Robust Point Estimation Research Articles

Robust point and variance estimation for meta‐analyses with selective reporting and dependent effect sizes

Abstract Meta‐analysis produces a quantitative synthesis of evidence‐based knowledge, shaping not only research trends but also policies and practices in biology. However, two statistical issues, selective reporting and statistical dependence, can severely distort meta‐analytic parameter estimation and inference. Here, we re‐analyse 448 meta‐analyses to demonstrate a new two‐step procedure to deal with two common challenges in biological meta‐analyses that often occur simultaneously: publication bias and non‐independence. First, we employ bias‐robust weighting schemes under the generalized least square estimator to obtain average effect sizes that are more robust to selective reporting. We then use cluster‐robust variance estimation to account for statistical dependence, reducing bias in estimating standard errors and ensuring valid statistical inference. The first step of our approach demonstrates comparable performance in estimating average effect sizes to the existing publication‐bias adjustment methods in the presence of selective reporting. This equivalence holds across two publication bias selection processes. The second step achieves estimates of standard errors consistent with the multilevel meta‐analytic model, a benchmark method with adequate control of Type I error rates for multiple, statistically dependent effect sizes. Re‐analyses of 448 meta‐analyses show that ignoring these two issues tends to overestimate effect sizes by an average of 110% and underestimate standard errors by 120%. To facilitate implementation, we have developed a website including a step‐by‐step tutorial. Complementing current meta‐analytic workflows with the proposed method as a sensitivity analysis can facilitate a transition to a more robust approach in quantitative evidence synthesis.

Model-assisted sensitivity analysis for treatment effects under unmeasured confounding via regularized calibrated estimation.

Consider sensitivity analysis for estimating average treatment effects under unmeasured confounding, assumed to satisfy a marginal sensitivity model. At the population level, we provide new representations for the sharp population bounds and doubly robust estimating functions. We also derive new, relaxed population bounds, depending on weighted linear outcome quantile regression. At the sample level, we develop new methods and theory for obtaining not only doubly robust point estimators for the relaxed population bounds with respect to misspecification of a propensity score model or an outcome mean regression model, but also model-assisted confidence intervals which are valid if the propensity score model is correctly specified, but the outcome quantile and mean regression models may be misspecified. The relaxed population bounds reduce to the sharp bounds if outcome quantile regression is correctly specified. For a linear outcome mean regression model, the confidence intervals are also doubly robust. Our methods involve regularized calibrated estimation, with Lasso penalties but carefully chosen loss functions, for fitting propensity score and outcome mean and quantile regression models. We present a simulation study and an empirical application to an observational study on the effects of right-heart catheterization. The proposed method is implemented in the R package RCALsa.

Model-Assisted Inference for Covariate-Specific Treatment Effects with High-dimensional Data

Covariate-specific treatment effects (CSTEs) represent heterogeneous treatment effects across subpopulations defined by certain selected covariates. In this article, we consider marginal structural models where CSTEs are linearly represented using a set of basis functions of the selected covariates. We develop a new approach in high-dimensional settings to obtain not only doubly robust point estimators of CSTEs, but also model-assisted confidence intervals, which are valid when a propensity score model is correctly specified but an outcome regression model may be misspecified. With a linear outcome model and subpopulations defined by discrete covariates, both point estimators and confidence intervals are doubly robust for CSTEs. In contrast, confidence intervals from existing high-dimensional methods are valid only when both the propensity score and outcome models are correctly specified. We establish asymptotic properties of the proposed point estimators and the associated confidence intervals. We present simulation studies and empirical applications which demonstrate the advantages of the proposed method compared with competing ones.

Zonotope-based Fault Estimation for Uncertain Discrete-Time Switched Linear Systems

This paper investigates actuator fault estimation for discrete-time switched linear systems subject to unknown but bounded disturbances and measurement noises. By taking the fault as an auxiliary state vector, the proposed method consists of two steps. First, a switched L∞-based descriptor observer attenuating the effect of uncertainties is designed to obtain simultaneous point estimate of the system state and the fault term. Second, interval estimation is achieved by integrating robust point estimation with zonotopic analysis techniques. The observer gains are calculated by solving Linear Matrix Inequality (LMI) derived using a common Lyapunov function. Finally, the effectiveness of the proposed approach is demonstrated through a numerical example.

Online Patient Education Materials Related to Lipoprotein(a): Readability Assessment.

BackgroundLipoprotein(a) (Lp(a)) is a highly proatherogenic lipid fraction that is a clinically significant risk modifier. Patients wanting to learn more about Lp(a) are likely to use online patient educational materials (OPEMs). However, the readability of OPEMs may exceed the health literacy of the public.ObjectiveThis study aims to assess the readability of OPEMs related to Lp(a). We hypothesized that the readability of these online materials would exceed the sixth grade level recommended by the American Medical Association.MethodsUsing an online search engine, we queried the top 20 search results from 10 commonly used Lp(a)-related search terms to identify a total of 200 websites. We excluded duplicate websites, advertised results, research journal articles, or non–patient-directed materials, such as those intended only for health professionals or researchers. Grade level readability was calculated using 5 standard readability metrics (automated readability index, SMOG index, Coleman-Liau index, Gunning Fog score, Flesch-Kincaid score) to produce robust point (mean) and interval (CI) estimates of readability. Generalized estimating equations were used to model grade level readability by each search term, with the 5 readability scores nested within each OPEM.ResultsA total of 27 unique websites were identified for analysis. The average readability score for the aggregated results was a 12.2 (95% CI 10.9798-13.3978) grade level. OPEMs were grouped into 6 categories by primary source: industry, lay press, research foundation and nonprofit organizations, university or government, clinic, and other. The most readable category was OPEMs published by universities or government agencies (9.0, 95% CI 6.8-11.3). The least readable OPEMs on average were the ones published by the lay press (13.0, 95% CI 11.2-14.8). All categories exceeded the sixth grade reading level recommended by the American Medical Association.ConclusionsLack of access to readable OPEMs may disproportionately affect patients with low health literacy. Ensuring that online content is understandable by broad audiences is a necessary component of increasing the impact of novel therapeutics and recommendations regarding Lp(a).

Prevalence of anxiety and depression in people with different types of cancer or haematologic malignancies: a cross-sectional study.

Cancer patients often present with psychological symptoms that affect their quality of life, physical health outcomes and survival. Two of the most frequent psychiatric comorbidities are anxiety and depression. However, the prevalence of these disorders among cancer patients remains unclear, as studies frequently report varying rates. In the present study, we aimed to provide robust point estimates for the prevalence of anxiety and depression for both a mixed cancer sample and for 13 cancer types separately, considering confounding variables. In a sample of 7509 cancer outpatients (51.4% female), we used the Hospital Anxiety and Depression Scale to assess rates of anxiety and depression. Applying ordinal logistic regression models, we compared the prevalence of anxiety and depression between different cancer types, controlling for age and gender. About one third of our sample showed symptoms of anxiety (35.2%) or depression (27.9%), and every sixth patient had a very likely psychiatric condition, with women being more frequently affected. Elderly patients more often showed signs of depression. The prevalence of anxiety and depression was significantly higher in lung and brain cancer patients, than in other cancer patients. Lowest depression rates were found in breast cancer patients. The prevalence of anxiety and depression is high in cancer patients. Type of cancer is an important predictor for anxiety and depressive symptoms, with lung and brain cancer patients being highly burdened. Considering a personalised medicine approach, physicians should take into account the high prevalence of psychiatric comorbidities and include psychiatric consultations in the treatment plan.

Robust control point estimation with an out-of-focus camera calibration pattern

Abstract The calibration of a zoom lens camera depends on the precision of the localization of control points. At a long focal length, the narrow depth-of-field (DOF) causes defocused blurring and an inevitable decrease in accuracy in control points localization. In particular, the camera calibration requires multiple control points defined on calibration patterns acquired at various camera angles. However, clear pattern images are difficult to obtain owing to the narrow DOF. We propose a robust and intuitive method to accurately estimate the control points in blurred images. To obtain control points that are less affected by blurring, we dynamically varied the circle size in the patterns and identified the local maximum point using the intensity gradient of accumulated concentric circles. This approach is robust to blurring and can be employed at all zoom levels. In our experiments, the error of the control point estimation was measured while varying the angles of the calibration patterns and the degree of blurring. Compared with the conventional checker pattern method, the performance of the proposed method in the estimation of the control points was better and its related camera parameters with severely defocused images were settled.

Sensitivity of the Posterior Mean on the Prior Assumptions: An Application of the Ellipsoid Bound Theorem

This study examines the sensitivity of the posterior mean to change in the prior assumptions. Three plausible choices of prior which include informative, relative-non informative and non-informative priors are considered. The paper considers information level for a prior to cause a notable change in the Bayesian posterior point estimate. The study develops a framework for evaluating a bound for a robust posterior point estimate. The Ellipsoid Bound theorem is employed to derive the Ellipsoid Bound for an independent normal gamma prior distribution. The proposed modification ellipsoid bound for the large prior was establised by varrying different variance co-variance sizes for the independent normal gamma prior. This bound represents the range for the posterior mean when is insensitive and when it’s sensitive in both location and spread. The result shows that; for a large prior parameter value (greater than the OLS estimate) with a positive definite prior variance covariance matrix, and prior parameter values interval which contains the OLS estimate then, the posterior estimate will be less than both the OLS and the prior estimates. Similarly, if the lower bound of the prior parameter values range is greater than the OLS estimate then: The posterior estimate will be greater than the OLS estimate but smaller than the prior estimate. Furthermore, it is observed that no matter the degrees of confidence in the prior values, data information is powerful enough to modify it.

Robust bivariate random-effects model for accommodating outlying and influential studies in meta-analysis of diagnostic test accuracy studies.

Due to the inevitable inter-study correlation between test sensitivity (Se) and test specificity (Sp), mostly because of threshold variability, hierarchical or bivariate random-effects models are widely used to perform a meta-analysis of diagnostic test accuracy studies. Conventionally, these models assume that the random-effects follow the bivariate normal distribution. However, the inference made using the well-established bivariate random-effects models, when outlying and influential studies are present, may lead to misleading conclusions, since outlying or influential studies can extremely influence parameter estimates due to their disproportional weight. Therefore, we developed a new robust bivariate random-effects model that accommodates outlying and influential observations and gives robust statistical inference by down-weighting the effect of outlying and influential studies. The marginal model and the Monte Carlo expectation-maximization algorithm for our proposed model have been derived. A simulation study has been carried out to validate the proposed method and compare it against the standard methods. Regardless of the parameters varied in our simulations, the proposed model produced robust point estimates of Se and Sp compared to the standard models. Moreover, our proposed model resulted in precise estimates as it yielded the narrowest confidence intervals. The proposed model also generated a similar point and interval estimates of Se and Sp as the standard models when there are no outlying and influential studies. Two published meta-analyses have also been used to illustrate the methods.

Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. We develop new methods and theory to obtain not only doubly robust point estimators for average treatment effects, which remain consistent if either the propensity score model or the outcome regression model is correctly specified, but also model-assisted confidence intervals, which are valid when the propensity score model is correctly specified but the outcome model may be misspecified. With a linear outcome model, the confidence intervals are doubly robust, that is, being also valid when the outcome model is correctly specified but the propensity score model may be misspecified. Our methods involve regularized calibrated estimators with Lasso penalties but carefully chosen loss functions, for fitting propensity score and outcome regression models. We provide high-dimensional analysis to establish the desired properties of our methods under comparable sparsity conditions to previous results, which give valid confidence intervals when both the propensity score and outcome models are correctly specified. We present simulation studies and an empirical application which demonstrate advantages of the proposed methods compared with related methods based on regularized maximum likelihood estimation. The methods are implemented in the R package $\mathtt{RCAL}$.

Refined National Institutes of Health response algorithm for chronic graft-versus-host disease in joints and fascia

AbstractImplementation of the 2014 National Institutes of Health (NIH) response algorithm for joint/fascia graft-versus-host disease (GVHD) has identified real-world limits to its application. To refine the 2014 NIH response algorithm, we analyzed multicenter prospective observational data from the Chronic GVHD Consortium. The training cohort included 209 patients and the replication cohort included 191 patients with joint/fascia involvement during their course of chronic GVHD. Linear mixed models with random patient effect were used to evaluate correlations between response categories and clinician- or patient-perceived changes in joint status as an anchor of response. Analysis of the training cohort showed that a 2-point change in total photographic range of motion (P-ROM) score was clinically meaningful. The results also suggested that a change from 0 to 1 on the NIH joint/fascia score should not be considered as worsening and suggested that both the NIH joint/fascia score and total P-ROM score, but not individual P-ROM scores, should be used for response assessment. On the basis of these results, we developed an evidence-based refined algorithm, the utility of which was examined in an independent replication cohort. Using the refined algorithm, ∼40% of responses were reclassified, largely mitigating most divergent responses among individual joints and changes from 0 to 1 on the NIH joint/fascia score. The refined algorithm showed robust point estimates and tighter 95% confidence intervals associated with clinician- or patient-perceived changes, compared with the 2014 NIH algorithm. The refined algorithm provides a superior, evidence-based method for measuring therapeutic response in joint/fascia chronic GVHD.

Robust change point estimation in two-phase linear regression models: An application to metabolic pathway data

In this study, we develop robust versions of the change point estimation methods given by Hudson (1966) and Muggeo (2003) in the two-phase linear regression model. We use a modified maximum likelihood (MML) methodology originated by Tiku (1967, 1968) when the error terms of a two-phase linear regression model are independently and identically distributed as long-tailed symmetric. Proposed estimators are shown to be more efficient and robust using the Monte-Carlo simulation. Julious’s (Julious, 2001) metabolic pathway data is analyzed in the application part of the study. It is shown that for this data using a LS estimator is inappropriate since there is an outlying observation. We therefore use proposed robust estimators instead of LS estimators and obtain more reliable results.

PSY112 - Healthcare Resource Use (HRU) Associated with Severe Adverse Events (AES) Of Interest in Adults With Relapsed or Refractory (R/R) B-Precursor Acute Lymphoblastic Leukemia (All) In Eu-4 Countries

To estimate HRU associated with severe AEs of interest in adults with R/R B-precursor ALL in EU-4 countries (France, Italy, Spain and UK). A Delphi-based methodology was employed which comprised two phases: a questionnaire administered to clinicians (phase 1) and a country-specific panel to discuss the phase 1 results to generate robust point estimates (phase 2). Physicians must be board certified and have at least 5-years’ experience with R/R ALL. Four types of grade 3/4 AEs (vascular events, infections, cytopenia and gastrointestinal events) were evaluated. Outcomes included number of outpatient day visits, length of stay (LOS) in hospital and LOS in intense care unit (ICU) (in days). Four clinicians from UK, and three clinicians from Spain, France, and Italy were enrolled with a median of 10 years’ experience treating R/R ALL. In France, average number of outpatient day visits was highest for diarrhea (2.5), while veno-occlusive disease (VOD) and septic shock (SS) led to longest average LOS in hospital (17.5). SS also required longest LOS in ICU (4.5). In Italy, viral infection needed highest number of outpatient day visits (7.3) and VOD had longest inpatient LOS (22.5). SS had longest LOS in ICU (13.7). In Spain, thrombocytopenia incurred highest number of outpatient day visits (3.3) and VOD had longest inpatient LOS (16.0). SS led to highest LOS in ICU (9). In the UK, fungal infection incurred highest average number of outpatient day visits (3.8) while VOD led to longest inpatient LOS (16.8). Again, SS needed longest LOS in ICU (7.5). In the EU-4 countries, severe VOD universally incurred the highest LOS in hospital (16~22.5 days) and severe SS had highest LOS in ICU (4~13.7 days) among adults with R/R B-precursor ALL. Novel therapies that can improve outcomes while reducing the incidence of these AEs are needed.

A Meta-Analysis of Major Foodborne Pathogens in Chinese Food Commodities Between 2006 and 2016

Prevalence of pathogenic bacteria in food commodities in China have been reported in numerous publications over time. However, the results are scattered and varied. To calculate a robust point estimate with a higher statistical power, we applied meta-analytic approach for investigating the prevalence of common foodborne pathogens in major food items in China. Data, on prevalence of bacteria in various food commodities were extracted and analyzed from 361 (132 English and 229 Chinese) publications. Prevalence of eight most frequently reported pathogens on six broad food categories was used for pooled and subgroup meta-analysis by DerSimonian-Laird method in random-effects model. The estimated overall prevalence of pathogens in the foods was 8.5% (95% CI 8.2-8.7). The highest prevalence, irrespective of the pathogen type, was in the aquatic produce at 12.8% (12.0-13.5), while the least was in the vegetables at 3.0% (2.6-3.4). Among the pathogens, the most prevalent was Vibrio at 21.3% (19.6-23.1), whereas the least was pathogenic Escherichia coli at 4.3% (3.3-5.2). The major food pathogens in Chinese foods in decreasing order of prevalence were Vibrio parahaemolyticus, Campylobacter, Bacillus cereus, Staphylococcus aureus, Salmonella, Enterobacter, Listeria monocytogenes, and pathogenic E. coli. Presence of these organisms in foods equates the risk of microbiological food safety in China with other developed countries rather than the developing countries. This justifies the need of novel perspectives for formulating policies on microbiological food safety and risk mitigation.

Dairy products and bone health: how strong is the scientific evidence?

The relevance of dairy produce for the diminishment of osteoporotic risk is still a matter of scientific debate due to the outcome of a few single observational studies. This review will address the most robust point estimate on the role of dairy products, as reported in systematic reviews and meta-analyses on randomised controlled trials in the case of bone mineralisation or prospective studies in the case of fracture risk. Plain dairy products or those fortified with Ca and/or vitamin D improve total body bone mineral content (BMC) by 45-50 g over 1 year when the daily baseline Ca intake is lower than 750 mg in Caucasians and Chinese girls. In Caucasian and Chinese women, Ca from (fortified) dairy products increases bone mineral density (BMD) by 0·7-1·8 % over 2 years dependent on the site of measurement. Despite the results on BMC, there are currently no studies that have investigated the potential of dairy products to reduce fracture risk in children. In adult Caucasian women, daily intake of 200-250 ml of milk is associated with a reduction in fracture risk of 5 % or higher. In conclusion, the role of dairy products for BMC or BMD has been sufficiently established in Chinese and Caucasian girls and women. In Caucasian women, drinking milk also reduces fracture risk. More research on the role of dairy products within the context of bone health-promoting diets is needed in specific ethnicities, other than Chinese and Caucasians, and in men.

Fiscal Consolidation, Growth and Employment: International Evidence and Implications for India

The paper argues that many national governments, including the one in India, focus on insufficiently robust point estimates pertaining to specific debt/deficit thresholds that create a fiscal consolidation bias. This is costly in terms of output and employment losses. The paper points out that labour market reforms to support fiscal consolidation are often advocated by international agencies, but one should not ignore the high short-run costs of such reforms. These lessons of international experience are highly pertinent to India as it is poised to implement a new fiscal framework. The paper emphasizes that India faces the major challenge of providing productive and durable jobs for its burgeoning work force while ensuring improved social indicators. Adequate and sustainable financing of such critical development needs ought to be at the centre of any fiscal framework.

The benefit of pacemaker therapy in patients with neurally mediated syncope and documented asystole: a meta-analysis of implantable loop recorder studies

Although the efficacy of cardiac pacing in patients with neurally mediated syncope (NMS) and documented asystole is established, a more robust point estimate of the benefit, which is not possible with any individual study, is lacking. We undertook a meta-analysis of individual participant data from four studies that reported follow-up data on syncope recurrence with cardiac pacing in patients with NMS who had had an electrocardiographic (ECG) documentation of an asystolic event by means of implantable loop recorder (ILR). Of a total of 1046 patients, who had ILR implanted, 383 (36.6%) patients had an ECG documentation of a diagnostic event during mean follow-up of 13 ± 10 months. Of these, 201 (52%) patients, corresponding to 19.2% of the total ILRs, had an asystolic event of 12.8 ± 11.0 s duration documented and met the criteria for pacemaker therapy. Follow-up was available in 121 (60%) of those patients with asystolic events. Syncope recurred after pacing in 18 (14.9%) patients with an actuarial rate of 13% [95% confidence interval (CI) ±6] at 1 year, 21% (95%CI ±10) at 2 years, and 24% (95%CI ±11) at 3 years. On multivariable Cox regression analysis, positive tilt test response was the only significant predictor of syncope recurrence with a hazard ratio (95% CI) of 4.3 (1.4-13). On the contrary, type of asystolic event (sinus arrest or atrioventricular block), prodrome, cardiac abnormalities, number and duration of history of syncope, age, and gender were not predictors of recurrence of syncope. A long asystolic pause, suitable for pacemaker therapy, was found in one of five patients with ILR. After pacemaker implantation, most of these patients remained free of syncope recurrence for up to 3 years. The benefit of pacemaker was greater in patients with negative tilt test.

Rdrobust: Software for Regression-discontinuity Designs

We describe a major upgrade to the Stata (and R) rdrobust package, which provides a wide array of estimation, inference, and falsification methods for the analysis and interpretation of regression-discontinuity designs. The main new features of this upgraded version are as follows: i) covariate-adjusted bandwidth selection, point estimation, and robust bias-corrected inference, ii) cluster–robust bandwidth selection, point estimation, and robust bias-corrected inference, iii) weighted global polynomial fits and pointwise confidence bands in regression-discontinuity plots, and iv) several new bandwidth selection methods, including different bandwidths for control and treatment groups, coverage error-rate optimal bandwidths, and optimal bandwidths for fuzzy designs. In addition, the upgraded package has superior performance because of several numerical and implementation improvements. We also discuss issues of backward compatibility and provide a companion R package with the same syntax and capabilities.

Abstract 335: Dynamic biochemical tissue analysis of novel P-selectin ligands expressed by colon cancer

Abstract Selectin/selectin ligand interactions have been implicated in mediating the adhesion of circulating tumor cells to distant sites during metastasis. Previous work from our lab has demonstrated the limitations of static biochemical tissue analysis (SBTA), using both selectins and antibodies against glycotopes, in detecting functional selectin ligands expressed on tissue. To address these shortcomings, we developed a novel tissue interrogation method, termed dynamic biochemical tissue analysis (DBTA), in which selectin-coated microspheres are perfused over tissues in a microfluidic device to detect functional selectin ligands in situ. In this work, DBTA using P-selectin microspheres was performed on cancer tissue sections in conjunction with SBTA using antibodies against P-selectin ligands CD24, CD44, and PSGL-1. Using DBTA, calcium-dependent selectin/selectin ligand adhesive interactions in the form of P-selectin microsphere rolling was observed on four distinct cases of colorectal cancer tissue. Examination of serial sections with SBTA in the same regions of tissue displaying P-selectin microsphere rolling revealed no detectable levels of CD24, CD44, or PSGL-1 epitopes, while only one case displayed CD44 expression that was in agreement with DBTA. However, not all regions displaying specific reactivity with the P-selectin microspheres used in DBTA were recognized with the CD44 antibody in SBTA. These results imply the presence of novel P-selectin ligands in the tissue section. Follow-up CD45 SBTA ruled out the possibility of microsphere interaction with infiltrated leukocytes, in agreement with the lack of PSGL-1 detection. Consistent with our DBTA studies using microspheres coated with E- and L-selectin on other types of cancer tissue, DBTA reveals unequivocal detection of functional P-selectin ligands by generating results distinct from SBTA. To further characterize the adhesion of P-selectin-coated microspheres to functional selectin ligands that were not identified with SBTA, a more refined method of interaction analysis that discretizes rolling into a sequence of succinct pauses (i.e., brief stationary adhesion) was used. In this method, microsphere rolling recorded at 300 frames per second was assessed using a cross-correlation tracking algorithm to obtain a robust point estimate that represents the off-rate bond breakage of the ensemble of receptor-ligand complexes that mediate microsphere adhesion to the tissue surface. This adhesion parameter lays the framework for potentially correlating the density and type of functional ligand(s) expressed with tumor stage and/or aggressiveness, furthering our understanding of aberrantly expressed functional selectin ligands as potential cancer biomarkers. Citation Format: Eric Martin, Ramiro Malgor, Douglas Goetz, Monica Burdick. Dynamic biochemical tissue analysis of novel P-selectin ligands expressed by colon cancer. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 335. doi:10.1158/1538-7445.AM2015-335

Optimal probabilistic energy management in a typical micro-grid based-on robust optimization and point estimate method

Uncertainty can be defined as the probability of difference between the forecasted value and the real value. As this probability is small, the operation cost of the power system will be less. This purpose necessitates modeling of system random variables (such as the output power of renewable resources and the load demand) with appropriate and practicable methods. In this paper, an adequate procedure is proposed in order to do an optimal energy management on a typical micro-grid with regard to the relevant uncertainties. The point estimate method is applied for modeling the wind power and solar power uncertainties, and robust optimization technique is utilized to model load demand uncertainty. Finally, a comparison is done between deterministic and probabilistic management in different scenarios and their results are analyzed and evaluated.