This study presents the results of a Monte Carlo simulation to compare the statistical power of Siegel-Tukey and Savage tests.The main purpose of the study is to evaluate the statistical power of both tests in scenari...This study presents the results of a Monte Carlo simulation to compare the statistical power of Siegel-Tukey and Savage tests.The main purpose of the study is to evaluate the statistical power of both tests in scenarios involving Normal,Platykurtic and Skewed distributions over different sample sizes and standard deviation values.In the study,standard deviation ratios were set as 2,3,4,1/2,1/3 and 1/4 and power comparisons were made between small and large sample sizes.For equal sample sizes,small sample sizes of 5,8,10,12,16 and 20 and large sample sizes of 25,50,75 and 100 were used.For different sample sizes,the combinations of(4,16),(8,16),(10,20),(16,4),(16,8)and(20,10)small sample sizes and(10,30),(30,10),(50,75),(50,100),(75,50),(75,100),(100,50)and(100,75)large sample sizes were examined in detail.According to the findings,the power analysis under variance heterogeneity conditions shows that the Siegel-Tukey test has a higher statistical power than the other nonparametric Savage test at small and large sample sizes.In particular,the Siegel-Tukey test was reported to offer higher precision and power under variance heterogeneity,regardless of having equal or different sample sizes.展开更多
In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fi...In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.展开更多
Regression estimates are biased when potential confounders are omitted or when there are other similar risks to validity.The instrumental variable(IV)method can be used instead to obtain less biased estimates or to st...Regression estimates are biased when potential confounders are omitted or when there are other similar risks to validity.The instrumental variable(IV)method can be used instead to obtain less biased estimates or to strengthen causal inferences.One key assumption critical to the validity of the IV method is the exclusion assumption,which requires instruments to be correlated with the outcome variable only through endogenous predictors.The chi-square test of model fit is widely used as a diagnostic test for this assumption.Previous simulation studies assessed the power of this diagnostic test only in situations with strong violations of the exclusion assumption.However,low to moderate levels of assumption violation are not uncommon in reality,especially when the exclusion assumption is violated indirectly.In this study,we showed through Monte Carlo simulations that the chi-square model fit test suffered from a severe lack of power(<30%)to detect violations of the exclusion assumption when the level of violation was of typical size,and the IV causal inferences were severely inaccurate and misleading in this case.We thus advise using the IV method with caution unless there is a chance for thorough assumption diagnostics,like in meta-analyses or experiments.展开更多
Alignment-based database search and sequence comparison are commonly used to detect horizontal gene transfer(HGT).However,with the rapid increase of sequencing depth,hundreds of thousands of contigs are routinely asse...Alignment-based database search and sequence comparison are commonly used to detect horizontal gene transfer(HGT).However,with the rapid increase of sequencing depth,hundreds of thousands of contigs are routinely assembled from metagenomics studies,which challenges alignment-based HGT analysis by overwhelming the known reference sequences.Detecting HGT by k-mer statistics thus becomes an attractive alternative.These alignment-free statistics have been demonstrated in high performance and efficiency in wholegenome and transcriptome comparisons.To adapt k-mer statistics for HGT detection,we developed two aggregative statistics T^(S)_(sum ) and T^(*)_(sum),which subsample metagenome contigs by their representative regions,and summarize the regional D^(S) _(2) and D^(*)_(2)metrics by their upper bounds.We systematically studied the aggregative statistics’power at different k-mer size using simulations.Our analysis showed that,in general,the power of T^(S)_(sum) and T^(*)_(sum) increases with sequencing coverage,and reaches a maximum power>80%at k=6,with 5%Type-I error and the coverage ratio>0.2x.The statistical power ofT^(S)_(sum) and T^(*)_(sum) was evaluated with realistic simulations of HGT mechanism,sequencing depth,read length,and base error.We expect these statistics to be useful distance metrics for identifying HGT in metagenomic studies.展开更多
In this paper, we study an energy efficient multi-antenna unmanned aerial vehicle(UAV)-enabled half-duplex mobile relaying system under Rician fading channels. By assuming that the UAV follows a circular trajectory at...In this paper, we study an energy efficient multi-antenna unmanned aerial vehicle(UAV)-enabled half-duplex mobile relaying system under Rician fading channels. By assuming that the UAV follows a circular trajectory at fixed altitude and applying the decode-and-forward relaying strategy, we maximize the energy efficiency by jointly designing beamforming, power allocation, circular radius and flight speed, subject to the sum transmit power constraint on source node and UAV relay node. First, we maximize the end-to-end signal-to-noise ratio by jointly designing beamforming and statistical power allocation. Based on the obtained beamforming and power allocation results, we then obtain a semi closed-form expression of energy efficiency, and finally maximize energy efficiency by optimizing flight speed and circular radius, allowing optimal circular radius to be obtained via numerical computation. Numerical results demonstrate that the proposed scheme can effectively enhance the system energy efficiency.展开更多
Statistical power, number of replicates and experiment complexity of semi-field and field studies on Apis and non-Apis bee species has become a major issue after publication of the draft European Food Safety Authori...Statistical power, number of replicates and experiment complexity of semi-field and field studies on Apis and non-Apis bee species has become a major issue after publication of the draft European Food Safety Authority （EFSA） Guidance on risk assessment of plant protection products （PPP） on bees （Apis mellifera, Bombus spp. and solitary bees）. According to this guidance document, field studies have to be designed to be able to detect significance differences as low as 7% for certain endpoints such as reduction in colony size. This will require an immense number of replicates which is obviously not feasible. In the present study, key endpoints such as mortality, termination rate and number of brood cells in honeybee studies, cocoon production and flight activity in solitary bee studies and number of gynes in bumble bee studies （just to mention some of the endpoints considered） in semi-field studies were analyzed, with Apis mellifera, Bombus terrestris and Osmia bicornis during the past five years （2013-2017）. The results indicate huge differences in the percentage minimal detectable differences （%MDDs） （MDD expressed as median of control value of the endpoint in percent） depending on endpoint and species tested. For honeybee semi-field studies, the lowest %MDDs recorded were between 10% and 15% for the endpoints foraging, number of brood cells and colony strength. The highest %MDDs were observed for the endpoint termination rate, with a %MDD of almost 50%. For the endpoints in bumble bee semi-field studies the %MDDs varied between 17% for bumble bee colony weight and 53% for average mortality during the exposure period in the tunnel. The %MDD for the number of gynes （young queens） was slightly below 25%. For the semi-field solitary bee test system, the %MDDs for the measured endpoints seem to be lower than those for the other two species tested. The %MDDs for the endpoints hatching of offspring, nest occupation and number of cocoons were 8%, 13% and 14%, respectively. Most of the %MDDs were between 10% and 30% indicating clearly that the currently performed experimental design for the semi-field pollinator studies allowed to determine relatively small effects on key study endpoints. The analysis indicated that for all the three bee species tested, the semi-field test design detected low %MDDs for most of the endpoints. It was also observed that detectable differences between the control and PPP treatments were much lower in semi-field test designs than in field studies with these bee species. The “perfect sample size” really does not exist but test design and statistical analysis can be adapted to lower the %MDDs. Measured and simulated （according to Student’s t-test-distribution） data and results showed that statistical evaluations parameter selection （e.g., alpha value）, data transformation （log10） and the number of replicates had a direct effect on the ability of the test design to detect lower or higher %MDD values. It could show that a change of alpha value from 0.05 to 0.1, increases the ability of the studies to detect lower %MDDs. For most of the measured endpoints, increasing the number of replicates e.g., from four to eight, improved the power of the test design by decreasing the %MDD. The reduction magnitude of the %MDD is dependent on the endpoint and selection of statistical parameters such as the alpha value. Parameters that display effects at a biologically relevant scale will be a better indicator for effects than parameters that are able to detect minor differences that are not biologically relevant.展开更多
The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combination...The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combinations of the variables and their W- or W'-statistics with the Royston’s log-transformation and standardization, z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub>. Because the calculation of the probability of z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub> is to the right tail, negative values are truncated to 0 before doing their sum of squares. Independence in the sequence of these half-normally distributed values is required for the test statistic to follow a chi-square distribution. This assumption is checked using the robust Ljung-Box test. One degree of freedom is lost for each cancelled value. Defined the new test with its two variants (Q-test or Q'-test), 50 random samples with 4 variables and 20 participants were generated, 20% following a multivariate normal distribution and 80% deviating from this distribution. The new test was compared with Mardia’s, runs, and Royston’s tests. Central tendency differences in type II error and statistical power were tested using the Friedman’s test and pairwise comparisons using the Wilcoxon’s test. Differences in the frequency of successes in statistical decision making were compared using the Cochran’s Q test and pairwise comparisons using the McNemar’s test. Sensitivity, specificity and efficiency proportions were compared using the McNemar’s Z test. The generated 50 samples were classified into five ordered categories of deviation from multivariate normality, the correlation between this variable and p-value of each test was calculated using the Spearman’s coefficient and these correlations were compared. Family-wise error rate corrections were applied. The new test and the Royston’s test were the best choices, with a very slight advantage Q-test over Q'-test. Based on these promising results, further study and use of this new sensitive, specific and effective test are suggested.展开更多
While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if eve...While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if ever do so.In this paper,we review some of the quantitative tools and techniques which are available for use in digital forensic investigations,including Bayesian networks,complexity theory,information theory and probability theory,and indicate how they may be used to obtain likelihood ratios or odds ratios for the relative plausibility of alternative explanations for the creation of the recovered digital evidence.The potential benefits of such quantitative measures for modern digital forensics are also outlined.展开更多
This study aims to examine the effect of El Nino and La Nina on the monthly and seasonal climate of Hong Kong against the ENSO-neutral situation from a statistical perspective. Monthly and seasonal temperature and rai...This study aims to examine the effect of El Nino and La Nina on the monthly and seasonal climate of Hong Kong against the ENSO-neutral situation from a statistical perspective. Monthly and seasonal temperature and rainfall of Hong Kong and monthly number of tropical cyclones （TCs） coming within 500 km of the city over the 59-yr （1950–2008） period are examined under three ENSO situations, namely El Nino, La Nina, and ENSO-neutral. It is found that, compared with the ENSO-neutral situation, El Nino tends to be associated with wetter winter （December–February） and spring （March–May） while La Nina tends to be associated with cooler autumn （September–November） and winter. El Nino tends to be associated with a later start of the tropical cyclone season of Hong Kong while La Nina tends to be associated with more TCs coming within 500 km of Hong Kong in August–October. It is also found that, for April and June–December, although the monthly number of TCs coming within 500 km of Hong Kong during El Nino is generally lower than that under the ENSO-neutral situation, the difference is not statistically significant based on the current data sample size.展开更多
Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different n...Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics|Mn,r|p are established.An alternative method is presented to estimate the probability of the r-th extremes.Numerical analyses are provided to support the main results.展开更多
Background:The presence of delayed treatment effects(DTE)is common in immuno-oncology trials.However,conventional trial designs often overlook the potential presence of DTE,which can result in an underestimation of th...Background:The presence of delayed treatment effects(DTE)is common in immuno-oncology trials.However,conventional trial designs often overlook the potential presence of DTE,which can result in an underestimation of the required sample size and loss of statistical power.Conversely,when there is actually no apparent delay in treatment effects,alternative trial designs for addressing DTE may lead to an over-estimation of sample size and unnecessary prolongation of the trial duration.To mitigate this challenge,we propose the use of a DTE predicting(DTEP)model to better guide immuno-oncology trial designs.Methods:The DTEP model was developed and validated using data from 147 pub-lished randomized immuno-oncology trials.The eligible trials were divided into a training set(approximately 75%of the trials)and a test set(approximately 25%).We employed linear discriminant analysis(LDA)to develop the DTEP model for pre-dicting the DTE status using baseline characteristics available at the trial design stage.The receiver operating characteristic(ROC)curve was utilized to assess the ability of the model to distinguish between trials with and without DTE.We further re-conducted the JUPITER-02 trial in a simulation setting,employing three design approaches to assess the potential benefits of utilizing the DTEP model.Results:Baseline characteristics available during the trial design stage,including cancer type,line of treatment,and experimental and control arm regimens were incorporated,and high accuracy in predicting the DTE status in both the training set(area under the operating characteristic curve(AUC),0.79;95%confidence interval(CI),0.71-0.88)and test set(AUC,0.78;95%CI,0.66-0.90)was achieved.Notably,the model successfully predicted the DTE status in two randomized trials among the test sets that were conducted by our team(ESCORT-1st(absence of DTE)and JUPITER-02(presence of DTE)).In silico re-conduct of the JUPITER-02 trial further showed that the statistical power would be markedly improved when trial designs were guided by the DTEP model.Conclusions:The DTEP model can significantly enhance the precision and effectiveness of immuno-oncology trial designs,thereby facilitating the discovery of effective im-munotherapeutics in a more streamlined and expedited manner.展开更多
Background:Interventional trials in amyotrophic lateral sclerosis(ALS)sufer from the heterogeneity of the disease as it considerably reduces statistical power.We asked if blood neuroflament light chains(NfL)could be u...Background:Interventional trials in amyotrophic lateral sclerosis(ALS)sufer from the heterogeneity of the disease as it considerably reduces statistical power.We asked if blood neuroflament light chains(NfL)could be used to antici‑pate disease progression and increase trial power.Methods:In 125 patients with ALS from three independent prospective studies-one observational study and two interventional trials-we developed and externally validated a multivariate linear model for predicting disease pro‑gression,measured by the monthly decrease of the ALS Functional Rating Scale Revised(ALSFRS-R)score.We trained the prediction model in the observational study and tested the predictive value of the following parameters assessed at diagnosis:NfL levels,sex,age,site of onset,body mass index,disease duration,ALSFRS-R score,and monthly ALSFRS-R score decrease since disease onset.We then applied the resulting model in the other two study cohorts to assess the actual utility for interventional trials.We analyzed the impact on trial power in mixed-efects models and compared the performance of the NfL model with two currently used predictive approaches,which anticipate disease progression using the ALSFRS-R decrease during a three-month observational period(lead-in)or since disease onset(ΔFRS).Results:Among the parameters provided,the NfL levels(P<0.001)and the interaction with site of onset(P<0.01)contributed signifcantly to the prediction,forming a robust NfL prediction model(R=0.67).Model application in the trial cohorts confrmed its applicability and revealed superiority over lead-in andΔFRS-based approaches.The NfL model improved statistical power by 61%and 22%(95%confdence intervals:54%-66%,7%-29%).Conclusion:The use of the NfL-based prediction model to compensate for clinical heterogeneity in ALS could signif‑cantly increase the trial power.NCT00868166,registered March23,2009;NCT02306590,registered December 2,2014.展开更多
文摘This study presents the results of a Monte Carlo simulation to compare the statistical power of Siegel-Tukey and Savage tests.The main purpose of the study is to evaluate the statistical power of both tests in scenarios involving Normal,Platykurtic and Skewed distributions over different sample sizes and standard deviation values.In the study,standard deviation ratios were set as 2,3,4,1/2,1/3 and 1/4 and power comparisons were made between small and large sample sizes.For equal sample sizes,small sample sizes of 5,8,10,12,16 and 20 and large sample sizes of 25,50,75 and 100 were used.For different sample sizes,the combinations of(4,16),(8,16),(10,20),(16,4),(16,8)and(20,10)small sample sizes and(10,30),(30,10),(50,75),(50,100),(75,50),(75,100),(100,50)and(100,75)large sample sizes were examined in detail.According to the findings,the power analysis under variance heterogeneity conditions shows that the Siegel-Tukey test has a higher statistical power than the other nonparametric Savage test at small and large sample sizes.In particular,the Siegel-Tukey test was reported to offer higher precision and power under variance heterogeneity,regardless of having equal or different sample sizes.
文摘In this study, the statistical powers of Kolmogorov-Smimov two-sample （KS-2） and Wald Wolfowitz （WW） tests, non-parametric tests used in testing data from two independent samples, have been compared in terms of fixed skewness and fixed kurtosis by means of Monte Carlo simulation. This comparison has been made when the ratio of variance is two as well as with equal and different sample sizes for large sample volumes. The sample used in the study is： （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 25）, （50, 50）, （50, 75）, （50, 100）, （75, 25）, （75, 50）, （75, 75）, （75, 100）, （100, 25）, （100, 50）, （100, 75）, and （100, 100）. According to the results of the study, it has been observed that the statistical power of both tests decreases when the coefficient of kurtosis is held fixed and the coefficient of skewness is reduced while it increases when the coefficient of skewness is held fixed and the coefficient of kurtosis is reduced. When the ratio of skewness is reduced in the case of fixed kurtosis, the WW test is stronger in sample volumes （25, 25）, （25, 50）, （25, 75）, （25, 100）, （50, 75）, and （50, 100） while KS-2 test is stronger in other sample volumes. When the ratio of kurtosis is reduced in the case of fixed skewness, the statistical power of WW test is stronger in volume samples （25, 25）, （25, 75）, （25, 100）, and （75, 25） while KS-2 test is stronger in other sample volumes.
基金supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515011986)National Natural Science Foundation of China(Grant No.31700986).
文摘Regression estimates are biased when potential confounders are omitted or when there are other similar risks to validity.The instrumental variable(IV)method can be used instead to obtain less biased estimates or to strengthen causal inferences.One key assumption critical to the validity of the IV method is the exclusion assumption,which requires instruments to be correlated with the outcome variable only through endogenous predictors.The chi-square test of model fit is widely used as a diagnostic test for this assumption.Previous simulation studies assessed the power of this diagnostic test only in situations with strong violations of the exclusion assumption.However,low to moderate levels of assumption violation are not uncommon in reality,especially when the exclusion assumption is violated indirectly.In this study,we showed through Monte Carlo simulations that the chi-square model fit test suffered from a severe lack of power(<30%)to detect violations of the exclusion assumption when the level of violation was of typical size,and the IV causal inferences were severely inaccurate and misleading in this case.We thus advise using the IV method with caution unless there is a chance for thorough assumption diagnostics,like in meta-analyses or experiments.
基金L.C.X.was supported by the Innovation in Cancer Informatics Fund.
文摘Alignment-based database search and sequence comparison are commonly used to detect horizontal gene transfer(HGT).However,with the rapid increase of sequencing depth,hundreds of thousands of contigs are routinely assembled from metagenomics studies,which challenges alignment-based HGT analysis by overwhelming the known reference sequences.Detecting HGT by k-mer statistics thus becomes an attractive alternative.These alignment-free statistics have been demonstrated in high performance and efficiency in wholegenome and transcriptome comparisons.To adapt k-mer statistics for HGT detection,we developed two aggregative statistics T^(S)_(sum ) and T^(*)_(sum),which subsample metagenome contigs by their representative regions,and summarize the regional D^(S) _(2) and D^(*)_(2)metrics by their upper bounds.We systematically studied the aggregative statistics’power at different k-mer size using simulations.Our analysis showed that,in general,the power of T^(S)_(sum) and T^(*)_(sum) increases with sequencing coverage,and reaches a maximum power>80%at k=6,with 5%Type-I error and the coverage ratio>0.2x.The statistical power ofT^(S)_(sum) and T^(*)_(sum) was evaluated with realistic simulations of HGT mechanism,sequencing depth,read length,and base error.We expect these statistics to be useful distance metrics for identifying HGT in metagenomic studies.
基金supported in part by the National Science Foundation (NSFC) for Distinguished Young Scholars of China with Grant 61625106the National Natural Science Foundation of China under Grant 61531011
文摘In this paper, we study an energy efficient multi-antenna unmanned aerial vehicle(UAV)-enabled half-duplex mobile relaying system under Rician fading channels. By assuming that the UAV follows a circular trajectory at fixed altitude and applying the decode-and-forward relaying strategy, we maximize the energy efficiency by jointly designing beamforming, power allocation, circular radius and flight speed, subject to the sum transmit power constraint on source node and UAV relay node. First, we maximize the end-to-end signal-to-noise ratio by jointly designing beamforming and statistical power allocation. Based on the obtained beamforming and power allocation results, we then obtain a semi closed-form expression of energy efficiency, and finally maximize energy efficiency by optimizing flight speed and circular radius, allowing optimal circular radius to be obtained via numerical computation. Numerical results demonstrate that the proposed scheme can effectively enhance the system energy efficiency.
文摘Statistical power, number of replicates and experiment complexity of semi-field and field studies on Apis and non-Apis bee species has become a major issue after publication of the draft European Food Safety Authority （EFSA） Guidance on risk assessment of plant protection products （PPP） on bees （Apis mellifera, Bombus spp. and solitary bees）. According to this guidance document, field studies have to be designed to be able to detect significance differences as low as 7% for certain endpoints such as reduction in colony size. This will require an immense number of replicates which is obviously not feasible. In the present study, key endpoints such as mortality, termination rate and number of brood cells in honeybee studies, cocoon production and flight activity in solitary bee studies and number of gynes in bumble bee studies （just to mention some of the endpoints considered） in semi-field studies were analyzed, with Apis mellifera, Bombus terrestris and Osmia bicornis during the past five years （2013-2017）. The results indicate huge differences in the percentage minimal detectable differences （%MDDs） （MDD expressed as median of control value of the endpoint in percent） depending on endpoint and species tested. For honeybee semi-field studies, the lowest %MDDs recorded were between 10% and 15% for the endpoints foraging, number of brood cells and colony strength. The highest %MDDs were observed for the endpoint termination rate, with a %MDD of almost 50%. For the endpoints in bumble bee semi-field studies the %MDDs varied between 17% for bumble bee colony weight and 53% for average mortality during the exposure period in the tunnel. The %MDD for the number of gynes （young queens） was slightly below 25%. For the semi-field solitary bee test system, the %MDDs for the measured endpoints seem to be lower than those for the other two species tested. The %MDDs for the endpoints hatching of offspring, nest occupation and number of cocoons were 8%, 13% and 14%, respectively. Most of the %MDDs were between 10% and 30% indicating clearly that the currently performed experimental design for the semi-field pollinator studies allowed to determine relatively small effects on key study endpoints. The analysis indicated that for all the three bee species tested, the semi-field test design detected low %MDDs for most of the endpoints. It was also observed that detectable differences between the control and PPP treatments were much lower in semi-field test designs than in field studies with these bee species. The “perfect sample size” really does not exist but test design and statistical analysis can be adapted to lower the %MDDs. Measured and simulated （according to Student’s t-test-distribution） data and results showed that statistical evaluations parameter selection （e.g., alpha value）, data transformation （log10） and the number of replicates had a direct effect on the ability of the test design to detect lower or higher %MDD values. It could show that a change of alpha value from 0.05 to 0.1, increases the ability of the studies to detect lower %MDDs. For most of the measured endpoints, increasing the number of replicates e.g., from four to eight, improved the power of the test design by decreasing the %MDD. The reduction magnitude of the %MDD is dependent on the endpoint and selection of statistical parameters such as the alpha value. Parameters that display effects at a biologically relevant scale will be a better indicator for effects than parameters that are able to detect minor differences that are not biologically relevant.
文摘The aim of this paper is to present a generalization of the Shapiro-Wilk W-test or Shapiro-Francia W'-test for application to two or more variables. It consists of calculating all the unweighted linear combinations of the variables and their W- or W'-statistics with the Royston’s log-transformation and standardization, z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub>. Because the calculation of the probability of z<sub>ln(1-W)</sub> or z<sub>ln(1-W</sub><sub>'</sub><sub>)</sub> is to the right tail, negative values are truncated to 0 before doing their sum of squares. Independence in the sequence of these half-normally distributed values is required for the test statistic to follow a chi-square distribution. This assumption is checked using the robust Ljung-Box test. One degree of freedom is lost for each cancelled value. Defined the new test with its two variants (Q-test or Q'-test), 50 random samples with 4 variables and 20 participants were generated, 20% following a multivariate normal distribution and 80% deviating from this distribution. The new test was compared with Mardia’s, runs, and Royston’s tests. Central tendency differences in type II error and statistical power were tested using the Friedman’s test and pairwise comparisons using the Wilcoxon’s test. Differences in the frequency of successes in statistical decision making were compared using the Cochran’s Q test and pairwise comparisons using the McNemar’s test. Sensitivity, specificity and efficiency proportions were compared using the McNemar’s Z test. The generated 50 samples were classified into five ordered categories of deviation from multivariate normality, the correlation between this variable and p-value of each test was calculated using the Spearman’s coefficient and these correlations were compared. Family-wise error rate corrections were applied. The new test and the Royston’s test were the best choices, with a very slight advantage Q-test over Q'-test. Based on these promising results, further study and use of this new sensitive, specific and effective test are suggested.
文摘While the conventional forensic scientists routinely validate and express the results of their investigations quantitatively using statistical measures from probability theory,digital forensics examiners rarely if ever do so.In this paper,we review some of the quantitative tools and techniques which are available for use in digital forensic investigations,including Bayesian networks,complexity theory,information theory and probability theory,and indicate how they may be used to obtain likelihood ratios or odds ratios for the relative plausibility of alternative explanations for the creation of the recovered digital evidence.The potential benefits of such quantitative measures for modern digital forensics are also outlined.
文摘This study aims to examine the effect of El Nino and La Nina on the monthly and seasonal climate of Hong Kong against the ENSO-neutral situation from a statistical perspective. Monthly and seasonal temperature and rainfall of Hong Kong and monthly number of tropical cyclones （TCs） coming within 500 km of the city over the 59-yr （1950–2008） period are examined under three ENSO situations, namely El Nino, La Nina, and ENSO-neutral. It is found that, compared with the ENSO-neutral situation, El Nino tends to be associated with wetter winter （December–February） and spring （March–May） while La Nina tends to be associated with cooler autumn （September–November） and winter. El Nino tends to be associated with a later start of the tropical cyclone season of Hong Kong while La Nina tends to be associated with more TCs coming within 500 km of Hong Kong in August–October. It is also found that, for April and June–December, although the monthly number of TCs coming within 500 km of Hong Kong during El Nino is generally lower than that under the ENSO-neutral situation, the difference is not statistically significant based on the current data sample size.
文摘Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics|Mn,r|p are established.An alternative method is presented to estimate the probability of the r-th extremes.Numerical analyses are provided to support the main results.
基金supported by the National Natural Science Foundation of China(82003269,82173128,81803327,81930065,and 81903406)the Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences(2019-I2M-5-036)the Young Faculty Development Project of Sun Yat-sen University(84000-31660002).
文摘Background:The presence of delayed treatment effects(DTE)is common in immuno-oncology trials.However,conventional trial designs often overlook the potential presence of DTE,which can result in an underestimation of the required sample size and loss of statistical power.Conversely,when there is actually no apparent delay in treatment effects,alternative trial designs for addressing DTE may lead to an over-estimation of sample size and unnecessary prolongation of the trial duration.To mitigate this challenge,we propose the use of a DTE predicting(DTEP)model to better guide immuno-oncology trial designs.Methods:The DTEP model was developed and validated using data from 147 pub-lished randomized immuno-oncology trials.The eligible trials were divided into a training set(approximately 75%of the trials)and a test set(approximately 25%).We employed linear discriminant analysis(LDA)to develop the DTEP model for pre-dicting the DTE status using baseline characteristics available at the trial design stage.The receiver operating characteristic(ROC)curve was utilized to assess the ability of the model to distinguish between trials with and without DTE.We further re-conducted the JUPITER-02 trial in a simulation setting,employing three design approaches to assess the potential benefits of utilizing the DTEP model.Results:Baseline characteristics available during the trial design stage,including cancer type,line of treatment,and experimental and control arm regimens were incorporated,and high accuracy in predicting the DTE status in both the training set(area under the operating characteristic curve(AUC),0.79;95%confidence interval(CI),0.71-0.88)and test set(AUC,0.78;95%CI,0.66-0.90)was achieved.Notably,the model successfully predicted the DTE status in two randomized trials among the test sets that were conducted by our team(ESCORT-1st(absence of DTE)and JUPITER-02(presence of DTE)).In silico re-conduct of the JUPITER-02 trial further showed that the statistical power would be markedly improved when trial designs were guided by the DTEP model.Conclusions:The DTEP model can significantly enhance the precision and effectiveness of immuno-oncology trial designs,thereby facilitating the discovery of effective im-munotherapeutics in a more streamlined and expedited manner.
基金Open Access funding enabled and organized by Projekt DEAL。
文摘Background:Interventional trials in amyotrophic lateral sclerosis(ALS)sufer from the heterogeneity of the disease as it considerably reduces statistical power.We asked if blood neuroflament light chains(NfL)could be used to antici‑pate disease progression and increase trial power.Methods:In 125 patients with ALS from three independent prospective studies-one observational study and two interventional trials-we developed and externally validated a multivariate linear model for predicting disease pro‑gression,measured by the monthly decrease of the ALS Functional Rating Scale Revised(ALSFRS-R)score.We trained the prediction model in the observational study and tested the predictive value of the following parameters assessed at diagnosis:NfL levels,sex,age,site of onset,body mass index,disease duration,ALSFRS-R score,and monthly ALSFRS-R score decrease since disease onset.We then applied the resulting model in the other two study cohorts to assess the actual utility for interventional trials.We analyzed the impact on trial power in mixed-efects models and compared the performance of the NfL model with two currently used predictive approaches,which anticipate disease progression using the ALSFRS-R decrease during a three-month observational period(lead-in)or since disease onset(ΔFRS).Results:Among the parameters provided,the NfL levels(P<0.001)and the interaction with site of onset(P<0.01)contributed signifcantly to the prediction,forming a robust NfL prediction model(R=0.67).Model application in the trial cohorts confrmed its applicability and revealed superiority over lead-in andΔFRS-based approaches.The NfL model improved statistical power by 61%and 22%(95%confdence intervals:54%-66%,7%-29%).Conclusion:The use of the NfL-based prediction model to compensate for clinical heterogeneity in ALS could signif‑cantly increase the trial power.NCT00868166,registered March23,2009;NCT02306590,registered December 2,2014.
