Elevated extracellular matrix protein 1 in circulating extracellular vesicles supports breast cancer progression under obesity conditions.

The cargo content in small extracellular vesicles (sEVs) changes under pathological conditions. Our data shows that in obesity, extracellular matrix protein 1 (ECM1) protein levels are significantly increased in circulating sEVs, which is dependent on integrin-ß2. Knockdown of integrin-ß2 does not affect cellular ECM1 protein levels but significantly reduces ECM1 protein levels in the sEVs released by these cells. In breast cancer (BC), overexpressing ECM1 increases matrix metalloproteinase 3 (MMP3) and S100A/B protein levels. Interestingly, sEVs purified from high-fat diet-induced obesity mice (D-sEVs) deliver more ECM1 protein to BC cells compared to sEVs from control diet-fed mice. Consequently, BC cells secrete more ECM1 protein, which promotes cancer cell invasion and migration. D-sEVs treatment also significantly enhances ECM1-mediated BC metastasis and growth in mouse models, as evidenced by the elevated tumor levels of MMP3 and S100A/B. Our study reveals a mechanism and suggests sEV-based strategies for treating obesity-associated BC.

A new method for estimating Sharpe ratio function via local maximum likelihood.

The Sharpe ratio function is a commonly used risk/return measure in financial econometrics. To estimate this function, most existing methods take a two-step procedure that first estimates the mean and volatility functions separately and then applies the plug-in method. In this paper, we propose a direct method via local maximum likelihood to simultaneously estimate the Sharpe ratio function and the negative log-volatility function as well as their derivatives. We establish the joint limiting distribution of the proposed estimators, and moreover extend the proposed method to estimate the multivariate Sharpe ratio function. We also evaluate the numerical performance of the proposed estimators through simulation studies, and compare them with existing methods. Finally, we apply the proposed method to the three-month US Treasury bill data and that captures a well-known covariate-dependent effect on the Sharpe ratio.

Detecting the skewness of data from the five-number summary and its application in meta-analysis.

For clinical studies with continuous outcomes, when the data are potentially skewed, researchers may choose to report the whole or part of the five-number summary (the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation. In the recent literature, it is often suggested to transform the five-number summary back to the sample mean and standard deviation, which can be subsequently used in a meta-analysis. However, if a study contains skewed data, this transformation and hence the conclusions from the meta-analysis are unreliable. Therefore, we introduce a novel method for detecting the skewness of data using only the five-number summary and the sample size, and meanwhile, propose a new flow chart to handle the skewed studies in a different manner. We further show by simulations that our skewness tests are able to control the type I error rates and provide good statistical power, followed by a simulated meta-analysis and a real data example that illustrate the usefulness of our new method in meta-analysis and evidence-based medicine.

Efficacy and safety of Chinese patent medicine Xiao Yao San in polycystic ovary syndrome: A systematic review and meta-analysis.

ETHNOPHARMACOLOGICAL RELEVANCE: Polycystic ovary syndrome (PCOS) is one of the most common endocrine-metabolic disorders in women of reproductive age worldwide. Previous studies using randomized controlled trials (RCTs) have revealed that Xiao Yao San (XYS), a classic Chinese patent medicine formula, can effectively treat PCOS. However, the entire evidence has yet to be systematically summarized. AIM OF THE STUDY: The aim of this systematic review and meta-analysis of clinical trials was to assess the effect of XYS for the treatment of PCOS. MATERIALS AND METHODS: 7 databases were thoroughly reviewed for RCTs published from inception to July 2022, assessing the effect of XYS in treating PCOS, including Cochrane Library, PubMed, Embase, Wan Fang Database, Chinese Biomedical Database, China National Knowledge Infrastructure, and China Science and Technology Journal Database. Outcome measures included ovulation rate, pregnancy rate, hormonal levels, and glycemic parameters. Either a random-effects model or a fixed-effect models was used to pool data. Pooled effect sizes were reported as odds ratios (ORs) or standardized mean differences (SMDs) with their 95% confidence intervals (CIs). RESULTS: A total of 9 trials including 736 PCOS patients met the selection criteria. Our results indicate that XYS plus conventional medicines for PCOS significantly improved ovulation rate (OR = 2.45, 95% CI = 1.94 to 3.08, P < 0.001) and pregnancy rate (OR = 2.65, 95% CI = 1.87 to 3.75, P < 0.001), meanwhile decreased levels of fasting insulin (FINS) (SMD = - 0.46, 95% CI: 0.65 to - 0.27, P < 0.001) and homeostatic model assessment for insulin resistance (HOMA-IR) (SMD = - 0.65, 95% CI = - 0.93 to - 0.37, P < 0.001). XYS plus conventional medicines for PCOS did not have a significant impact on levels of total testosterone (T), follicle-stimulating hormone (FSH), luteinizing hormone (LH), and fasting plasma glucose (FPG). No serious adverse reactions were observed. CONCLUSION: XYS combined with conventional medicines can improve ovulation and pregnancy rates, decrease FINS and HOMA-IR in PCOS patients, indicating that XYS treatment may be used as a promising adjuvant therapy to the conventional medicines of PCOS. However, due to significant heterogeneity and methodological shortcomings, these results should be interpreted with great caution. Larger, higher quality RCTs are needed to rigorously assess the effect of XYS as a complementary therapy in managing PCOS.

Omics approach to reveal the effects of obesity on the protein profiles of the exosomes derived from different adipose depots.

BACKGROUND: Obesity affects the cargo packaging of the adipocyte-derived exosomes. Furthermore, adipocytes in different adipose tissues have different genetic makeup, the cargo contents of the exosomes derived from different adipose tissues under obesity conditions should be different, and hence their impacts on the pathophysiological conditions. METHODS AND RESULTS: iTRAQ-based quantitative proteomics show that obesity has more prominent effects on the protein profiles of the exosomes derived from subcutaneous adipose tissue (SAT-Exos) in the high fat diet-induced obesity (DIO) mice than those derived from epididymal adipose tissue (EAT-Exos) and visceral adipose tissue (VAT-Exos). The differentially expressed proteins (DEPs) in SAT-Exos and VAT-Exos are mainly involved in metabolism. Subsequent untargeted metabolomic and lipidomics analyses reveal that injection of these SAT-Exos into the B6/J-Rab27a-Cas9-KO mice significantly affects the mouse metabolism such as fatty acid metabolism. Some of the DEPs in SAT-Exos are correlated with fatty acid metabolism including ADP-ribosylation factor and mitogen-activated protein kinase kinase kinase-3. Pathway analysis also shows that SAT-Exos affect adipocyte lipolysis and glycerophospholipid metabolism, which is in parallel with the enhanced plasma levels of fatty acids, diglycerides, monoglycerides and the changes in glycerophospholipid levels in DIO mice. CONCLUSION: Our data provide scientific evidence to suggest SAT-Exos contribute to the changes in plasma lipid profiles under obesity conditions.

scDLC: a deep learning framework to classify large sample single-cell RNA-seq data.

BACKGROUND: Using single-cell RNA sequencing (scRNA-seq) data to diagnose disease is an effective technique in medical research. Several statistical methods have been developed for the classification of RNA sequencing (RNA-seq) data, including, for example, Poisson linear discriminant analysis (PLDA), negative binomial linear discriminant analysis (NBLDA), and zero-inflated Poisson logistic discriminant analysis (ZIPLDA). Nevertheless, few existing methods perform well for large sample scRNA-seq data, in particular when the distribution assumption is also violated. RESULTS: We propose a deep learning classifier (scDLC) for large sample scRNA-seq data, based on the long short-term memory recurrent neural networks (LSTMs). Our new scDLC does not require a prior knowledge on the data distribution, but instead, it takes into account the dependency of the most outstanding feature genes in the LSTMs model. LSTMs is a special recurrent neural network, which can learn long-term dependencies of a sequence. CONCLUSIONS: Simulation studies show that our new scDLC performs consistently better than the existing methods in a wide range of settings with large sample sizes. Four real scRNA-seq datasets are also analyzed, and they coincide with the simulation results that our new scDLC always performs the best. The code named "scDLC" is publicly available at https://github.com/scDLC-code/code .

Development of a Method for Quantitative Evaluation of Facial Swelling in a Rat Model of Cerebral Ischemia by Facial Image Processing.

A quantitative method for the evaluation of facial swelling in rats with middle cerebral artery occlusion (MCAO) was established using a mathematical method for the first time. The rat model of MCAO was established via bilateral common carotid artery ligation. Three groups of rats with the same baseline were selected (model group, positive drug group, and control group) according to their behavioral score and body weight 24 h after surgery. Drug administration was initiated on post-MCAO day 8 and was continued for 28 days. Mobile phones were used to collect facial images at different time points after surgery. In facial image analysis, the outer canthi of both eyes were used as the facial dividing line, and the outer edge of the rat's face was framed using the marking method, and the framed part was regarded as the facial area (S) of the rats. The histogram created with Photoshop CS5 was used to measure the face area in pixels. The distance between the outer canthi of both eyes (Le) and vertical line from the tip of the nose to the line joining the eyes was recorded as H1, and the line from the tip of the nose to the midpoint of the line joining the eyes was recorded as H2. The facial area was calibrated based on the relationship between H1 and H2. The distance between the eyes was inversely proportional to the distance between the rats and mobile phone such that the face area was calibrated by unifying Le. The size of Le between the eyes was inversely proportional to the distance between the rats and mobile phone. This was used to calibrate the face area. When compared with the control group, the facial area of the model group gradually increased from postoperative day 1 to day 7, and there was a significant difference in the facial area of the model group on postoperative day 7. Hence, positive drugs exhibited the effect of improving facial swelling. H1 and H2 can reflect the state of turning the head and raising the head of the rats, respectively. Facial area was calibrated according to the relationship between H1 and H2, which had no obvious effect on the overall conclusion. Furthermore, mobile phone lens was used to capture the picture of rat face, and the distance between the eyes and H1 and H2 was used to calibrate the facial area. Hence, this method is convenient and can be used to evaluate subjective judgment of the human eyes via a quantitative method.

Meta-Analyzing Multiple Omics Data With Robust Variable Selection.

High-throughput omics data are becoming more and more popular in various areas of science. Given that many publicly available datasets address the same questions, researchers have applied meta-analysis to synthesize multiple datasets to achieve more reliable results for model estimation and prediction. Due to the high dimensionality of omics data, it is also desirable to incorporate variable selection into meta-analysis. Existing meta-analyzing variable selection methods are often sensitive to the presence of outliers, and may lead to missed detections of relevant covariates, especially for lasso-type penalties. In this paper, we develop a robust variable selection algorithm for meta-analyzing high-dimensional datasets based on logistic regression. We first search an outlier-free subset from each dataset by borrowing information across the datasets with repeatedly use of the least trimmed squared estimates for the logistic model and together with a hierarchical bi-level variable selection technique. We then refine a reweighting step to further improve the efficiency after obtaining a reliable non-outlier subset. Simulation studies and real data analysis show that our new method can provide more reliable results than the existing meta-analysis methods in the presence of outliers.

Meta-analysis with zero-event studies: a comparative study with application to COVID-19 data.

BACKGROUND: Meta-analysis is a statistical method to synthesize evidence from a number of independent studies, including those from clinical studies with binary outcomes. In practice, when there are zero events in one or both groups, it may cause statistical problems in the subsequent analysis. METHODS: In this paper, by considering the relative risk as the effect size, we conduct a comparative study that consists of four continuity correction methods and another state-of-the-art method without the continuity correction, namely the generalized linear mixed models (GLMMs). To further advance the literature, we also introduce a new method of the continuity correction for estimating the relative risk. RESULTS: From the simulation studies, the new method performs well in terms of mean squared error when there are few studies. In contrast, the generalized linear mixed model performs the best when the number of studies is large. In addition, by reanalyzing recent coronavirus disease 2019 (COVID-19) data, it is evident that the double-zero-event studies impact the estimate of the mean effect size. CONCLUSIONS: We recommend the new method to handle the zero-event studies when there are few studies in a meta-analysis, or instead use the GLMM when the number of studies is large. The double-zero-event studies may be informative, and so we suggest not excluding them.

Estimating the reference interval from a fixed effects meta-analysis.

A reference interval provides a basis for physicians to determine whether a measurement is typical of a healthy individual. It can be interpreted as a prediction interval for a new individual from the overall population. However, a reference interval based on a single study may not be representative of the broader population. Meta-analysis can provide a general reference interval based on the overall population by combining results from multiple studies. Methods for estimating the reference interval from a random effects meta-analysis have been recently proposed to incorporate the within and between-study variation, but a random effects model may give imprecise estimates of the between-study variation with only few studies. In addition, the normal distribution of underlying study-specific means, and equal within-study variance assumption in these methods may be inappropriate in some settings. In this article, we aim to estimate the reference interval based on the fixed effects model assuming study effects are unrelated, which is useful for a meta-analysis with only a few studies (e.g., ≤5). We propose a mixture distribution method only assuming parametric distributions (e.g., normal) for individuals within each study and integrating them to form the overall population distribution. This method is compared to an empirical method only assuming a parametric overall population distribution. Simulation studies have shown that both methods can estimate a reference interval with coverage close to the targeted value (i.e., 95%). Meta-analyses of women daytime urination frequency and frontal subjective postural vertical measurements are reanalyzed to demonstrate the application of our methods.

[Efficacy of curcumin in the treatment of oral submucous fibrosis: a Meta-analysis].

OBJECTIVES: This study was performed to review the efficacy of curcumin in the treatment of oral submucous fibrosis systematically. METHODS: We searched seven databases, including Web of Science, PubMed, EBSCO, The Cochrane Library, CNKI, WanFang Data, and VIP, to obtain randomized controlled trials related to the treatment of oral submucous fibrosis by curcumin. Each database was searched from inception to 30 June 2019. RevMan 5.3 software was used for the meta-analysis. RESULTS: Six randomized controlled trials involving 350 patients were included in this study. Meta-analysis showed that curcumin can increase the maximal mouth opening and improve burning sensation compared with placebo treatment. Curcumin was not as effective as the controls in achieving maximal mouth opening after 1 month of treatment. However, no statistically significant difference was observed between the treatments from 2 months to 6 months. Curcumin significantly improved burning sensation compared with the controls after 3 months of treatment. No statistically significant diffe-rence in burning sensation was observed between the curcumin and control groups after 1, 2, and 6 months of treatment. CONCLUSIONS: The current evidence shows that curcumin is an effective treatment for improving maximal mouth opening and burning sensation in patients with oral submucous fibrosis. Given the limited number and low quality of the included studies, however, more high-quality studies are needed to verify these findings.

Efficacy and safety of Si-Jun-Zi-Tang-based therapies for functional (non-ulcer) dyspepsia: a meta-analysis of randomized controlled trials.

BACKGROUND: The traditional Chinese medicine formula Si-Jun-Zi-Tang (SJZT) has a long history of application in the treatment of functional dyspepsia (non-ulcer dyspepsia, FD)-like symptoms. SJZT-based therapies have been claimed to be beneficial in managing FD. This study aimed to assess the efficacy and safety of SJZT-based therapies in treating FD by meta-analysis. METHODS: Systematic searches for RCTs were conducted in seven databases (up to February 2019) without language restrictions. Data were analyzed using Cochrane RevMan software version 5.3.0 and Stata software version 13.1, and reported as relative risk (RR) or odds ratio (OR) with 95% confidence intervals (CIs). The primary outcome was response rate and the secondary outcomes were gastric emptying, quality of life, adverse effects and relapse rate. The quality of evidence was evaluated according to criteria from the Cochrane risk of bias. RESULTS: A total of 341 potentially relevant publications were identified, and 12 RCTs were eligible for inclusion. For the response rate, there was a statically significant benefit in favor of SJZT-based therapies (RR = 1.23; 95% CI 1.17 to 1.30). However, the benefit was limited to modified SJZT (MSJZT). The relapse rate of FD patients received SJZT-based therapies was lower than that of patients who received conventional medicines (OR = 0.23; 95% CI 0.10 to 0.51). No SJZT-based therapies-related adverse effect was reported. CONCLUSION: SJZT-based prescriptions may be effective in treating FD and no serious side-effects were identified, but the effect on response rate appeared to be limited to MSJZT. The results should be interpreted with caution as all the included studies were considered at a high risk of bias. Standardized, large-scale and strictly designed RCTs are needed to further validate the benefits of SJZT-based therapies for FD management. TRIAL REGISTRATION: Systematic review registration: [PROSPERO registration: CRD42019139136 ].

Optimally estimating the sample standard deviation from the five-number summary.

When reporting the results of clinical studies, some researchers may choose the five-number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. For these studies, when included in a meta-analysis, it is often desired to convert the five-number summary back to the sample mean and SD. For this purpose, several methods have been proposed in the recent literature and they are increasingly used nowadays. In this article, we propose to further advance the literature by developing a smoothly weighted estimator for the sample SD that fully utilizes the sample size information. For ease of implementation, we also derive an approximation formula for the optimal weight, as well as a shortcut formula for the sample SD. Numerical results show that our new estimator provides a more accurate estimate for normal data and also performs favorably for non-normal data. Together with the optimal sample mean estimator in Luo et al., our new methods have dramatically improved the existing methods for data transformation, and they are capable to serve as "rules of thumb" in meta-analysis for studies reported with the five-number summary. Finally for practical use, an Excel spreadsheet and an online calculator are also provided for implementing our optimal estimators.

Testing for heteroskedasticity in two-way fixed effects panel data models.

In this paper, we propose a new method for testing heteroskedasticity in two-way fixed effects panel data models under two important scenarios where the cross-sectional dimension is large and the temporal dimension is either large or fixed. Specifically, we will develop test statistics for both cases under the conditional moment framework, and derive their asymptotic distributions under both the null and alternative hypotheses. The proposed tests are distribution free and can easily be implemented using the simple auxiliary regressions. Simulation studies and two real data analyses demonstrate that our proposed tests perform well in practice, and may have the potential for wide application in econometric models with panel data.

Pathway-Based Single-Cell RNA-Seq Classification, Clustering, and Construction of Gene-Gene Interactions Networks Using Random Forests.

Single-cell RNA-Sequencing (scRNA-Seq), an advanced sequencing technique, enables biomedical researchers to characterize cell-specific gene expression profiles. Although studies have adapted machine learning algorithms to cluster different cell populations for scRNA-Seq data, few existing methods have utilized machine learning techniques to investigate functional pathways in classifying heterogeneous cell populations. As genes often work interactively at the pathway level, studying the cellular heterogeneity based on pathways can facilitate the interpretation of biological functions of different cell populations. In this paper, we propose a pathway-based analytic framework using Random Forests (RF) to identify discriminative functional pathways related to cellular heterogeneity as well as to cluster cell populations for scRNA-Seq data. We further propose a novel method to construct gene-gene interactions (GGIs) networks using RF that illustrates important GGIs in differentiating cell populations. The co-occurrence of genes in different discriminative pathways and 'cross-talk' genes connecting those pathways are also illustrated in our networks. Our novel pathway-based framework clusters cell populations, prioritizes important pathways, highlights GGIs and pivotal genes bridging cross-talked pathways, and groups co-functional genes in networks. These features allow biomedical researchers to better understand the functional heterogeneity of different cell populations and to pinpoint important genes driving heterogeneous cellular functions.

A statistical normalization method and differential expression analysis for RNA-seq data between different species.

BACKGROUND: High-throughput techniques bring novel tools and also statistical challenges to genomic research. Identifying genes with differential expression between different species is an effective way to discover evolutionarily conserved transcriptional responses. To remove systematic variation between different species for a fair comparison, normalization serves as a crucial pre-processing step that adjusts for the varying sample sequencing depths and other confounding technical effects. RESULTS: In this paper, we propose a scale based normalization (SCBN) method by taking into account the available knowledge of conserved orthologous genes and by using the hypothesis testing framework. Considering the different gene lengths and unmapped genes between different species, we formulate the problem from the perspective of hypothesis testing and search for the optimal scaling factor that minimizes the deviation between the empirical and nominal type I errors. CONCLUSIONS: Simulation studies show that the proposed method performs significantly better than the existing competitor in a wide range of settings. An RNA-seq dataset of different species is also analyzed and it coincides with the conclusion that the proposed method outperforms the existing method. For practical applications, we have also developed an R package named "SCBN", which is freely available at http://www.bioconductor.org/packages/devel/bioc/html/SCBN.html .

The association of depression following percutanous coronary intervention with adverse cardiovascular events: Protocol for a systematic review and meta-analysis.

INTRODUCTION: Percutanous coronary intervention (PCI) has been increasingly used for patients suffered from severe coronary artery disease. However, physical trauma and potential adverse events related to the procedure often result in detrimental psychological stress. Accumulating evidences have shown that depression is closely related to coronary artery disease. However, the association of depression following percutanous coronary intervention with adverse cardiovascular events is still unknown. OBJECTIVE: This review is designed to assess the prognostic association of depression following PCI with adverse cardiac events. METHODS AND ANALYSIS: The following databases will be searched, PubMed, the EMBASE, CINAHL and Web of Science of English-language publications from inception to 30 October 2018. Cross-referencing from retrieved studies will be conducted additionally, and observational studies were included. Two independent review authors will do the study selection on the basis of the study eligibility criteria. Extracted data will be used for quantitative and qualitative evidence synthesis as well as to assess methodological quality of studies using the Newcastle-Ottawa checklist. The primary objective of this review is adverse cardiac events, presented as a composition of myocardial infarction, repeat coronary revascularization, cardiac readmission, and cardiac death. The accumulated evidence is evaluated and graded according to Grading of Recommendations, Assessment, Development and Evaluation (GRADE). RESULTS AND CONCLUSIONS: This review will explain the association of depression following percutanous coronary intervention with adverse cardiovascular events, and provide physicians with scientific evidence for psychological intervention in patients after PCI. PROSPERO REGISTRATION NUMBER: CRD42018112486.

Diagonal likelihood ratio test for equality of mean vectors in high-dimensional data.

We propose a likelihood ratio test framework for testing normal mean vectors in high-dimensional data under two common scenarios: the one-sample test and the two-sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log-transformed squared t-statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods.

Weight reduction and cardiovascular benefits: Protocol for a systematic review and meta-analysis.

BACKGROUND: There is widespread obesity paradox in cardiovascular diseases, the cardiovascular influence from weight management remains controversial. Moreover, previous publications indicating that different weight reduction extent might lead to various results. Thus, it is of importance to reassess the cardiovascular benefits of weight management strategies. OBJECTIVES: This review is designed to assess the association between weight loss and cardiovascular outcomes. METHODS: Clinical trials including randomized control trials, observational studies reported a weight change before and after weight interventions including lifestyle intervention, as well as pharmacotherapies were included. Three major databases will be searched to retrieve the appropriate studies. Dual selection and abstraction of data will be conducted by 2 authors independently. The population, intervention, comparator, outcomes, study characteristics framework will be used to extract all the necessary data from included studies. The risk of bias assessment will be conducted in duplicate based on the Cochrane risk of bias guideline for randomized controlled trials (RCTs) and the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement for observational studies respectively. The primary outcomes will be the cardiovascular mortality, and the secondary outcomes are all-cause mortality and new cardiovascular events. A meta-analysis will be considered if there is sufficient homogeneity among selected studies. Follow the criteria of Grading of Recommendations, Assessment, Development and Evaluation (GRADE), the quality of the cumulative evidence will be evaluated. RESULTS AND CONCLUSIONS: The results of this systematic review could provide reliable and concrete evidence for weight loss and its cardiovascular benefits.Prospero registration number: CRD42018108582.

Optimally estimating the sample mean from the sample size, median, mid-range, and/or mid-quartile range.

The era of big data is coming, and evidence-based medicine is attracting increasing attention to improve decision making in medical practice via integrating evidence from well designed and conducted clinical research. Meta-analysis is a statistical technique widely used in evidence-based medicine for analytically combining the findings from independent clinical trials to provide an overall estimation of a treatment effectiveness. The sample mean and standard deviation are two commonly used statistics in meta-analysis but some trials use the median, the minimum and maximum values, or sometimes the first and third quartiles to report the results. Thus, to pool results in a consistent format, researchers need to transform those information back to the sample mean and standard deviation. In this article, we investigate the optimal estimation of the sample mean for meta-analysis from both theoretical and empirical perspectives. A major drawback in the literature is that the sample size, needless to say its importance, is either ignored or used in a stepwise but somewhat arbitrary manner, e.g. the famous method proposed by Hozo et al. We solve this issue by incorporating the sample size in a smoothly changing weight in the estimators to reach the optimal estimation. Our proposed estimators not only improve the existing ones significantly but also share the same virtue of the simplicity. The real data application indicates that our proposed estimators are capable to serve as "rules of thumb" and will be widely applied in evidence-based medicine.