metastases as dichotomous variables, resulting in underestimation of the extent of risk variation and substantial loss of statistical power. The aim of this study was to develop and validate a new prognostic model for patients undergoing liver resection including largest diameter and number of colorectal liver metastases as continuous variables. A prognostic model was developed using data from patients who underwent liver resection for colorectal liver metastases at MD Anderson Cancer Center and had RAS mutational data. A Cox proportional hazards model analysis was used to develop a model based on largest colorectal liver metastasis diameter and number of metastases as continuous variables. The model results were shown using contour plots, and validated externally in an international multi-institutional cohort. A total of 810 patients met the inclusion criteria. Largest colorectal liver metastasis diameter (hazard ratio (HR) 1.11, 95 per cent confidence interval 1.06 to 1.16; P < 0.001), number of colorectal liver metastases (HR 1.06, 1.03 to 1.09; P < 0.001), and RAS mutation status (HR 1.76, 1.42 to 2.18; P < 0.001) were significantly associated with overall survival, together with age, primary lymph node metastasis, and prehepatectomy chemotherapy. The model performed well in the external validation cohort, with predicted overall survival values almost lying within 10 per cent of observed values. Wild-type RAS was associated with better overall survival than RAS mutation even when liver resection was performed for larger and/or multiple colorectal liver metastases. The contour prognostic model, based on diameter and number of lesions considered as continuous variables along with RAS mutation, predicts overall survival after resection of colorectal liver metastasis.

Impact of covariate omission and categorization from the Fine–Gray model in randomized-controlled trials

In this paper, we study the statistical issues related to the omission and categorization of important covariates in the context of the Fine–Gray model in randomized-controlled trials with competing risks. We show that the omission of an important covariate from the Fine–Gray model leads to attenuated estimates for treatment effect and loss of proportionality in general. Our simulation studies reveal substantial attenuation in the estimate for treatment effect and the loss of statistical power, while dichotomizing a continuous covariate leads to similar but less pronounced impact. Our results are illustrated using data from a randomized clinical trial of HIV-infected individuals. The relative merits of conducting an adjusted versus an unadjusted analysis of treatment effect in light of both statistical and practical considerations are discussed.

Best Practices for Binary and Ordinal Data Analyses.

The measurement of many human traits, states, and disorders begins with a set of items on a questionnaire. The response format for these questions is often simply binary (e.g., yes/no) or ordered (e.g., high, medium or low). During data analysis, these items are frequently summed or used to estimate factor scores. In clinical applications, such assessments are often non-normally distributed in the general population because many respondents are unaffected, and therefore asymptomatic. As a result, in many cases these measures violate the statistical assumptions required for subsequent analyses. To reduce the influence of the non-normality and quasi-continuous assessment, variables are frequently recoded into binary (affected-unaffected) or ordinal (mild-moderate-severe) diagnoses. Ordinal data therefore present challenges at multiple levels of analysis. Categorizing continuous variables into ordered categories typically results in a loss of statistical power, which represents an incentive to the data analyst to assume that the data are normally distributed, even when they are not. Despite prior zeitgeists suggesting that, e.g., variables with more than 10 ordered categories may be regarded as continuous and analyzed as if they were, we show via simulation studies that this is not generally the case. In particular, using Pearson product-moment correlations instead of maximum likelihood estimates of polychoric correlations biases the estimated correlations towards zero. This bias is especially severe when a plurality of the observations fall into a single observed category, such as a score of zero. By contrast, estimating the ordinal correlation by maximum likelihood yields no estimation bias, although standard errors are (appropriately) larger. We also illustrate how odds ratios depend critically on the proportion or prevalence of affected individuals in the population, and therefore are sub-optimal for studies where comparisons of association metrics are needed. Finally, we extend these analyses to the classical twin model and demonstrate that treating binary data as continuous will underestimate genetic and common environmental variance components, and overestimate unique environment (residual) variance. These biases increase as prevalence declines. While modeling ordinal data appropriately may be more computationally intensive and time consuming, failing to do so will likely yield biased correlations and biased parameter estimates from modeling them.

Study on the Missing Data Mechanisms and Imputation Methods

The absence of some data values in any observed dataset has been a real hindrance to achieving valid results in statistical research. This paper aimed at the missing data widespread problem faced by analysts and statisticians in academia and professional environments. Some data-driven methods were studied to obtain accurate data. Projects that highly rely on data face this missing data problem. And since machine learning models are only as good as the data used to train them, the missing data problem has a real impact on the solutions developed for real-world problems. Therefore, in this dissertation, there is an attempt to solve this problem using different mechanisms. This is done by testing the effectiveness of both traditional and modern data imputation techniques by determining the loss of statistical power when these different approaches are used to tackle the missing data problem. At the end of this research dissertation, it should be easy to establish which methods are the best when handling the research problem. It is recommended that using Multivariate Imputation by Chained Equations (MICE) for MAR missingness is the best approach to dealing with missing data.

IMIX: a multivariate mixture model approach to association analysis through multi-omics data integration.

Integrative genomic analysis is a powerful tool used to study the biological mechanisms underlying a complex disease or trait across multiplatform high-dimensional data, such as DNA methylation, copy number variation and gene expression. It is common to perform large-scale genome-wide association analysis of an outcome for each data type separately and combine the results ad hoc, leading to loss of statistical power and uncontrolled overall false discovery rate (FDR). We propose a multivariate mixture model (IMIX) framework that integrates multiple types of genomic data and allows modeling of inter-data-type correlations. We investigated the across-data-type FDR control in IMIX and demonstrated lower misclassification rates at controlled overall FDR than established individual data type analysis strategies, such as the Benjamini-Hochberg FDR control, the q-value and the local FDR control by extensive simulations. IMIX features statistically principled model selection, FDR control and computational efficiency. Applications to The Cancer Genome Atlas data provided novel multi-omics insights into the genes and mechanisms associated with the luminal and basal subtypes of bladder cancer and the prognosis of pancreatic cancer. We have implemented our method in R package 'IMIX' available at https://github.com/ziqiaow/IMIX, as well as CRAN soon. Supplementary data are available at Bioinformatics online.

DCTRGAN: improving the precision of generative models with reweighting

Significant advances in deep learning have led to more widely used and precise neural network-based generative models such as Generative Adversarial Networks (GANS). We introduce a post-hoc correction to deep generative models to further improve their fidelity, based on the Deep neural networks using the Classification for Tuning and Reweighting (DCTR) protocol. The correction takes the form of a reweighting function that can be applied to generated examples when making predictions from the simulation. We illustrate this approach using GANS trained on standard multimodal probability densities as well as calorimeter simulations from high energy physics. We show that the weighted GAN examples significantly improve the accuracy of the generated samples without a large loss in statistical power. This approach could be applied to any generative model and is a promising refinement method for high energy physics applications and beyond.

Hybrid of Restricted and Penalized Maximum Likelihood Method for Efficient Genome-Wide Association Study.

In genome-wide association studies, linear mixed models (LMMs) have been widely used to explore the molecular mechanism of complex traits. However, typical association approaches suffer from several important drawbacks: estimation of variance components in LMMs with large scale individuals is computationally slow; single-locus model is unsatisfactory to handle complex confounding and causes loss of statistical power. To address these issues, we propose an efficient two-stage method based on hybrid of restricted and penalized maximum likelihood, named HRePML. Firstly, we performed restricted maximum likelihood (REML) on single-locus LMM to remove unrelated markers, where spectral decomposition on covariance matrix was used to fast estimate variance components. Secondly, we carried out penalized maximum likelihood (PML) on multi-locus LMM for markers with reasonably large effects. To validate the effectiveness of HRePML, we conducted a series of simulation studies and real data analyses. As a result, our method always had the highest average statistical power compared with multi-locus mixed-model (MLMM), fixed and random model circulating probability unification (FarmCPU), and genome-wide efficient mixed model association (GEMMA). More importantly, HRePML can provide higher accuracy estimation of marker effects. HRePML also identifies 41 previous reported genes associated with development traits in Arabidopsis, which is more than was detected by the other methods.