Modelling competing risks in cancer studies

Oncology Clinical Trial Design Planning Based on a Multistate Model That Jointly Models Progression-Free and Overall Survival Endpoints

When planning an oncology clinical trial, the usual approach is to assume proportional hazards and even an exponential distribution for time-to-event endpoints. Often, besides the gold-standard endpoint overall survival (OS), progression-free survival (PFS) is considered as a second confirmatory endpoint. We use a survival multistate model to jointly model these two endpoints and find that neither exponential distribution nor proportional hazards will typically hold for both endpoints simultaneously. The multistate model provides a stochastic process approach to model the dependency of such endpoints neither requiring latent failure times nor explicit dependency modeling such as copulae. We use the multistate model framework to simulate clinical trials with endpoints OS and PFS and show how design planning questions can be answered using this approach. In particular, nonproportional hazards for at least one of the endpoints are a consequence of OS and PFS being dependent and are naturally modeled to improve planning. We then illustrate how clinical trial design can be based on simulations from a multistate model. Key applications are coprimary endpoints and group-sequential designs. Simulations for these applications show that the standard simplifying approach may very well lead to underpowered or overpowered clinical trials. Our approach is quite general and can be extended to more complex trial designs, further endpoints, and other therapeutic areas. An R package is available on CRAN.

Accounting for Competing Events When Evaluating Long-Term Outcomes in Survivors of Critical Illness

The clinical trajectory of survivors of critical illness after hospital discharge can be complex and highly unpredictable. Assessing long-term outcomes after critical illness can be challenging because of possible competing events, such as all-cause death during follow-up (which precludes the occurrence of an event of particular interest). In this perspective, we explore challenges and methodological implications of competing events during the assessment of long-term outcomes in survivors of critical illness. In the absence of competing events, researchers evaluating long-term outcomes commonly use the Kaplan-Meier method and the Cox proportional hazards model to analyze time-to-event (survival) data. However, traditional analytical and modeling techniques can yield biased estimates in the presence of competing events. We present different estimands of interest and the use of different analytical approaches, including changes to the outcome of interest, Fine and Gray regression models, cause-specific Cox proportional hazards models, and generalized methods (such as inverse probability weighting). Finally, we provide code and a simulated dataset to exemplify the application of the different analytical strategies in addition to overall reporting recommendations.

Regression modeling of restricted mean survival time for left-truncated right-censored data

The restricted mean survival time (RMST) is a clinically meaningful summary measure in studies with survival outcomes. Statistical methods have been developed for regression analysis of RMST to investigate impacts of covariates on RMST, which is a useful alternative to the Cox regression analysis. However, existing methods for regression modeling of RMST are not applicable to left-truncated right-censored data that arise frequently in prevalent cohort studies, for which the sampling bias due to left truncation and informative censoring induced by the prevalent sampling scheme must be properly addressed. The pseudo-observation (PO) approach has been used in regression modeling of RMST for right-censored data and competing-risks data. For left-truncated right-censored data, we propose to directly model RMST as a function of baseline covariates based on POs under general censoring mechanisms. We adjust for the potential covariate-dependent censoring or dependent censoring by the inverse probability of censoring weighting method. We establish large sample properties of the proposed estimators and assess their finite sample performances by simulation studies under various scenarios. We apply the proposed methods to a prevalent cohort of women diagnosed with stage IV breast cancer identified from surveillance, epidemiology, and end results-medicare linked database.

Risk Factors Associated with Malignant Transformation of Astrocytoma: Competing Risk Regression Analysis

Background  Malignant transformation (MT) of low-grade astrocytoma (LGA) triggers a poor prognosis in benign tumors. Currently, factors associated with MT of LGA have been inconclusive. The present study aims to explore the risk factors predicting LGA progressively differentiated to malignant astrocytoma.

Methods  The study design was a retrospective cohort study of medical record reviews of patients with LGA. Using the Fire and Gray method, the competing risk regression analysis was performed to identify factors associated with MT, using both univariate and multivariable analyses. Hence, the survival curves of the cumulative incidence of MT of each covariate were constructed following the final model.

Results  Ninety patients with LGA were included in the analysis, and MT was observed in 14.4% of cases in the present study. For MT, 53.8% of patients with MT transformed to glioblastoma, while 46.2% differentiated to anaplastic astrocytoma. Factors associated with MT included supratentorial tumor (subdistribution hazard ratio [SHR] 4.54, 95% confidence interval [CI] 1.08–19.10), midline shift > 1 cm (SHR 8.25, 95% CI 2.18–31.21), and nontotal resection as follows: subtotal resection (SHR 5.35, 95% CI 1.07–26.82), partial resection (SHR 10.90, 95% CI 3.13–37.90), and biopsy (SHR 11.10, 95% CI 2.88–42.52).

Conclusion  MT in patients with LGA significantly changed the natural history of the disease to an unfavorable prognosis. Analysis of patients' clinical characteristics from the present study identified supratentorial LGA, a midline shift more than 1 cm, and extent of resection as risk factors associated with MT. The more extent of resection would significantly help to decrease tumor burden and MT. In addition, future molecular research efforts are warranted to explain the pathogenesis of MT.

Direct modeling of the crude probability of cancer death and the number of life years lost due to cancer without the need of cause of death: a pseudo-observation approach in the relative survival setting

In population-based cancer studies, net survival is a crucial measure for population comparison purposes. However, alternative measures, namely the crude probability of death (CPr) and the number of life years lost (LYL) due to death according to different causes, are useful as complementary measures for reflecting different dimensions in terms of prognosis, treatment choice, or development of a control strategy. When the cause of death (COD) information is available, both measures can be estimated in competing risks setting using either cause-specific or subdistribution hazard regression models or with the pseudo-observation approach through direct modeling. We extended the pseudo-observation approach in order to model the CPr and the LYL due to different causes when information on COD is unavailable or unreliable (i.e., in relative survival setting). In a simulation study, we assessed the performance of the proposed approach in estimating regression parameters and examined models with different link functions that can provide an easier interpretation of the parameters. We showed that the pseudo-observation approach performs well for both measures and we illustrated their use on cervical cancer data from the England population-based cancer registry. A tutorial showing how to implement the method in R software is also provided.

Pooled Cohort Equations and the competing risk of cardiovascular disease versus cancer: Multi-Ethnic study of atherosclerosis

BACKGROUND

many of the modifiable variables in the Pooled Cohort Equations (PCE) are shared risk factors for cardiovascular disease (CVD) and cancer, which are the two leading causes of death in the United States. We sought to determine the utility of the PCE risk for the synergistic risk prediction of CVD and cancer.

METHODS

we identified 5,773 participants (61.5 years and 53% women) without baseline CVD or cancer from the Multi-Ethnic study of atherosclerosis. The primary outcome was time to first event of either incident CVD or incident cancer. We calculated competing risk and cause-specific hazard models to examine the association of the PCE groups (<7.5%, 7.5-<20%, ≥20%) with the competing risk of CVD and cancer.

RESULTS

the rate of incident CVD and cancer was higher with higher PCE risk, but the absolute event rate was low for both CVD and cancer when the PCE risk was <7.5%. Participants with a PCE <7.5% had a higher rate of cancer (4.8) compared to CVD (3.3) per 1000 person-years, while the rate of CVD (11.5) was higher than cancer (8.6) for PCE between 7.5 and <20%. The ratio of CVD to cancer increased in a logarithmic manner and at a PCE risk of approximately 7.2% the risk for CVD and cancer was equal. In adjusted competing risk modeling, a PCE risk of ≥20% compared to <7.5% was associated with a greater risk of both CVD [7.18 (95% CI 5.77-8.94)] and cancer [3.59 (95% CI 2.91-4.43)].

CONCLUSIONS

these findings highlight the importance of age and modifiable risk factors for CVD and cancer prevention. In addition, it suggests that the PCE can provide important information for both CVD and cancer risk stratification, which may guide a synergistic approach to screening and preventive therapies for the two leading causes of death in the United States.

Estimating the hazard rate difference from case-cohort studies

The case-cohort design, among many two-phase sampling designs, substantially reduces the cost of an epidemiological study by selecting more informative participants within the full cohort for expensive variable measurements. Despite their benefits, additive hazards models, which estimate hazard differences, have rarely been used for the analysis of case-cohort studies due to the lack of software and application examples. In this paper, we describe a newly developed estimation method that fits the additive hazards models to general two-phase sampling studies along with the R package addhazard that implements it. It allows for missing covariates among cases, cohort stratification, robust variances, and the incorporation of auxiliary information from the full cohort to enhance inference precision. We demonstrate the use of this tool to estimate the association of the risk of coronary heart disease (CHD) with biomarkers high-sensitivity C-reactive protein (hs-CRP) and Lipoprotein-associated phospholipase A₂ (Lp-PLA₂) by analyzing the Atherosclerosis Risk in Communities Study, which adopted a two-phase sampling design for studying these two biomarkers. We show that the use of auxiliary variables from the full cohort based on calibration techniques improves the precision of the hazard difference being estimated. We observe a synergistic effect of the two biomarkers among participants with lower LDL cholesterol (LDL-C): the CHD hazard rate attributable to the combined action of high hs-CRP and high Lp-PLA₂ exceeded the sum of the CHD hazard rate attributable to each one independently by 11.58 (95% CI 2.16-21.01) cases per 1000 person-years. With higher LDL-C, we observe the CHD hazard rate attributable to the combined action of high hs-CRP and medium Lp-PLA₂ was less than the sum of their individual effects by 13.42 (95% CI 2.44-24.40) cases per 1000 person-years. This demonstration serves the dual purposes of illustrating analysis techniques and providing insights about the utility of hs-CRP and Lp-PLA₂ for identifying the high-risk population of CHD that the traditional risk factors such as the LDL-C may miss. Epidemiologists are encouraged to use this new tool to analyze other case-cohort studies and incorporate auxiliary variables embedded in the full cohort in their analysis.

Application of additive hazards models for analyzing survival of breast cancer patients

BACKGROUND

Survival rates for breast cancer (BC) are often based on the outcomes of this disease. The aim of this study was to compare the performance of three survival models, namely Cox regression, Aalen's, and Lin and Ying's additive hazards (AH) models for identifying the prognostic factors regarding the survival time of BC patients.

MATERIALS AND METHODS

This study was a historical cohort study which used 1025 females' medical records that underwent modified radical mastectomy or breast saving. These patients were admitted to Besat and Chamran Hospitals, Tehran, Iran, during 2010-2015 and followed until 2017. The Aalen's and Lin and Ying's AH models and also traditional Cox model were applied for analysis of time to death of BC patients using R 3.5.1 software.

RESULTS

In Aalen's and also Lin and Ying's AH models, age at diagnosis, history of disease, number of lymph nodes, metastasis, hormonal therapy, and evacuation lymph nodes were prognostic factors for the survival of BC patients (P < 0.05). In addition, in the Lin and Ying's AH model tumor size (P = 0.048) was also identified as a significant factor. According to Aalen's plot, metastasis, age at diagnosis, and number of lymph nodes had a time-varying effect on survival time. These variables had a different slope as the times go on.

CONCLUSION

AH model may yield new insights in prognostic studies of survival time of patients with BC over time. Because of the positive slope of estimated cumulative regression function in Aalen's plot, metastasis, higher age at diagnosis, and high number of lymph nodes are important factors in reducing the survival BC, and then based on these factors, the therapists should consider a special therapeutic protocol for BC patients.

Multistate modeling of clinical hold in randomized clinical trials

A clinical hold order by the Food and Drug Administration (FDA) to the sponsor of a clinical trial is a measure to delay a proposed or to suspend an ongoing clinical investigation. The phase III clinical trial START serves as motivating data example to explore implications and potential statistical approaches for a trial continuing after a clinical hold is lifted. In spite of a modified intention-to-treat (ITT) analysis introduced to account for the clinical hold by excluding patients potentially affected most by the clinical hold, results of the trial did not show a significant improvement of overall survival duration, and the question remains whether the negative result was an effect of the clinical hold. In this paper, we propose a multistate model incorporating the clinical hold as well as disease progression as intermediate events to investigate the impact of the clinical hold on the treatment effect. Moreover, we consider a simple counterfactual censoring approach as alternative strategy to the modified ITT analysis to deal with a clinical hold. Using a realistic simulation study informed by the START data and with a design based on our multistate model, we show that the modified ITT analysis used in the START trial was reasonable. However, the censoring approach will be shown to have some benefits in terms of power and flexibility.

Association between oral leukoplakia and risk of upper gastrointestinal cancer death: A follow-up study of the Linxian General Population Trial

Background

This study was conducted to explore the association between oral leukoplakia (OL) and the risk of upper gastrointestinal cancer death in the Linxian General Population Trial Cohort.

Methods

A prospective cohort study of the Linxian General Population Trial Cohort was performed. Participants with OL were treated as an exposed group, and the remainder was selected as a control group. All subjects were followed monthly by village health workers and reviewed quarterly by the Linxian Cancer Registry. Hazard ratios (HRs) and 95% confidence interval (CIs) were evaluated using proportional hazard and proportional subdistribution hazard models, respectively.

Results

Over a median of 27 years of observation, 29 476 subjects were followed‐up. A total of 17 473 deaths occurred, including 2345 esophageal squamous cell carcinoma (ESCC), 1139 gastric cardia carcinoma, and 506 gastric non‐cardia carcinoma deaths. Significant increased ESCC mortality was observed in subjects with OL (exposed 9.66% vs. unexposed 7.39%; P < 0.0001). Furthermore, subjects with OL had a 22% higher risk of death from ESCC (HR 1.22, 95% CI 1.10–1.34; P = 0.0001) after adjusted covariates. In subjects aged ≤52 at the baseline, OL was significantly associated with an elevated risk of ESCC mortality (HR 1.32, 95% CI 1.13–1.54; P = 0.0005). No significant associations were observed for gastric cardia carcinoma and non‐cardia carcinoma mortality.

Conclusions

OL may increase the risk of ESCC mortality, especially in the younger population. These associations should be investigated in further studies.

Joint Inference for Competing Risks Survival Data

This article develops joint inferential methods for the cause-specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the time to the type of failure of interest in the presence of competing risks. Joint inference for the two functions are needed in practice because (i) they describe different characteristics of a given type of failure, (ii) they do not uniquely determine each other, and (iii) the effects of a variable on the two functions can be different and one often does not know which effects are to be expected. We study both the group comparison problem and the regression problem. We also discuss joint inference for other related functions. Our simulation shows that our joint tests can be considerably more powerful than the Bonferroni method, which has important practical implications to the analysis and design of clinical studies with competing risks data. We illustrate our method using a Hodgkin disease data and a lymphoma data. Supplementary materials for this article are available online.

Identification and utilization of donor and recipient genetic variants to predict survival after HCT: are we ready for primetime?

Overall survival following hematopoietic cell transplantation (HCT) has improved over the past two decades through better patient selection and advances in HLA typing, supportive care, and infection prophylaxis. Nonetheless, mortality rates are still unsatisfactory and transplant-related mortality remains a major cause of death after unrelated allogeneic HCT. Since there are no known pre-HCT, non-HLA biologic predictors of survival following transplant, for over a decade, scientists have been investigating the role of non-HLA germline genetic variation in survival and treatment-related mortality after HCT. Variation in single nucleotide polymorphisms (SNPs) has the potential to impact chemotherapy, radiation, and immune responses, leading to different post-HCT survival outcomes. In this paper, we address the current knowledge of the contribution of genetic variation to survival following HCT and discuss study design and methodology for investigating HCT survival on a genomic scale.

Assessment of nutritional status and health-related quality of life before and after liver transplantation

Background

Patients with chronic liver disease frequently suffer from malnutrition, together with a decline in their health-related quality of life.

This study was carried out with the aim of evaluating the nutritional status, complications of medical and surgical care, anxiety, health-related quality of life and dependence level on basic and instrumental activities of daily living in pre- and post-liver transplant patients.

Methods/Design

A prospective observational study with follow-up of patients on the waiting list for liver transplants who subsequently received a transplant at the University Hospital Complex in A Coruña during the period 2012–2014 (n = 110).

All the patients will be followed-up for a maximum of 6 months. For survivors, assessments will be re-evaluated at one, three and six months post- transplant.

Informed consent of the patient and ethical review board approval was obtained (Code: 2010/081 and 2010/082).

The following variables will be studied: socio-demographic data, reason for the transplant, comorbidity (Charlson Score), analytical parameters, time on transplant waiting list and post-transplant complications. A trained nurse will evaluate the following for each patient: nutritional indices, anthropometric variables and handgrip strength. Validated questionnaires will be used to determine the patients’ nutritional status (Subjective Global Assessment), anxiety (STAI questionnaire), Health-Related Quality of Life (LDQoL 1.0 questionnaire), dependence (Barthel Index and Lawton-Brody Scale), nursing diagnoses (NANDA) and post-transplant quality indicators.

Multiple linear/logistic regression models will be used to identify variables associated with the events of interest. Changes in nutritional status, quality of life and dependence over time will be analysed with linear mixed-effects regression models.

Actuarial survival analysis using Kaplan-Meier curves, Cox regression and competitive risk will be performed

Concordance between the different scores that assess nutritional status and interobserver agreement regarding nursing diagnoses will be studied using the statistical Kappa index and Bland Altman method.

Discussion

The risk of malnutrition can be considered as a possible prognostic factor in transplant outcomes, associated with anxiety, health-related quality of life and dependence.

For this reason we consider interesting to perform a prospective follow-up study of patients who require a transplant to survive, studying their nutritional status and health-related quality of life.

Electronic supplementary material

The online version of this article (doi:10.1186/s12876-015-0232-3) contains supplementary material, which is available to authorized users.

Simple analysis of non-Markov models: A case study on heart transplant data

In transplantation studies, often several response measurements are collected for patients while they are on the waiting list. In this settings it is often of primary interest to assess whether the available history of a patient can be used for predicting patient survival as well as further performance on the list. In this work, we use a multi-state model approach to analyze the performance of patients described by their urgency status that changes in time while waiting for a new organ. We use the pseudo-value approach introduced by Andersen et al. ( 2003 ) and apply it for the Aalen-Johansen estimator of the state occupation probabilities since the transition probabilities were found to depend on the history. This approach allows us to study the impact of baseline information on the occupation probabilities treating the dependence on the history as a nuisance. It was found that the previous state, the current state and time from the moment of entering the waiting list had an impact on the future performance of the patient. Depending on those, patients were more likely to come back to the particular status in which they were before, die or get a transplant. To address the problem of those competing events, a multinomial approach was used for the next state given the previous state observed.

Events per variable for risk differences and relative risks using pseudo-observations

A method based on pseudo-observations has been proposed for direct regression modeling of functionals of interest with right-censored data, including the survival function, the restricted mean and the cumulative incidence function in competing risks. The models, once the pseudo-observations have been computed, can be fitted using standard generalized estimating equation software. Regression models can however yield problematic results if the number of covariates is large in relation to the number of events observed. Guidelines of events per variable are often used in practice. These rules of thumb for the number of events per variable have primarily been established based on simulation studies for the logistic regression model and Cox regression model. In this paper we conduct a simulation study to examine the small sample behavior of the pseudo-observation method to estimate risk differences and relative risks for right-censored data. We investigate how coverage probabilities and relative bias of the pseudo-observation estimator interact with sample size, number of variables and average number of events per variable.

Regression modeling of the cumulative incidence function with missing causes of failure using pseudo-values

Competing risks arise when patients may fail from several causes. Strategies for modeling event-specific quantities often assume that the cause of failure is known for all patients, but this is seldom the case. Several authors have addressed the problem of modeling the cause-specific hazard rates with missing causes of failure. In contrast, direct modeling of the cumulative incidence function has received little attention.We provide a general framework for regression modeling of this function in the missing cause setting, encompassing key models such as the Fine and Gray and additive models, by considering two extensions of the Andersen–Klein pseudo-value approach. The first extension is a novel inverse probability weighting method, whereas the second extension is based on a previously proposed multiple imputation procedure.We evaluated the gain in using these approaches with small samples in an extensive simulation study. We analyzed the data from an Eastern Cooperative Oncology Group breast cancer treatment clinical trial to illustrate the practical value and ease of implementation of the proposed methods.

Modeling cumulative incidence function for competing risks data

A frequent occurrence in medical research is that a patient is subject to different causes of failure, where each cause is known as a competing risk. The cumulative incidence curve is a proper summary curve, showing the cumulative failure rates over time due to a particular cause. A common question in medical research is to assess the covariate effects on a cumulative incidence function. The standard approach is to construct regression models for all cause-specific hazard rate functions and then model a covariate-adjusted cumulative incidence curve as a function of all cause-specific hazards for a given set of covariates. New methods have been proposed in recent years, emphasizing direct assessment of covariate effects on cumulative incidence function. Fine and Gray proposed modeling the effects of covariates on a subdistribution hazard function. A different approach is to directly model a covariate-adjusted cumulative incidence function, including a pseudovalue approach by Andersen and Klein and a direct binomial regression by Scheike, Zhang and Gerds. In this paper, we review the standard and new regression methods for modeling a cumulative incidence function, and give the sources of computer packages/programs that implement these regression models. A real bone marrow transplant data set is analyzed to illustrate various regression methods.

Clinical endpoints in allogeneic hematopoietic stem cell transplantation studies: the cost of freedom

When designing a study for allogeneic hematopoietic stem cell transplantation (HSCT), many choices must be made, including conditioning regimen, stem cell source, and graft-versus-host disease (GVHD) prevention method. For each of these, there are a growing number of options, which can be combined into a bewildering number of possible HSCT protocols. To properly interpret the results of a given strategy and compare them with others, it is essential that there be agreement on the definitions and estimation methods of HSCT endpoints. We report a survey of the recent HSCT literature that confirms the heterogeneity of endpoint definitions and estimation methods used. Unfortunately, this heterogeneity may lead to significant biases in the estimates of key endpoints, including nonrelapse mortality, relapse, GVHD, or engraftment. This can preclude adequate comparisons among studies, even though such comparisons are the major tool with which to improve HSCT outcome. In the context of our survey, we discuss some of the statistical issues that arise when dealing with HSCT endpoints and the ramifications of the choice of endpoint definition, when the endpoint occurs in the context of competing risks. Our hope is to generate discussion and motivate a search for consensus among those who perform transplantations and statisticians.

A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions

Competing risks endpoints are frequently encountered in hematopoietic stem cell transplantation where patients are exposed to relapse and treatment-related mortality. Both cause-specific hazards and direct models for the cumulative incidence functions have been used for analyzing such competing risks endpoints. For both approaches, the popular models are of a proportional hazards type. Such models have been used for studying prognostic factors in acute and chronic leukemias. We argue that a complete understanding of the event dynamics requires that both hazards and cumulative incidence be analyzed side by side, and that this is generally the most rigorous scientific approach to analyzing competing risks data. That is, understanding the effects of covariates on cause-specific hazards and cumulative incidence functions go hand in hand. A case study illustrates our proposal.

Relationship of race/ethnicity and survival after single umbilical cord blood transplantation for adults and children with leukemia and myelodysplastic syndromes

The relationship of race/ethnicity with outcomes of umbilical cord blood transplantation (UCBT) is not well known. We analyzed the association between race/ethnicity and outcomes of unrelated single UCBT for leukemia and myelodysplastic syndromes. Our retrospective cohort study consisted of 885 adults and children (612 whites, 145 blacks, and 128 Hispanics) who received unrelated single UCBT for leukemia and myelodysplastic syndromes between 1995 and 2006 and were reported to the Center for International Blood and Marrow Transplant Research. A 5-6/6 HLA-matched unit with a total nucleated cell count infused of ≥2.5 × 10(7)/kg was given to 40% white and 42% Hispanic, but only 21% black patients. Overall survival at 2 years was 44% for whites, 34% for blacks, and 46% for Hispanics (P = .008). In multivariate analysis adjusting for patient, disease, and treatment factors (including HLA match and cell dose), blacks had inferior overall survival (relative risk of death, 1.31; P = .02), whereas overall survival of Hispanics was similar (relative risk, 1.03; P = .81) to that of whites. For all patients, younger age, early-stage disease, use of units with higher cell dose, and performance status ≥80 were independent predictors of improved survival. Black patients and white patients infused with well-matched cords had comparable survival; similarly, black and white patients receiving units with adequate cell dose had similar survival. These results suggest that blacks have inferior survival to whites after single UCBT, but outcomes are improved when units with a higher cell dose are used.

HLA-matched sibling transplantation for severe aplastic anemia: impact of HLA DR15 antigen status on engraftment, graft-versus-host disease, and overall survival

The HLA class II DRB1 antigen DR15 (common alleles *1501, *1502) is an important marker in the pathobiology of severe aplastic anemia (SAA). We studied 1204 recipients of HLA-matched sibling bone marrow transplantation for SAA to determine whether HLA DR15 status (as determined by allele-level typing) affected hematopoietic recovery, graft-versus-host disease (GVHD), or overall survival (OS). In multivariate analysis, secondary graft failure rate at 2 years was lower in patients who were HLA DR15+ (hazard ratio = 0.46, P = .01). However, neutrophil recovery at day -28, platelet recovery at day -100, acute GVHD, chronic GVHD, and overall mortality were independent of DR15 status. The 5-year probabilities of OS, after adjusting for age, race, performance score, transplant-conditioning regimen, and year of transplantation, were 78% and 81% for patients who were HLA DR15+ and HLA DR15-, respectively (P = .35). In conclusion, DR15 status is associated with secondary graft failure after HLA-matched sibling bone marrow transplantation for SAA but has no significant impact on survival.

How to handle mortality when investigating length of hospital stay and time to clinical stability

BACKGROUND

Hospital length of stay (LOS) and time for a patient to reach clinical stability (TCS) have increasingly become important outcomes when investigating ways in which to combat Community Acquired Pneumonia (CAP). Difficulties arise when deciding how to handle in-hospital mortality. Ad-hoc approaches that are commonly used to handle time to event outcomes with mortality can give disparate results and provide conflicting conclusions based on the same data. To ensure compatibility among studies investigating these outcomes, this type of data should be handled in a consistent and appropriate fashion.

METHODS

Using both simulated data and data from the international Community Acquired Pneumonia Organization (CAPO) database, we evaluate two ad-hoc approaches for handling mortality when estimating the probability of hospital discharge and clinical stability: 1) restricting analysis to those patients who lived, and 2) assigning individuals who die the "worst" outcome (right-censoring them at the longest recorded LOS or TCS). Estimated probability distributions based on these approaches are compared with right-censoring the individuals who died at time of death (the complement of the Kaplan-Meier (KM) estimator), and treating death as a competing risk (the cumulative incidence estimator). Tests for differences in probability distributions based on the four methods are also contrasted.

RESULTS

The two ad-hoc approaches give different estimates of the probability of discharge and clinical stability. Analysis restricted to patients who survived is conceptually problematic, as estimation is conditioned on events that happen at a future time. Estimation based on assigning those patients who died the worst outcome (longest LOS and TCS) coincides with the complement of the KM estimator based on the subdistribution hazard, which has been previously shown to be equivalent to the cumulative incidence estimator. However, in either case the time to in-hospital mortality is ignored, preventing simultaneous assessment of patient mortality in addition to LOS and/or TCS. The power to detect differences in underlying hazards of discharge between patient populations differs for test statistics based on the four approaches, and depends on the underlying hazard ratio of mortality between the patient groups.

CONCLUSIONS

Treating death as a competing risk gives estimators which address the clinical questions of interest, and allows for simultaneous modelling of both in-hospital mortality and TCS / LOS. This article advocates treating mortality as a competing risk when investigating other time related outcomes.

Competing risk models to estimate the excess mortality and the first recurrent-event hazards

BACKGROUND

In medical research, one common competing risks situation is the study of different types of events, such as disease recurrence and death. We focused on that situation but considered death under two aspects: "expected death" and "excess death", the latter could be directly or indirectly associated with the disease.

METHODS

The excess hazard method allows estimating an excess mortality hazard using the population (expected) mortality hazard. We propose models combining the competing risks approach and the excess hazard method. These models are based on a joint modelling of each event-specific hazard, including the event-free excess death hazard. The proposed models are parsimonious, allow time-dependent hazard ratios, and facilitate comparisons between event-specific hazards and between covariate effects on different events. In a simulation study, we assessed the performance of the estimators and showed their good properties with different drop-out censoring rates and different sample sizes.

RESULTS

We analyzed a population-based dataset on French colon cancer patients who have undergone curative surgery. Considering three competing events (local recurrence, distant metastasis, and death), we showed that the recurrence-free excess mortality hazard reached zero six months after treatment. Covariates sex, age, and cancer stage had the same effects on local recurrence and distant metastasis but a different effect on excess mortality.

CONCLUSIONS

The proposed models consider the excess mortality within the framework of competing risks. Moreover, the joint estimation of the parameters allow (i) direct comparisons between covariate effects, and (ii) fitting models with common parameters to obtain more parsimonious models and more efficient parameter estimators.

Practical methods for competing risks data: a review

Competing risks data arise naturally in medical research, when subjects under study are at risk of more than one mutually exclusive event such as death from different causes. The competing risks framework also includes settings where different possible events are not mutually exclusive but the interest lies on the first occurring event. For example, in HIV studies where seropositive subjects are receiving highly active antiretroviral therapy (HAART), treatment interruption and switching to a new HAART regimen act as competing risks for the first major change in HAART. This article introduces competing risks data and critically reviews the widely used statistical methods for estimation and modelling of the basic (estimable) quantities of interest. We discuss the increasingly popular Fine and Gray model for subdistribution hazard of interest, which can be readily fitted using standard software under the assumption of administrative censoring. We present a simulation study, which explores the robustness of inference for the subdistribution hazard to the assumption of administrative censoring. This shows a range of scenarios within which the strictly incorrect assumption of administrative censoring has a relatively small effect on parameter estimates and confidence interval coverage. The methods are illustrated using data from HIV-1 seropositive patients from the collaborative multicentre study CASCADE (Concerted Action on SeroConversion to AIDS and Death in Europe).

Methods of competing risks analysis of end-stage renal disease and mortality among people with diabetes

BACKGROUND

When a patient experiences an event other than the one of interest in the study, usually the probability of experiencing the event of interest is altered. By contrast, disease-free survival time analysis by standard methods, such as the Kaplan-Meier method and the standard Cox model, does not distinguish different causes in the presence of competing risks. Alternative approaches use the cumulative incidence estimator by the Cox models on cause-specific and on subdistribution hazards models. We applied cause-specific and subdistribution hazards models to a diabetes dataset with two competing risks (end-stage renal disease (ESRD) or death without ESRD) to measure the relative effects of covariates and cumulative incidence functions.

RESULTS

In this study, the cumulative incidence curve of the risk of ESRD by the cause-specific hazards model was revealed to be higher than the curves generated by the subdistribution hazards model. However, the cumulative incidence curves of risk of death without ESRD based on those three models were very similar.

CONCLUSIONS

In analysis of competing risk data, it is important to present both the results of the event of interest and the results of competing risks. We recommend using either the cause-specific hazards model or the subdistribution hazards model for a dominant risk. However, for a minor risk, we do not recommend the subdistribution hazards model and a cause-specific hazards model is more appropriate. Focusing the interpretation on one or a few causes and ignoring the other causes is always associated with a risk of overlooking important features which may influence our interpretation.

Diagnosis delay and follow-up strategies in colorectal cancer. Prognosis implications: a study protocol

Background

Controversy exists with regard to the impact that the different components of diagnosis delay may have on the degree of invasion and prognosis in patients with colorectal cancer. The follow-up strategies after treatment also vary considerably. The aims of this study are: a) to determine if the symptoms-to-diagnosis interval and the treatment delay modify the survival of patients with colorectal cancer, and b) to determine if different follow-up strategies are associated with a higher survival rate.

Methods/Design

Multi-centre study with prospective follow-up in five regions in Spain (Galicia, Balearic Islands, Catalonia, Aragón and Valencia) during the period 2010-2012. Incident cases are included with anatomopathological confirmation of colorectal cancer (International Classification of Diseases 9th revision codes 153-154) that formed a part of a previous study (n = 953).

At the time of diagnosis, each patient was given a structured interview. Their clinical records will be reviewed during the follow-up period in order to obtain information on the explorations and tests carried out after treatment, and the progress of these patients.

Symptoms-to-diagnosis interval is defined as the time calculated from the diagnosis of cancer and the first symptoms attributed to cancer. Treatment delay is defined as the time elapsed between diagnosis and treatment. In non-metastatic patients treated with curative intention, information will be obtained during the follow-up period on consultations performed in the digestive, surgery and oncology departments, as well as the endoscopies, tumour markers and imaging procedures carried out.

Local recurrence, development of metastases in the follow-up, appearance of a new tumour and mortality will be included as outcome variables.

Actuarial survival analysis with Kaplan-Meier curves, Cox regression and competitive risk survival analysis will be performed.

Discussion

This study will make it possible to verify if the different components of delay have an impact on survival rate in colon cancer and rectal cancer. In consequence, this multi-centre study will be able to detect the variability present in the follow-up of patients with colorectal cancer, and if this variability modifies the prognosis. Ideally, this study could determine which follow-up strategies are associated with a better prognosis in colorectal cancer.

Estimating subject-specific dependent competing risk profile with censored event time observations

In a longitudinal study, suppose that the primary endpoint is the time to a specific event. This response variable, however, may be censored by an independent censoring variable or by the occurrence of one of several dependent competing events. For each study subject, a set of baseline covariates is collected. The question is how to construct a reliable prediction rule for the future subject's profile of all competing risks of interest at a specific time point for risk-benefit decision making. In this article, we propose a two-stage procedure to make inferences about such subject-specific profiles. For the first step, we use a parametric model to obtain a univariate risk index score system. We then estimate consistently the average competing risks for subjects who have the same parametric index score via a nonparametric function estimation procedure. We illustrate this new proposal with the data from a randomized clinical trial for evaluating the efficacy of a treatment for prostate cancer. The primary endpoint for this study was the time to prostate cancer death, but had two types of dependent competing events, one from cardiovascular death and the other from death of other causes.

Proportional subdistribution hazards modeling offers a summary analysis, even if misspecified

Competing risks model time-to-first-event and the event type. Our motivating data example is the ONKO-KISS study on the occurrence of infections in neutropenic patients after stem-cell transplantation with first-event-types 'infection' and 'end of neutropenia'. The standard approach to study the effects of covariates in competing risks is to assume each event-specific hazard (ESH) to follow a proportional hazards model. However, a summarizing probability interpretation of the different event-specific effects of one covariate can be challenging. This difficulty has led to the development of the proportional subdistribution hazards model of a competing event of interest. However, one model specification usually precludes the other. Assuming proportional ESHs, we find that the subdistribution log-hazard ratio may show a pronounced time-dependency, even changing sign. Still, the subdistribution analysis is useful by estimating the least false parameter (LFP), a time-averaged effect on the cumulative event probabilities. In examples, we find that the LFP offers a robust summary of the effects on the ESHs for different observation periods, ranging from heavy censoring to no censoring at all. In particular, if there is no effect on the competing ESH, the subdistribution log-hazard ratio is close to the event-specific log-hazard ratio of interest. We reanalyze an interpretationally challenging example from the ONKO-KISS study and conduct a simulation study, where we find that the LFP is reliably estimated by the subdistribution analysis even for moderate sample sizes.

Recent decrease in acute graft-versus-host disease in children with leukemia receiving unrelated donor bone marrow transplants

Unrelated donor (URD) bone marrow transplantation (BMT) is an effective treatment for leukemia in children, but its success is threatened by graft-versus-host disease (GVHD) and relapse. In this report, we describe the incidence of and risk factors for GVHD over time in children receiving URD BMT. We analyzed outcomes of 638 myeloablative URD BMTs performed between 1990 and 2003 to treat acute myelogenous leukemia (AML), acute lymphoblastic leukemia (ALL), chronic myelogenous leukemia, or myelodysplastic syndrome MDS, using the Center for International Blood and Marrow Transplant Research (CIBMTR) database. All recipients were under age 18 years and had available high-resolution HLA typing for HLA-A, -B, -C, and -DRB1. Overall, 27% of the recipients developed acute GVHD (aGVHD) grade III-IV; the risk was significantly higher in children receiving T cell-replete grafts compared with those receiving T cell-depleted grafts (odds ratio [OR] = 3.12; 95% confidence interval [CI] = 2.02 to 4.83; P < .0001). Acute GVHD significantly reduced the risk of relapse in children with ALL (OR = 0.34; 95% CI = 0.13 to 0.86; P = .0052), but not in those with AML (OR = 0.58; 95% CI = 0.22 to 2.98; P = .26). The risk of aGVHD was higher in children undergoing transplantation in 1990-1998 (n = 365) compared with those doing so in 1999-2003 (OR = 1.93; 95% CI = 1.27 to 2.91; P = .002). We conclude that outcomes have changed significantly over time, with a reduced risk of aGVHD associated with the more recent transplantations.

Semi-parametric additive risk models: application to injury duration study

In survival analysis, the Cox model is a multiplicative model and widely used in survival analysis. However, the assumption of proportional hazards in the Cox multiplicative model is a crucial one that needs to be fulfilled for the results to be meaningful. When proportionality is a questionable assumption, an alternative but less widely used method is additive model. The additive hazards model assumes that covariates act in an additive manner on an unknown baseline hazard rate. Using the emergency department (ED) visits data, we demonstrated the additive hazards regression models and showed the differences in estimates obtained by the additive hazards models and the Cox model. In our study, the Cox model gave a higher estimate than the additive hazards model. However, both models revealed similar results with regard to covariates selected to remain in the model and the estimated survival functions based on the Cox and additive hazards models were almost identical. Since Cox and additive hazards models give different aspects of the association between risk factors and the study outcome, it seems desirable to use together to give a more comprehensive understanding of data.

Donor and recipient CMV serostatus and outcome of pediatric allogeneic HSCT for acute leukemia in the era of CMV-preemptive therapy

In the era of cytomegalovirus (CMV)-preemptive therapy, it is unclear whether CMV serostatus of donor or recipient affects outcome of allogeneic hematopoietic stem cell transplantation (HSCT) among children with leukemia. To investigate, consecutive patients aged 0-18 who underwent primary HSCT for acute leukemia in 1997-2007 (HLA-matched sibling or unrelated donor, myeloablative conditioning, unmanipulated bone marrow or peripheral blood, preemptive therapy, no CMV prophylaxis) were followed retrospectively through January 2008. Treatment failure (relapse or death) was analyzed using survival-based proportional hazards regression. Competing risks (relapse and nonrelapse mortality, NRM) were analyzed using generalized linear models of cumulative incidence-based proportional hazards. Excluding 4 (2.8%) patients lacking serostatus of donor or recipient, there were 140 subjects, of whom 50 relapsed and 24 died in remission. Pretransplant CMV seroprevalence was 55.7% in recipients, 57.1% in donors. Thirty-five (25.0%) grafts were from seronegative donor to seronegative recipient (D-/R-). On univariate analysis, D-/R- grafts were associated with shorter relapse-free survival (RFS) than other grafts (median 1.06 versus 3.15 years, P < .05). Adjusted for donor type, diagnosis, disease stage, recipient and donor age, female-to-male graft, graft source, and year, D-/R- graft was associated with relapse (hazards ratio 3.15, 95% confidence interval 1.46-6.76) and treatment failure (2.45, 1.46-4.12) but not significantly with NRM (2.00, 0.44-9.09). In the current era, children who undergo allogeneic HSCT for acute leukemia have reduced risk of relapse and superior RFS when recipient and/or donor is CMV-seropositive before transplantation. However, no net improvement in RFS would be gained from substituting seropositive unrelated for seronegative sibling donors.

Statistical methods for analysing longitudinal data in delirium studies

Delirium is an often acute and highly fluctuating syndrome that can be transient or in some cases associated with prolonged disturbances. The best way to capture its natural course is to conduct studies with longitudinal design, but data analysis in longitudinal studies is difficult, as often the measured variables of each subject are correlated over the course of time. As such, there has been limited application of such methods for analysing longitudinal data in the study of delirium. This overview considers simple traditional approaches along with more complex methods that involve modelling of data. The relative merits of survival analysis, structural equation modelling, and path analysis are reviewed. Furthermore, two flexible modelling techniques are considered; the mixed effects model and generalized estimating equations with emphasis on their use with binary outcomes, as often the outcome in delirium studies is delirium/no delirium. Their contrasting approach to parameter interpretation and methods for accounting for correlation and dealing with missing data are detailed. Information on available software is provided. Delirium research will be substantially enhanced by incorporating such methods.