Adaptive design with bayesian informed interim decisions: application to a randomized trial of mechanical circulatory support

Abstract Background Cardiovascular trials increasingly require large sample sizes and long follow-up periods. Several approaches have been developed to optimize sample size such as adaptive group sequential trials, samples size re-estimation based on the promising zone, and the win ratio. Traditionally, the log-rank or the Cox proportional hazards model is used to test for treatment effects, based on a constant hazard rate and proportional hazards alternatives, which however, may not always hold. Large sample sizes and/or long follow up periods are especially challenging for trials evaluating the efficacy of acute care interventions. Purpose We propose an adaptive design wherein using interim data, Bayesian computation of predictive power guides the increase in sample size and/or the minimum follow-up duration. These computations do not depend on the constant hazard rate and proportional hazards assumptions, thus yielding more robust interim decision making for the future course of the trial. Methods PROTECT IV is designed to evaluate mechanical circulatory support with the Impella CP device vs. standard of care during high-risk PCI. The primary endpoint is a composite of all-cause death, stroke, MI or hospitalization for cardiovascular causes with initial minimum follow-up of 12 months and initial enrolment of 1252 patients with expected recruitment in 24 months. The study will employ an adaptive increase in sample size and/or minimum follow-up at the Interim analysis when ∼80% of patients have been enrolled. The adaptations utilize extensive simulations to choose a new sample size up to 2500 and new minimal follow-up time up to 36 months that provides a Bayesian predictive power of 85%. Bayesian calculations are based on patient-level information rather than summary statistics therefore enabling more reliable interim decisions. Constant or proportional hazard assumptions are not required for this approach because two separate Piece-wise Constant Hazard Models with Gamma-priors are fitted to the interim data. Bayesian predictive power is then calculated using Monte-Carlo methodology. Via extensive simulations, we have examined the utility of the proposed design for situations with time varying hazards and non-proportional hazards ratio such as situations of delayed treatment effect (Figure) and crossing of survival curves. The heat map of Bayesian predictive power obtained when the interim Kaplan-Meier curves reflected delayed response shows that for this scenario an optimal combination of increased sample size and increased follow-up time would be needed to attain 85% predictive power. Conclusion A proposed adaptive design with sample size and minimum follow-up period adaptation based on Bayesian predictive power at interim looks allows for de-risking the trial of uncertainties regarding effect size in terms of control arm outcome rate, hazard ratio, and recruitment rate. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Abiomed, Inc Figure 1

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Risk Factors for Survival After Heart Transplantation in Children and Young Adults: A 22-Year Study of 179 Transplants

World Journal for Pediatric and Congenital Heart Surgery ◽

10.1177/2150135118782190 ◽

2018 ◽

Vol 9 (5) ◽

pp. 557-564 ◽

Cited By ~ 3

Author(s):

Shawn Shah ◽

Alfred Asante-Korang ◽

Sharon R. Ghazarian ◽

Gary Stapleton ◽

Carrie Herbert ◽

...

Keyword(s):

Risk Factors ◽

Cardiac Surgery ◽

Heart Transplantation ◽

Mechanical Circulatory Support ◽

Proportional Hazards ◽

Cox Proportional Hazards ◽

Circulatory Support ◽

Kaplan Meier ◽

Diagnostic Characteristics

Background: This article reviews all patients who underwent heart transplantation (HTx) within a single institution (172 patients underwent 179 HTx [167 first-time HTxs, 10 second HTxs, 2 third HTxs]) to describe diagnostic characteristics, management protocols, and risk factors for mortality. Methods: Descriptive analysis was performed for the entire cohort using mean, standard deviation, median, interquartile range, and overall range, as appropriate. Univariable and multivariable Cox proportional hazards models were performed to identify prognostic factors for outcomes over time. The primary outcome of interest was mortality, which was modeled by Kaplan-Meier analysis. Results: Median age at HTx was 263 days (range, 5 days to 24 years; mean = 4.63 ± 5.95 years; 18 neonates, 79 infants). Median weight at HTx was 7.5 kg (range, 2.2-113 kg; mean = 19.36 ± 23.54). Diagnostic categories were cardiomyopathy (n = 62), primary transplantation for hypoplastic left heart syndrome (HLHS) or HLHS-related malformation (n = 33), transplantation after cardiac surgery for HLHS or HLHS-related malformation (n = 17), non-HLHS congenital heart disease (n = 55), and retransplant (n = 12). Operative mortality was 10.1% (18 patients). Cumulative total follow-up is 1,355 years. Late mortality was 18.4% (33 patients). Overall Kaplan-Meier five-year survival was 76.2%. One hundred twenty-one patients are alive with a mean follow-up of 7.61 ± 6.46 years. No survival differences were seen among the five diagnostic subgroups ( P = .064) or between immunosensitized patients (n = 31) and nonimmunosensitized patients (n = 141; P = .422). Conclusions: Excellent results are expected for children undergoing HTx with comparable results among diagnostic groups. Pretransplant mechanical circulatory support and posttransplant mechanical circulatory support are risk factors for decreased survival. Survival after transplantation for HLHS or HLHS-related malformation is better with primary HTx in comparison to HTx after prior cardiac surgery.

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Developing a composite outcome measure for frailty prevention trials – rationale, derivation and sample size comparison with other candidate measures

10.21203/rs.2.13602/v2 ◽

2020 ◽

Author(s):

Miles D. Witham ◽

James Wason ◽

Richard M Dodds ◽

Avan A Sayer

Keyword(s):

Sample Size ◽

Transition Probabilities ◽

Adverse Outcomes ◽

Transition Rates ◽

Composite Outcome ◽

Composite Measure ◽

Sample Sizes ◽

Loss To Follow Up ◽

Prevention Trials

Abstract Introduction Frailty is the loss of ability to withstand a physiological stressor, and is associated with multiple adverse outcomes in older people. Trials to prevent or ameliorate frailty are in their infancy. A range of different outcome measures have been proposed, but current measures require either large sample sizes, long follow-up, or do not directly measure the construct of frailty. Methods We propose a composite outcome for frailty prevention trials, comprising progression to the frail state, death, or being too unwell to continue in a trial. To determine likely event rates, we used data from the English Longitudinal Study for Ageing, collected 4 years apart. We calculated transition rates between non-frail, prefrail, frail or loss to follow up due to death or illness. We used Markov state transition models to interpolate one- and two-year transition rates, and performed sample size calculations for a range of differences in transition rates using simple and composite outcomes. Results The frailty category was calculable for 4650 individuals at baseline (2226 non-frail, 1907 prefrail, 517 frail); at follow up, 1282 were non-frail, 1108 were prefrail, 318 were frail and 1936 had dropped out or were unable to complete all tests for frailty. Transition probabilities for those prefrail at baseline, measured at wave 4 were respectively 0.176, 0.286, 0.096 and 0.442 to non-frail, prefrail, frail and dead/dropped out. Interpolated transition probabilities were 0.159, 0.494, 0.113 and 0.234 at two years, and 0.108, 0.688, 0.087 and 0.117 at one year. Required sample sizes for a two-year outcome were between 1000 and 7200 for transition from prefrailty to frailty alone, 250 to 1600 for transition to the composite measure, and 75 to 350 using the composite measure with an ordinal logistic regression approach. Conclusion Use of a composite outcome for frailty trials offers reduced sample sizes and could ameliorate the effect of high loss to follow up inherent in such trials due to death and illness.

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Developing a composite outcome measure for frailty prevention trials – rationale, derivation and sample size comparison with other candidate measures

10.21203/rs.2.13602/v1 ◽

2019 ◽

Author(s):

Miles D. Witham ◽

James Wason ◽

Richard M Dodds ◽

Avan A Sayer

Keyword(s):

Sample Size ◽

Transition Probabilities ◽

Adverse Outcomes ◽

Transition Rates ◽

Composite Outcome ◽

Composite Measure ◽

Sample Sizes ◽

Loss To Follow Up ◽

Prevention Trials

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Concentration inequalities for the empirical distribution of discrete distributions: beyond the method of types

Information and Inference A Journal of the IMA ◽

10.1093/imaiai/iaz025 ◽

2019 ◽

Vol 9 (4) ◽

pp. 813-850 ◽

Cited By ~ 7

Author(s):

Jay Mardia ◽

Jiantao Jiao ◽

Ervin Tánczos ◽

Robert D Nowak ◽

Tsachy Weissman

Keyword(s):

Sample Size ◽

Empirical Distribution ◽

Discrete Distributions ◽

Concentration Inequalities ◽

Sample Sizes ◽

Alphabet Size ◽

Large Sample ◽

Kl Divergence ◽

The Difference ◽

True Distribution

Abstract We study concentration inequalities for the Kullback–Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes of sample size $n$ and alphabet size $k$, and the improvement becomes more significant when $k$ is large. We discuss the applications of our results in obtaining tighter concentration inequalities for $L_1$ deviations of the empirical distribution from the true distribution, and the difference between concentration around the expectation or zero. We also obtain asymptotically tight bounds on the variance of the KL divergence between the empirical and true distribution, and demonstrate their quantitatively different behaviours between small and large sample sizes compared to the alphabet size.

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Long-term follow-up of pediatric cardiac patients requiring mechanical circulatory support

The Annals of Thoracic Surgery ◽

10.1016/s0003-4975(99)01194-7 ◽

2000 ◽

Vol 69 (1) ◽

pp. 186-192 ◽

Cited By ~ 120

Author(s):

Andra E Ibrahim ◽

Brian W Duncan ◽

Elizabeth D Blume ◽

Richard A Jonas

Keyword(s):

Mechanical Circulatory Support ◽

Cardiac Patients ◽

Circulatory Support ◽

Long Term Follow Up

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Postoperative Mechanical Circulatory Support with Biomedicus Centrifugal Pump

Asian Cardiovascular and Thoracic Annals ◽

10.1177/021849230501300109 ◽

2005 ◽

Vol 13 (1) ◽

pp. 38-41 ◽

Cited By ~ 4

Author(s):

Murat Mert ◽

Atif Akcevin ◽

Cenk E Yildiz ◽

Kaya Suzer

Keyword(s):

Centrifugal Pump ◽

Mechanical Circulatory Support ◽

Myocardial Protection ◽

Survival Rates ◽

Surgical Techniques ◽

Cost Effective ◽

Circulatory Support ◽

Hospital Death ◽

Ventricular Assistance

Despite advances in surgical techniques, myocardial protection, and management protocols, approximately 1% of patients undergoing open heart operations still need mechanical circulatory support for severe cardiac dysfunction. The Biomedicus centrifugal pump, available in most cardiovascular centers, is a highly effective and relatively inexpensive system compared to other more sophisticated devices for the same purpose. Of 10 patients aged 5 to 61 years who were supported for 22 to 168 hours with a Biomedicus centrifugal pump, 7 (70%) were weaned from support, there was one hospital death, and 6 patients were discharged from hospital. Two sudden deaths occurred in the first 8 months after discharge. Four patients (40%) were still alive after follow-up of 11–55 months, with no restriction in their daily activities. The centrifugal pump is a very cost-effective support system with survival rates comparable to those of more sophisticated devices in short-term ventricular assistance.

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Follow-up of survivors of mechanical circulatory support

Journal of Thoracic and Cardiovascular Surgery ◽

10.1016/s0022-5223(19)35299-7 ◽

1988 ◽

Vol 96 (1) ◽

pp. 72-80 ◽

Cited By ~ 35

Author(s):

Kirk R. Kanter ◽

Shelly A. Ruzevich ◽

D. Glenn Pennington ◽

Lawrence R. McBride ◽

Marc T. Swartz ◽

...

Keyword(s):

Mechanical Circulatory Support ◽

Circulatory Support

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Long-Term Follow-Up of Children with Cardiac Disease Requiring Mechanical Circulatory Support

Mechanical Support for Cardiac and Respiratory Failure in Pediatric Patients ◽

10.1201/9781482270143-16 ◽

2001 ◽

pp. 223-238

Keyword(s):

Cardiac Disease ◽

Mechanical Circulatory Support ◽

Circulatory Support ◽

Long Term Follow Up

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Some thoughts on sample size: A Bayesian-frequentist hybrid approach

Clinical Trials ◽

10.1177/1740774512453784 ◽

2012 ◽

Vol 9 (5) ◽

pp. 561-569 ◽

Cited By ~ 12

Author(s):

KK Gordan Lan ◽

Janet T Wittes

Keyword(s):

Sample Size ◽

High Power ◽

Effect Size ◽

Fixed Effect ◽

Phase 2 ◽

Sample Sizes ◽

Phase 3 ◽

Large Sample ◽

Truncated Normal ◽

Effect Method

Background Traditional calculations of sample size do not formally incorporate uncertainty about the likely effect size. Use of a normal prior to express that uncertainty, as recently recommended, can lead to power that does not approach 1 as the sample size approaches infinity. Purpose To provide approaches for calculating sample size and power that formally incorporate uncertainty about effect size. The relevant formulas should ensure that power approaches one as sample size increases indefinitely and should be easy to calculate. Methods We examine normal, truncated normal, and gamma priors for effect size computationally and demonstrate analytically an approach to approximating the power for a truncated normal prior. We also propose a simple compromise method that requires a moderately larger sample size than the one derived from the fixed effect method. Results Use of a realistic prior distribution instead of a fixed treatment effect is likely to increase the sample size required for a Phase 3 trial. The standard fixed effect method for moving from estimates of effect size obtained in a Phase 2 trial to the sample size of a Phase 3 trial ignores the variability inherent in the estimate from Phase 2. Truncated normal priors appear to require unrealistically large sample sizes while gamma priors appear to place too much probability on large effect sizes and therefore produce unrealistically high power. Limitations The article deals with a few examples and a limited range of parameters. It does not deal explicitly with binary or time-to-failure data. Conclusions Use of the standard fixed approach to sample size calculation often yields a sample size leading to lower power than desired. Other natural parametric priors lead either to unacceptably large sample sizes or to unrealistically high power. We recommend an approach that is a compromise between assuming a fixed effect size and assigning a normal prior to the effect size.

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