Distributed Cox proportional hazards regression using summary-level information

Communication-efficient federated learning of temporal effects on opioid use disorder with data from distributed research networks

OBJECTIVE

To develop a distributed algorithm to fit multi-center Cox regression models with time-varying coefficients to facilitate privacy-preserving data integration across multiple health systems.

MATERIALS AND METHODS

The Cox model with time-varying coefficients relaxes the proportional hazards assumption of the usual Cox model and is particularly useful to model time-to-event outcomes. We proposed a One-shot Distributed Algorithm to fit multi-center Cox regression models with Time varying coefficients (ODACT). This algorithm constructed a surrogate likelihood function to approximate the Cox partial likelihood function, using patient-level data from a lead site and aggregated data from other sites. The performance of ODACT was demonstrated by simulation and a real-world study of opioid use disorder (OUD) using decentralized data from a large clinical research network across 5 sites with 69 163 subjects.

RESULTS

The ODACT method precisely estimated the time-varying effects over time. In the simulation study, ODACT always achieved estimation close to that of the pooled analysis, while the meta-estimator showed considerable amount of bias. In the OUD study, the bias of the estimated hazard ratios by ODACT are smaller than those of the meta-estimator for all 7 risk factors at almost all of the time points from 0 to 2.5 years. The greatest bias of the meta-estimator was for the effects of age ≥65 years, and smoking.

CONCLUSION

ODACT is a privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data which allows the covariates' effects to be time-varying. ODACT provides estimates close to the pooled estimator and substantially outperforms the meta-analysis estimator.

DISCUSSION

The proposed ODACT is a privacy-preserving distributed algorithm for fitting Cox models with time-varying coefficients. The limitations of ODACT include that privacy-preserving via aggregate data does rely on relatively large number of data at each individual site, and rigorous quantification of the risk of privacy leaks requires further investigation.

Association of Urinary Metals With Cardiovascular Disease Incidence and All-Cause Mortality in the Multi-Ethnic Study of Atherosclerosis (MESA)

BACKGROUND

Exposure to metals has been associated with cardiovascular disease (CVD) end points and mortality, yet prospective evidence is limited beyond arsenic, cadmium, and lead. In this study, we assessed the prospective association of urinary metals with incident CVD and all-cause mortality in a racially diverse population of US adults from MESA (the Multi-Ethnic Study of Atherosclerosis).

METHODS

We included 6599 participants (mean [SD] age, 62.1 [10.2] years; 53% female) with urinary metals available at baseline (2000 to 2001) and followed through December 2019. We used Cox proportional hazards models to estimate the adjusted hazard ratio and 95% CI of CVD and all-cause mortality by baseline urinary levels of cadmium, tungsten, and uranium (nonessential metals), and cobalt, copper, and zinc (essential metals). The joint association of the 6 metals as a mixture and the corresponding 10-year survival probability was calculated using Cox Elastic-Net.

RESULTS

During follow-up, 1162 participants developed CVD, and 1844 participants died. In models adjusted by behavioral and clinical indicators, the hazard ratios (95% CI) for incident CVD and all-cause mortality comparing the highest with the lowest quartile were, respectively: 1.25 (1.03, 1.53) and 1.68 (1.43, 1.96) for cadmium; 1.20 (1.01, 1.42) and 1.16 (1.01, 1.33) for tungsten; 1.32 (1.08, 1.62) and 1.32 (1.12, 1.56) for uranium; 1.24 (1.03, 1.48) and 1.37 (1.19, 1.58) for cobalt; 1.42 (1.18, 1.70) and 1.50 (1.29, 1.74) for copper; and 1.21 (1.01, 1.45) and 1.38 (1.20, 1.59) for zinc. A positive linear dose-response was identified for cadmium and copper with both end points. The adjusted hazard ratios (95% CI) for an interquartile range (IQR) increase in the mixture of these 6 urinary metals and the corresponding 10-year survival probability difference (95% CI) were 1.29 (1.11, 1.56) and -1.1% (-2.0, -0.05) for incident CVD and 1.66 (1.47, 1.91) and -2.0% (-2.6, -1.5) for all-cause mortality.

CONCLUSIONS

This epidemiological study in US adults indicates that urinary metal levels are associated with increased CVD risk and mortality. These findings can inform the development of novel preventive strategies to improve cardiovascular health.

Centralized and Federated Models for the Analysis of Clinical Data

The progress of precision medicine research hinges on the gathering and analysis of extensive and diverse clinical datasets. With the continued expansion of modalities, scales, and sources of clinical datasets, it becomes imperative to devise methods for aggregating information from these varied sources to achieve a comprehensive understanding of diseases. In this review, we describe two important approaches for the analysis of diverse clinical datasets, namely the centralized model and federated model. We compare and contrast the strengths and weaknesses inherent in each model and present recent progress in methodologies and their associated challenges. Finally, we present an outlook on the opportunities that both models hold for the future analysis of clinical data.

Covariate balance-related propensity score weighting in estimating overall hazard ratio with distributed survival data

BACKGROUND

When data is distributed across multiple sites, sharing information at the individual level among sites may be difficult. In these multi-site studies, propensity score model can be fitted with data within each site or data from all sites when using inverse probability-weighted Cox regression to estimate overall hazard ratio. However, when there is unknown heterogeneity of covariates in different sites, either approach may lead to potential bias or reduced efficiency. In this study, we proposed a method to estimate propensity score based on covariate balance-related criterion and estimate the overall hazard ratio while overcoming data sharing constraints across sites.

METHODS

The proposed propensity score was generated by choosing between global and local propensity score based on covariate balance-related criterion, combining the global propensity score fitted in the entire population and the local propensity score fitted within each site. We used this proposed propensity score to estimate overall hazard ratio of distributed survival data with multiple sites, while requiring only the summary-level information across sites. We conducted simulation studies to evaluate the performance of the proposed method. Besides, we applied the proposed method to real-world data to examine the effect of radiation therapy on time to death among breast cancer patients.

RESULTS

The simulation studies showed that the proposed method improved the performance in estimating overall hazard ratio comparing with global and local propensity score method, regardless of the number of sites and sample size in each site. Similar results were observed under both homogeneous and heterogeneous settings. Besides, the proposed method yielded identical results to the pooled individual-level data analysis. The real-world data analysis indicated that the proposed method was more likely to find a significant effect of radiation therapy on mortality compared to the global propensity score method and local propensity score method.

CONCLUSIONS

The proposed covariate balance-related propensity score in multi-site distributed survival data outperformed the global propensity score estimated using data from the entire population or the local propensity score estimated within each site in estimating the overall hazard ratio. The proposed approach can be performed without individual-level data transfer between sites and would yield the same results as the corresponding pooled individual-level data analysis.

Accommodating time-varying heterogeneity in risk estimation under the Cox model: a transfer learning approach

Transfer learning has attracted increasing attention in recent years for adaptively borrowing information across different data cohorts in various settings. Cancer registries have been widely used in clinical research because of their easy accessibility and large sample size. Our method is motivated by the question of how to utilize cancer registry data as a complement to improve the estimation precision of individual risks of death for inflammatory breast cancer (IBC) patients at The University of Texas MD Anderson Cancer Center. When transferring information for risk estimation based on the cancer registries (i.e., source cohort) to a single cancer center (i.e., target cohort), time-varying population heterogeneity needs to be appropriately acknowledged. However, there is no literature on how to adaptively transfer knowledge on risk estimation with time-to-event data from the source cohort to the target cohort while adjusting for time-varying differences in event risks between the two sources. Our goal is to address this statistical challenge by developing a transfer learning approach under the Cox proportional hazards model. To allow data-adaptive levels of information borrowing, we impose Lasso penalties on the discrepancies in regression coefficients and baseline hazard functions between the two cohorts, which are jointly solved in the proposed transfer learning algorithm. As shown in the extensive simulation studies, the proposed method yields more precise individualized risk estimation than using the target cohort alone. Meanwhile, our method demonstrates satisfactory robustness against cohort differences compared with the method that directly combines the target and source data in the Cox model. We develop a more accurate risk estimation model for the MD Anderson IBC cohort given various treatment and baseline covariates, while adaptively borrowing information from the National Cancer Database to improve risk assessment.

Larynx cancer survival model developed through open-source federated learning

INTRODUCTION

Federated learning has the potential to perfrom analysis on decentralised data; however, there are some obstacles to survival analyses as there is a risk of data leakage. This study demonstrates how to perform a stratified Cox regression survival analysis specifically designed to avoid data leakage using federated learning on larynx cancer patients from centres in three different countries.

METHODS

Data were obtained from 1821 larynx cancer patients treated with radiotherapy in three centres. Tumour volume was available for all 786 of the included patients. Parameter selection among eleven clinical and radiotherapy parameters were performed using best subset selection and cross-validation through the federated learning system, AusCAT. After parameter selection, β regression coefficients were estimated using bootstrap. Calibration plots were generated at 2 and 5-years survival, and inner and outer risk groups' Kaplan-Meier curves were compared to the Cox model prediction.

RESULTS

The best performing Cox model included log(GTV), performance status, age, smoking, haemoglobin and N-classification; however, the simplest model with similar statistical prediction power included log(GTV) and performance status only. The Harrell C-indices for the simplest model were for Odense, Christie and Liverpool 0.75[0.71-0.78], 0.65[0.59-0.71], and 0.69[0.59-0.77], respectively. The values are slightly higher for the full model with C-index 0.77[0.74-0.80], 0.67[0.62-0.73] and 0.71[0.61-0.80], respectively. Smoking during treatment has the same hazard as a ten-years older nonsmoking patient.

CONCLUSION

Without any patient-specific data leaving the hospitals, a stratified Cox regression model based on data from centres in three countries was developed without data leakage risks. The overall survival model is primarily driven by tumour volume and performance status.