Proposed Sample Size Research Articles

Sample size estimation for modified Poisson analysis of cluster randomized trials with a binary outcome.

The modified Poisson regression coupled with a robust sandwich variance has become a viable alternative to log-binomial regression for estimating the marginal relative risk in cluster randomized trials. However, a corresponding sample size formula for relative risk regression via the modified Poisson model is currently not available for cluster randomized trials. Through analytical derivations, we show that there is no loss of asymptotic efficiency for estimating the marginal relative risk via the modified Poisson regression relative to the log-binomial regression. This finding holds both under the independence working correlation and under the exchangeable working correlation provided a simple modification is used to obtain the consistent intraclass correlation coefficient estimate. Therefore, the sample size formulas developed for log-binomial regression naturally apply to the modified Poisson regression in cluster randomized trials. We further extend the sample size formulas to accommodate variable cluster sizes. An extensive Monte Carlo simulation study is carried out to validate the proposed formulas. We find that the proposed formulas have satisfactory performance across a range of cluster size variability, as long as suitable finite-sample corrections are applied to the sandwich variance estimator and the number of clusters is at least 10. Our findings also suggest that the sample size estimate under the exchangeable working correlation is more robust to cluster size variability, and recommend the use of an exchangeable working correlation over an independence working correlation for both design and analysis. The proposed sample size formulas are illustrated using the Stop Colorectal Cancer (STOP CRC) trial.

Power and sample size for GEE analysis of incomplete paired outcomes in 2 × 2 crossover trials.

The 2 × 2 crossover trial uses subjects as their own control to reduce the intersubject variability in the treatment comparison, and typically requires fewer subjects than a parallel design. The generalized estimating equations (GEE) methodology has been commonly used to analyze incomplete discrete outcomes from crossover trials. We propose a unified approach to the power and sample size determination for the Wald Z-test and t-test from GEE analysis of paired binary, ordinal and count outcomes in crossover trials. The proposed method allows misspecification of the variance and correlation of the outcomes, missing outcomes, and adjustment for the period effect. We demonstrate that misspecification of the working variance and correlation functions leads to no or minimal efficiency loss in GEE analysis of paired outcomes. In general, GEE requires the assumption of missing completely at random. For bivariate binary outcomes, we show by simulation that the GEE estimate is asymptotically unbiased or only minimally biased, and the proposed sample size method is suitable under missing at random (MAR) if the working correlation is correctly specified. The performance of the proposed method is illustrated with several numerical examples. Adaption of the method to other paired outcomes is discussed.

Sample size and power considerations for cluster randomized trials with count outcomes subject to right truncation.

Cluster randomized trials (CRTs) are widely used in epidemiological and public health studies assessing population-level effect of group-based interventions. One important application of CRTs is the control of vector-borne disease, such as malaria. However, a particular challenge for designing these trials is that the primary outcome involves counts of episodes that are subject to right truncation. While sample size formulas have been developed for CRTs with clustered counts, they are not directly applicable when the counts are right truncated. To address this limitation, we discuss two marginal modeling approaches for the analysis of CRTs with truncated counts and develop two corresponding closed-form sample size formulas to facilitate the design of such trials. The proposed sample size formulas allow investigators to explore the power under a large number of scenarios without computationally intensive simulations. The proposed formulas are validated in extensive simulations. We further explore the implication of right truncation on power and apply the proposed formulas to illustrate the power calculation for a malaria control CRT where the primary outcome is subject to righttruncation.

Sample size considerations for matched-pair cluster randomization design with incomplete observations of continuous outcomes

Matched-pair cluster randomization design is becoming increasingly used in clinical and health behavioral studies. Investigators often encounter incomplete observations in the data collected. Statistical inference for matched-pair cluster randomization design with incomplete observations has been extensively studied in literature. However, sample size method for such study design is sparsely available. We propose a closed-form sample size formula for matched-pair cluster randomization design with continuous outcomes, based on the generalized estimating equation approach by treating incomplete observations as missing data in a marginal linear model. The sample size formula is flexible to accommodate different correlation structures, missing patterns, and magnitude of missingness. In the presence of missing data, the proposed method would lead to a more accurate sample size estimation than the crude adjustment method. Simulation studies are conducted to evaluate the finite-sample performance of the proposed sample size method under various design configurations. We use bias-corrected variance estimators to address the issue of inflated type I error when the number of clusters per group is small. A real application example of physical fitness study in Ecuadorian adolescents is presented for illustration.

EIGHT-WEEK SET-PIECES AND DOUBLE-TEAMING TRAINING ON SCORING PRECISION OF UNIVERSITY OF IBADAN FOOTBALL PLAYERS, IBADAN, NIGERIA

This study sought to investigate the effect of eight-week set-pieces and double-teaming training on scoring precision of the University of Ibadan football players. The proposed sample size for this study was twenty one football players of the University of Ibadan. All the participants completed the intervention programme. Randomised pretest-posttest experimental research design of 3 X 2 X 3 factorial matrix was used for the study. Descriptive statistics of frequency counts and percentages was used to analyse the demographic data and research questions while inferential statistics of Analysis of Covariance (ANCOVA) was used to test hypotheses at 0.05 level of significance. Two research questions were answered while seven hypotheses were tested. Findings from this study revealed that there was a significant main effect of treatment on scoring precision of the football players. (F = 65.120, p<.05, η2=.963). The eta value of 0.963 showed that 96.3% of the variance in the participant’s score was accounted for by the intervention. It was also observed that there was a variance of 87.5 percent accounted for by the independent variables combined together. There was no significant main effect of playing position on scoring precision. Likewise, there was no significant main effect of playing experience on scoring precision. The interaction effect of the two moderating variables was not significant. The study also concluded that the interaction effect of treatment, playing position and playing experience has no significant effect on scoring precision of the University of Ibadan players. Based on the findings of this study, it was concluded that the treatment was effective on scoring precision among football players. However, it was noted that double-teaming was better on scoring precision than set-pieces.
 
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The many faces of recruitment in a randomized controlled trial

BackgroundThoughtful approaches to study recruitment are a critical step in designing and implementing randomized controlled trials. Delays and challenges in recruitment can be costly and can result in smaller than proposed sample sizes which have downstream effects, such as underpowered studies. PurposeThe current study evaluated recruitment methods (e.g., targeted mailings, brochures/flyers, social media) and their relationship to eligibility, randomization, participant characteristics and retention at end of a randomized controlled trial of physical activity adoption and maintenance among breast cancer survivors. MethodsScreening data from 874 women was analyzed for recruitment method, study eligibility, randomization and retention through end of treatment. Costs per randomized participant were calculated by recruitment method. Baseline participant characteristics were compared across recruitment methods and between randomized and retained participants. ResultsRates of participant accrual from eligibility screening through randomization differed statistically significantly depending on recruitment method (p < .05). The highest randomization rates were obtained via targeted mailings (88.2%) and lowest via brochure/flyer (0.4%). Among the randomized sample, there were no differences in demographic characteristics between recruitment methods, however, there were differences within the targeted mailings category (registries vs. organizational recruitment). There were statistically significant differences in costs between recruitment methods (p < .001) with lowest (non-negligible) cost being targeted mailings. ConclusionsThe current RCT of breast cancer survivors successfully recruited and retained participants, highlighting the need to combine recruitment methods to achieve accrual goals. Recruitment methods differed substantially in their cost and their ability to attract individuals who would ultimately be randomized.

Sample size for estimating organism concentration in ballast water: A Bayesian approach

Estimation of microorganism concentration in ballast water tanks is important to evaluate and possibly to prevent the introduction of invasive species in stable ecosystems. For such purpose, the number of organisms in ballast water aliquots must be counted and used to estimate their concentration with some precision requirement. Poisson and negative binomial models have been employed to describe the organism distribution in the tank, but determination of sample sizes required to generate estimates with pre-specified precision is still not well established. A Bayesian approach is a flexible alternative to accommodate adequate models that account for the heterogeneous distribution of the organisms and may provide a sequential way of enhancing the estimation procedure by updating the prior distribution along the ballast water discharging process. We adopt such an approach to compute sample sizes required to construct credible intervals obtained via two optimality criteria that have not been employed in this context. Such intervals may be used in the decision with respect to compliance with the D-2 standard of the Ballast Water Management Convention. We also conduct a simulation study to verify whether the credible intervals obtained with the proposed sample sizes satisfy the precision criteria.

Combining Model-Based Clinical Trial Simulation, Pharmacoeconomics, and Value of Information to Optimize Trial Design.

The Bayesian decision‐analytic approach to trial design uses prior distributions for treatment effects, updated with likelihoods for proposed trial data. Prior distributions for treatment effects based on previous trial results risks sample selection bias and difficulties when a proposed trial differs in terms of patient characteristics, medication adherence, or treatment doses and regimens. The aim of this study was to demonstrate the utility of using pharmacometric‐based clinical trial simulation (CTS) to generate prior distributions for use in Bayesian decision‐theoretic trial design. The methods consisted of four principal stages: a CTS to predict the distribution of treatment response for a range of trial designs; Bayesian updating for a proposed sample size; a pharmacoeconomic model to represent the perspective of a reimbursement authority in which price is contingent on trial outcome; and a model of the pharmaceutical company return on investment linking drug prices to sales revenue. We used a case study of febuxostat versus allopurinol for the treatment of hyperuricemia in patients with gout. Trial design scenarios studied included alternative treatment doses, inclusion criteria, input uncertainty, and sample size. Optimal trial sample sizes varied depending on the uncertainty of model inputs, trial inclusion criteria, and treatment doses. This interdisciplinary framework for trial design and sample size calculation may have value in supporting decisions during later phases of drug development and in identifying costly sources of uncertainty, and thus inform future research and development strategies.

An Empirical Research on Pilgrims Wayfinding Satisfaction Study: A Consideration for Improving Wayfinding Experience in Al Masjid Al Haram

Millions of Muslims visit Makkah Al-Mukarramah every year for Hajj and Umrah. It is a mandatory part of both Hajj and Umrah rituals to visit Al Masjid Al Haram for various activities. Huge crowds and lack of prominent wayfinding signs make Hajis spend more time inside Haram trying to find their way that too in a tense and panicky state of mind. This paper aims at assessing the gravity of wayfinding associated challenges faced by Hajis by applying the well-known Customer Satisfaction Model and proposing possible solutions to minimize potential adverse effects. Convenience sampling was used to collect the data from the proposed sample size of 2000 from various nationalities and regions. A total of 618 responses were received. The structural equation modeling (SEM) method was used for path analysis using AMOS 21 analytical tool and results revealed a reasonable fit between data collected and the model used: chi2 (485.95), chi2 / DF (3.77), RMSEA (0.07), CFI (0.92), and all values of Cronbach's alpha are greater than 0.78. The results substantiated that Hajis face problems in wayfinding inside Haram, which leads to Hajis finding it challenging to navigate in the Haram area. When the respondents were presented with alternative solutions to improve their wayfinding inside Haram, the results showed a statistically significant improvement in the satisfaction level.

Sample Size Determination for Credibility Estimation

The credibility estimator has been successfully and widely applied by practitioners in the insurance industry for decades. However, an important issue remains unresolved: what sample size should the actuary choose when he/she applies the credibility estimator? In particular, is the size of a given claims data set large enough for the credibility estimator to be accurate? This paper aims to address this issue by first suggesting a sample size criterion for the credibility estimator and then proposing a sample size based upon that. The proposed sample size is easy to apply, and it guarantees provable accuracy for credibility estimation.

Sample size calculation based on discrete Weibull and zero-inflated discrete Weibull regression models

In this paper, we present a sample size determination for count data based on discrete Weibull and zero-inflated discrete Weibull regression models. The discrete Weibull regression can be used under various dispersion of count data, but its attractive feature is not sufficiently revealed. Discrete Weibull regression has a desirable feature in that it can be used for both over and under dispersed data, and thus a researcher can use a unified model with having low risk of failing to cope with the dispersion type of the data. Although the sample size calculation for Poisson, negative binomial regression has been previously introduced in many papers, there is no study that deals with discrete Weibull or zero-inflated discrete Weibull regression. We modified the method by Channouf, Fredette, and MacGibbon (2014) to calculate the required sample size for the two models. By using these two models, one can incorporate the effect of skewness, dispersion type and zero-inflated structure of the data when calculating the required sample size. Through the simulation studies, it was shown that our proposed sample size calculation method gives accurate results and also sample size is affected by the skewness of the distribution, covariance structure of covariates and amount of zeros. For illustration of our methods, the hospital length of stay study was used.

Sample size determination for Bayesian analysis of small n sequential, multiple assignment, randomized trials (snSMARTs) with three agents

ABSTRACT The small n, Sequential, Multiple Assignment, Randomized Trial (snSMART) is a two-stage clinical trial design for rare diseases motivated by the comparison of three active treatments for isolated skin vasculitis in the ongoing clinical trial ARAMIS (a randomized multicenter study for isolated skin vasculitis, NCT09239573). In Stage 1, all patients are randomized to one of three treatments. In Stage 2, patients who respond to their initial treatment receive the same treatment again, while those who fail to respond are re-randomized to one of the two remaining treatments. A Bayesian method for estimating the response rate of each individual treatment in a three-arm snSMART demonstrated efficiency gains for a given sample size relative to other existing frequentist approaches. However, these efficiency gains are dependent upon knowing how many subjects are required to determine a specific difference in the treatment response rates. Because few sample size calculation methods for snSMARTs exist, we propose a Bayesian sample size calculation for an snSMART designed to distinguish the best treatment from the second-best treatment. Although our methods are based on asymptotic approximations, we demonstrate via simulations that our proposed sample size calculation approach produces the desired statistical power, even in small samples. Moreover, our methods and applet produce sample sizes quickly, thereby saving time relative to using simulations to determine the appropriate sample size. We compare our proposed sample size to an existing frequentist method based upon a weighted -statistic and demonstrate that the Bayesian method requires far fewer patients than the frequentist method for a study with the same design parameters.

English

The objective of this study is to assess the challenges of business income tax administration with special emphasis on collection process in the case of Hadiya zone, Hossana town. To answer the research questions, the researcher used both primary and secondary data as a source of information. Initially, by using proportionally stratified sampling technique, 341 tax payers were selected as a sample size from the total population of 3077 tax payers of which 131, 163, and 2783 were categories &ldquo;A&rdquo;, &ldquo;B&rdquo;, and &ldquo;C&rdquo;, respectively. All the proposed sample size (341) was distributed to respondents. However, from the total distributed sample size, 280 (82% response rate) questionnaires were accurately responded and returned back. The descriptive statistical method was employed as a method of data analysis. As the results of this study revealed, there are some major challenges in the business income tax collection process such as: challenges associated with business income tax collection procedures, challenges associated with tax payers&rsquo; attitude towards tax system, lack of good tax administration and implementation; tax collectors unethical practice during tax collection; availability of unregistered traders or illegal traders; tax evasion and avoidance. Finally, the researcher gave some recommendations like distributing the tax laws and procedures to tax payers, increasing awareness to tax payers both in a short run and long run plan, developing tax authority&rsquo;s administrative capacity using advanced technology to collect tax, revision of tax policy and others. &nbsp; Key words: Tax administration challenges, business income tax compliance, tax payers&rsquo; attitude, tax payers&rsquo; perception, income tax collection procedure.

Sample size requirements for detecting treatment effect heterogeneity in cluster randomized trials.

Cluster randomized trials (CRTs) refer to experiments with randomization carried out at the cluster or the group level. While numerous statistical methods have been developed for the design and analysis of CRTs, most of the existing methods focused on testing the overall treatment effect across the population characteristics, with few discussions on the differential treatment effect among subpopulations. In addition, the sample size and power requirements for detecting differential treatment effect in CRTs remain unclear, but are helpful for studies planned with such an objective. In this article, we develop a new sample size formula for detecting treatment effect heterogeneity in two-level CRTs for continuous outcomes, continuous or binary covariates measured at cluster or individual level. We also investigate the roles of two intraclass correlation coefficients (ICCs): the adjusted ICC for the outcome of interest and the marginal ICC for the covariate of interest. We further derive a closed-form design effect formula to facilitate the application of the proposed method, and provide extensions to accommodate multiple covariates. Extensive simulations are carried out to validate the proposed formula in finite samples. We find that the empirical power agrees well with the prediction across a range of parameter constellations, when data are analyzed by a linear mixed effects model with a treatment-by-covariate interaction. Finally, we use data from the HF-ACTION study to illustrate the proposed sample size procedure for detecting heterogeneous treatment effects.

Incorporating pragmatic features into power analysis for cluster randomized trials with a count outcome.

Cluster randomized designs are frequently employed in pragmatic clinical trials which test interventions in the full spectrum of everyday clinical settings in order to maximize applicability and generalizability. In this study, we propose to directly incorporate pragmatic features into power analysis for cluster randomized trials with count outcomes. The pragmatic features considered include arbitrary randomization ratio, overdispersion, random variability in cluster size, and unequal lengths of follow-up over which the count outcome is measured. The proposed method is developed based on generalized estimating equation (GEE) and it is advantageous in that the sample size formula retains a closed form, facilitating its implementation in pragmatic trials. We theoretically explore the impact of various pragmatic features on sample size requirements. An efficient Jackknife algorithm is presented to address the problem of underestimated variance by the GEE sandwich estimator when the number of clusters is small. We assess the performance of the proposed sample size method through extensive simulation and an application example to a real clinical trial is presented.

Calculating the Expected Value of Sample Information in Practice: Considerations from 3 Case Studies.

Background. Investing efficiently in future research to improve policy decisions is an important goal. Expected value of sample information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of a range of different studies. Estimating EVSI with the standard nested Monte Carlo algorithm has a notoriously high computational burden, especially when using a complex decision model or when optimizing over study sample sizes and designs. Recently, several more efficient EVSI approximation methods have been developed. However, these approximation methods have not been compared, and therefore their comparative performance across different examples has not been explored. Methods. We compared 4 EVSI methods using 3 previously published health economic models. The examples were chosen to represent a range of real-world contexts, including situations with multiple study outcomes, missing data, and data from an observational rather than a randomized study. The computational speed and accuracy of each method were compared. Results. In each example, the approximation methods took minutes or hours to achieve reasonably accurate EVSI estimates, whereas the traditional Monte Carlo method took weeks. Specific methods are particularly suited to problems where we wish to compare multiple proposed sample sizes, when the proposed sample size is large, or when the health economic model is computationally expensive. Conclusions. As all the evaluated methods gave estimates similar to those given by traditional Monte Carlo, we suggest that EVSI can now be efficiently computed with confidence in realistic examples. No systematically superior EVSI computation method exists as the properties of the different methods depend on the underlying health economic model, data generation process, and user expertise.

Novel Coronavirus COVID-19: Current Evidence and Evolving Strategies.

Novel Coronavirus COVID-19: Current Evidence and Evolving Strategies.

Sequential parallel comparison design with two coprimary endpoints.

A placebo-controlled randomized clinical trial is required to demonstrate that an experimental treatment is superior to its corresponding placebo on multiple coprimary endpoints. This is particularly true in the field of neurology. In fact, clinical trials for neurological disorders need to show the superiority of an experimental treatment over a placebo in two coprimary endpoints. Unfortunately, these trials often fail to detect a true treatment effect for the experimental treatment versus the placebo owing to an unexpectedly high placebo response rate. Sequential parallel comparison design (SPCD) can be used to address this problem. However, the SPCD has not yet been discussed in relation to clinical trials with coprimary endpoints. In this article, our aim was to develop a hypothesis-testing method and a method for calculating the corresponding sample size for the SPCD with two coprimary endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the nominal type I error rate and power and that the proposed sample size calculation method has adequate power accuracy. In addition, the usefulness of our methods is confirmed by returning to an SPCD trial with a single primary endpoint of Alzheimer disease-related agitation.

SMARTp: A SMART design for nonsurgical treatments of chronic periodontitis with spatially referenced and nonrandomly missing skewed outcomes.

This paper proposes dynamic treatment regimes (DTRs) as effective individualized treatment strategies for managing chronic periodontitis. The proposed DTRs are studied via SMARTp-a two-stage sequential multiple assignment randomized trial (SMART) design. For this design, we propose a statistical analysis plan and a novel cluster-level sample size calculation method that factors in typical features of periodontal responses such as non-Gaussianity, spatial clustering, and nonrandom missingness. Here, each patient is viewed as a cluster, and a tooth within a patient's mouth is viewed as an individual unit inside the cluster, with the tooth-level covariance structure described by a conditionally autoregressive structure. To accommodate possible skewness and tail behavior, the tooth-level clinical attachment level (CAL) response is assumed to be skew-t, with the nonrandomly missing structure captured via a shared parameter model corresponding to the missingness indicator. The proposed method considers mean comparison for the regimes with or without sharing an initial treatment, where the expected values and corresponding variances or covariance for the sample means of a pair of DTRs are derived by the inverse probability weighting and method of moments. Simulation studies are conducted to investigate the finite-sample performance of the proposed sample size formulas under a variety of outcome-generating scenarios. An R package SMARTp implementing our sample size formula is available at the Comprehensive R Archive Network for freedownload.

Testing two variances for superiority/non-inferiority and equivalence: Using the exhaustion algorithm for sample size allocation with cost.

The equality of two group variances is frequently tested in experiments. However, criticisms of null hypothesis statistical testing on means have recently arisen and there is interest in other types of statistical tests of hypotheses, such as superiority/non-inferiority and equivalence. Although these tests have become more common in psychology and social sciences, the corresponding sample size estimation for these tests is rarely discussed, especially when the sampling unit costs are unequal or group sizes are unequal for two groups. Thus, for finding optimal sample size, the present study derived an initial allocation by approximating the percentiles of an F distribution with the percentiles of the standard normal distribution and used the exhaustion algorithm to select the best combination of group sizes, thereby ensuring the resulting power reaches the designated level and is maximal with a minimal total cost. In this manner, optimization of sample size planning is achieved. The proposed sample size determination has a wide range of applications and is efficient in terms of Type I errors and statistical power in simulations. Finally, an illustrative example from a report by the Health Survey for England, 1995-1997, is presented using hypertension data. For ease of application, four R Shiny apps are provided and benchmarks for setting equivalence margins are suggested.