Landmark Estimation of Survival and Treatment Effect in a Randomized Clinical Trial

Tackling dynamic prediction of death in patients with recurrent cardiovascular events

In the field of cardiovascular disease, recurrent events such as stroke or myocardial infarction (MI) are often encountered, leading to an increase in the risk of death. Accurately evaluating the prognosis of patients and dynamically predicting the risk of death by considering the historical recurrent events can improve medical decisions and lead to better health care outcomes. Recently proposed joint modeling approaches within the Bayesian framework have inspired the development of a dynamic prediction tool, which can be applied for subject-level prediction of death with implementation in software packages. The prediction model incorporates subject heterogeneity with subject-level random effects that account for unobserved time-invariant factors and an extra copula function capturing the part caused by unmeasured time-dependent factors. Thereafter, given the prespecified landmark timet ' $$ {t}^{\prime } $$ , the survival probability for a prediction horizon time of interestt $$ t $$ can be estimated for each individual. The prediction accuracy is assessed by time-dependent receiving operating characteristic curve and the area under the curve and the Brier score with calibration plots is compared to traditional joint frailty models. Finally, the tool is applied to patients with multiple attacks of stroke or MI in the Cardiovascular Health study and the Atherosclerosis Risk in Communities study for illustration.

Semi-supervised calibration of noisy event risk (SCANER) with electronic health records

OBJECTIVE

Electronic health records (EHR), containing detailed longitudinal clinical information on a large number of patients and covering broad patient populations, open opportunities for comprehensive predictive modeling of disease progression and treatment response. However, since EHRs were originally constructed for administrative purposes not for research, in the EHR-linked studies, it is often not feasible to capture reliable information for analytical variables, especially in the survival setting, when both accurate event status and event times are needed for model building. For example, progression-free survival (PFS), a commonly used survival outcome for cancer patients, often involves complex information embedded in free-text clinical notes and cannot be extracted reliably. Proxies of PFS time such as time to the first mention of progression in the notes are at best good approximations to the true event time. This leads to difficulty in efficiently estimating event rates for an EHR patient cohort. Estimating survival rates based on error-prone outcome definitions can lead to biased results and hamper the power in the downstream analysis. On the other hand, extracting accurate event time information via manual annotation is time and resource intensive. The objective of this study is to develop a calibrated survival rate estimator using noisy outcomes from EHR data.

MATERIALS AND METHODS

In this paper, we propose a two-stage semi-supervised calibration of noisy event rate (SCANER) estimator that can effectively overcome censoring induced dependency and attains more robust performance (i.e., not sensitive to misspecification of the imputation model) by fully utilizing both a small-labeled set of gold-standard survival outcomes annotated via manual chart review and a set of proxy features automatically captured via EHR in the unlabeled set. We validate the SCANER estimator by estimating the PFS rates for a virtual cohort of lung cancer patients from one large tertiary care center and the ICU-free survival rates for COVID patients from two large tertiary care centers.

RESULTS

In terms of survival rate estimates, the SCANER had very similar point estimates compared to the complete-case Kaplan Meier estimator. On the other hand, other benchmark methods for comparison, which fail to account for the induced dependency between event time and the censoring time conditioning on surrogate outcomes, produced biased results across all three case studies. In terms of standard errors, the SCANER estimator was more efficient than the KM estimator, with up to 50% efficiency gain.

CONCLUSION

The SCANER estimator achieves more efficient, robust, and accurate survival rate estimates compared to existing approaches. This promising new approach can also improve the resolution (i.e., granularity of event time) by using labels conditioning on multiple surrogates, particularly among less common or poorly coded conditions.

Regression of nonalcoholic fatty liver disease is associated with reduced risk of incident diabetes: A longitudinal cohort study

OBJECTIVE

Non-alcoholic fatty liver disease (NAFLD) is potentially reversible. However, whether improvement of NAFLD leads to clinical benefits remains uncertain. We investigated the association between regression of NAFLD and the risk of incident diabetes in a longitudinal way.

METHODS

A cohort of 11,260 adults who had NAFLD at in an initial exam, had the second evaluation for NAFLD status at 1~2 years from an initial exam were followed up for incident diabetes from 2001 and 2016. NAFLD was diagnosed with abdominal ultrasound.

RESULTS

At baseline, NAFLD was regressed in 2,559 participants (22.7%). During 51,388 person-years of follow-up (median 4 years), 1,768 participants developed diabetes. The fully adjusted hazard ratio (HR) for incident diabetes in participants with regressed NAFLD compared to those with persistent NAFLD was 0.81 [95% confidence interval (CI) 0.72-0.92]. When assessed by NAFLD severity, among participants with a low NAFLD fibrosis score (NFS) (< -1.455), participants with regressed NAFLD had a lower risk of incident diabetes than those with persistent NAFLD (HR 0.77, 95% CI 0.68-0.88). However, in participants with an intermediate to high NFS (≥ -1.455), the risk of incident diabetes was not different between NAFLD regression and persistence groups (HR 1.12, 95% CI 0.82-1.51).

CONCLUSIONS

Regression of NAFLD was associated with decreased risk of incident diabetes compared to persistent NAFLD. However, the benefit was evident only for NAFLD patients with low NFS. This suggests that early intervention for NAFLD, before advanced fibrosis is present, may maximize the metabolic benefit from NAFLD regression.

More efficient and inclusive time-to-event trials with covariate adjustment: a simulation study

Adjustment for prognostic covariates increases the statistical power of randomized trials. The factors influencing the increase of power are well-known for trials with continuous outcomes. Here, we study which factors influence power and sample size requirements in time-to-event trials. We consider both parametric simulations and simulations derived from the Cancer Genome Atlas (TCGA) cohort of hepatocellular carcinoma (HCC) patients to assess how sample size requirements are reduced with covariate adjustment. Simulations demonstrate that the benefit of covariate adjustment increases with the prognostic performance of the adjustment covariate (C-index) and with the cumulative incidence of the event in the trial. For a covariate that has an intermediate prognostic performance (C-index=0.65), the reduction of sample size varies from 3.1% when cumulative incidence is of 10% to 29.1% when the cumulative incidence is of 90%. Broadening eligibility criteria usually reduces statistical power while our simulations show that it can be maintained with adequate covariate adjustment. In a simulation of adjuvant trials in HCC, we find that the number of patients screened for eligibility can be divided by 2.4 when broadening eligibility criteria. Last, we find that the Cox-Snell [Formula: see text] is a conservative estimation of the reduction in sample size requirements provided by covariate adjustment. Overall, more systematic adjustment for prognostic covariates leads to more efficient and inclusive clinical trials especially when cumulative incidence is large as in metastatic and advanced cancers. Code and results are available at https://github.com/owkin/CovadjustSim .

Optimising precision and power by machine learning in randomised trials with ordinal and time-to-event outcomes with an application to COVID-19

The rapid finding of effective therapeutics requires efficient use of available resources in clinical trials. Covariate adjustment can yield statistical estimates with improved precision, resulting in a reduction in the number of participants required to draw futility or efficacy conclusions. We focus on time-to-event and ordinal outcomes. When more than a few baseline covariates are available, a key question for covariate adjustment in randomised studies is how to fit a model relating the outcome and the baseline covariates to maximise precision. We present a novel theoretical result establishing conditions for asymptotic normality of a variety of covariate-adjusted estimators that rely on machine learning (e.g.,ℓ 1 -regularisation, Random Forests, XGBoost, and Multivariate Adaptive Regression Splines [MARS]), under the assumption that outcome data are missing completely at random. We further present a consistent estimator of the asymptotic variance. Importantly, the conditions do not require the machine learning methods to converge to the true outcome distribution conditional on baseline variables, as long as they converge to some (possibly incorrect) limit. We conducted a simulation study to evaluate the performance of the aforementioned prediction methods in COVID-19 trials. Our simulation is based on resampling longitudinal data from over 1500 patients hospitalised with COVID-19 at Weill Cornell Medicine New York Presbyterian Hospital. We found that usingℓ 1 -regularisation led to estimators and corresponding hypothesis tests that control type 1 error and are more precise than an unadjusted estimator across all sample sizes tested. We also show that when covariates are not prognostic of the outcome,ℓ 1 -regularisation remains as precise as the unadjusted estimator, even at small sample sizes (n = 100 ). We give an R package adjrct that performs model-robust covariate adjustment for ordinal and time-to-event outcomes.

Evaluation of Surrogate Endpoints Using Information-Theoretic Measure of Association Based on Havrda and Charvat Entropy

Surrogate endpoints have been used to assess the efficacy of a treatment and can potentially reduce the duration and/or number of required patients for clinical trials. Using information theory, Alonso et al. (2007) proposed a unified framework based on Shannon entropy, a new definition of surrogacy that departed from the hypothesis testing framework. In this paper, a new family of surrogacy measures under Havrda and Charvat (H-C) entropy is derived which contains Alonso’s definition as a particular case. Furthermore, we extend our approach to a new model based on the information-theoretic measure of association for a longitudinally collected continuous surrogate endpoint for a binary clinical endpoint of a clinical trial using H-C entropy. The new model is illustrated through the analysis of data from a completed clinical trial. It demonstrates advantages of H-C entropy-based surrogacy measures in the evaluation of scheduling longitudinal biomarker visits for a phase 2 randomized controlled clinical trial for treatment of multiple sclerosis.

Improving precision and power in randomized trials for COVID-19 treatments using covariate adjustment, for binary, ordinal, and time-to-event outcomes

Time is of the essence in evaluating potential drugs and biologics for the treatment and prevention of COVID-19. There are currently 876 randomized clinical trials (phase 2 and 3) of treatments for COVID-19 registered on clinicaltrials.gov. Covariate adjustment is a statistical analysis method with potential to improve precision and reduce the required sample size for a substantial number of these trials. Though covariate adjustment is recommended by the U.S. Food and Drug Administration and the European Medicines Agency, it is underutilized, especially for the types of outcomes (binary, ordinal, and time-to-event) that are common in COVID-19 trials. To demonstrate the potential value added by covariate adjustment in this context, we simulated two-arm, randomized trials comparing a hypothetical COVID-19 treatment versus standard of care, where the primary outcome is binary, ordinal, or time-to-event. Our simulated distributions are derived from two sources: longitudinal data on over 500 patients hospitalized at Weill Cornell Medicine New York Presbyterian Hospital and a Centers for Disease Control and Prevention preliminary description of 2449 cases. In simulated trials with sample sizes ranging from 100 to 1000 participants, we found substantial precision gains from using covariate adjustment-equivalent to 4-18% reductions in the required sample size to achieve a desired power. This was the case for a variety of estimands (targets of inference). From these simulations, we conclude that covariate adjustment is a low-risk, high-reward approach to streamlining COVID-19 treatment trials. We provide an R package and practical recommendations for implementation.

Dynamic Survival Analysis for EHR Data with Personalized Parametric Distributions

The widespread availability of high-dimensional electronic healthcare record (EHR) datasets has led to significant interest in using such data to derive clinical insights and make risk predictions. More specifically, techniques from machine learning are being increasingly applied to the problem of dynamic survival analysis, where updated time-to-event risk predictions are learned as a function of the full covariate trajectory from EHR datasets. EHR data presents unique challenges in the context of dynamic survival analysis, involving a variety of decisions about data representation, modeling, interpretability, and clinically meaningful evaluation. In this paper we propose a new approach to dynamic survival analysis which addresses some of these challenges. Our modeling approach is based on learning a global parametric distribution to represent population characteristics and then dynamically locating individuals on the time-axis of this distribution conditioned on their histories. For evaluation we also propose a new version of the dynamic C-Index for clinically meaningful evaluation of dynamic survival models. To validate our approach we conduct dynamic risk prediction on three real-world datasets, involving COVID-19 severe outcomes, cardiovascular disease (CVD) onset, and primary biliary cirrhosis (PBC) time-to-transplant. We find that our proposed modeling approach is competitive with other well-known statistical and machine learning approaches for dynamic risk prediction, while offering potential advantages in terms of interepretability of predictions at the individual level.

Dynamic Survival Analysis with Individualized Truncated Parametric Distributions

Dynamic survival analysis is a variant of traditional survival analysis where time-to-event predictions are updated as new information arrives about an individual over time. In this paper we propose a new approach to dynamic survival analysis based on learning a global parametric distribution, followed by individualization via truncating and renormalizing that distribution at different locations over time. We combine this approach with a likelihood-based loss that includes predictions at every time step within an individual's history, rather than just including one term per individual. The combination of this loss and model results in an interpretable approach to dynamic survival, requiring less fine tuning than existing methods, while still achieving good predictive performance. We evaluate the approach on the problem of predicting hospital mortality for a dataset with over 6900 COVID-19 patients.

Evaluating multiple surrogate markers with censored data

The utilization of surrogate markers offers the opportunity to reduce the length of required follow-up time and/or costs of a randomized trial examining the effectiveness of an intervention or treatment. There are many available methods for evaluating the utility of a single surrogate marker including both parametric and nonparametric approaches. However, as the dimension of the surrogate marker increases, a completely nonparametric procedure becomes infeasible due to the curse of dimensionality. In this paper, we define a quantity to assess the value of multiple surrogate markers in a time-to-event outcome setting and propose a robust estimation approach for censored data. We focus on surrogate markers that are measured at some landmark time, t₀ , which occurs earlier than the end of the study. Our approach is based on a dimension reduction procedure with an option to incorporate weights to guard against potential misspecification of the working model, resulting in three different proposed estimators, two of which can be shown to be double robust. We examine the finite sample performance of the estimators under various scenarios using a simulation study. We illustrate the estimation and inference procedures using data from the Diabetes Prevention Program (DPP) to examine multiple potential surrogate markers for diabetes.

Long-term β-blocker therapy and clinical outcomes after acute myocardial infarction in patients without heart failure: nationwide cohort study

Aims

To investigate the association between long-term β-blocker therapy and clinical outcomes in patients without heart failure (HF) after acute myocardial infarction (AMI).

Method and results

Between 2010 and 2015, a total of 28 970 patients who underwent coronary revascularization for AMI with β-blocker prescription at hospital discharge and were event-free from death, recurrent myocardial infarction (MI), or HF for 1 year were enrolled from Korean nationwide medical insurance data. The primary outcome was all-cause death. The secondary outcomes were recurrent MI, hospitalization for new HF, and a composite of all-cause death, recurrent MI, or hospitalization for new HF. Outcomes were compared between β-blocker therapy for ≥1 year (N = 22 707) and β-blocker therapy for &lt;1 year (N = 6263) using landmark analysis at 1 year after index MI. Compared with patients receiving β-blocker therapy for &lt;1 year, those receiving β-blocker therapy for ≥1 year had significantly lower risks of all-cause death [adjusted hazard ratio (HR) 0.81; 95% confidence interval (CI) 0.72–0.91] and composite of all-cause death, recurrent MI, or hospitalization for new HF (adjusted HR 0.82; 95% CI 0.75–0.89), but not the risks of recurrent MI or hospitalization for new HF. The lower risk of all-cause death associated with persistent β-blocker therapy was observed beyond 2 years (adjusted HR 0.86; 95% CI 0.75–0.99) but not beyond 3 years (adjusted HR 0.87; 95% CI 0.73–1.03) after MI.

Conclusion

In this nationwide cohort, β-blocker therapy for ≥1 year after MI was associated with reduced all-cause death among patients with AMI without HF.

Improving Precision and Power in Randomized Trials for COVID-19 Treatments Using Covariate Adjustment, for Binary, Ordinal, and Time-to-Event Outcomes

Time is of the essence in evaluating potential drugs and biologics for the treatment and prevention of COVID-19. There are currently over 400 clinical trials (phase 2 and 3) of treatments for COVID-19 registered on clinicaltrials.gov. Covariate adjustment is a statistical analysis method with potential to improve precision and reduce the required sample size for a substantial number of these trials. Though covariate adjustment is recommended by the U.S. Food and Drug Administration and the European Medicines Agency, it is underutilized, especially for the types of outcomes (binary, ordinal and time-to-event) that are common in COVID-19 trials. To demonstrate the potential value added by covariate adjustment in this context, we simulated two-arm, randomized trials comparing a hypothetical COVID-19 treatment versus standard of care, where the primary outcome is binary, ordinal, or time-to-event. Our simulated distributions are derived from two sources: longitudinal data on over 500 patients hospitalized at Weill Cornell Medicine New York Presbyterian Hospital, and a Centers for Disease Control and Prevention (CDC) preliminary description of 2449 cases. We found substantial precision gains from using covariate adjustment--equivalent to 9-21% reductions in the required sample size to achieve a desired power--for a variety of estimands (targets of inference) when the trial sample size was at least 200. We provide an R package and practical recommendations for implementing covariate adjustment. The estimators that we consider are robust to model misspecification.

Improved Landmark Dynamic Prediction Model to Assess Cardiovascular Disease Risk in On-Treatment Blood Pressure Patients: A Simulation Study and Post Hoc Analysis on SPRINT Data

Landmark model (LM) is a dynamic prediction model that uses a longitudinal biomarker in time-to-event data to make prognosis prediction. This study was designed to improve this model and to apply it to assess the cardiovascular risk in on-treatment blood pressure patients. A frailty parameter was used in LM, landmark frailty model (LFM), to account the frailty of the patients and measure the correlation between different landmarks. The proposed model was compared with LM in different scenarios respecting data missing status, sample size (100, 200, and 400), landmarks (6, 12, 24, and 48), and failure percentage (30, 50, and 100%). Bias of parameter estimation and mean square error as well as deviance statistic between models were compared. Additionally, discrimination and calibration capability as the goodness of fit of the model were evaluated using dynamic concordance index (DCI), dynamic prediction error (DPE), and dynamic relative prediction error (DRPE). The proposed model was performed on blood pressure data, obtained from systolic blood pressure intervention trial (SPRINT), in order to calculate the cardiovascular risk. Dynpred, coxme, and coxphw packages in the R.3.4.3 software were used. It was proved that our proposed model, LFM, had a better performance than LM. Parameter estimation in LFM was closer to true values in comparison to that in LM. Deviance statistic showed that there was a statistically significant difference between the two models. In the landmark numbers 6, 12, and 24, the LFM had a higher DCI over time and the three landmarks showed better performance in discrimination. Both DPE and DRPE in LFM were lower in comparison to those in LM over time. It was indicated that LFM had better calibration in comparison to its peer. Moreover, real data showed that the structure of prognostic process was predicted better in LFM than in LM. Accordingly, it is recommended to use the LFM model for assessing cardiovascular risk due to its better performance.

Dynamic landmark prediction for mixture data

In kin-cohort studies, clinicians want to provide their patients with the most current cumulative risk of death arising from a rare deleterious mutation. Estimating the cumulative risk is difficult when the genetic mutation status is unknown and only estimated probabilities of a patient having the mutation are available. We estimate the cumulative risk for this scenario using a novel nonparametric estimator that incorporates covariate information and dynamic landmark prediction. Our estimator has improved prediction accuracy over existing estimators that ignore covariate information. It is built within a dynamic landmark prediction framework whereby we can obtain personalized dynamic predictions over time. Compared to current standards, a simple transformation of our estimator provides more efficient estimates of marginal distribution functions in settings where patient-specific predictions are not the main goal. We show our estimator is unbiased and has more predictive accuracy compared to methods that ignore covariate information and landmarking. Applying our method to a Huntington disease study of mortality, we develop dynamic survival prediction curves incorporating gender and familial genetic information.

Evaluating radiological response in pancreatic neuroendocrine tumours treated with sunitinib: comparison of Choi versus RECIST criteria (CRIPNET_ GETNE1504 study)

BACKGROUND

The purpose of our study was to analyse the usefulness of Choi criteria versus RECIST in patients with pancreatic neuroendocrine tumours (PanNETs) treated with sunitinib.

METHOD

A multicentre, prospective study was conducted in 10 Spanish centres. Computed tomographies, at least every 6 months, were centrally evaluated until tumour progression.

RESULTS

One hundred and seven patients were included. Median progression-free survival (PFS) by RECIST and Choi were 11.42 (95% confidence interval [CI], 9.7-15.9) and 15.8 months (95% CI, 13.9-25.7). PFS by Choi (Kendall's τ = 0.72) exhibited greater correlation with overall survival (OS) than PFS by RECIST (Kendall's τ = 0.43). RECIST incorrectly estimated prognosis in 49.6%. Partial response rate increased from 12.8% to 47.4% with Choi criteria. Twenty-four percent of patients with progressive disease according to Choi had stable disease as per RECIST, overestimating treatment effect. Choi criteria predicted PFS/OS. Changes in attenuation occurred early and accounted for 21% of the variations in tumour volume. Attenuation and tumour growth rate (TGR) were associated with improved survival.

CONCLUSION

Choi criteria were able to capture sunitinib's activity in a clinically significant manner better than RECIST; their implementation in standard clinical practice shall be strongly considered in PanNET patients treated with this drug.

Statistical inference for data-adaptive doubly robust estimators with survival outcomes

The consistency of doubly robust estimators relies on the consistent estimation of at least one of two nuisance regression parameters. In moderate-to-large dimensions, the use of flexible data-adaptive regression estimators may aid in achieving this consistency. However, n^1/2 -consistency of doubly robust estimators is not guaranteed if one of the nuisance estimators is inconsistent. In this paper, we present a doubly robust estimator for survival analysis with the novel property that it converges to a Gaussian variable at an n^1/2 -rate for a large class of data-adaptive estimators of the nuisance parameters, under the only assumption that at least one of them is consistently estimated at an n^1/4 -rate. This result is achieved through the adaptation of recent ideas in semiparametric inference, which amount to (i) Gaussianizing (ie, making asymptotically linear) a drift term that arises in the asymptotic analysis of the doubly robust estimator and (ii) using cross-fitting to avoid entropy conditions on the nuisance estimators. We present the formula of the asymptotic variance of the estimator, which allows for the computation of doubly robust confidence intervals and p values. We illustrate the finite-sample properties of the estimator in simulation studies and demonstrate its use in a phase III clinical trial for estimating the effect of a novel therapy for the treatment of human epidermal growth factor receptor 2 (HER2)-positive breast cancer.

Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards

We present a new estimator of the restricted mean survival time in randomized trials where there is right censoring that may depend on treatment and baseline variables. The proposed estimator leverages prognostic baseline variables to obtain equal or better asymptotic precision compared to traditional estimators. Under regularity conditions and random censoring within strata of treatment and baseline variables, the proposed estimator has the following features: (i) it is interpretable under violations of the proportional hazards assumption; (ii) it is consistent and at least as precise as the Kaplan-Meier and inverse probability weighted estimators, under identifiability conditions; (iii) it remains consistent under violations of independent censoring (unlike the Kaplan-Meier estimator) when either the censoring or survival distributions, conditional on covariates, are estimated consistently; and (iv) it achieves the nonparametric efficiency bound when both of these distributions are consistently estimated. We illustrate the performance of our method using simulations based on resampling data from a completed, phase 3 randomized clinical trial of a new surgical treatment for stroke; the proposed estimator achieves a 12% gain in relative efficiency compared to the Kaplan-Meier estimator. The proposed estimator has potential advantages over existing approaches for randomized trials with time-to-event outcomes, since existing methods either rely on model assumptions that are untenable in many applications, or lack some of the efficiency and consistency properties (i)-(iv). We focus on estimation of the restricted mean survival time, but our methods may be adapted to estimate any treatment effect measure defined as a smooth contrast between the survival curves for each study arm. We provide R code to implement the estimator.

Using a surrogate marker for early testing of a treatment effect

The development of methods to identify, validate, and use surrogate markers to test for a treatment effect has been an area of intense research interest given the potential for valid surrogate markers to reduce the required costs and follow-up times of future studies. Several quantities and procedures have been proposed to assess the utility of a surrogate marker. However, few methods have been proposed to address how one might use the surrogate marker information to test for a treatment effect at an earlier time point, especially in settings where the primary outcome and the surrogate marker are subject to censoring. In this paper, we propose a novel test statistic to test for a treatment effect using surrogate marker information measured prior to the end of the study in a time-to-event outcome setting. We propose a robust nonparametric estimation procedure and propose inference procedures. In addition, we evaluate the power for the design of a future study based on surrogate marker information. We illustrate the proposed procedure and relative power of the proposed test compared to a test performed at the end of the study using simulation studies and an application to data from the Diabetes Prevention Program.

Protons versus Photons for Unresectable Hepatocellular Carcinoma: Liver Decompensation and Overall Survival

PURPOSE

Ablative radiation therapy is increasingly being used for hepatocellular carcinoma (HCC) resulting in excellent local control rates; however, patients without evidence of disease progression often die from liver failure. The clinical benefit of proton- over photon-based radiation therapy is unclear. We therefore sought to compare clinical outcomes of proton versus photon ablative radiation therapy in patients with unresectable HCC.

METHODS AND MATERIALS

This is a single-institution retrospective study of patients treated during 2008 to 2017 with nonmetastatic, unresectable HCC not previously treated with liver-directed radiation therapy and who did not receive further liver-directed radiation therapy within 12 months after completion of index treatment. The primary outcome, overall survival (OS), was assessed using Cox regression. Secondary endpoints included incidence of non-classic radiation-induced liver disease (defined as increase in baseline Child-Pugh score by ≥2 points at 3 months posttreatment), assessed using logistic regression, and locoregional recurrence, assessed using Fine-Gray regression for competing risks. All outcomes were measured from radiation start date.

RESULTS

The median follow-up was 14 months. Of 133 patients with median age 68 years and 75% male, 49 (37%) were treated with proton radiation therapy. Proton radiation therapy was associated with improved OS (adjusted hazard ratio, 0.47; P = .008; 95% confidence interval [CI], 0.27-0.82). The median OS for proton and photon patients was 31 and 14 months, respectively, and the 24-month OS for proton and photon patients was 59.1% and 28.6%, respectively. Proton radiation therapy was also associated with a decreased risk of non-classic radiation-induced liver disease (odds ratio, 0.26; P = .03; 95% CI, 0.08-0.86). Development of nonclassic RILD at 3 months was associated with worse OS (adjusted hazard ratio, 3.83; P < .001; 95% CI, 2.12-6.92). There was no difference in locoregional recurrence, including local failure, between protons and photons.

CONCLUSIONS

Proton radiation therapy was associated with improved survival, which may be driven by decreased incidence of posttreatment liver decompensation. Our findings support prospective investigations comparing proton versus photon ablative radiation therapy for HCC.

Augmented estimation for t-year survival with censored regression models

Reliable and accurate risk prediction is fundamental for successful management of clinical conditions. Estimating comprehensive risk prediction models precisely, however, is a difficult task, especially when the outcome of interest is time to a rare event and the number of candidate predictors, p, is not very small. Another challenge in developing accurate risk models arises from potential model misspecification. Time-specific generalized linear models estimated with inverse censoring probability weighting are robust to model misspecification, but may be inefficient in the rare event setting. To improve the efficiency of such robust estimation procedures, various augmentation methods have been proposed in the literature. These procedures can also leverage auxiliary variables such as intermediate outcomes that are predictive of event risk. However, most existing methods do not perform well in the rare event setting, especially when p is not small. In this article, we propose a two-step, imputation-based augmentation procedure that can improve estimation efficiency and that is robust to model misspecification. We also develop regularized augmentation procedures for settings where p is not small, along with procedures to improve the estimation of individualized treatment effect in risk reduction. Numerical studies suggest that our proposed methods substantially outperform existing methods in efficiency gains. The proposed methods are applied to an AIDS clinical trial for treating HIV-infected patients.

Landmark estimation of survival and treatment effects in observational studies

Clinical studies aimed at identifying effective treatments to reduce the risk of disease or death often require long term follow-up of participants in order to observe a sufficient number of events to precisely estimate the treatment effect. In such studies, observing the outcome of interest during follow-up may be difficult and high rates of censoring may be observed which often leads to reduced power when applying straightforward statistical methods developed for time-to-event data. Alternative methods have been proposed to take advantage of auxiliary information that may potentially improve efficiency when estimating marginal survival and improve power when testing for a treatment effect. Recently, Parast et al. (J Am Stat Assoc 109(505):384-394, 2014) proposed a landmark estimation procedure for the estimation of survival and treatment effects in a randomized clinical trial setting and demonstrated that significant gains in efficiency and power could be obtained by incorporating intermediate event information as well as baseline covariates. However, the procedure requires the assumption that the potential outcomes for each individual under treatment and control are independent of treatment group assignment which is unlikely to hold in an observational study setting. In this paper we develop the landmark estimation procedure for use in an observational setting. In particular, we incorporate inverse probability of treatment weights (IPTW) in the landmark estimation procedure to account for selection bias on observed baseline (pretreatment) covariates. We demonstrate that consistent estimates of survival and treatment effects can be obtained by using IPTW and that there is improved efficiency by using auxiliary intermediate event and baseline information. We compare our proposed estimates to those obtained using the Kaplan-Meier estimator, the original landmark estimation procedure, and the IPTW Kaplan-Meier estimator. We illustrate our resulting reduction in bias and gains in efficiency through a simulation study and apply our procedure to an AIDS dataset to examine the effect of previous antiretroviral therapy on survival.

Joint model imputation to estimate the treatment effect on long-term survival using auxiliary events

Clinical trial duration may be a concern in clinical research, especially in cancer trials where the endpoint is overall survival. A surrogate endpoint can be used as an auxiliary variable to analyze the treatment effect earlier. At an early time point, the high number of censored observations can be compensated by the imputation of the unobserved deaths times. We propose to use predictions of the risk of death from a joint model for a recurrent event and a terminal event, which account for disease relapse information. Two imputation methods were compared: sampling from the estimated parametric distribution of the survival time and sampling using its nonparametric estimation. The treatment effect and its standard error were estimated via multiple imputations. The performances of the two methods were compared in terms of bias in the estimates, standard errors, and coverage probability. Both methods were then retrospectively applied to two randomized clinical trials studying the effect of adjuvant chemotherapy in breast cancer patients.

Sizing clinical trials when comparing bivariate time-to-event outcomes

Clinical trials with multiple primary time-to-event outcomes are common. Use of multiple endpoints creates challenges in the evaluation of power and the calculation of sample size during trial design particularly for time-to-event outcomes. We present methods for calculating the power and sample size for randomized superiority clinical trials with two correlated time-to-event outcomes. We do this for independent and dependent censoring for three censoring scenarios: (i) the two events are non-fatal; (ii) one event is fatal (semi-competing risk); and (iii) both are fatal (competing risk). We derive the bivariate log-rank test in all three censoring scenarios and investigate the behavior of power and the required sample sizes. Separate evaluations are conducted for two inferential goals, evaluation of whether the test intervention is superior to the control on: (1) all of the endpoints (multiple co-primary) or (2) at least one endpoint (multiple primary). Copyright © 2017 John Wiley & Sons, Ltd.

Estimating the average treatment effect on survival based on observational data and using partly conditional modeling

Treatments are frequently evaluated in terms of their effect on patient survival. In settings where randomization of treatment is not feasible, observational data are employed, necessitating correction for covariate imbalances. Treatments are usually compared using a hazard ratio. Most existing methods which quantify the treatment effect through the survival function are applicable to treatments assigned at time 0. In the data structure of our interest, subjects typically begin follow-up untreated; time-until-treatment, and the pretreatment death hazard are both heavily influenced by longitudinal covariates; and subjects may experience periods of treatment ineligibility. We propose semiparametric methods for estimating the average difference in restricted mean survival time attributable to a time-dependent treatment, the average effect of treatment among the treated, under current treatment assignment patterns. The pre- and posttreatment models are partly conditional, in that they use the covariate history up to the time of treatment. The pre-treatment model is estimated through recently developed landmark analysis methods. For each treated patient, fitted pre- and posttreatment survival curves are projected out, then averaged in a manner which accounts for the censoring of treatment times. Asymptotic properties are derived and evaluated through simulation. The proposed methods are applied to liver transplant data in order to estimate the effect of liver transplantation on survival among transplant recipients under current practice patterns.