Sample Size Calculation Method Research Articles

Sample size calculations for single-arm survival studies using transformations of the Kaplan-Meier estimator.

In single-arm clinical trials with survival outcomes, the Kaplan-Meier estimator and its confidence interval are widely used to assess survival probability and median survival time. Since the asymptotic normality of the Kaplan-Meier estimator is a common result, the sample size calculation methods have not been studied in depth. An existing sample size calculation method is founded on the asymptotic normality of the Kaplan-Meier estimator using the log transformation. However, the small sample properties of the log transformed estimator are quite poor in small sample sizes (which are typical situations in single-arm trials), and the existing method uses an inappropriate standard normal approximation to calculate sample sizes. These issues can seriously influence the accuracy of results. In this paper, we propose alternative methods to determine sample sizes based on a valid standard normal approximation with several transformations that may give an accurate normal approximation even with small sample sizes. In numerical evaluations via simulations, some of the proposed methods provided more accurate results, and the empirical power of the proposed method with the arcsine square-root transformation tended to be closer to a prescribed power than the other transformations. These results were supported when methods were applied to data from three clinical trials.

Instructional strategies and students’ entrepreneurial empowerment through Marketing Trade subject in Lagos State, Nigeria

The increasing occurrences of youth unemployment and the associated vices led to the introduction of Marketing Trade subject, and other trade/entrepreneurship subjects, at senior secondary schools in Nigeria. Therefore, this study was carried out to assess the instructional strategies and students’ entrepreneurship empowerment through the acquisition of competences in Marketing Trade subject. The study raised and answered two related research questions and also formulated and tested one relevant research on the null hypothesis (H0). The descriptive survey research design was adopted for the study. The population for the study comprised 1367 students of Marketing Trade subject in the randomly selected public senior secondary schools under Education District IV of Lagos State, Nigeria. Using Taro Yamane’s sample size calculation method, the sample size was 309 respondents, but 308 was returned eventually. The research instrument used was structured questionnaire. The Cronbach Alpha correlation coefficient used to determine the internal consistency of the research instrument yielded an average index of 0.88. The research questions and hypotheses data were analysed using mean and Pearson Product Moment of Correction statistical tools respectively. The findings show that recommended instructional strategies were not used appropriately, and as a result, the expected marketing competences were not acquired to the extent that they can empower students for entrepreneurship. It was therefore recommended that Government, Ministry of Education, teachers, and other relevant stakeholders should collaborate to ensure that Marketing Trade subject is ideally implemented to empower students with the requisite competences needed to achieve its goals and objectives in Nigeria.

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.

Randomized controlled trials in non-pharmacological rehabilitation research: a scoping review of the reporting of sample size calculation, randomization procedure, and statistical analyses.

The randomized controlled trials (RCTs) are often considered as the gold standard for clinical trials and researchers argue that the quality of RCT reports should be of the highest standards due to their clinical significance. To review the quality of reporting of the sample size calculation methods, and randomization procedures, and assess whether the statistical analyses correlate as reported in the trials' Evidence acquisition and Evidence synthesis sections in non-pharmacological, physiological rehabilitation RCT interventions. A systematic electronic search was conducted in Cochrane Central from 1 January 2019 to 16 December 2019. Titles and abstracts were analyzed for inclusion independently by two authors, and disagreements were resolved by a third reader. Studies were included if they met the following criteria: 1) assessed and reported a type of non-pharmacological rehabilitation RCT (e.g. physiotherapy); 2) randomized intervention to patients with a disease comparing to healthy or patients without intervention as the comparison group; 3) published in an indexed journal; and 4) original research, available full text, human study, published in 2019, and written in English. The following information was extracted from the included articles: journal impact factor (JIF), sample size calculation methods (SS), randomization procedure (RND), and statistical analyses (STAT) reported. Analyzing the full text, whether SS and RND were reported or not and whether the STAT correlated with the Methods and Results sections. The prevalence of each statistical method was derived from the Methods section of the report and compared if it was reported in the Results section. The continuous variable of JIF was tested for normality and used for independent t-test for equality of means between categories. In addition, using Downs and Black checklist the methodological quality of the articles was assessed and categorized to be poor, fair, good, and excellent based on the checklist's score. Finally, the association between the assessed quality (categorical variable) of the articles and the reporting variables (categorical variables) was analyzed utilizing the Pearson χ2. One hundred and nighty-four articles were retrieved from the systematic search out of which 99 (51%) were included for data extraction and further analyses. About one in five (20.2%) and two in five (37.4%) did not properly and adequately report the SS and RND while one in five (19.2%) there was at least one mismatch in STAT. The JIF was not significantly associated to the quality of reporting of SS (t=1.974, P=0.051), RND (t=0.309, P=0.758), and STAT (t=-0.275, P=0.784). This finding could indicate that the quality of the journal did not assure the quality of the reporting these methods. However, there was a significant association between the assessed quality of the article measured with the Down's and Black checklist and the reporting of SS (χ2=29.149, DF=2, P<0.0001), RND (χ2=55.079, df=2, P<0.0001) and STAT (χ2=25.778, df=2, P<0.0001). Recent reporting quality of non-pharmacological rehabilitation RCTs was investigated. We found that the quality of the article but not the quality of the journal in which it is published in may be associated to the quality of reporting in sample size methods, randomization processes, and statistical analyses reporting. The quality of study reporting may be enhanced utilizing a guideline that addresses the required information in sample size calculation, randomization of individuals, and proper statistical analyses used and reported.

Sample size calculation for logrank test and prediction of number of events over time.

We review and compare existing methods for sample size calculation based on the logrank statistic and recommend the method of Lakatos for its accuracy and flexibility in allowing time-dependent rates of event, loss to follow-up, and noncompliance. We extend the Lakatos method to allow a general follow-up scheme, to handle non-inferiority tests, and to predict the number of events over calendar time. We apply the Lakatos method to the simple nonproportional hazard situation of delayed treatment effect to facilitate the comparison of different weighting methods and to evaluate the performance of the maximum combination tests. We use simulation studies to confirm the validity of the Lakatos method and its extensions.

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.

A method for sample size calculation via E-value in the planning of observational studies.

Confounding adjustment plays a key role in designing observational studies such as cross-sectional studies, case-control studies, and cohort studies. In this article, we propose a simple method for sample size calculation in observational research in the presence of confounding. The method is motivated by the notion of E-value, using some bounding factor to quantify the impact of confounders on the effect size. The method can be applied to calculate the needed sample size in observational research when the outcome variable is binary, continuous, or time-to-event. The method can be implemented straightforwardly using existing commercial software such as the PASS software. We demonstrate the performance of the proposed method through numerical examples, simulation studies, and a real application, which show that the proposed method is conservative in providing a slightly bigger sample size than what it needs to achieve a given power.

A guide to human microbiome research: study design, sample collection, and bioinformatics analysis.

The purpose of this review is to provide medical researchers, especially those without a bioinformatics background, with an easy-to-understand summary of the concepts and technologies used in microbiome research. First, we define primary concepts such as microbiota, microbiome, and metagenome. Then, we discuss study design schemes, the methods of sample size calculation, and the methods for improving the reliability of research. We emphasize the importance of negative and positive controls in this section. Next, we discuss statistical analysis methods used in microbiome research, focusing on problems with multiple comparisons and ways to compare β-diversity between groups. Finally, we provide step-by-step pipelines for bioinformatics analysis. In summary, the meticulous study design is a key step to obtaining meaningful results, and appropriate statistical methods are important for accurate interpretation of microbiome data. The step-by-step pipelines provide researchers with insights into newly developed bioinformatics analysis methods.

Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances

This work presents a statistically principled method for estimating the required number of instances in the experimental comparison of multiple algorithms on a given problem class of interest. This approach generalises earlier results by allowing researchers to design experiments based on the desired best, worst, mean or median-case statistical power to detect differences between algorithms larger than a certain threshold. Holm’s step-down procedure is used to maintain the overall significance level controlled at desired levels, without resulting in overly conservative experiments. This paper also presents an approach for sampling each algorithm on each instance, based on optimal sample size ratios that minimise the total required number of runs subject to a desired accuracy in the estimation of paired differences. A case study investigating the effect of 21 variants of a custom-tailored Simulated Annealing for a class of scheduling problems is used to illustrate the application of the proposed methods for sample size calculations in the experimental comparison of algorithms.

Sample Size Calculation for “Gold-Standard” Noninferiority Trials With Fixed Margins and Negative Binomial Endpoints

For clinical trials in patients with asthma, chronic obstructive pulmonary disease, and relapsing-remitting multiple sclerosis, regulatory guidelines state that a noninferiority clinical trial is an option. Aiming at establishing assay sensitivity, a three-arm noninferiority trial, including an experimental treatment, a reference treatment, and a placebo, the so-called gold-standard noninferiority trial, is recommended. In addition, in the clinical trials for the above diseases, the number of events per unit time is often used as a primary or key secondary endpoint. There are two issues to be addressed in determining the sample size for gold-standard noninferiority trials: the hypotheses to be tested for assay sensitivity, and overdispersion of the number of events. To address these two issues, we propose a sample size calculation method for gold-standard noninferiority trials with two fixed margins and negative binomial endpoints. In a simulation, we show that the proposed hypothesis-testing method achieves the target power, while controlling the Type I error rate at a nominal level, and that the sample size calculation method has adequate power accuracy. Moreover, we illustrate an application of our proposed method for a clinical trial of mild asthma.

An Improved Sample Size Calculation Method for Score Tests in Generalized Linear Models

Self and Mauritsen developed a sample size determination procedure for score tests in generalized linear models under contiguous alternatives. Its performance may deteriorate when the effect size is large. We propose a modification of the Self–Mauritsen method by taking into account of the variance of the score statistic under both the null and alternative hypotheses, and extend the method to noninferiority trials. The modified approach is employed to calculate the sample size for the logistic regression and negative binomial regression in superiority and noninferiority trials. We further explain why the formulae recently derived by Zhu and Lakkis tend to underestimate the required sample size for the negative binomial regression. Numerical examples are used to demonstrate the accuracy of the proposed method.

Sample size calculations for noninferiority trials for time-to-event data using the concept of proportional time

Noninferiority trials intend to show that a new treatment is ‘not worse' than a standard-of-care active control and can be used as an alternative when it is likely to cause fewer side effects compared to the active control. In the case of time-to-event endpoints, existing methods of sample size calculation are done either assuming proportional hazards between the two study arms, or assuming exponentially distributed lifetimes. In scenarios where these assumptions are not true, there are few reliable methods for calculating the sample sizes for a time-to-event noninferiority trial. Additionally, the choice of the non-inferiority margin is obtained either from a meta-analysis of prior studies, or strongly justifiable ‘expert opinion', or from a ‘well conducted' definitive large-sample study. Thus, when historical data do not support the traditional assumptions, it would not be appropriate to use these methods to design a noninferiority trial. For such scenarios, an alternate method of sample size calculation based on the assumption of Proportional Time is proposed. This method utilizes the generalized gamma ratio distribution to perform the sample size calculations. A practical example is discussed, followed by insights on choice of the non-inferiority margin, and the indirect testing of superiority of treatment compared to placebo.

Sample size calculation and re-estimation based on the prevalence in a single-arm confirmatory diagnostic accuracy study.

In a confirmatory diagnostic accuracy study, sensitivity and specificity are considered as co-primary endpoints. For the sample size calculation, the prevalence of the target population must be taken into account to obtain a representative sample. In this context, a general problem arises. With a low or high prevalence, the study may be overpowered in one subpopulation. One further issue is the correct pre-specification of the true prevalence. With an incorrect assumption about the prevalence, an over- or underestimated sample size will result. To obtain the desired power independent of the prevalence, a method for an optimal sample size calculation for the comparison of a diagnostic experimental test with a prespecified minimum sensitivity and specificity is proposed. To face the problem of an incorrectly pre-specified prevalence, a blinded one-time re-estimation design of the sample size based on the prevalence and a blinded repeated re-estimation design of the sample size based on the prevalence are evaluated by a simulation study. Both designs are compared to a fixed design and additionally among each other. The type I error rates of both blinded re-estimation designs are not inflated. Their empirical overall power equals the desired theoretical power and both designs offer unbiased estimates of the prevalence. The repeated re-estimation design reveals no advantages concerning the mean squared error of the re-estimated prevalence or sample size compared to the one-time re-estimation design. The appropriate size of the internal pilot study in the one-time re-estimation design is 50% of the initially calculated sample size. A one-time re-estimation design of the prevalence based on the optimal sample size calculation is recommended in single-arm diagnostic accuracy studies.

Dynamic treatment regimens in small n, sequential, multiple assignment, randomized trials: An application in focal segmental glomerulosclerosis

Focal segmental glomerulosclerosis (FSGS) is a rare kidney disease with an annual incidence of 0.2–1.8 cases per 100,000 individuals. Most rare diseases like FSGS lack effective treatments, and it is difficult to implement clinical trials to study rare diseases because of the small sample sizes and difficulty in recruitment. A novel clinical trial design, a small sample, sequential, multiple assignment, randomized trial (snSMART) has been proposed to efficiently identify effective treatments for rare diseases. In this work, we review and expand the snSMART design applied to studying treatments for FSGS. The snSMART is a multistage trial that randomizes participants to one of three active treatments in the first stage and then re-randomizes those who do not respond to the initial treatment to one of the other two treatments in the second stage. A Bayesian joint stage model efficiently shares information across the stages to find the best first stage treatment. In this setting, we modify the previously presented design and methods (Wei et al. 2018) such that the proposed design includes a standard of care as opposed to three active treatments. We present Bayesian and frequentist models to compare the two novel therapies to the standard of care. Additionally, we show for the first time how we should estimate and compare tailored sequences of treatments or dynamic treatment regimens (DTRs) and contrast the results from our methods to existing methods for analyzing DTRs from a SMART. We also propose a sample size calculation method for our snSMART design when implementing the frequentist model with Dunnett's correction.

Sample size recalculation in multicenter randomized controlled clinical trials based on noncomparative data.

Many late-phase clinical trials recruit subjects at multiple study sites. This introduces a hierarchical structure into the data that can result in a power-loss compared to a more homogeneous single-center trial. Building on a recently proposed approach to sample size determination, we suggest a sample size recalculation procedure for multicenter trials with continuous endpoints. The procedure estimates nuisance parameters at interim from noncomparative data and recalculates the sample size required based on these estimates. In contrast to other sample size calculation methods for multicenter trials, our approach assumes a mixed effects model and does not rely on balanced data within centers. It is therefore advantageous, especially for sample size recalculation at interim. We illustrate the proposed methodology by a study evaluating a diabetes management system. Monte Carlo simulations are carried out to evaluate operation characteristics of the sample size recalculation procedure using comparative as well as noncomparative data, assessing their dependence on parameters such as between-center heterogeneity, residual variance of observations, treatment effect size and number of centers. We compare two different estimators for between-center heterogeneity, an unadjusted and a bias-adjusted estimator, both based on quadratic forms. The type 1 error probability as well as statistical power are close to their nominal levels for all parameter combinations considered in our simulation study for the proposed unadjusted estimator, whereas the adjusted estimator exhibits some type 1 error rate inflation. Overall, the sample size recalculation procedure can be recommended to mitigate risks arising from misspecified nuisance parameters at the planningstage.

Abstract OT2-01-04: Phase IB-II combination neoadjuvant chemotherapy with docetaxel plus atezolizumab plus herceptin SC and pertuzumab (TAHP) for patients with HER2-positive early breast cancer and subsequent atezolizumab plus herceptin SC and pertuzumab (AHP) adjuvant therapy after surgery (Neo-PATH)

Abstract Background Dual HER2-targeting with trastuzumab and pertuzumab combined with cytotoxic chemotherapy as neoadjuvant treatment increased rate of pathologic complete response to 50-65%. Subset of HER2-positive breast cancer has shown adaptive immune infiltrates which was correlated with better prognosis, including whom treated with dual anti-HER2 treatment. Immune checkpoint inhibitor including anti-PD-L1 modulate tumor microenvironment to restore tumor-induced or antibody-treatment induced immunosuppression. Here we investigate an efficacy of combining immunotherapy with anti-HER2 treatment as a neoadjuvant treatment in clinical stage II-III, HER2-positive breast cancer. Trial design This is a Phase Ib-II single arm study of six cycles of neoadjuvant docetaxel, atezolizumab, trastuzumab SC, and pertuzumab combination in patients with HER2-positive breast cancer. After 6 cycles of TAHP, surgery followed by 12 cycles of adjuvant atezolizumab, trastuzumab SC, and pertuzumab(AHP) will be performed. Patients without pCR will receive additional four cycles of doxorubicin and cyclophosphamide between surgery and adjuvant AHP. Eligibility criteria - Locally advanced, inflammatory, or early stage histologically confirmed invasive carcinoma of breast - HER2-positive breast cancer (immunohistochemistry score 3+, or HER2 SISH (or FISH, CISH) positive) - Primary tumor size&amp;gt;2cm or histologically or cytologically confirmed ipsilateral axillary lymph node metastases by fine needle aspiration (clinical stage IIA-IIIC by TNM 7th staging system) - ECOG Performance status 0-1 Specific aims Primary endpoint is a rate of pathologic complete response (pCR) after neoadjuvant docetaxel, atezolizumab, trastuzumab SC, and pertuzumab. Secondary endpoints are comparison of 3-year event free survival rate, disease free survival, and overall survival according to pCR achievement, toxicities, quality of life parameters, biomarker analyses (PD-L1 expression, immune signature, PIK3CA pathway, tumor mutation burden) for pCR and survival, multiomic profiling of tumor tissue using F1CDx. Statistical methods For sample size calculation, we used a Simon’s two-stage optimal design, with a 80 % power and 10% significance. The expected sample size is 60 to test the null hypothesis of pCR rate of ≤ 50% versus the alternative hypothesis of pCR rate of ≥ 65%. Stage 1: If pCR were observed in ≤ 12 patients among the first 23 patients, the alternative hypothesis will be rejected and the study will be discontinued Stage 2: If pCR were observed in ≥ 13 patients among the first 23 patients, additional 37 patients will be accrued (a total of 60 patients). If pCR were observed in &amp;gt; 34 patients, the null hypothesis will be rejected. Considering drop-out rate of 10%, we will accrue 67 patients. Our planned study duration is 42 months (patients accrual 6 months, follow up duration 36 months). Citation Format: Hee Kyung Ahn, Ji- Yeon Kim, Koung Jin Suh, Gun Min Kim, Sung Hoon Sim, Ki Hyeong Lee, Kyung Hae Jung, Seok- Ah Im, Yeon Hee Park. Phase IB-II combination neoadjuvant chemotherapy with docetaxel plus atezolizumab plus herceptin SC and pertuzumab (TAHP) for patients with HER2-positive early breast cancer and subsequent atezolizumab plus herceptin SC and pertuzumab (AHP) adjuvant therapy after surgery (Neo-PATH) [abstract]. In: Proceedings of the 2019 San Antonio Breast Cancer Symposium; 2019 Dec 10-14; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2020;80(4 Suppl):Abstract nr OT2-01-04.

On powerful exact nonrandomized tests for the Poisson two-sample setting.

In the case of two independent samples from Poisson distributions, the natural target parameter for hypothesis testing is the ratio of the two population means. The conditional tests which have been derived for this class of problems already in the 1940s are well known to be optimal in terms of power only when randomized decisions between hypotheses are admitted at the boundary of the respective rejection regions. The major objective of this contribution is to show how the approach used by Boschloo in 1970 for constructing a powerful nonrandomized version of Fisher's exact test for hypotheses about the odds ratio between two binomial parameters can successfully be adapted for the Poisson case. The resulting procedure, which we propose to term Poisson-Boschloo test, depends on some cutoff for the observed total number of events, the variable upon which conditioning has to be done. We show that for any fixed specific alternative, this cutoff can be chosen in such a way that the resulting nonrandomized test falls short in power of the randomized UMPU test only by a negligible amount. Thus, sample size calculation for the Poisson-Boschloo test can be carried out nearly exactly by means of the same computational procedure as has to be used for the randomized UMPU test. Since the power of the latter is accessible to elementary computational tools, this result makes approximate methods of sample size calculation for the Poisson-Boschloo test dispensable. It is furthermore shown how the construction of a Poisson-Boschloo type test extends to the case that interest is in establishing equivalence in the strict, two-sided sense rather than noninferiority. Although proceeding to two-sided equivalence considerably complicates the construction, comparing the resulting test procedure in terms of power with the exact randomized UMPU test leads essentially to the same conclusions as in the noninferiority case.

Basics of statistics-3: Sample size calculation – (i)

Introduction: From a practicing oncologist's perspective, sample size calculation is a very intriguing aspect of medical statistics. Methods: Basic aspects of sample size calculation in relevant case scenarios are discussed. Results: The formulae are illustrated with examples for easier understanding. Discussion: This article is a brief account of sample size calculation methods in different clinical research scenarios. The derivation of formulae is beyond the scope of this article. The discussion is kept simple by illustrations matching real life studies. More complex methods will be discussed in the next session of this series.

Basics of statistics – 4: Sample size calculation (ii): A narrative review

Sample size calculation is one of the most crucial aspects of planning clinical trials. Through this series, we aim to delve into the basic concepts of sample size calculation and the various methodologies used for it. For the purpose of this review, a thorough study and selection of the available literature from various sources including PubMed and Medline was conducted. The search terms used were “sample size,” “calculation,” and “oncology,” and 1370 articles were screened. The relevant material has been presented in a simplified format along with appropriate examples mimicking real-world clinical situations. This review article provides a brief overview of the sample size calculation methods used when designing clinical studies. Extensive details about the methods have been avoided to keep the write-up short, crisp, and directed toward the focus. The intricacies of complex topics will be dealt with in the subsequent issues.

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.