Traditional Survival Analysis Research Articles

Challenges and shifting paradigms in clinical trials in oncology: the case for immunological and targeted therapies.

The advent of immunotherapy has undoubtedly changed the current standard for cancer treatment. Immunotherapy offers the possibility of achieving excellent results—a new alternative for patients with advanced-stage or relapsed disease. Nowadays, the progress made in tumour biology has led to multiple advances in clinical and translational cancer research. Many oncogenic pathways responsible for tumour growth and metastases have been described and, consequently, multiple new cancer therapeutic agents have been developed and are under current investigation. Due to this rapid increase in knowledge and pharmaceutical development, traditional clinical trials designs have encountered major limitations. The pharmacological differences (in toxicity profiles and effectiveness patterns) between immunotherapy and chemotherapy have caused traditional clinical trials to evolve in order to meet this emerging need. This review focuses on the different options pertaining to clinical trial design that have arisen in the field of immuno-oncology, as well as the challenges of accurately interpreting traditional survival analyses within this novel area of cancer medicine.

Abstract 1928: Radiation response in preclinical orthotopic models of brain cancer

Abstract Glioblastoma (GBM) is a fast-growing, aggressive type of central nervous system tumor that forms on the supportive tissue of the brain. Primary treatment options for patients with GBMs have not changed much in many years, and still include surgery, radiation and/or chemotherapy treatment with temozolomide (TMZ). GBM is an incurable disease where there is a desperate need for continued development of novel therapeutic options. A number of preclinical models exist to support the early work needed to develop these new drugs. Here we describe three different preclinical models of brain cancer, U87MG-Luc, GL261-Luc and BT142. Each model was evaluated following orthotopic implantation into the brain. As radiation therapy remains a steadfast approach to GBM, we evaluated each model for its response to radiation and tracked disease progression and response to treatment with either bioluminescence imaging (BLI) or magnetic resonance imaging (MRI) along with traditional survival (morbidity/mortality) analysis. U87MG-Luc is a human glioblastoma cell line that was developed from an astrocytoma. We found that orthotopic implant of U87MG-luc results in reliable growth with a tumor doubling time of 4 days and a median survival time of 45 days. We tested this model with radiation therapy (2.5Gy for 5 days on, 2 days off, for 2 cycles) and found a 70% partial response rate as measured by BLI. We also tested this model with TMZ therapy (33.3mg/kg; orally every day for 5 days) and found a significant delay in disease progression, resulting in a 93% increase in life span. GL261-Luc is a murine glioblastoma model that grows quite aggressively in the mouse brain. We find a tumor volume doubling time of 2 days and a median survival time of 14 days. As this model grows in a mouse strain with an intact immune system it allowed us to evaluate the tumor infiltrating immune cell populations. While we found a low number of CD45+ cells infiltrating into GL261-Luc tumors, immune population changes over time will be described. In this model we tested increasing doses of radiation and found that a single dose of 15Gy was curative whereas the tumors were more moderately responsive to a single dose of 7.5Gy (30% tumor regressions). We then combined 7.5Gy with the immune checkpoint inhibitor anti-PD-1 and saw an improved outcome with a 100% response rate. BT142 is a human anaplastic oligoastroytoma that is relatively unique due to its isocitrate dehydrogenase (IDH1/2) mutational status which results in an accumulation of the oncometabolite 2-hydroxygluarate (2-HG) in the tumor. This tumor line grows in the NOD SCID mouse strain and we found a tumor doubling time of 5 days, as measured by MRI. The BT142 model has proven to be sensitive to radiation following a single dose of 10Gy but less responsive when lower dosage levels were administered on a fractionated schedule. Thus, a variety of human and mouse GBM models exist to enable further drug discovery and development efforts for this intractable disease. Citation Format: Erin E. Trachet, Sumithra Urs, Alden Wong, Scott Wise, Maryland Rosenfeld Franklin. Radiation response in preclinical orthotopic models of brain cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 1928.

Clinical Significance of Fractional Anisotropy Measured in Peritumoral Edema as a Biomarker of Overall Survival in Glioblastoma: Evidence Using Correspondence Analysis.

Fractional anisotropy (FA), a diffusion tensor image (DTI) derived biomarker is related to invasion, infiltration, and extension of glioblastoma (GB). We aimed to evaluate FA values and their association with intervals of overall survival (OS). Retrospective study conducted in 36 patients with GB included 23 (63.9%) males, 46 ± 14 y; and 13 (36.1%) females, 53 ± 13; followed up for 36 months. We measured FA at edema, enhancing rim, and necrosis. We created two categorical variables using levels of FA and intervals of OS to evaluate their relationships. Kaplan-Meier method and correspondence analysis evaluated the association between OS (grouped in 7 six-month intervals) and FA measurements. Median FA values were higher in healthy brain regions (0.351), followed by peritumoral edema (0.190), enhancing ring (0.116), and necrosis (0.071). Pair-wise comparisons among tumor regions showed a significant difference, P < 0.001. The median OS for all patients was 19.3 months; variations in the OS curves among subgroups was significant χ2 (3) = 8.48, P = 0.037. Correspondence analysis showed a significant association between FA values in the edema region and the survival intervals χ2 (18) = 30.996, P = 0.029. Alternative multivariate assessment using correspondence analysis might supplement the traditional survival analysis in patients with GB. A close follow-up of the variability of FA in the peritumoral edema region is predictive of the OS within specific six-month interval subgroup. Further studies should focus on predictive models combining surgical and DTI biomarkers.

Stabilizing cumulative incidence estimation of pregnancy outcome with delayed entries.

A pregnancy may end up with (at least) three possible events: live birth, spontaneous abortion, or elective termination, yielding a competing risks issue when studying an association between a risk factor and a pregnancy outcome. Cumulative incidences (probabilities to end up with the different outcomes depending on gestational age) can be estimated via the Aalen-Johansen estimate. Another issue is that women are usually not entering such an observational study from the first day of pregnancy, resulting in delayed entries. As in traditional survival analysis, this can be solved by considering "at risk" at a given gestational age only for those women who entered the study before that age. However, the number of women at risk at an early gestational age might be extremely low, such that the estimates of cumulative incidence may increase exaggeratedly at that age because of a single event. One solution to reduce the problem has been recently proposed in the literature, which is to ignore simply those early events, creating a small mean bias but enhancing stability of estimates. In the present paper, we propose an alternative computationally simple approach to tackle this problem that consists to postpone to later gestational ages (rather than to ignore) those early events. The two approaches are compared with respect to bias, stability, and sensitivity on the smoothing parameter via simulations reproducing realistic pregnancy scenarios, and are illustrated with data from a study on the effects of statins on pregnancy outcomes. We also outline that all three approaches are asymptotically equivalent.

Impact of Competing Risk of Mortality on Association of Cognitive Impairment With Risk of Hip Fracture in Older Women.

Previous studies examining the association of cognitive impairment and dementia with fracture outcomes in older adults have usually used standard approaches that did not take into account the competing risk of mortality. However, ignoring mortality may not provide accurate estimates of risk of fracture because dementia in older adults strongly predicts death, making mortality a competing risk. A total of 1491 women (mean age 87.6 years) participating in the prospective Study of Osteoporotic Fractures (SOF) Year 20 exam were cognitively assessed and followed to ascertain vital status (deaths verified by death certificates) and hip fractures (confirmed by radiographic reports). Cognitive status was categorized as normal, mild cognitive impairment (MCI), or dementia, based on a standardized evaluation. Absolute probability of hip fracture by category of cognitive function was estimated using traditional Kaplan-Meier method and cumulative incidence function accounting for competing mortality risk. Risk of hip fracture by cognitive function category was determined using conventional Cox proportional hazards regression and subdistribution hazards models with death as a competing risk. During an average follow-up of 5.6 years, 139 (9.3%) women experienced a hip fracture and 990 (66.4%) died before experiencing this outcome. Among women with dementia, the risk of hip fracture was 11.7% (95% confidence interval [CI] 7.3-17.2) at 5 years and 18.6% (95% CI 9.1-30.9) at 10 years using traditional survival analysis versus 7.9% (95% CI 5.1-11.6) at 5 years and 8.8% (95% CI 5.8-12.8) at 9.8 years using a competing risk approach. Results were similar for women with MCI. Women with MCI and dementia have a higher risk of hip fractures than women with normal cognition. However, not taking into account the competing risk of mortality significantly overestimates the risk of hip fracture in women in the ninth and tenth decades of life with cognitive impairment. © 2018 American Society for Bone and Mineral Research.

Survival Weibull regression model for mismeasured outcomes

ABSTRACTIn some survival studies, the exact time of the event of interest is unknown, but the event is known to have occurred during a particular period of time (interval-censored data). If the diagnostic tool used to detect the event of interest is not perfectly sensitive and specific, outcomes may be mismeasured; a healthy subject may be diagnosed as sick and a sick one may be diagnosed as healthy. In such cases, traditional survival analysis methods produce biased estimates for the time-to-failure distribution parameters (Paggiaro and Torelli 2004). In this context, we developed a parametric model that incorporates sensitivity and specificity into a grouped survival data analysis (a case of interval-censored data in which all subjects are tested at the same predetermined time points). Inferential aspects and properties of the methodology, such as the likelihood function and identifiability, are discussed in this article. Assuming known and non differential misclassification, Monte Carlo simulations showed that the proposed model performed well in the case of mismeasured outcomes; the estimates of the relative bias of the model were lower than those provided by the naive method that assumes perfect sensitivity and specificity. The proposed methodology is illustrated by a study related to mango tree lifetimes.

Weighted win loss approach for analyzing prioritized outcomes.

To analyze prioritized outcomes, Buyse (2010) and Pocock etal. (2012) proposed the win loss approach. In this paper, we first study the relationship between the win loss approach and the traditional survival analysis on the time to the first event. We then propose the weighted win loss statistics to improve the efficiency of the unweighted methods. A closed-form variance estimator of the weighted win loss statistics is derived to facilitate hypothesis testing and study design. We also calculated the contribution index to better interpret the results of the weighted win loss approach. Simulation studies and real data analysis demonstrated the characteristics of the proposed statistics. Copyright © 2017 John Wiley & Sons, Ltd.

Condition prediction and estimation of service life in the presence of data censoring and dependent competing risks

An accurate estimation of service life is of primary interest in pavement management systems limiting the time frame for maintenance and rehabilitation (M&R) treatments. Common condition prediction models are derived by regression analysis at the road network level based on empirical data from periodic condition surveys. If a particular section has not failed prior to the last survey or the condition has improved (e.g. due to treatment), it is considered as censored. If censoring is neglected the performance functions, service lives and estimated costs may show substantial bias. The authors who acknowledge this problem have used standard statistical (survival analysis) techniques accounting for censoring. However, any road section may fail due to different but dependent competing failure causes (risks), each leading to treatments. This constitutes a special type of censoring that cannot be addressed with traditional survival analysis methods relying on the assumption of independent censoring. As the number of failure causes usually exceeds one (e.g. fatigue, permanent deformation, thermal cracking), this case is quite common. Moreover, the time until a first failure depends on the sign and degree of correlation between present failure types being modelled by the overall survival function. This paper presents a critical review and comparison of common regression, Markov chain and survival analysis models with and without correlated competing risks based on computer-generated data. Using performance history and distress progression models at the section level in combination with survival analysis improves the accuracy of predictions in comparison. Furthermore, the paper proposes a simultaneous modelling of joint and marginal service life distributions based on copula functions as generalised solution accounting for dependence between competing risks. As the focus of this paper is on condition prediction with censored data, the distress-specific planning and optimisation of treatments will be covered in forthcoming papers.

Estimating time to event characteristics via longitudinal threshold regression models - an application to cervical dilation progression.

In longitudinal studies, it is sometimes of interest to estimate the distribution of the time a longitudinal process takes to traverse from one threshold to another. For example, the distribution of the time it takes a woman's cervical dilation to progress from 3 to 4cm can aid the decision-making of obstetricians as to whether a stalled labor should be allowed to proceed or stopped in favor of other options. Often researchers treat this type of data structure as interval censored and employ traditional survival analysis methods. However, the traditional interval censoring approaches are inefficient in that they do not use all of the available data. In this paper, we propose utilizing a longitudinal threshold model to estimate the distribution of the elapsed time between two thresholds of the longitudinal process from repeated measurements. We extend this modeling framework to be used with multiple thresholds. A Wiener process under the first hitting time framework is used to represent survival distribution. We demonstrate our model through simulation studies and an analysis of data from the Consortium on Safe Labor study. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Conditional probability of long-term survival after resection of hilar cholangiocarcinoma

BackgroundWhile traditional survival analyses focus on factors determined at the time of surgery, conditional survival (CS) estimates prognosis relative to time following treatment. We sought to compare actuarial and CS among patients undergoing curative intent surgery for hilar cholangiocarcinoma. Methods242 patients undergoing surgery between 2000 and 2014 were identified using a multi-institutional database. CS was calculated as the probability of surviving an additional 3 years, given that the patient had already survived “x” years from surgery. ResultsMedian patient age was 67 years (IQR: 57–73) and most patients were male (n = 140, 57.9%). Lymph node metastases were noted in 79 (32.6%) patients while an R0 margin was obtained in 66.1% (n = 160). Median OS was 22.3 months. Actuarial survival decreased over time from 46.3% at 2 years following surgery to 18.2% at 5 years; in contrast, the 3-year CS (CS3) increased with time (CS3 at 2 years was 39.3% versus 54.4% at 5 years). CS3 exceeded actuarial survival for high-risk patients with patients with perineural invasion demonstrating an actuarial survival of 15.4% at 5 years versus CS3 of 37.6% at 2 years following surgery (Δ = 22.2%). ConclusionsCS provides a more accurate, dynamic estimate for survival, especially among high-risk patients.

Estimating the Time to Benefit for Preventive Drugs with the Statistical Process Control Method: An Example with Alendronate.

BackgroundFor physicians dealing with patients with a limited life expectancy, knowing the time to benefit (TTB) of preventive medication is essential to support treatment decisions.ObjectiveThe aim of this study was to investigate the usefulness of statistical process control (SPC) for determining the TTB in relation to fracture risk with alendronate versus placebo in postmenopausal women.MethodsWe performed a post hoc analysis of the Fracture Intervention Trial (FIT), a randomized, controlled trial that investigated the effect of alendronate versus placebo on fracture risk in postmenopausal women. We used SPC, a statistical method used for monitoring processes for quality control, to determine if and when the intervention group benefited significantly more than the control group. SPC discriminated between the normal variations over time in the numbers of fractures in both groups and the variations that were attributable to alendronate. The TTB was defined as the time point from which the cumulative difference in the number of clinical fractures remained greater than the upper control limit on the SPC chart.ResultsFor the total group, the TTB was defined as 11 months. For patients aged ≥70 years, the TTB was 8 months [absolute risk reduction (ARR) = 1.4 %]; for patients aged <70 years, it was 19 months (ARR = 0.7 %).ConclusionSPC is a clear and understandable graphical method to determine the TTB. Its main advantage is that there is no need to define a prespecified time point, as is the case in traditional survival analyses. Prescribing alendronate to patients who are aged ≥70 years is useful because the TTB shows that they will benefit after 8 months. Investigators should report the TTB to simplify clinical decision making.

Conditional survival probability of long-term survival after resection of peri-hilar cholangiocarcinoma.

212 Background: Traditional survival analyses focus on factors determined at the time of surgery and may not be accurate over time. Conditional survival (CS) estimates future prognosis based on survival time accrued following treatment. We sought to define differences between actuarial and CS among patients after resection of peri-hilar cholangiocarcinoma (PHCC). Methods: 242 patients who underwent resection for PHCC between 2000-2014 were identified from 10 major HPB centers. Cox regression models were used to evaluate factors associated with overall survival. CS was calculated as the probability of surviving an additional 3 years at “x” years after surgery using the formula CS3=S(x+3)/Sx. Results: Median patient age was 67 yrs (IQR:57-73) and the majority (73.6%) of patients had a major hepatic resection. Surgical margin status was R0 (n=160; 66.1%) or R1 (n=82; 33.9%). Tumor grade was well- (n=43; 19.1%), moderate- (n=131; 58.2%) or poorly- (n=51; 22.6%) differentiated. Most patients had T1 (13.8%) or T2 (66.4%) disease, while a smaller subset had T3 (17.3%) or T4 (2.6%) disease. Lymph node metastases were present in 79 (32.6%) patients. While actuarial survival decreased over time from 46.3% at 2 years to 18.2% at 5 years following surgery, 3-year CS increased over time among those patients who survived. The CS3 at 2 years (i.e. the probability of surviving to postoperative year 5 after having already survived to year 2) was 39.3% and increased to 54.4% at year 5 (Table). Factors associated with worse OS included lymph node metastases (HR 1.71; 95%CI, 1.24-2.36) and perineural invasion (HR 1.54; 95%CI, 1.02-2.33) (both P&lt;0.05). CS3 for high-risk patients exceeded the actuarial survival, e.g. patients with perineural invasion had an actuarial survival of 15.4% at 5 years vs. a CS3 at 2 years of 37.6% (Δ=22.2%). Conclusions: CS provides a more dynamic means to estimate future survival among patients who have accrued survival time, especially in high-risk patients who were predicted to have short survival times. [Table: see text]

What Cure Models Can Teach us About Genome-Wide Survival Analysis.

The aim of logistic regression is to estimate genetic effects on disease risk, while survival analysis aims to determine effects on age of onset. In practice, genetic variants may affect both types of outcomes. A cure survival model analyzes logistic and survival effects simultaneously. The aim of this simulation study is to assess the performance of logistic regression and traditional survival analysis under a cure model and to investigate the benefits of cure survival analysis. We simulated data under a cure model and varied the percentage of subjects at risk for disease (cure fraction), the logistic and survival effect sizes, and the contribution of genetic background risk factors. We then computed the error rates and estimation bias of logistic, Cox proportional hazards (PH), and cure PH analysis, respectively. The power of logistic and Cox PH analysis is sensitive to the cure fraction and background heritability. Our results show that traditional Cox PH analysis may erroneously detect age of onset effects if no such effects are present in the data. In the presence of genetic background risk even the cure model results in biased estimates of both the odds ratio and the hazard ratio. Cure survival analysis takes cure fractions into account and can be used to simultaneously estimate the effect of genetic variants on disease risk and age of onset. Since genome-wide cure survival analysis is not computationally feasible, we recommend this analysis for genetic variants that are significant in a traditional survival analysis.

Do statins reduce the risk of myocardial infarction in patients with heart failure? A pooled individual-level reanalysis of CORONA and GISSI-HF.

Current guidelines do not explicitly recommend statin use in heart failure (HF). Relatively low numbers of atherothrombotic events among HF patients, in the context of their elevated competing risks for non-atherothrombotic causes of death, may have prevented previous analyses of clinical trials from detecting a benefit for statins. We pooled data from two landmark trials of HF patients not on statin therapy randomized to rosuvastatin 10 mg daily vs. placebo, CORONA and GISSI-HF, in order to improve our power to detect statistically significant differences in atherothrombotic events. We also accounted for competing risks from other causes of death. We used competing risks analyses to evaluate atherothrombotic events in the context of death from other cardiovascular and non-cardiovascular causes. We also performed traditional Cox survival analyses of the same data with the intention that these statistical approaches would be complementary. CORONA participants (n = 5011, median follow-up 32.8 months) were older and sicker than GISSI-HF participants (n = 4574, median follow-up 46.9 months) by design. Rosuvastatin decreased risk for myocardial infarction (MI) among CORONA and GISSI-HF participants with ischaemic aetiology of HF (hazard ratio 0.81, 95% confidence interval 0.66-0.99, P < 0.05). There were no significant differences between rosuvastatin and placebo in risks for stroke or death from other causes. This individual-level reanalysis of two landmark trials demonstrates a small but statistically significant decreased risk for MI among patients with ischaemic HF randomized to rosuvastatin vs. placebo. Rosuvastatin appears to be effective in preventing MI in ischaemic HF patients not already on statins.

A discrete-time Multiple Event Process Survival Mixture (MEPSUM) model.

Traditional survival analysis was developed to investigate the occurrence and timing of a single event, but researchers have recently begun to ask questions about the order and timing of multiple events. A multiple event process survival mixture model is developed here to analyze nonrepeatable events measured in discrete-time that may occur at the same point in time. Building on both traditional univariate survival analysis and univariate survival mixture analysis, the model approximates the underlying multivariate distribution of hazard functions via a discrete-point finite mixture in which the mixing components represent prototypical patterns of event occurrence. The model is applied in an empirical analysis concerning transitions to adulthood, where the events under study include parenthood, marriage, beginning full-time work, and obtaining a college degree. Promising opportunities, as well as possible limitations of the model and future directions for research, are discussed.

Competing risk: An illustration with aspiration pneumonia in head and neck cancer patients undergoing radical radiotherapy: A biostatistician's perspective.

Interest in survival analysis is to look and capture the information about the occurrence of events, i.e., death. In human life different types of events may happen at the same time. Sometimes, few events completely interrupt or make subtle changes on the occurrence of an event of interest. The method to capture information about the specific event of interest along with other events is known as competing risk modeling. This paper is dedicated to explore the application of competing risk model in oncology practice. It is aimed in near future that more and more survival analysis will be performed through application of competing risk modeling instead of traditional survival analysis to generate robust statistical inference.

The need for novel strategies to analyze the dynamic pattern of worker’s health over time and the consequences for sustained employability

The need for novel strategies to analyze the dynamic pattern of worker’s health over time and the consequences for sustained employability

A complex adaptive system using statistical learning theory as an inline preprocess for clinical survival analysis

New advances in medicine have led to a disparity between the existing information about patients and the ability of clinicians to utilize it. Lack of training and incompatibility with clinical techniques has made the use of the complex adaptive systems approach difficult. To avoid this, we used statistical learning theory as an inline preprocess between existing data collection methods and clinical analysis of data. Clinicians would be able to use this system without any changes to their techniques, while improving accuracy. We used data from CT scans of patients with metastatic carcinoma to predict prognosis. Specifically, we used the standard for evaluating response to treatment, RECIST, and new qualitative and quantitative features. An Evolutionary Programming trained Support Vector Machine (EP-SVM), was used to preprocess the data for two traditional survival analysis techniques: Cox Proportional Hazard Models and Kaplan Meier curves. This was compared to Logistic Regression (LR) and using cutoff points. Analyses were also done to compare different inputs and different radiologists. The EP-SVM outperformed both LR and the cutoff method significantly and allowed us to both intelligently combine data from multiple sources and identify the most predictive features without necessitating changes in clinical methods.

A competing risks analysis of the duration of federal target funds rates

The behaviour of short term interest rates has been the focus of extensive studies in economics and finance. This paper analyses the duration between changes in the Intended Federal Funds Rate (IFFR) taking into account different factors and the possibility of two outcomes (rate increase and rate decrease). Due to the lack of independence between these outcomes, the use of traditional survival analysis was ruled out and a novel approach based on competing risks is used. The estimation results show the influence of the current interest rate level, US GDP growth rate, US inflation rate, inflation rate differential with Euro-zone and the sign of the previous interest rate change. Test results also confirm that the duration previous to small changes (of a quarter point) and to large changes (above a quarter point) are statistically different for both rate hikes and rate cuts. Accurate confidence intervals for the Cumulative Incidence Function (CIF) are provided even with small sample size under non-normality.

Competing Risk of Death: An Important Consideration in Studies of Older Adults

Clinical studies often face the difficult problem of how to account for participants who die without experiencing the study outcome of interest. In a geriatric population with considerable comorbidities, the competing risk of death is especially high. Traditional approaches to describe risk of disease include Kaplan-Meier survival analysis and Cox proportional hazards regression, but these methods can overestimate risk of disease by failing to account for the competing risk of death. This report discusses traditional survival analysis and competing risk analysis as used to estimate risk of disease in geriatric studies. Furthermore, it illustrates a competing risk approach to estimate risk of second hip fracture in the Framingham Osteoporosis Study and compares the results with traditional survival analysis. In this example, survival analysis overestimated the 5-year risk of second hip fracture by 37% and the 10-year risk by 75% compared with competing risk estimates. In studies of older individuals in which a substantial number of participants die during a long follow-up, the cumulative incidence competing risk estimate and competing risk regression should be used to determine incidence and effect estimates. Use of a competing risk approach is critical to accurately determining disease risk for elderly individuals and therefore best inform clinical decision-making.