Sample Size Determination and Study Design Impact on Dose-Scale Pharmacodynamic Bioequivalence: a Case Study Using Orlistat.

Dose-scale pharmacodynamic bioequivalence is recommended for evaluating the consistency of generic and innovator formulations of certain locally acting drugs, such as orlistat. This study aimed to investigate the standard methodology for sample size determination and the impact of study design on dose-scale pharmacodynamic bioequivalence using orlistat as the model drug. A population pharmacodynamic model of orlistat was developed using NONMEM 7.5.1 and utilized for subsequent simulations. Three different study designs were evaluated across various predefined relative bioavailability ratios of test/reference (T/R) formulations. These designs included Study Design 1 (2×1 crossover with T1 60 mg, R1 60 mg, and R2 120 mg), Study Design 2 (2×1 crossover with T2 120 mg, R1 60 mg, and R2 120 mg), and Study Design 3 (2×2 crossover with T1 60 mg, T2 120 mg, R1 60 mg, and R2 120 mg). Sample sizes were determined using a stochastic simulation and estimation approach. Under the same T/R ratio and power, Study Design 3 required the minimum sample size for bioequivalence, followed by Study Design 1, while Study Design 2 performed the worst. For Study Designs 1 and 3, a larger sample size was needed on the T/R ratio < 1.0 side for the same power compared to that on the T/R ratio > 1.0 side. The opposite asymmetry was observed for Study Design 2. We demonstrated that Study Design 3 is most effective for reducing the sample size for orlistat bioequivalence studies, and the impact of T/R ratio on sample size shows asymmetry.

Determining sample size in a personalized randomized controlled (PRACTical) trial.

In clinical settings with no commonly accepted standard-of-care, multiple treatment regimens are potentially useful, but some treatments may not be appropriate for some patients. A personalized randomized controlled trial (PRACTical) design has been proposed for this setting. For a network of treatments, each patient is randomized only among treatments which are appropriate for them. The aim is to produce treatment rankings that can inform clinical decisions about treatment choices for individual patients. Here we propose methods for determining sample size in a PRACTical design, since standard power-based methods are not applicable. We derive a sample size by evaluating information gained from trials of varying sizes. For a binary outcome, we quantify how many adverse outcomes would be prevented by choosing the top-ranked treatment for each patient based on trial results rather than choosing a random treatment from the appropriate personalized randomization list. In simulations, we evaluate three performance measures: mean reduction in adverse outcomes using sample information, proportion of simulated patients for whom the top-ranked treatment performed as well or almost as well as the best appropriate treatment, and proportion of simulated trials in which the top-ranked treatment performed better than a randomly chosen treatment. We apply the methods to a trial evaluating eight different combination antibiotic regimens for neonatal sepsis (NeoSep1), in which a PRACTical design addresses varying patterns of antibiotic choice based on disease characteristics and resistance. Our proposed approach produces results that are more relevant to complex decision making by clinicians and policy makers.

How many Monte Carlo samples are needed for probabilistic cost-effectiveness analyses?

OBJECTIVE: Probabilistic sensitivity analysis (PSA) is conducted to account for the uncertainty in cost and effect of decision options under consideration. PSA involves obtaining a large sample of input parameter values (N) to estimate the expected cost and effect of each alternative in the presence of parameter uncertainty. When the analysis involves using stochastic models (e.g., individual-level models), the model is further replicated P times for each sampled parameter set. We study how N and P should be determined. METHODS: We show that PSA could be structured such that P can be an arbitrary number (say, P=1). To determine N, we derive a formula based on Chebyshev's inequality such that the error in estimating the incremental cost-effectiveness ratio (ICER) of alternatives (or equivalently, the willingness-to-pay value at which the optimal decision option changes) is within a desired level of accuracy. We described two methods to confirmed, visually and quantitatively, that the N informed by this method results in ICER estimates within the specified level of accuracy. RESULTS: When N is arbitrarily selected, the estimated ICERs could be substantially different from the true ICER (even as P increases), which could lead misleading conclusions. Using a simple resource allocation model, we demonstrate that the proposed approach can minimize the potential for this error. CONCLUSIONS: The number of parameter samples in probabilistic CEAs should not be arbitrarily selected. We describe three methods to ensure that enough parameter samples are used in probabilistic CEAs.

Sample Size Calculation for an Individual Stepped-Wedge Randomized Trial.

In the individual stepped-wedge randomized trial (ISW-RT), subjects are allocated to sequences, each sequence being defined by a control period followed by an experimental period. The total follow-up time is the same for all sequences, but the duration of the control and experimental periods varies among sequences. To our knowledge, there is no validated sample size calculation formula for ISW-RTs unlike stepped-wedge cluster randomized trials (SW-CRTs). The objective of this study was to adapt the formula used for SW-CRTs to the case of individual randomization and to validate this adaptation using a Monte Carlo simulation study. The proposed sample size calculation formula for an ISW-RT design yielded satisfactory empirical power for most scenarios except scenarios with operating characteristic values near the boundary (i.e., smallest possible number of periods, very high or very low autocorrelation coefficient). Overall, the results provide useful insights into the sample size calculation for ISW-RTs.

The score-goldilocks design for phase 3 clinical trials.

In this paper, we propose a new Bayesian adaptive design, score-goldilocks design, which has the same algorithmic idea as goldilocks design. The score-goldilocks design leads to a uniform formula for calculating the probability of trial success for different endpoint trials by using the normal approximation. The simulation results show that the score-goldilocks design is not only very similar to the goldilocks design in terms of operating characteristics such as type 1 error, power, average sample size, probability of stop for futility, and probability of early stop for success, but also greatly saves the calculation time and improves the operation efficiency.

Sample Size Estimation Using a Partially Clustered Frailty Model for Biomarker-Strategy Designs With Multiple Treatments.

Biomarker-guided therapy is a growing area of research in medicine. To optimize the use of biomarkers, several study designs including the biomarker-strategy design (BSD) have been proposed. Unlike traditional designs, the emphasis here is on comparing treatment strategies and not on treatment molecules as such. Patients are assigned to either a biomarker-based strategy (BBS) arm, in which biomarker-positive patients receive an experimental treatment that targets the identified biomarker, or a non-biomarker-based strategy (NBBS) arm, in which patients receive treatment regardless of their biomarker status. We proposed a simulation method based on a partially clustered frailty model (PCFM) as well as an extension of Freidlin formula to estimate the sample size required for BSD with multiple targeted treatments. The sample size was mainly influenced by the heterogeneity of treatment effect, the proportion of biomarker-negative patients, and the randomization ratio. The PCFM is well suited for the data structure and offers an alternative to traditional methodologies.

Strategy for Designing In Vivo Dose-Response Comparison Studies.

In preclinical drug discovery, at the step of lead optimization of a compound, in vivo experimentation can differentiate several compounds in terms of efficacy and potency in a biological system of whole living organisms. For the lead optimization study, it may be desirable to implement a dose-response design so that compound comparisons can be made from nonlinear curves fitted to the data. A dose-response design requires more thought relative to a simpler study design, needing parameters for the number of doses, the dose values, and the sample size per dose. This tutorial illustrates how to calculate statistical power, choose doses, and determine sample size per dose for a comparison of two or more dose-response curves for a future in vivo study.

Calculating the power of a planned individual participant data meta-analysis to examine prognostic factor effects for a binary outcome.

Collecting data for an individual participant data meta-analysis (IPDMA) project can be time consuming and resource intensive and could still have insufficient power to answer the question of interest. Therefore, researchers should consider the power of their planned IPDMA before collecting IPD. Here we propose a method to estimate the power of a planned IPDMA project aiming to synthesise multiple cohort studies to investigate the (unadjusted or adjusted) effects of potential prognostic factors for a binary outcome. We consider both binary and continuous factors and provide a three-step approach to estimating the power in advance of collecting IPD, under an assumption of the true prognostic effect of each factor of interest. The first step uses routinely available (published) aggregate data for each study to approximate Fisher's information matrix and thereby estimate the anticipated variance of the unadjusted prognostic factor effect in each study. These variances are then used in step 2 to estimate the anticipated variance of the summary prognostic effect from the IPDMA. Finally, step 3 uses this variance to estimate the corresponding IPDMA power, based on a two-sided Wald test and the assumed true effect. Extensions are provided to adjust the power calculation for the presence of additional covariates correlated with the prognostic factor of interest (by using a variance inflation factor) and to allow for between-study heterogeneity in prognostic effects. An example is provided for illustration, and Stata code is supplied to enable researchers to implement the method.

Determining an Appropriate Sample Size for Qualitative Interviews to Achieve True and Near Code Saturation: Secondary Analysis of Data.

BACKGROUND: In-depth interviews are a common method of qualitative data collection, providing rich data on individuals' perceptions and behaviors that would be challenging to collect with quantitative methods. Researchers typically need to decide on sample size a priori. Although studies have assessed when saturation has been achieved, there is no agreement on the minimum number of interviews needed to achieve saturation. To date, most research on saturation has been based on in-person data collection. During the COVID-19 pandemic, web-based data collection became increasingly common, as traditional in-person data collection was possible. Researchers continue to use web-based data collection methods post the COVID-19 emergency, making it important to assess whether findings around saturation differ for in-person versus web-based interviews. OBJECTIVE: We aimed to identify the number of web-based interviews needed to achieve true code saturation or near code saturation. METHODS: The analyses for this study were based on data from 5 Food and Drug Administration-funded studies conducted through web-based platforms with patients with underlying medical conditions or with health care providers who provide primary or specialty care to patients. We extracted code- and interview-specific data and examined the data summaries to determine when true saturation or near saturation was reached. RESULTS: The sample size used in the 5 studies ranged from 30 to 70 interviews. True saturation was reached after 91% to 100% (n=30-67) of planned interviews, whereas near saturation was reached after 33% to 60% (n=15-23) of planned interviews. Studies that relied heavily on deductive coding and studies that had a more structured interview guide reached both true saturation and near saturation sooner. We also examined the types of codes applied after near saturation had been reached. In 4 of the 5 studies, most of these codes represented previously established core concepts or themes. Codes representing newly identified concepts, other or miscellaneous responses (eg, "in general"), uncertainty or confusion (eg, "don't know"), or categorization for analysis (eg, correct as compared with incorrect) were less commonly applied after near saturation had been reached. CONCLUSIONS: This study provides support that near saturation may be a sufficient measure to target and that conducting additional interviews after that point may result in diminishing returns. Factors to consider in determining how many interviews to conduct include the structure and type of questions included in the interview guide, the coding structure, and the population under study. Studies with less structured interview guides, studies that rely heavily on inductive coding and analytic techniques, and studies that include populations that may be less knowledgeable about the topics discussed may require a larger sample size to reach an acceptable level of saturation. Our findings also build on previous studies looking at saturation for in-person data collection conducted at a small number of sites.

Sample size calculation for data reliability and diagnostic performance: a go-to review.

Sample size, namely the number of subjects that should be included in a study to reach the desired endpoint and statistical power, is a fundamental concept of scientific research. Indeed, sample size must be planned a priori, and tailored to the main endpoint of the study, to avoid including too many subjects, thus possibly exposing them to additional risks while also wasting time and resources, or too few subjects, failing to reach the desired purpose. We offer a simple, go-to review of methods for sample size calculation for studies concerning data reliability (repeatability/reproducibility) and diagnostic performance. For studies concerning data reliability, we considered Cohen's κ or intraclass correlation coefficient (ICC) for hypothesis testing, estimation of Cohen's κ or ICC, and Bland-Altman analyses. With regards to diagnostic performance, we considered accuracy or sensitivity/specificity versus reference standards, the comparison of diagnostic performances, and the comparisons of areas under the receiver operating characteristics curve. Finally, we considered the special cases of dropouts or retrospective case exclusions, multiple endpoints, lack of prior data estimates, and the selection of unusual thresholds for α and ß errors. For the most frequent cases, we provide example of software freely available on the Internet.Relevance statement Sample size calculation is a fundamental factor influencing the quality of studies on repeatability/reproducibility and diagnostic performance in radiology.Key points• Sample size is a concept related to precision and statistical power.• It has ethical implications, especially when patients are exposed to risks.• Sample size should always be calculated before starting a study.• This review offers simple, go-to methods for sample size calculations.

Global Perfusion Practice Survey: Readiness of On-Call and Emergency Operation Rooms.

INTRODUCTION: Perfusion safety in cardiac surgery is vital, and this survey explores perfusion practices, perspectives, and challenges related to it. Specifically, it examines the readiness of on-call and emergency operation rooms for perfusion-related procedures during urgent situations. The aim is to identify gaps and enhance perfusion safety protocols, ultimately improving patient care. METHODS: This was a preliminary survey conducted as an initial exploration before committing to a comprehensive study. The sample size was primarily determined based on a one-month time frame. The survey collected data from 236 healthcare professionals, including cardiac surgeons, perfusionists, and anesthetists, using an online platform. Ethical considerations ensured participant anonymity and voluntary participation. The survey comprised multiple-choice and open-ended questions to gather quantitative and qualitative data. RESULTS: The survey found that 53% preferred a dry circuit ready for emergencies, 19.9% preferred primed circuits, and 19.1% chose not to have a ready pump at all. Various reasons influenced these choices, including caseload variations, response times, historical practices, surgeon preferences, and backup perfusionist availability. Infection risk, concerns about error, and team dynamics were additional factors affecting circuit readiness. CONCLUSION: This survey sheds light on current perfusion practices and challenges, emphasizing the importance of standardized protocols in regards to readiness of on-call and emergency operation rooms. It provides valuable insights for advancing perfusion safety and patient care while contributing to the existing literature on the subject.

Hypothesis testing and sample size considerations for the test-negative design.

The test-negative design (TND) is an observational study design to evaluate vaccine effectiveness (VE) that enrolls individuals receiving diagnostic testing for a target disease as part of routine care. VE is estimated as one minus the adjusted odds ratio of testing positive versus negative comparing vaccinated and unvaccinated patients. Although the TND is related to case-control studies, it is distinct in that the ratio of test-positive cases to test-negative controls is not typically pre-specified. For both types of studies, sparse cells are common when vaccines are highly effective. We consider the implications of these features on power for the TND. We use simulation studies to explore three hypothesis-testing procedures and associated sample size calculations for case-control and TND studies. These tests, all based on a simple logistic regression model, are a standard Wald test, a continuity-corrected Wald test, and a score test. The Wald test performs poorly in both case-control and TND when VE is high because the number of vaccinated test-positive cases can be low or zero. Continuity corrections help to stabilize the variance but induce bias. We observe superior performance with the score test as the variance is pooled under the null hypothesis of no group differences. We recommend using a score-based approach to design and analyze both case-control and TND. We propose a modification to the TND score sample size to account for additional variability in the ratio of controls over cases. This work enhances our understanding of the data generating mechanism in a test-negative design (TND) and how it is distinct from that of a case-control study due to its passive recruitment of controls.

An evaluation of sample size requirements for developing risk prediction models with binary outcomes.

BACKGROUND: Risk prediction models are routinely used to assist in clinical decision making. A small sample size for model development can compromise model performance when the model is applied to new patients. For binary outcomes, the calibration slope (CS) and the mean absolute prediction error (MAPE) are two key measures on which sample size calculations for the development of risk models have been based. CS quantifies the degree of model overfitting while MAPE assesses the accuracy of individual predictions. METHODS: Recently, two formulae were proposed to calculate the sample size required, given anticipated features of the development data such as the outcome prevalence and c-statistic, to ensure that the expectation of the CS and MAPE (over repeated samples) in models fitted using MLE will meet prespecified target values. In this article, we use a simulation study to evaluate the performance of these formulae. RESULTS: We found that both formulae work reasonably well when the anticipated model strength is not too high (c-statistic < 0.8), regardless of the outcome prevalence. However, for higher model strengths the CS formula underestimates the sample size substantially. For example, for c-statistic = 0.85 and 0.9, the sample size needed to be increased by at least 50% and 100%, respectively, to meet the target expected CS. On the other hand, the MAPE formula tends to overestimate the sample size for high model strengths. These conclusions were more pronounced for higher prevalence than for lower prevalence. Similar results were drawn when the outcome was time to event with censoring. Given these findings, we propose a simulation-based approach, implemented in the new R package 'samplesizedev', to correctly estimate the sample size even for high model strengths. The software can also calculate the variability in CS and MAPE, thus allowing for assessment of model stability. CONCLUSIONS: The calibration and MAPE formulae suggest sample sizes that are generally appropriate for use when the model strength is not too high. However, they tend to be biased for higher model strengths, which are not uncommon in clinical risk prediction studies. On those occasions, our proposed adjustments to the sample size calculations will be relevant.

Primary outcomes and anticipated effect sizes in randomised clinical trials assessing adjuncts to peripheral nerve blocks: A scoping review.

BACKGROUND: Prolonging effects of adjuncts to local anaesthetics in peripheral nerve blocks have been demonstrated in randomised clinical trials. The chosen primary outcome and anticipated effect size have major impact on the clinical relevance of results in these trials. This scoping review aims to provide an overview of frequently used outcomes and anticipated effect sizes in randomised trials on peripheral nerve block adjuncts. METHODS: For our scoping review, we searched MEDLINE, Embase and CENTRAL for trials assessing effects of adjuncts for peripheral nerve blocks published in 10 major anaesthesia journals. We included randomised clinical trials assessing adjuncts for single-shot ultrasound-guided peripheral nerve blocks, regardless of the type of interventional adjunct and control group, local anaesthetic used and anatomical localization. Our primary outcome was the choice of primary outcomes and corresponding anticipated effect size used for sample size estimation. Secondary outcomes were assessor of primary outcomes, the reporting of sample size calculations and statistically significant and non-significant results related to the anticipated effect sizes. RESULTS: Of 11,854 screened trials, we included 59. The most frequent primary outcome was duration of analgesia (35/59 trials, 59%) with absolute and relative median (interquartile range) anticipated effect sizes for adjunct versus placebo/no adjunct: 240 min (180-318) and 30% (25-40) and for adjunct versus active comparator: 210 min (180-308) and 17% (15-28). Adequate sample size calculations were reported in 78% of trials. Statistically significant results were reported for primary outcomes in 45/59 trials (76%), of which 22% did not reach the anticipated effect size. CONCLUSION: The reported outcomes and associated anticipated effect sizes can be used in future trials on adjuncts for peripheral nerve blocks to increase methodological homogeneity.

Merging Data with Modeling: An Example from Fatigue.

It is well known that errors are inevitable in experimental observations, but it is equally unavoidable to eliminate errors in modeling the process leading to the experimental observations. If estimation and prediction are to be done with reasonable accuracy, the accumulated errors must be adequately managed. Research in fatigue is challenging because modeling can be quite complex. Furthermore, experimentation is time-consuming, which frequently yields limited data. Both of these exacerbate the magnitude of the potential error. The purpose of this paper is to demonstrate a procedure that combines modeling with independent experimental data to improve the estimation of the cumulative distribution function (cdf) for fatigue life. Subsequently, the effect of intrinsic error will be minimized. Herein, a simplified fatigue crack growth modeling is used. The data considered are a well-known collection of fatigue lives for an aluminum alloy. For lower applied stresses, the fatigue lives can range over an order of magnitude and up to 107 cycles. For larger applied stresses, the scatter in the lives is considerably reduced. Consequently, modeling must encompass a variety of conditions. The primary conclusion of the effort is that merging independent experimental data with a reasonably acceptable model vastly improves the accuracy of the calibrated cdfs for fatigue life, given the loading conditions. This allows for improved life estimation and prediction. For the aluminum data, the calibrated cdfs are shown to be quite good by using statistical goodness-of-fit tests, stress-life (S-N) analysis, and confidence bounds estimated using the mean square error (MSE) method. A short investigation into the effect of sample size is also included. Thus, the proposed methodology is warranted.

Determination of sample size for various study designs in medical research: A practical primer.

Formulating a research question and selecting an appropriate study design for answering that question are crucial initial steps in the research process. The population, intervention, control group, and outcomes measures (PICO time and setting [TS]) framework provides a practical guide in this regard, which stands for population, intervention, control, outcome, type of research question, and study design. The various study designs have their own merits and demerits, and implementing the methodology meticulously requires knowledge of all of these. Similarly, different methods of sample size calculation are warranted based on the most appropriate study design and outcome variables of interest. Sometimes, a post hoc power analysis can be performed after the sample size calculation, to check whether the study was adequately powered or not. There are multiple validated free software tools for sample size calculation, including Open-Epi, R, StatCalc, etc. The practice by most researchers of reporting significant P values is to be replaced by reporting effect sizes, as the latter is a much better estimate of the strength of association. This review provides a comprehensive, ready reckoner for busy family physicians to quickly identify the appropriate study design for answering any applied research questions in their minds and estimating the sample size required for the same.

Group sequential design for time-to-event outcome with non-proportional hazards using the concept of relative time utilizing two different Weibull distributions.

A group sequential design allows investigators to sequentially monitor efficacy and safety as part of interim testing in phase III trials. Literature is well developed in the case of continuous and binary outcomes, however, in case of trials with a time-to-event outcome, popular methods of sample size calculation often assume proportional hazards. In situations where the proportional hazards assumption is inappropriate as indicated by historical data, these popular methods are very restrictive. In this paper, a novel simulation-based group sequential design is proposed for a two-arm randomized phase III clinical trial with a survival endpoint for the non-proportional hazards scenario. By assuming that the survival times for each treatment arm follow two different Weibull distributions, the proposed method utilizes the concept of Relative Time to calculate the efficacy and safety boundaries at selected interim testing points. The test statistic used to generate these boundaries is asymptotically normal, allowing p-value calculation at each boundary. Many design features specific to time-to-event data can be incorporated with ease. Additionally, the proposed method allows the flexibility of having the accelerated failure time model and the proportional hazards model as constrained special cases. Real life applications are discussed demonstrating the practicality of the proposed method.

Key insights and challeneges in noninferiority trials.

Noninferiority clinical trials are crucial for evaluating the effectiveness of new interventions compared to standard interventions. By establishing statistical and clinical comparability, these trials can be conducted to demonstrate that a new intervention is not significantly inferior to the standard intervention. However, selecting appropriate noninferiority margins and study designs are essential to ensuring valid and reliable results. Moreover, employing the Consolidated Standards of Reporting Trials (CONSORT) statement for reporting noninferiority clinical trials enhances the quality and transparency of research findings. This article addresses key considerations and challenges faced by investigators in planning, conducting, and interpreting the results of noninferiority clinical trials.

Sample size in multistakeholder Delphi surveys: at what minimum sample size do replicability of results stabilise?

BACKGROUND: The minimum sample size for multistakeholder Delphi surveys remains understudied. Drawing from three large international multistakeholder Delphi surveys, this study aimed to: 1) investigate the effect of increasing sample size on replicability of results; 2) assess whether the level of replicability of results differed with participant characteristics: e.g., gender, age, profession. METHODS: We used data from Delphi surveys to develop guidance for improved reporting of healthcare intervention trials: SPIRIT (Standard Protocol Items: Recommendations for Interventional Trials) and CONSORT (Consolidated Standards of Reporting Trials) extension for surrogate endpoints (n=175, 22 items rated); CONSORT-SPI, extension for social and psychological interventions (n=333, 77 items rated); and core outcome set for burn care (n=553, 88 items rated). Resampling with replacement was used to draw random subsamples from the participant data set in each of the three surveys. For each subsample, the median value of all rated survey items was calculated and compared to the medians from the full participant data set. The median number (and interquartile range) of medians replicated was used to calculate the percentage replicability (and variability). High replicability was defined as ≥80% and moderate as 60% and <80% RESULTS: The average median replicability (variability) as a percentage of total number of items rated from the three datasets was 81% (10%) at a sample size of 60. In one of the datasets (CONSORT-SPI), a ≥80% replicability was reached at a sample size of 80. On average, increasing the sample size from 80 to 160 increased the replicability of results by a further 3% and reduced variability by 1%. For subgroup analysis based on participant characteristics (e.g. gender, age, professional role), using resampled samples of 20 to 100 showed that a sample size of 20 to 30 resulted to moderate replicability levels of 64 to 77%. CONCLUSION: We found that a minimum sample size of 60 to 80 participants in multistakeholder Delphi surveys provide a high level of replicability (≥80%) in the results. For Delphi studies limited to individual stakeholder groups (such as researchers, clinicians, patients), a sample size of 20 to 30 per group may be sufficient.

Bayesian sample size determination for coefficient of variation of normal distribution.

Sample size determination is an active area of research in statistics. Generally, Bayesian methods provide relatively smaller sample sizes than the classical techniques, particularly average length criterion is more conventional and gives relatively small sample sizes under the given constraints. The objective of this study is to utilize major Bayesian sample size determination techniques for the coefficient of variation of normal distribution and assess their performance by comparing the results with the freqentist approach. To this end, we noticed that the average coverage criterion is the one that provides relatively smaller sample sizes than the worst outcome criterion. By comparing with the existing frequentist studies, we show that a smaller sample size is required in Bayesian methods to achieve the same efficiency.