Power and Sample Size for Dose-Finding Studies with Survival Endpoints Under Model Uncertainty

Deng, Qi; Bai, Xiaofei; Liu, Dacheng; Roy, Dooti; Ying, Zhiliang; Lin, Danyu

doi:10.1111/biom.12968

Cited by 3 publications

(15 citation statements)

References 11 publications

(37 reference statements)

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“…To evaluate the role of testosterone levels in predicting clinical adverse arrhythmic events, we performed a follow‐up study among 68 ARVC male patients. During 17 months 9–29 of follow‐up, 5 were withdrawn, 16 patients experienced SSPE, and 22 developed malignant arrhythmic events ( Table 3 ). Amid two patients with both malignant arrhythmic events and SSPE, plasma testosterone levels (TT = 6.05 ng/mL, 4.90 ng/mL separately) were significantly lower than the average level in malignant arrhythmic events (TT = 11.73 ng/mL)—but were more similar with the expression levels in SSPE—and we included these patients in the malignant arrhythmic events group.…”

Section: Resultsmentioning

confidence: 99%

“…(A–C) ROC curve to distinguish patients with or without Malignant arrhythmic events during follow‐up. (D–F) Patients with above cut‐off concentrations of testosterone showed significantly elevated malignant arrhythmic events during follow‐up of 17 months 9–29 [log‐rank (Mantel–Cox) test, P < 0.0001].…”

Section: Resultsmentioning

confidence: 99%

“…The following formulas are used to calculate the sample size and power, respectively 23

n_{A} = κ n_{B} and n_{B} = ((), 1 + \frac{1}{κ}) {(σ \frac{Z_{1 - α / 2} + Z_{1 - β}}{{normalμ}_{A} - {normalμ}_{B}})}^{2}

1 - β = Φ ((), Z - Z_{1 - α / 2}) + Φ ((), - Z - Z_{1 - α / 2}), Z = \frac{μ_{A} - μ_{B}}{σ \sqrt{\frac{1}{n_{A}} + \frac{1}{n_{B}}}}

where κ = n A / n B is the matching ratio, σ is a standard deviation, Φ is the standard normal distribution function, α is Type I error, β is Type II error.…”

Section: Methodsmentioning

confidence: 99%

“…ARVC patients with ventricular dysfunction had a high probability of undergoing heart transplantation or death during follow‐up in the Fuwai cohort; 7 therefore, according to the previous literature, 8 we defined the significant structural progression event (SSPE) as a numerical reduction of 10% in LVEF based on echocardiography, heart transplantation, or death due to end‐stage heart failure. The patients were followed‐up for a median of 17 (interquartile ranges, IQR) months 9–29 in order to assess the role of plasma testosterone in survival outcome stratification. This study was approved by the Ethics Committee of Fuwai Hospital, Beijing, China.…”

Section: Methodsmentioning

confidence: 99%

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Plasma testosterone and arrhythmic events in male patients with arrhythmogenic right ventricular cardiomyopathy

Ren

Chen

et al. 2020

ESC Heart Failure

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Aims Arrhythmogenic right ventricular cardiomyopathy (ARVC) is associated with life-threatening ventricular arrhythmia and progressive ventricular dysfunction. Previous studies suggested that sex hormones play an important role in the onset and prognosis of ARVC. This study aimed to investigate the role of testosterone in predicting major adverse cardiac events in the Chinese ARVC cohort. Methods and results Ninety-nine ARVC patients (median age, 40 years; 70.7% male) and 96 healthy controls (median age, 41 years; 62.5% male) were enrolled. The circulating levels of testosterone were measured by enzyme-linked immunosorbent assays (ELISA). The median follow-up time of all ARVC male patients was 17 months (interquartile range/IQR 9-29). Cox proportional hazards regression was used to analyse the effect of plasma testosterone and other well-described risk factors on malignant arrhythmic events in male ARVC patients. The male ARVC patients had significantly elevated levels of total testosterone [TT, 6.390 (4.438-8.768) ng/mL vs. 3.617 (2.073-4.479) ng/mL, P < 0.0001, data shown as the median with IQR], bioavailable testosterone [BT, 4.11 (1.990-6.545) ng/mL vs. 1.32 (0.7965-2.0350) ng/mL, P < 0.0001, median with IQR], and free testosterone [FT, 0.2055 (0.1000-0.4073) ng/mL vs. 0.0768 (0.0405-0.1105) ng/mL, P < 0.0001, median with IQR] than healthy male volunteer, whereas no differences were observed among female counterparts. There was no significant correlation between the baseline clinical characteristics and testosterone levels in male ARVC patients (Spearman's correlation test, P > 0.05). During the follow-up, the levels of testosterone were higher in male patients who experienced malignant arrhythmic events (N = 22) than in those who did not (N = 25) [TT, 9.034 (7.222-15.370) ng/mL vs. 4.633 (3.363-6.375) ng/mL, P < 0.001; BT, 7.485 (2.070-9.163) ng/mL vs. 3.300 (1.685-4.690) ng/mL, P < 0.05; FT, 0.453 (0.221-0.758) ng/mL vs. 0.161 (0.075-0.337) ng/mL P < 0.05, data expressed as median (IQR) and adjusted by Dunn's multiple comparisons test], whereas such distinction was not observed among patients with significant structural progression events (N = 16). Through multivariable adjustments, the Cox regression analysis showed the level of plasma total testosterone (HR = 1.325, 95% confidence interval = 1.171-1.498, P < 0.001) was an independent predictor for malignant arrhythmic events. Conclusions The levels of plasma testosterone in ARVC male patients are higher than those in healthy males. Testosterone level, without relation to the baseline cardiac function and future significant structural progression events, is a strong predictor of future adverse arrhythmic events in male patients with ARVC. Therefore, our results suggest that testosterone may be a useful biomarker in arrhythmic risk prediction in the ARVC.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

“…The following formulas are used to calculate the sample size and power, respectively 23

n_{A} = κ n_{B} and n_{B} = ((), 1 + \frac{1}{κ}) {(σ \frac{Z_{1 - α / 2} + Z_{1 - β}}{{normalμ}_{A} - {normalμ}_{B}})}^{2}

1 - β = Φ ((), Z - Z_{1 - α / 2}) + Φ ((), - Z - Z_{1 - α / 2}), Z = \frac{μ_{A} - μ_{B}}{σ \sqrt{\frac{1}{n_{A}} + \frac{1}{n_{B}}}}

where κ = n A / n B is the matching ratio, σ is a standard deviation, Φ is the standard normal distribution function, α is Type I error, β is Type II error.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Plasma testosterone and arrhythmic events in male patients with arrhythmogenic right ventricular cardiomyopathy

Ren

Chen

et al. 2020

ESC Heart Failure

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“…Subsequently, Pinheiro et al 7 provided an overview of sample size determination under both strategies and illustrated its implementation using the sampSizeMCT and planMod functions in the DoseFinding 8 R package. For time‐to‐event endpoints, Deng et al 9 derived the sample size formulas using MCP‐Mod based on the power of testing PoC.…”

Section: Introductionmentioning

confidence: 99%

Calculation of Phase 2 dose‐finding study sample size for reliable Phase 3 dose selection

Liu

Zhao

Rodgers

et al. 2023

Pharmaceutical Statistics

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Sample sizes of Phase 2 dose‐finding studies, usually determined based on a power requirement to detect a significant dose–response relationship, will generally not provide adequate precision for Phase 3 target dose selection. We propose to calculate the sample size of a dose‐finding study based on the probability of successfully identifying the target dose within an acceptable range (e.g., 80%–120% of the target) using the multiple comparison and modeling procedure (MCP‐Mod). With the proposed approach, different design options for the Phase 2 dose‐finding study can also be compared. Due to inherent uncertainty around an assumed true dose–response relationship, sensitivity analyses to assess the robustness of the sample size calculations to deviations from modeling assumptions are recommended. Planning for a hypothetical Phase 2 dose‐finding study is used to illustrate the main points. Codes for the proposed approach is available at https://github.com/happysundae/posMCPMod.

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Sample size calculation for multi-arm parallel design with restricted mean survival time

Chen,

Lam,

2023

Stat Methods Med Res

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With the recent advances in oncology treatment, restricted mean survival time (RMST) is increasingly being used to replace the routine approach based on hazard ratios in randomized controlled trials for time-to-event outcomes. While RMST has been widely applied in single-arm and two-arm designs, challenges still exist in comparing RMST in multi-arm trials with three or more groups. In particular, it is unclear in the literature how to compare more than one intervention simultaneously or perform multiple testing based on RMST, and sample size determination is a major obstacle to its penetration to practice. In this paper, we propose a novel method of designing multi-arm clinical trials with right-censored survival endpoint based on RMST that can be applied in both phase II/III settings using a global [Formula: see text] test as well as a modeling-based multiple comparison procedure. The framework provides a closed-form sample size formula built upon a multi-arm global test and a sample size determination procedure based on multiple-comparison in the phase II dose-finding study. The proposed method enjoys strong robustness and flexibility as it requires less a priori set-up than conventional work, and obtains a smaller sample size while achieving the target power. In the assessment of sample size, we also incorporate practical considerations, including the presence of non-proportional hazards and staggered patient entry. We evaluate the validity of our method through simulation studies under various scenarios. Finally, we demonstrate the accuracy and stability of our method by implementing it in the design of two real clinical trial examples.

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Power and Sample Size for Dose-Finding Studies with Survival Endpoints Under Model Uncertainty

Cited by 3 publications

References 11 publications

Plasma testosterone and arrhythmic events in male patients with arrhythmogenic right ventricular cardiomyopathy

Plasma testosterone and arrhythmic events in male patients with arrhythmogenic right ventricular cardiomyopathy

Calculation of Phase 2 dose‐finding study sample size for reliable Phase 3 dose selection

Sample size calculation for multi-arm parallel design with restricted mean survival time

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