Analyzing differences between restricted mean survival time curves using pseudo-values

Flexible quantitative bias analysis for unmeasured confounding in subject-level indirect treatment comparisons with proportional hazards violation

BACKGROUND

Indirect treatment comparisons can provide evidence of relative efficacy for novel therapies when implementation of a randomised controlled trial is infeasible. However, such comparisons are vulnerable to unmeasured confounding bias due to incomplete data collection and non-random treatment assignment. Quantitative bias analysis (QBA) is a framework used to assess the sensitivity of a study's conclusions to unmeasured confounding. As indirect comparisons between therapies with differing treatment modalities may result in violation of the proportional hazards (PH) assumption, QBA methods that are applicable in this context are required. However, few QBA methods are valid under PH violation.

METHODS

We proposed a simulation-based QBA framework which quantifies the sensitivity of the difference in restricted mean survival time (dRMST) to unmeasured confounding, and is therefore valid under violation of the PH assumption. The proposed framework utilises Bayesian data augmentation for the multiple imputation of an unmeasured confounder with user-specified characteristics. Adjustment of dRMST is then implemented in a weighted analysis using the imputed values. The accuracy and precision of our proposed imputation-based adjustment method was assessed through a simulation study. Confounded data was simulated using a common non-PH data generating process, and imputation-based effect estimates were compared against estimates obtained following adjustment for all confounders. Implementation of the proposed QBA framework was also illustrated using a data from an external control arm study demonstrating clear PH violation.

RESULTS

Imputation-based adjustment using Bayesian data augmentation was observed to estimate the true adjusted dRMST with minimal bias. Moreover, the bias was comparable to that observed under adjustment when all confounders were measured. Application of the proposed QBA framework to an indirect treatment comparison study enabled identification of the characteristics of an unmeasured confounder that would be required to nullify the study's conclusions.

CONCLUSIONS

Imputation-based adjustment can accurately recover the true adjusted dRMST in the presence of unmeasured confounding with known exposure and outcome associations. Therefore, the proposed QBA framework can correctly determine the characteristics required by an unmeasured confounder to invalidate a study's conclusions. Consequently, this framework enables the construction of sensitivity analyses to investigate the robustness of relative efficacy evidence derived from indirect treatment comparisons which exhibit PH violation.

Long-Term Survival in Patients With Low-Risk Cervical Cancer After Simple, Modified, or Radical Hysterectomy

Importance

Three-year pelvic recurrence rate in women with low-risk cervical carcinoma was not inferior following simple hysterectomy (SH) vs modified radical hysterectomy (MRH) or radical hysterectomy (RH) in the Simple Hysterectomy and Pelvic Node Assessment randomized clinical trial, but the survival analysis of the trial was underpowered.

Objective

To evaluate long-term survival in low-risk cervical carcinoma following SH vs MRH or RH.

Design, Setting, and Participants

This cohort study included women undergoing SH, MRH or RH in US Commission on Cancer-accredited facilities participating in the National Cancer Database who received a diagnosis between January 2010 and December 2017 of International Federation of Gynecology and Obstetrics 2009 stage IA2 or IB1 squamous cell carcinoma, adenocarcinoma, or adenosquamous carcinoma of the cervix (≤2 cm) and clinically negative lymph nodes.

Exposure

SH, MRH, or RH following diagnosis of stage IA2 or IB1 squamous cell carcinoma, adenocarcinoma, or adenosquamous carcinoma of the cervix.

Main Outcomes and Measures

Survival was the primary end point, evaluated with and without propensity score balancing. Survival rates, survival distributions, adjusted hazard ratio (aHR) of death, and restricted mean survival times (RMST) were analyzed as of September 2024. Two multivariable models were fitted. Model 1 included the hysterectomy type and 9 baseline factors (age, comorbidity score, race and ethnicity, insurance status, treatment facility, stage, histologic subtype, tumor grade, and surgical approach). Model 2 included the model 1 variables plus 4 additional clinical factors (surgical margin, LVSI, pathologic LN metastasis, and adjuvant treatment).

Results

This cohort study evaluated 2636 women (mean [SD] age, 45.4 [11.4] years; median [IQR] follow-up, 85 [64-110] months), including 982 with SH, 300 with MRH, 927 with traditional RH, and 427 with unspecified MRH or RH. Survival was similar following SH vs MRH or RH (7 year survival rate, 93.9%; 95% CI, 91.9%-95.4% vs 95.3%; 95% CI, 94.0%-96.3%%; P = .07) and SH vs MRH vs RH (7 year survival rate, 93.9%; 95% CI, 91.9%-95.4% vs 94.2%; 95% CI, 90.1%-96.7% vs 95.4%; 95% CI, 93.6%-96.6%; P = .15). Risk of death following either SH vs MRH or RH, SH vs RH, or MRH vs RH remained similar after adjusting for baseline covariates alone or baseline covariates plus clinical factors. Survival remained similar within subsets by age, comorbidity score, race and ethnicity, facility type, stage, histologic subtype, tumor grade, surgical approach, and year of diagnosis. Adjusted survival remained similar in patients with SH vs MRH or RH after propensity score balancing for baseline covariates (aHR, 1.19; 95% CI, 0.86-1.65; P = .31) with similar 3-year (98.3%; 95% CI, 97.2%-99.0% vs 97.6%; 95% CI, 96.6%-98.2%), 5-year (95.9%; 95% CI, 94.3%-97.1% vs 96.5%; 95% CI, 95.5%-97.3%), 7-year (94.5%; 95% CI, 92.5%-95.9% vs 95.1%; 95% CI, 93.7%-96.1%), and 10-year (89.8%; 95% CI, 86.3%-92.5% vs 91.7%; 95% CI, 89.4%-93.4%) survival rates. Sensitivity analysis for patients who received a diagnosis between 2010 and 2013 documented similar 10-year RMST following SH vs MRH or RH, SH vs RH, SH vs MRH, and MRH vs RH.

Conclusions and Relevance

In this cohort study, long-term survival was similar following SH vs MRH or RH, supporting the use of SH in select patients with low-risk early-stage cervical carcinoma.

Matching-Adjusted Indirect Comparison of Arterial FOLFOX and Atezolizumab-Bevacizumab in Unresectable Hepatocellular Carcinoma

Introduction

A previous phase 3 FOHAIC-1 study demonstrated that hepatic arterial infusion chemotherapy (HAIC) of FOLFOX regimen displayed favorable outcomes in advanced hepatocellular carcinoma (HCC) patients, including those with high-risk features (main portal tumor invasion and >50% liver infiltration). This study aimed to compare the treatment efficacy of HAIC-FOLFOX versus atezolizumab-bevacizumab in HCC patients.

Methods

Individual patient data from the Chinese FOHAIC-1 study and aggregate data from the global IMbrave150 study were used to conduct an anchored matching-adjusted indirect comparison. Hazard ratios (HR) and restricted mean survival times (RMST) were calculated to assess survival differences. Landmark analysis was performed to evaluate time-sensitive treatment effects, and simulated treatment comparison (STC) was conducted as a sensitivity analysis. Rates of treatment-related adverse events (TRAEs) and TRAE-related discontinuations were also compared.

Results

After matching baseline characteristics, HAIC showed a numerical OS benefit (HR 0.57, 95% CI, 0.30-1.08) and similar PFS benefit (HR 0.79, 95% CI, 0.43-1.47) compared to atezolizumab-bevacizumab in the overall population. In high-risk patients, HAIC demonstrated significantly improved OS (HR 0.30, 95% CI, 0.12-0.72) and 2.89-month longer RMST compared to atezolizumab-bevacizumab (95% CI, 0.15-5.64 months). Additionally, HAIC showed superior PFS (HR 0.25, 95% CI, 0.10-0.64) and 2.88-month longer RMST over atezolizumab-bevacizumab (95% CI, 0.90-4.86). Landmark analysis in the high-risk group revealed that HAIC was associated with significant improvements in both OS (HR 0.32, 95% CI, 0.13-0.79) and PFS (HR 0.24, 95% CI, 0.09-0.63) during the 0-12 months following treatment initiation. Sensitivity analysis using the anchored STC analysis yielded consistent results. HAIC was associated with lower rates of grade 3-4 TRAEs and TRAE-related discontinuation in both the overall population and the high-risk group.

Conclusion

HAIC treatment provided superior survival benefits and a favorable safety profile compared to atezolizumab-bevacizumab in high-risk HCC patients.

Single (375 mg/m2) vs. double dose of rituximab along with mycophenolate mofetil for children with steroid-dependent/frequently relapsing nephrotic syndrome: a multicentre open-label randomized controlled trial

BACKGROUND

Optimal dosing of rituximab when given with mycophenolate mofetil (MMF) for frequently relapsing nephrotic syndrome/steroid-dependent nephrotic syndrome (FRNS/SDNS) remains uncertain.

METHODS

This was a prospective, non-inferiority, open-label randomized controlled multicentre study. Children (2-18 years old) with difficult FRNS/SDNS were randomized to group A (rituximab 375 mg/m2 once) or group B (rituximab 375 mg/m2 twice; 7-14 days apart) followed by continuous MMF and 3 months of tapered steroids. Primary outcome at an 18-month follow-up was time to first relapse. Secondary outcomes included post rituximab time to CD19 repopulation, sustained remission and significant adverse events (SAEs).

RESULTS

Ninety-six children (median age 8.6 years; IQR 6.4 to 11.3 years, 72% male) were randomized, 48 per arm. CD19 depletion (< 1%) was achieved in both groups. Three from single dose and two from double dose arm were lost to follow-up or withdrew. After 18 months, although non-inferiority could not be demonstrated, there was no difference in primary outcome either by intention-to-treat or per-protocol analysis. The restricted mean time to first relapse was 14.5 months (95% CI 13.1-15.9) in group A and 14.8 months (95% CI 13.5-16.1) in group B (p = 0.69). Relapse rate was similar between group A (19/45; 42%) and group B (16/46; 35%) (p = 0.53, hazard ratio 0.86 (95% CI 0.46-1.6)). Secondary outcomes were also similar between the groups.

CONCLUSIONS

Among children with FRNS/SDNS although non-inferiority could not be demonstrated, no statistically significant difference in outcome was found between 375 and 750 mg/m2 rituximab when accompanied with MMF.

Modeling the Restricted Mean Survival Time Using Pseudo-Value Random Forests

The restricted mean survival time (RMST) has become a popular measure to summarize event times in longitudinal studies. Defined as the area under the survival function up to a time horizonτ > 0 $$ \tau >0 $$ , the RMST can be interpreted as the life expectancy within the time interval[ 0 , τ ] $$ \left[0,\tau \right] $$ . In addition to its straightforward interpretation, the RMST allows for the definition of valid estimands for the causal analysis of treatment contrasts in medical studies. In this work, we introduce a non-parametric approach to model the RMST conditional on a set of baseline variables (including, e.g., treatment variables and confounders). Our method is based on a direct modeling strategy for the RMST, using leave-one-out jackknife pseudo-values within a random forest regression framework. In this way, it can be employed to obtain precise estimates of both patient-specific RMST values and confounder-adjusted treatment contrasts. Since our method (termed "pseudo-value random forest", PVRF) is model-free, RMST estimates are not affected by restrictive assumptions like the proportional hazards assumption. Particularly, PVRF offers a high flexibility in detecting relevant covariate effects from higher-dimensional data, thereby expanding the range of existing pseudo-value modeling techniques for RMST estimation. We investigate the properties of our method using simulations and illustrate its use by an application to data from the SUCCESS-A breast cancer trial. Our numerical experiments demonstrate that PVRF yields accurate estimates of both patient-specific RMST values and RMST-based treatment contrasts.

Cross-Sectoral Comparisons of Process Quality Indicators of Health Care Across Residential Regions Using Restricted Mean Survival Time

BACKGROUND

Practice guidelines recommend patient management based on scientific evidence. Quality indicators gauge adherence to such recommendations and assess health care quality. They are usually defined as adverse event rates, which may not fully capture guideline adherence over time.

METHODS

For assessing process indicators where compliance to the recommended treatment can be assessed by evaluating a patient's trace in linked routine databases, we propose using restricted mean survival time or restricted mean time lost, which are applicable even in competing risk situations. We demonstrate their application by assessing the compliance of patients with acute myocardial infarction (AMI) to high-power statins over 12 months in Austria's political districts, using pseudo-observations and employing causal inference methods to achieve regional comparability.

RESULTS

We analyzed the compliance of 31,678 AMI patients from Austria's 116 political districts with index AMI between 2011 and 2015. The results revealed considerable compliance variations across districts but also plausible spatial similarities.

CONCLUSIONS

Restricted mean survival time and restricted mean time lost provide interpretable estimates of patients' expected time in compliance (lost), well-suited for risk-adjusted entity comparisons in the presence of (measurable) confounding, censoring, and competing risks.

Comparison of baseline covariate adjustment methods for restricted mean survival time

The restricted mean survival time provides a straightforward clinical measure that dispenses with the need for proportional hazards assumptions. We focus on two strategies to directly model the survival time and adjust covariates. Firstly, pseudo-survival time is calculated for each subject using a leave-one-out approach, followed by a model analysis that adjusts for covariates using all pseudo-values. This method is used to reflect information of censored subjects in the model analysis. The second approach adjusts for covariates for those subjects with observed time-to-event while incorporating censored subjects using inverse probability of censoring weighting (IPCW). This paper evaluates these methods' power to detect group differences through computer simulations. We find the interpretation of pseudo-values challenging with the pseudo-survival time method and confirm that pseudo-survival times deviate from actual data in a primary biliary cholangitis clinical trial, mainly due to extensive censoring. Simulations reveal that the IPCW method is more robust, unaffected by the balance of censors, whereas pseudo-survival time is influenced by this balance. The IPCW method retains a nominal significance level for the type-1 error rate, even amidst group differences concerning censor incidence rates and covariates. Our study concludes that IPCW and pseudo-survival time methods differ significantly in handling censored data, impacting parameter estimations. Our findings suggest that the IPCW method provides more robust results than pseudo-survival time and is recommended, even when censor probabilities vary between treatment groups. However, pseudo-survival time remains a suitable choice when censoring probabilities are balanced.

Patient years lost due to cytomegalovirus serostatus mismatching in the scientific registry of transplant recipients

Background

The cytomegalovirus (CMV) mismatch rate in deceased donor kidney transplant (DDKT) recipients in the US remains above 40%. Since CMV mismatching is common in DDKT recipients, the cumulative effects may be significant in the context of overall patient and graft survival. Our primary objective was to describe the short- and long-term risks associated with high-risk CMV donor positive/recipient negative (D+/R-) mismatching among DDKT recipients with the explicit goal of deriving a mathematical mismatching penalty.

Methods

We conducted a retrospective, secondary analysis of the Scientific Registry of Transplant Recipients (SRTR) database using donor-matched DDKT recipient pairs (N=105,608) transplanted between 2011-2022. All-cause mortality and graft failure hazard ratios were calculated from one year to ten years post-DDKT. All-cause graft failure included death events. Survival curves were calculated using the Kaplan-Meier estimation at 10 years post-DDKT and extrapolated to 20 years to provide the average graft days lost (aGDL) and average patient days lost (aPDL) due to CMV D+/R- serostatus mismatching. We also performed an age-based stratification analysis to compare the relative risk of CMV D+ mismatching by age.

Results

Among 31,518 CMV D+/R- recipients, at 1 year post-DDKT, the relative risk of death increased by 29% (p<0.001), and graft failure increased by 17% (p<0.001) as compared to matched CMV D+/R+ group (N=31,518). Age stratification demonstrated a significant increase in the risk associated with CMV mismatching in patients 40 years of age and greater. The aGDL per patient due to mismatching was 125 days and the aPDL per patient was 100 days.

Conclusion

The risks of CMV D+/R- mismatching are seen both at 1 year post-DDKT period and accumulated throughout the lifespan of the patient, with the average CMV D+/R- recipient losing more than three months of post-DDKT survival time. CMV D+/R- mismatching poses a more significant risk and a greater health burden than previously reported, thus obviating the need for better preventive strategies including CMV serodirected organ allocation to prolong lifespans and graft survival in high-risk patients.

Analysis of survival data with nonproportional hazards: A comparison of propensity-score-weighted methods

One of the most common ways researchers compare cancer survival outcomes across treatments from observational data is using Cox regression. This model depends on its underlying assumption of proportional hazards, but in some real-world cases, such as when comparing different classes of cancer therapies, substantial violations may occur. In this situation, researchers have several alternative methods to choose from, including Cox models with time-varying hazard ratios; parametric accelerated failure time models; Kaplan-Meier curves; and pseudo-observations. It is unclear which of these models are likely to perform best in practice. To fill this gap in the literature, we perform a neutral comparison study of candidate approaches. We examine clinically meaningful outcome measures that can be computed and directly compared across each method, namely, survival probability at time T, median survival, and restricted mean survival. To adjust for differences between treatment groups, we use inverse probability of treatment weighting based on the propensity score. We conduct simulation studies under a range of scenarios, and determine the biases, coverages, and standard errors of the average treatment effects for each method. We then demonstrate the use of these approaches using two published observational studies of survival after cancer treatment. The first examines chemotherapy in sarcoma, which has a late treatment effect (i.e., similar survival initially, but after 2 years the chemotherapy group shows a benefit). The other study is a comparison of surgical techniques for kidney cancer, where survival differences are attenuated over time.

Variable selection using inverse probability of censoring weighting

In this article, we propose two variable selection methods for adjusting the censoring information for survival times, such as the restricted mean survival time. To adjust for the influence of censoring, we consider an inverse probability of censoring weighted for subjects with events. We derive a least absolute shrinkage and selection operator (lasso)-type variable selection method, which considers an inverse weighting for of the squared losses, and an information criterion-type variable selection method, which applies an inverse weighting of the survival probability to the power of each density function in the likelihood function. We prove the consistency of the inverse probability of censoring weighted lasso estimator and the maximum inverse probability of censoring weighted likelihood estimator. The performance of the inverse probability of censoring weighted lasso and inverse probability of censoring weighted information criterion are evaluated via a simulation study with six scenarios, and then their variable selection ability is demonstrated using data from two clinical studies. The results confirm that inverse probability of censoring weighted lasso and the inverse probability of censoring weighted likelihood function produce good estimation accuracy and consistent variable selection. We conclude that our two proposed methods are useful variable selection tools for adjusting the censoring information for survival time analyses.

Restricted mean survival time to estimate an intervention effect in a cluster randomized trial

For time-to-event outcomes, the difference in restricted mean survival time is a measure of the intervention effect, an alternative to the hazard ratio, corresponding to the expected survival duration gain due to the intervention up to a predefined time t*. We extended two existing approaches of restricted mean survival time estimation for independent data to clustered data in the framework of cluster randomized trials: one based on the direct integration of Kaplan-Meier curves and the other based on pseudo-values regression. Then, we conducted a simulation study to assess and compare the statistical performance of the proposed methods, varying the number and size of clusters, the degree of clustering, and the magnitude of the intervention effect under proportional and non-proportional hazards assumption. We found that the extended methods well estimated the variance and controlled the type I error if there was a sufficient number of clusters (≥ 50) under both proportional and non-proportional hazards assumption. For cluster randomized trials with a limited number of clusters (< 50), a permutation test for pseudo-values regression was implemented and corrected the type I error. We also provided a procedure to estimate permutation-based confidence intervals which produced adequate coverage. All the extended methods performed similarly, but the pseudo-values regression offered the possibility to adjust for covariates. Finally, we illustrated each considered method with a cluster randomized trial evaluating the effectiveness of an asthma-control education program.