A Multi-state Model for Designing Clinical Trials for Testing Overall Survival Allowing for Crossover after Progression

Improved estimation of overall survival and progression-free survival for state transition modeling

Aim: National Institute for Health and Care Excellence guidance (Technical Support Document 19) highlights a key challenge of state transition models (STMs) being their difficulty in achieving a satisfactory fit to the observed within-trial endpoints. Fitting poorly to data over the trial period can then have implications for long-term extrapolations. A novel estimation approach is defined in which the predicted overall survival (OS) and progression-free survival (PFS) extrapolations from an STM are optimized to provide closer estimates of the within-trial endpoints. Materials & methods: An STM was fitted to the SQUIRE trial data in non-small-cell lung cancer (obtained from Project Data Sphere). Two methods were used: a standard approach whereby the maximum likelihood was utilized for the individual transitions and the best-fitting parametric model selected based on AIC/BIC, and a novel approach in which parameters were optimized by minimizing the area between the STM-predicted OS and PFS curves and the corresponding OS and PFS Kaplan-Meier curves. Sensitivity analyses were conducted to assess uncertainty. Results: The novel approach resulted in closer estimations to the OS and PFS Kaplan-Meier for all combinations of parametric distributions analyzed compared with the standard approach. Though the uncertainty associated with the novel approach was slightly larger, it provided better estimates to the restricted mean survival time in 10 of the 12 parametric distributions analyzed. Conclusion: A novel approach is defined which provides an alternative STM estimation method enabling improved fits to modeled endpoints, which can easily be extended to more complex model structures.

PubPredict: Prediction of progression and survival in oncology leveraging publications and early efficacy data

In oncology/hematology early phase clinical trials, efficacies were often observed in terms of response rate, depth, timing, and duration. However, the true clinical benefits that eventually support registrational purpose are progression-free survival (PFS) and/or overall survival (OS), the follow-up of which are typically not long enough in early phase trials. This gap imposes challenges in strategies for late phase drug development. In this article, we tackle the question by leveraging published study to establish a quantitative link between early efficacy outcomes and late phase efficacy endpoints. We used solid tumor cancer as disease model. We modeled the disease course of a RECISTv1.1 assessed solid tumor with a continuous Markov chain (CMC) model. We parameterize the transition intensity matrix of a CMC model based on published aggregate-level summary statistics, and then simulate subject-level time-to-event data. The simulated data is shown to have good approximation to published studies. PFS and/or OS could be predicted with the transition intensity matrix modified given clinical knowledge to reflect various assumptions on response rate, depth, timing, and duration. The authors have built a R shiny application named PubPredict, the tool implements the algorithm described above and allows customized features including multiple response levels, treatment crossover and varying follow-up duration. This toolset has been applied to advise phase 3 trial design when only early efficacy data are available from phase 1 or 2 studies.

A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards

Log-rank tests have been widely used to compare two survival curves in biomedical research. We describe a unified approach to power and sample size calculation for the unweighted and weighted log-rank tests in superiority, noninferiority and equivalence trials. It is suitable for both time-driven and event-driven trials. A numerical algorithm is suggested. It allows flexible specification of the patient accrual distribution, baseline hazards, and proportional or nonproportional hazards patterns, and enables efficient sample size calculation when there are a range of choices for the patient accrual pattern and trial duration. A confidence interval method is proposed for the trial duration of an event-driven trial. We point out potential issues with several popular sample size formulae. Under proportional hazards, the power of a survival trial is commonly believed to be determined by the number of observed events. The belief is roughly valid for noninferiority and equivalence trials with similar survival and censoring distributions between two groups, and for superiority trials with balanced group sizes. In unbalanced superiority trials, the power depends also on other factors such as data maturity. Surprisingly, the log-rank test usually yields slightly higher power than the Wald test from the Cox model under proportional hazards in simulations. We consider various nonproportional hazards patterns induced by delayed effects, cure fractions, and/or treatment switching. Explicit power formulae are derived for the combination test that takes the maximum of two or more weighted log-rank tests to handle uncertain nonproportional hazards patterns. Numerical examples are presented for illustration.

Design and sample size considerations for Alzheimer's disease prevention trials using multistate models

BACKGROUND/AIMS

Clinical trials for Alzheimer's disease have been aimed primarily at persons who have cognitive symptoms at enrollment. However, researchers are now recognizing that the pathophysiological process of Alzheimer's disease begins years, if not decades, prior to the onset of clinical symptoms. Successful intervention may require intervening early in the disease process. Critical issues arise in designing clinical trials for primary and secondary prevention of Alzheimer's disease including determination of sample sizes and follow-up duration. We address a number of these issues through application of a unifying multistate model for the preclinical course of Alzheimer's disease. A multistate model allows us to specify at which points during the long disease process the intervention exerts its effects.

METHODS

We used a nonhomogeneous Markov multistate model for the progression of Alzheimer's disease through preclinical disease states defined by biomarkers, mild cognitive impairment and Alzheimer's disease dementia. We used transition probabilities based on several published cohort studies. Sample size methods were developed that account for factors including the initial preclinical disease state of trial participants, the primary endpoint, age-dependent transition and mortality rates and specifications of which transition rates are the targets of the intervention.

RESULTS

We find that Alzheimer's disease prevention trials with a clinical primary endpoint of mild cognitive impairment or Alzheimer's disease dementia will require sample sizes of the order many thousands of individuals with at least 5 years of follow-up, which is larger than most Alzheimer's disease therapeutic trials conducted to date. The reasons for the large trial sizes include the long and variable preclinical period that spans decades, high rates of attrition among elderly populations due to mortality and losses to follow-up and potential selection effects, whereby healthier subjects enroll in prevention trials. A web application is available to perform sample size calculations using the methods reported here.

CONCLUSION

Sample sizes based on multistate models can account for the points in the disease process when interventions exert their effects and may lead to more accurate sample size determinations. We will need innovative strategies to help design Alzheimer's disease prevention trials with feasible sample size requirements and durations of follow-up.

Application of multi-state models in cancer clinical trials

Background/aims The goal of this article is to illustrate the utility of multi-state models in cancer clinical trials. Our specific aims are to describe multi-state models and how they differ from standard survival methods, to illustrate how multi-state models can facilitate deeper understanding of the treatment effect on multiple paths along the disease process that patients could experience in cancer clinical trials, to explain the differences between multi-state models and time-dependent Cox models, and to briefly describe available software to conduct such analyses. Methods Data from 717 newly diagnosed acute myeloid leukemia patients who enrolled in the CALGB 10603 trial were used as an illustrative example. The current probability-in-state was estimated using the Aalen-Johansen estimator. The restricted mean time in state was calculated as the area under the probability-in-state curves. Cox-type regression was used to evaluate the effect of midostaurin on the various clinical paths. Simulation was conducted using a newly constructed shiny application. All analyses were performed using the R software. Results Multi-state model analyses of CALGB 10603 suggested that the overall improvement in survival with midostaurin seen in the primary analysis possibly resulted from a higher complete remission rate in combination with a lower risk of relapse and of death after complete remission in patients treated with midostaurin. Simulation results, in a three-state illness-death without recovery model, demonstrate that multi-state models and time-dependent Cox models evaluate treatment effects from different frameworks. Conclusion Multi-state models allow detailed evaluation of treatment effects in complex clinical trial settings where patients can experience multiple paths between study enrollment and the final outcome. Multi-state models can be used as a complementary tool to standard survival analyses to provide deeper insights to the effects of treatment in trial settings with complex disease process.