Estimates of clinically useful measures in competing risks survival analysis

Additive subdistribution hazards regression for competing risks data in case-cohort studies

In survival data analysis, a competing risk is an event whose occurrence precludes or alters the chance of the occurrence of the primary event of interest. In large cohort studies with long-term follow-up, there are often competing risks. Further, if the event of interest is rare in such large studies, the case-cohort study design is widely used to reduce the cost and achieve the same efficiency as a cohort study. The conventional additive hazards modeling for competing risks data in case-cohort studies involves the cause-specific hazard function, under which direct assessment of covariate effects on the cumulative incidence function, or the subdistribution, is not possible. In this paper, we consider an additive hazard model for the subdistribution of a competing risk in case-cohort studies. We propose estimating equations based on inverse probability weighting methods for the estimation of the model parameters. Consistency and asymptotic normality of the proposed estimators are established. The performance of the proposed methods in finite samples is examined through simulation studies and the proposed approach is applied to a case-cohort dataset from the Sister Study.

Pseudo-value regression of clustered multistate current status data with informative cluster sizes

Multistate current status data presents a more severe form of censoring due to the single observation of study participants transitioning through a sequence of well-defined disease states at random inspection times. Moreover, these data may be clustered within specified groups, and informativeness of the cluster sizes may arise due to the existing latent relationship between the transition outcomes and the cluster sizes. Failure to adjust for this informativeness may lead to a biased inference. Motivated by a clinical study of periodontal disease, we propose an extension of the pseudo-value approach to estimate covariate effects on the state occupation probabilities for these clustered multistate current status data with informative cluster or intra-cluster group sizes. In our approach, the proposed pseudo-value technique initially computes marginal estimators of the state occupation probabilities utilizing nonparametric regression. Next, the estimating equations based on the corresponding pseudo-values are reweighted by functions of the cluster sizes to adjust for informativeness. We perform a variety of simulation studies to study the properties of our pseudo-value regression based on the nonparametric marginal estimators under different scenarios of informativeness. For illustration, the method is applied to the motivating periodontal disease dataset, which encapsulates the complex data-generation mechanism.

Adjusting for informative cluster size in pseudo-value-based regression approaches with clustered time to event data

Informative cluster size (ICS) arises in situations with clustered data where a latent relationship exists between the number of participants in a cluster and the outcome measures. Although this phenomenon has been sporadically reported in the statistical literature for nearly two decades now, further exploration is needed in certain statistical methodologies to avoid potentially misleading inferences. For inference about population quantities without covariates, inverse cluster size reweightings are often employed to adjust for ICS. Further, to study the effect of covariates on disease progression described by a multistate model, the pseudo-value regression technique has gained popularity in time-to-event data analysis. We seek to answer the question: "How to apply pseudo-value regression to clustered time-to-event data when cluster size is informative?" ICS adjustment by the reweighting method can be performed in two steps; estimation of marginal functions of the multistate model and fitting the estimating equations based on pseudo-value responses, leading to four possible strategies. We present theoretical arguments and thorough simulation experiments to ascertain the correct strategy for adjusting for ICS. A further extension of our methodology is implemented to include informativeness induced by the intracluster group size. We demonstrate the methods in two real-world applications: (i) to determine predictors of tooth survival in a periodontal study and (ii) to identify indicators of ambulatory recovery in spinal cord injury patients who participated in locomotor-training rehabilitation.

Development and validation of a dynamic 48-hour in-hospital mortality risk stratification for COVID-19 in a UK teaching hospital: a retrospective cohort study

OBJECTIVES

To develop a disease stratification model for COVID-19 that updates according to changes in a patient's condition while in hospital to facilitate patient management and resource allocation.

DESIGN

In this retrospective cohort study, we adopted a landmarking approach to dynamic prediction of all-cause in-hospital mortality over the next 48 hours. We accounted for informative predictor missingness and selected predictors using penalised regression.

SETTING

All data used in this study were obtained from a single UK teaching hospital.

PARTICIPANTS

We developed the model using 473 consecutive patients with COVID-19 presenting to a UK hospital between 1 March 2020 and 12 September 2020; and temporally validated using data on 1119 patients presenting between 13 September 2020 and 17 March 2021.

PRIMARY AND SECONDARY OUTCOME MEASURES

The primary outcome is all-cause in-hospital mortality within 48 hours of the prediction time. We accounted for the competing risks of discharge from hospital alive and transfer to a tertiary intensive care unit for extracorporeal membrane oxygenation.

RESULTS

Our final model includes age, Clinical Frailty Scale score, heart rate, respiratory rate, oxygen saturation/fractional inspired oxygen ratio, white cell count, presence of acidosis (pH <7.35) and interleukin-6. Internal validation achieved an area under the receiver operating characteristic (AUROC) of 0.90 (95% CI 0.87 to 0.93) and temporal validation gave an AUROC of 0.86 (95% CI 0.83 to 0.88).

CONCLUSIONS

Our model incorporates both static risk factors (eg, age) and evolving clinical and laboratory data, to provide a dynamic risk prediction model that adapts to both sudden and gradual changes in an individual patient's clinical condition. On successful external validation, the model has the potential to be a powerful clinical risk assessment tool.

TRIAL REGISTRATION

The study is registered as 'researchregistry5464' on the Research Registry (www.researchregistry.com).

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

Hazard ratios are ubiquitously used in time to event analysis to quantify treatment effects. Although hazard ratios are invaluable for hypothesis testing, other measures of association, both relative and absolute, may be used to fully elucidate study results. Restricted mean survival time (RMST) differences between groups have been advocated as useful measures of association. Recent work focused on model-free estimates of the difference in restricted mean survival through follow-up times, instead of focusing on a single time horizon. The resulting curve can be used to quantify the association in time units with a simultaneous confidence band. In this work a model-based estimate of the curve is proposed using pseudo-values allowing for possible covariate adjustment. The method is easily implementable with available software and makes possible to compute a simultaneous confidence region for the curve. The pseudo-values regression using multiple restriction times is in good agreement with the estimates obtained by standard direct regression models fixing a single restriction time. Moreover, the proposed method is flexible enough to reproduce the results of the non-parametric approach when no covariates are considered. Examples where it is important to adjust for baseline covariates will be used to illustrate the different methods together with some simulations.

Excess cumulative incidence estimation for matched cohort survival studies

We suggest a regression approach to estimate the excess cumulative incidence function (CIF) when matched data are available. In a competing risk setting, we define the excess risk as the difference between the CIF in the exposed group and the background CIF observed in the unexposed group. We show that the excess risk can be estimated through an extended binomial regression model that actively uses the matched structure of the data, avoiding further estimation of both the exposed and the unexposed CIFs. The method naturally deals with two time scales, age and time since exposure and simplifies how to deal with the left truncation on the age time-scale. The model makes it easy to predict individual excess risk scenarios and allows for a direct interpretation of the covariate effects on the cumulative incidence scale. After introducing the model and some theory to justify the approach, we show via simulations that our model works well in practice. We conclude by applying the excess risk model to data from the ALiCCS study to investigate the excess risk of late events in childhood cancer survivors.

Regression analysis in an illness-death model with interval-censored data: A pseudo-value approach

Pseudo-values provide a method to perform regression analysis for complex quantities with right-censored data. A further complication, interval-censored data, appears when events such as dementia are studied in an epidemiological cohort. We propose an extension of the pseudo-value approach for interval-censored data based on a semi-parametric estimator computed using penalised likelihood and splines. This estimator takes interval-censoring and competing risks into account in an illness-death model. We apply the pseudo-value approach to three mean value parameters of interest in studies of dementia: the probability of staying alive and non-demented, the restricted mean survival time without dementia and the absolute risk of dementia. Simulation studies are conducted to examine properties of pseudo-values based on this semi-parametric estimator. The method is applied to the French cohort PAQUID, which included more than 3,000 non-demented subjects, followed for dementia for more than 25 years.

Different competing risks models for different questions may give similar results in arthroplasty registers in the presence of few events

Background and purpose - In arthroplasty registry studies, the analysis of time to revision is complicated by the competing risk of death. There are no clear guidelines for the choice between the 2 main adjusted analysis methods, cause-specific Cox and Fine-Gray regression, for orthopedic data. We investigated whether there are benefits, such as insight into different aspects of progression to revision, to using either 1 or both regression methods in arthroplasty registry studies in general, and specifically when the length of follow-up is short relative to the expected survival of the implants. Patients and methods - Cause-specific Cox regression and Fine-Gray regression were performed on total hip (138,234 hips, 124,560 patients) and knee (139,070 knees, 125,213 patients) replacement data from the Dutch Arthroplasty Register (median follow-up 3.1 years, maximum 8 years), with sex, age, ASA score, diagnosis, and type of fixation as explanatory variables. The similarity of the resulting hazard ratios and confidence intervals was assessed visually and by computing the relative differences of the resulting subdistribution and cause-specific hazard ratios. Results - The outcomes of the cause-specific Cox and Fine-Gray regressions were numerically very close. The largest relative difference between the hazard ratios was 3.5%. Interpretation - The most likely explanation for the similarity is that there are relatively few events (revisions and deaths), due to the short follow-up compared with the expected failure-free survival of the hip and knee prostheses. Despite the similarity, we recommend always performing both cause-specific Cox and Fine-Gray regression. In this way, both etiology and prediction can be investigated.

Risk of stroke and bleeding in patients with heart failure and chronic kidney disease: a nationwide cohort study

Aims

The aim of this study was to assess the prognostic value of chronic kidney disease (CKD) in relation to ischaemic stroke, intracranial haemorrhage, major bleeding, and all‐cause death in heart failure patients without atrial fibrillation.

Methods and results

In this observational cohort study, heart failure patients without atrial fibrillation were identified using Danish nationwide registries. Risk of stroke, major haemorrhage, and death were calculated after 1 and 5 years to compare patients with and without CKD, ±dialysis [dialysis: CKD with renal replacement therapy (CKD‐RRT); no dialysis: CKD‐no RRT]. A total of 43 199 heart failure patients were included, among which 0.8% had CKD‐RRT and 5.9% had CKD‐no RRT. When compared with heart failure patients without CKD, both CKD‐RRT and CKD‐no RRT were associated with a higher 5 year rate of major bleeding (CKD‐RRT: adjusted hazard ratio (aHR): 2.91, 95% confidence interval (CI): 2.29 to 3.70; CKD‐no RRT: aHR: 1.28, 95% CI: 1.13 to 1.45) and all‐cause death (CKD‐RRT: aHR: 2.40, 95% CI: 2.07 to 2.77; CKD‐no RRT: aHR: 1.63, 95% CI: 1.55 to 1.73). For the endpoints of ischaemic stroke and intracranial bleeding, only CKD‐no RRT was associated with significantly higher 5 year rates (ischaemic stroke: aHR: 1.31, 95% CI: 1.13 to 1.52; intracranial haemorrhage: aHR: 1.66, 95% CI: 1.04 to 2.65).

Conclusions

Compared with patients without CKD, among incident heart failure patients without atrial fibrillation, CKD both with and without dialysis was associated with a higher rate of major bleeding and all‐cause death. Only CKD‐no RRT was associated with a higher rate of ischaemic stroke and intracranial bleeding.

Penalized estimation for competing risks regression with applications to high-dimensional covariates

High-dimensional regression has become an increasingly important topic for many research fields. For example, biomedical research generates an increasing amount of data to characterize patients' bio-profiles (e.g. from a genomic high-throughput assay). The increasing complexity in the characterization of patients' bio-profiles is added to the complexity related to the prolonged follow-up of patients with the registration of the occurrence of possible adverse events. This information may offer useful insight into disease dynamics and in identifying subset of patients with worse prognosis and better response to the therapy. Although in the last years the number of contributions for coping with high and ultra-high-dimensional data in standard survival analysis have increased (Witten and Tibshirani, 2010. Survival analysis with high-dimensional covariates. Statistical Methods in Medical Research19(1), 29–51), the research regarding competing risks is less developed (Binder and others, 2009. Boosting for high-dimensional time-to-event data with competing risks. Bioinformatics25(7), 890–896). The aim of this work is to consider how to do penalized regression in the presence of competing events. The direct binomial regression model of Scheike and others (2008. Predicting cumulative incidence probability by direct binomial regression. Biometrika95(1), 205–220) is reformulated in a penalized framework to possibly fit a sparse regression model. The developed approach is easily implementable using existing high-performance software to do penalized regression. Results from simulation studies are presented together with an application to genomic data when the endpoint is progression-free survival. An R function is provided to perform regularized competing risks regression according to the binomial model in the package timereg (Scheike and Martinussen, 2006. Dynamic Regression models for survival data. New York: Springer), available through CRAN.

Vascular Disease and Risk Stratification for Ischemic Stroke and All-Cause Death in Heart Failure Patients without Diagnosed Atrial Fibrillation: A Nationwide Cohort Study

Background

Stroke and mortality risk among heart failure patients previously diagnosed with different manifestations of vascular disease is poorly described. We conducted an observational study to evaluate the stroke and mortality risk among heart failure patients without diagnosed atrial fibrillation and with peripheral artery disease (PAD) or prior myocardial infarction (MI).

Methods

Population-based cohort study of patients diagnosed with incident heart failure during 2000–2012 and without atrial fibrillation, identified by record linkage between nationwide registries in Denmark. Hazard rate ratios of ischemic stroke and all-cause death after 1 year of follow-up were used to compare patients with either: a PAD diagnosis; a prior MI diagnosis; or no vascular disease.

Results

39,357 heart failure patients were included. When compared to heart failure patients with no vascular disease, PAD was associated with a higher 1-year rate of ischemic stroke (adjusted hazard rate ratio [HR]: 1.34, 95% confidence interval [CI]: 1.08–1.65) and all-cause death (adjusted HR: 1.47, 95% CI: 1.35–1.59), whereas prior MI was not (adjusted HR: 1.00, 95% CI: 0.86–1.15 and 0.94, 95% CI: 0.89–1.00, for ischemic stroke and all-cause death, respectively). When comparing patients with PAD to patients with prior MI, PAD was associated with a higher rate of both outcomes.

Conclusions

Among incident heart failure patients without diagnosed atrial fibrillation, a previous diagnosis of PAD was associated with a significantly higher rate of the ischemic stroke and all-cause death compared to patients with no vascular disease or prior MI. Prevention strategies may be particularly relevant among HF patients with PAD.

Factors Associated With Recurrence and Survival in Lymph Node-negative Gastric Adenocarcinoma: A 7-Institution Study of the US Gastric Cancer Collaborative

OBJECTIVES

To determine pathologic features associated with recurrence and survival in patients with lymph node-negative gastric adenocarcinoma.

STUDY DESIGN

Multi-institutional retrospective analysis.

BACKGROUND

Lymph node status is among the most important predictors of recurrence after gastrectomy for gastric adenocarcinoma. Pathologic features predictive of recurrence in patients with node-negative disease are less well established.

METHODS

Patients who underwent curative resection for gastric adenocarcinoma between 2000 and 2012 from 7 institutions of the US Gastric Cancer Collaborative were analyzed, excluding 30-day mortalities and stage IV disease. Competing risks regression and multivariate Cox regression were used to determine pathologic features associated with time to recurrence and overall survival. Differences in cumulative incidence of recurrence were assessed using the Gray method (for univariate nonparametric analyses) and the Fine and Gray method (for multivariate analyses) and shown as subhazard ratios (SHRs) and adjusted subhazard ratios (aSHRs), respectively.

RESULTS

Of 805 patients who met inclusion criteria, 317 (39%) had node-negative disease, of which 54 (17%) recurred. By 2 and 5 years, 66% and 88% of patients, respectively, experienced recurrence. On multivariate competing risks regression, only T-stage 3 or higher was associated with shorter time to recurrence [aSHR = 2.7; 95% confidence interval (CI), 1.5-5.2]. Multivariate Cox regression showed T-stage 3 or higher [hazard ratio (HR) = 1.8; 95% CI, 1.2-2.8], lymphovascular invasion (HR = 2.2; 95% CI, 1.4-3.4), and signet ring histology (HR = 2.1; 95% CI, 1.2-3.6) to be associated with decreased overall survival.

CONCLUSIONS

Despite absence of lymph node involvement, patients with T-stage 3 or higher have a significantly shorter time to recurrence. These patients may benefit from more aggressive adjuvant therapy and postoperative surveillance regimens.

Would increasing centre volumes improve patient outcomes in peritoneal dialysis? A registry-based cohort and Monte Carlo simulation study

OBJECTIVE

To estimate the association between centre volume and patient outcomes in peritoneal dialysis, explore robustness to residual confounding and predict the impact of policies to increase centre volumes.

DESIGN

Registry-based cohort study with probabilistic sensitivity analysis and Monte Carlo simulation of (hypothetical) intervention effects.

SETTING

112 secondary-care centres in France.

PARTICIPANTS

9602 adult patients initiating peritoneal dialysis.

MAIN OUTCOME MEASURES

Technique failure (ie, permanent transfer to haemodialysis), renal transplantation and death while on peritoneal dialysis within 5 years of initiating treatment. Associations with underlying risk measured by cause-specific HRs (cs-HRs) and with cumulative incidence by subdistribution HRs (sd-HRs). Intervention effects measured by predicted mean change in cumulative incidences.

RESULTS

Higher volume centres had more patients with diabetes and were more frequently academic centres or associative groupings of private physicians. Patients in higher volume centres had a reduced risk of technique failure (>60 patients vs 0-10 patients: adjusted cs-HR 0.46; 95% CI 0.43 to 0.69), with no changed risk of death or transplantation. Sensitivity analyses mitigated the cs-HRs without changing the findings. In higher volume centres, the cumulative incidence was reduced for technique failure (>60 patients vs 0-10 patients: adjusted sd-HR 0.49; 95% CI 0.29 to 0.85) but was increased for transplantation and death (>60 patients vs 0-10 patients: transplantation-adjusted sd-HR 1.53; 95% CI 1.04 to 2.24; death-adjusted sd-HR 1.28; 95% CI 1.00 to 1.63). The predicted reduction in cumulative incidence of technique failure was largest under a scenario of shifting all patients to the two highest volume centre groups (0.091 reduction) but lower for three more realistic interventions (around 0.06 reduction).

CONCLUSIONS

Patients initiating peritoneal dialysis in high-volume centres had a considerably reduced risk of technique failure but simulations of interventions to increase exposure to high-volume centres yielded only modest improvements.

Therapy prolongation improves outcome in multisystem Langerhans cell histiocytosis

Langerhans cell histiocytosis (LCH)-III tested risk-adjusted, intensified, longer treatment of multisystem LCH (MS-LCH), for which optimal therapy has been elusive. Stratified by risk organ involvement (high [RO+] or low [RO-] risk groups), > 400 patients were randomized. RO+ patients received 1 to 2 six-week courses of vinblastine+prednisone (Arm A) or vinblastine + prednisone + methotrexate (Arm B). Response triggered milder continuation therapy with the same combinations, plus 6-mercaptopurine, for 12 months total treatment. 6/12-week response rates (mean, 71%) and 5-year survival (84%) and reactivation rates (27%) were similar in both arms. Notably, historical comparisons revealed survival superior to that of identically stratified RO+ patients treated for 6 months in predecessor trials LCH-I (62%) or LCH-II (69%, P < .001), and lower 5-year reactivation rates than in LCH-I (55%) or LCH-II (44%, P < .001). RO- patients received vinblastine+prednisone throughout. Response by 6 weeks triggered randomization to 6 or 12 months total treatment. Significantly lower 5-year reactivation rates characterized the 12-month Arm D (37%) compared with 6-month Arm C (54%, P = .03) or to 6-month schedules in LCH-I (52%) and LCH-II (48%, P < .001). Thus, prolonging treatment decreased RO- patient reactivations in LCH-III, and although methotrexate added no benefit, RO+ patient survival and reactivation rates have substantially improved in the 3 sequential trials. (Trial No. NCT00276757 www.ClinicalTrials.gov).

Competing risks and the clinical community: irrelevance or ignorance?

Life expectancy has dramatically increased in industrialized nations over the last 200 hundred years. The aging of populations carries over to clinical research and leads to an increasing representation of elderly and multimorbid individuals in study populations. Clinical research in these populations is complicated by the fact that individuals are likely to experience several potential disease endpoints that prevent some disease-specific endpoint of interest from occurrence. Large developments in competing risks methodology have been achieved over the last decades, but we assume that recognition of competing risks in the clinical community is still marginal. It is the aim of this article to address translational aspects of competing risks to the clinical community. We describe clinical populations where competing risks issues may arise. We then discuss the importance of agreement between the competing risks methodology and the study aim, in particular the distinction between etiologic and prognostic research questions. In a review of 50 clinical studies performed in individuals susceptible to competing risks published in high-impact clinical journals, we found competing risks issues in 70% of all articles. Better recognition of issues related to competing risks and of statistical methods that deal with competing risks in accordance with the aim of the study is needed. Copyright © 2011 John Wiley & Sons, Ltd.

The impact of surgery on survival of patients with cutaneous melanoma: revisiting the role of primary tumor excision margins

OBJECTIVE

To quantify the impact of excision margins on disease-specific survival of patients with primary cutaneous melanoma.

BACKGROUND

Current guidelines recommend narrow margins for the treatment of primary melanoma, although available evidence on this subject is not unequivocal and not always appropriately analyzed.

METHODS

A systematic review of randomized controlled trials (RCT) addressing the issue of wide versus narrow excision margins was performed. Meta-analysis methods for time-to-event data were used to extract hazard ratios(HR) and their 95% confidence intervals (CI) from eligible studies, and ultimately to estimate the summary effect of excision margins on patients' survival.

RESULTS

The 5 eligible RCT enrolled a total of 3295 patients who were allocated to wide (3-5 cm) or narrow (1-2 cm) excision of their primary tumor. The data of locoregional disease-free (LDFS), disease-free (DFS),disease-specific (DSS), and overall (OS) survival were available for 3, 5, 3, and 5 RCT, respectively. The meta-analysis suggested that narrow margins might be associated with an increased risk of both locoregional disease recurrence (HR: 1.30, CI: 1.07-1.57; P = 0.01) and death by disease (HR: 1.28, CI:1.07-1.53, P = 0.01). As regards DFS, the borderline disadvantage (HR:1.13, CI: 0.995-1.28; P = 0.06) becomes significant when considering RCT that enrolled patients with thicker melanoma (HR: 1.19, CI: 1.02-1.39, P =0.03). When death by any cause (OS) was analyzed, no risk difference was found.

CONCLUSIONS

The lack of DSS data from all the available RCT does not allow to draw definitive conclusions. However, current evidence appears sufficient to question the common belief that narrow excision margins are as safe as wide margins in the management of primary melanoma, that calls for further investigation in this field.

Joint modeling of multivariate longitudinal data and the dropout process in a competing risk setting: application to ICU data

BACKGROUND

Joint modeling of longitudinal and survival data has been increasingly considered in clinical trials, notably in cancer and AIDS. In critically ill patients admitted to an intensive care unit (ICU), such models also appear to be of interest in the investigation of the effect of treatment on severity scores due to the likely association between the longitudinal score and the dropout process, either caused by deaths or live discharges from the ICU. However, in this competing risk setting, only cause-specific hazard sub-models for the multiple failure types data have been used.

METHODS

We propose a joint model that consists of a linear mixed effects submodel for the longitudinal outcome, and a proportional subdistribution hazards submodel for the competing risks survival data, linked together by latent random effects. We use Markov chain Monte Carlo technique of Gibbs sampling to estimate the joint posterior distribution of the unknown parameters of the model. The proposed method is studied and compared to joint model with cause-specific hazards submodel in simulations and applied to a data set that consisted of repeated measurements of severity score and time of discharge and death for 1,401 ICU patients.

RESULTS

Time by treatment interaction was observed on the evolution of the mean SOFA score when ignoring potentially informative dropouts due to ICU deaths and live discharges from the ICU. In contrast, this was no longer significant when modeling the cause-specific hazards of informative dropouts. Such a time by treatment interaction persisted together with an evidence of treatment effect on the hazard of death when modeling dropout processes through the use of the Fine and Gray model for sub-distribution hazards.

CONCLUSIONS

In the joint modeling of competing risks with longitudinal response, differences in the handling of competing risk outcomes appear to translate into the estimated difference in treatment effect on the longitudinal outcome. Such a modeling strategy should be carefully defined prior to analysis.