Constant Hazard Model Research Articles

Cancer incidence following non-neoplastic medical conditions: a prospective population-based cohort study.

Many non-neoplastic diseases have been established to be tumorigenic, and cancers are sometimes misdiagnosed as non-neoplastic diseases. We conducted a comprehensive registry-based study of site-specific cancer diagnosis risk following the diagnosis of any preceding medical condition (PMC) encoded by the International Classification of Diseases (ICD)-10 classification. We analyzed healthcare data and cancer data for a random population-based sample of 2.5 million individuals living in Finland on January 1, 2000. Hazard ratios for each PMC and cancer pair were estimated using piecewise constant hazard regression models. P-values were corrected for multiple testing with the Bonferroni method. Several lifestyle-related PMCs were associated with the risk of cancer diagnosis, exemplified by chronic obstructive pulmonary disease and subsequent lung cancer diagnosis risk (female hazard ratio [HR] = 9.91, 95% confidence interval [CI]: 9.18-19.7, p-adj. < 0.0001; male HR = 5.69, 95% CI: 5.43-5.96, p-adj. < 0.0001). Diagnosis risk of ill-defined cancers appeared to increase following diagnosis of Alzheimer's disease (AD). We identified rare PMCs of potential interest. A considerable proportion of the statistically significant associations were explainable by tobacco smoking and alcohol use. The enrichment of ill-defined cancer diagnoses in persons with AD, together with the overall inverse association between AD and cancer, may reflect underdiagnosis of cancer in this patient population. Our results provide a useful resource for research on the prevention and early detection of cancer.

Modified Bayesian survival analysis of Diabetes Mellitus in selected hospital facilities in Nasarawa, Nigeria

Diabetes mellitus is a global chronic health problem affecting over 400 million people. The study focused on the commonest type of Diabetes-Type II diabetes. The disease is associated with morbidity and mortality. Bayesian survival model may be utilized to assess the risk factors associated with Diabetes. The study utilized secondary data from 532 diabetic patients from two General Hospital facilities in Nasarawa State, Nigeria. The aim of the paper was to apply a Bayesian survival model on diabetic dataset to assess some risk factors pertaining to the disease. This Bayesian model was modified to Diabetic Additive Models (DAMS) and further extended to the Diabetic Additive Constant Hazard Model (DACHM), the coded version C. DACHM (when all metrical covariates were coded) and Diabetic Additive Accelerated Failure Time Model (DAAFTM). The results show that C.DACHM outperforms the other model with least values of Watanabe Akaike Information Criterion (WAIC), Deviance Information Criterion (DIC), and a large predictive power measured by the Log Pseudo Maximum Likelihood (LPML). The C.DACH model suggests that; good management of type II diabetes patients aged 40 years and above in both hospitals reduced the risk of death. Considerably, low Body Mass Index (BMI) increased the risk of death of patients with the disease. Body Mass Index, BMI greater than 24.9 (overweight) are 5.41E-17 times at risk of death from diabetes than those of normal weight. High Systolic Blood Pressure, SBP, greater than 140 (high) increases the risk of dying from the diseases by 1.51 times than those of normal SBP. High Diastolic Blood Pressure, DBP, greater than or equal to 90 (high) increases the risk of dying from the diseases by 7.81 times than those of normal DBP. Male patients were 1.28 times at risk of death from diabetes than their female patients. Patients of General Hospital Keffi experience are 1.02 times at risk of death than those of the General Hospital Nasarawa. The research recommends patients’ drug compliance especially for patients above 40 years, maintenance of a healthy body mass index and maintenance of a healthy blood pressure.

Abstract 29: Autoimmune diseases and the risk of cancer

Abstract Background: Many autoimmune diseases (AD) are known to be associated with comorbidities, and certain ADs have been suggested to influence cancer risk. Immunosuppression and dysregulation of the immune system promote the development of certain cancers, particularly hematological malignancies. There is also evidence on an increased risk of several types of solid tumors among individuals with an AD. The aim of this population-based cohort study was to evaluate the risk of any cancer, except non-melanoma skin cancer, in 31 different ADs. We explored associations between both common (such as rheumatoid arthritis) and rare (such as Behcet’s disease) ADs and cancer. Material and methods: The data consists of a population-based random sample of 2.5 million individuals who lived in Finland on January 1, 2000. It includes information on hospital diagnoses between 1970 and 2017 for each individual, with a total of 92 million hospital care records. There were 70 694 individuals with prevalent AD and 68 002 individuals with prevalent cancer. Those with prevalent cancer were removed from the analyses. Participants were followed up for subsequent occurrence of cancer, based on data from the nationwide cancer registry. We estimated relative risks (RRs) with 95% confidence intervals (CIs) using piecewise constant hazard regression models, adjusting for age, sex, and calendar period. Time since AD diagnosis was treated as a time-varying covariate. Results: During the follow-up, 222 211 primary cancers were diagnosed, 18 409 with and 203 802 without a pre-existing AD. Overall, the risk of cancer was 2.02 (95% CI 1.93-2.12) for &amp;lt;1 year since any AD diagnosis and 1.05 (1.03-1.07) for ≥10 years since diagnosis. The largest increase in cancer risk was observed for individuals with autoimmune hemolytic anemia, and there was evidence of a persisting risk even after 10 years since diagnosis (RR 8.53 (6.76-10.77) for &amp;lt;1 year since diagnosis and 1.62 (1.18-2.24) for ≥10 years since diagnosis). Long-term impact on cancer risk was also observed for autoimmune vasculitis, Crohn's disease, discoid lupus erythematosus, pemphigus, psoriasis, systemic lupus erythematosus and ulcerative colitis. For individuals with these ADs, cancer risk was still elevated after 10 or more years after AD diagnosis. Discussion: Cancer incidence was greatly dependent on AD duration. Cancer risk was increased soon (&amp;lt;1 year) after AD diagnosis in 24 different ADs and elevated risks were still observed after ≥10 years in 8 ADs. Cancer and comorbid diseases may have partly shared etiologies. Many lifestyle factors such as smoking, alcohol consumption, and obesity are established causes of many common diseases. Also, AD treatments may in some cases be tumorigenic. In conclusion, many ADs were associated with a significantly increased risk of cancer long after diagnosis, and this should be considered in patient counseling and monitoring. The findings also encourage search for shared risk factors underlying both diseases. Citation Format: Sanna Heikkinen, Tomas Tanskanen, Lauri Sipilä, Janne Pitkäniemi. Autoimmune diseases and the risk of cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 29.

Adaptive design with bayesian informed interim decisions: application to a randomized trial of mechanical circulatory support

Abstract Background Cardiovascular trials increasingly require large sample sizes and long follow-up periods. Several approaches have been developed to optimize sample size such as adaptive group sequential trials, samples size re-estimation based on the promising zone, and the win ratio. Traditionally, the log-rank or the Cox proportional hazards model is used to test for treatment effects, based on a constant hazard rate and proportional hazards alternatives, which however, may not always hold. Large sample sizes and/or long follow up periods are especially challenging for trials evaluating the efficacy of acute care interventions. Purpose We propose an adaptive design wherein using interim data, Bayesian computation of predictive power guides the increase in sample size and/or the minimum follow-up duration. These computations do not depend on the constant hazard rate and proportional hazards assumptions, thus yielding more robust interim decision making for the future course of the trial. Methods PROTECT IV is designed to evaluate mechanical circulatory support with the Impella CP device vs. standard of care during high-risk PCI. The primary endpoint is a composite of all-cause death, stroke, MI or hospitalization for cardiovascular causes with initial minimum follow-up of 12 months and initial enrolment of 1252 patients with expected recruitment in 24 months. The study will employ an adaptive increase in sample size and/or minimum follow-up at the Interim analysis when ∼80% of patients have been enrolled. The adaptations utilize extensive simulations to choose a new sample size up to 2500 and new minimal follow-up time up to 36 months that provides a Bayesian predictive power of 85%. Bayesian calculations are based on patient-level information rather than summary statistics therefore enabling more reliable interim decisions. Constant or proportional hazard assumptions are not required for this approach because two separate Piece-wise Constant Hazard Models with Gamma-priors are fitted to the interim data. Bayesian predictive power is then calculated using Monte-Carlo methodology. Via extensive simulations, we have examined the utility of the proposed design for situations with time varying hazards and non-proportional hazards ratio such as situations of delayed treatment effect (Figure) and crossing of survival curves. The heat map of Bayesian predictive power obtained when the interim Kaplan-Meier curves reflected delayed response shows that for this scenario an optimal combination of increased sample size and increased follow-up time would be needed to attain 85% predictive power. Conclusion A proposed adaptive design with sample size and minimum follow-up period adaptation based on Bayesian predictive power at interim looks allows for de-risking the trial of uncertainties regarding effect size in terms of control arm outcome rate, hazard ratio, and recruitment rate. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Abiomed, Inc Figure 1

Causal inference with a mediated proportional hazards regression model

The natural direct and indirect effects in causal mediation analysis with survival data having one mediator is addressed by VanderWeele. He derived an approach for (1) an accelerated failure time regression model in general cases and (2) a proportional hazards regression model when the time-to-event outcome is rare. If the outcome is not rare, then VanderWeele did not derive a simple closed-form expression for the log-natural direct and log-natural indirect effects for the proportional hazards regression model because the baseline cumulative hazard function does not approach zero. We develop two approaches to extend VanderWeele’s approach, in which the assumption of a rare outcome is not required. We obtain the natural direct and indirect effects for specific time points through numerical integration after we calculate the cumulative baseline hazard by (1) applying the Breslow method in the Cox proportional hazards regression model to estimate the unspecified cumulative baseline hazard; (2) assuming a piecewise constant baseline hazard model, yielding a parametric model, to estimate the baseline hazard and cumulative baseline hazard. We conduct simulation studies to compare our two approaches with other methods and illustrate our two approaches by applying them to data from the ASsessment, Serial Evaluation, and Subsequent Sequelae in Acute Kidney Injury (ASSESS-AKI) Consortium.

Adaptive design with bayesian informed interim decisions: application to a randomized trial of mechanical circulatory support

Abstract Background Cardiovascular trials increasingly require large sample sizes and long follow-up periods. Several approaches have been developed to optimize sample size such as adaptive group sequential trials, samples size re-estimation based on the promising zone, and the win ratio. Traditionally, the log-rank or the Cox proportional hazards model is used to test for treatment effects, based on a constant hazard rate and proportional hazards alternatives, which however, may not always hold. Large sample sizes and/or long follow up periods are especially challenging for trials evaluating the efficacy of acute care interventions. Purpose We propose an adaptive design wherein using interim data, Bayesian computation of predictive power guides the increase in sample size and/or the minimum follow-up duration. These computations do not depend on the constant hazard rate and proportional hazards assumptions, thus yielding more robust interim decision making for the future course of the trial. Methods PROTECT IV is designed to evaluate mechanical circulatory support with the Impella CP device vs. standard of care during high-risk PCI. The primary endpoint is a composite of all-cause death, stroke, MI or hospitalization for cardiovascular causes with initial minimum follow-up of 12 months and initial enrolment of 1252 patients with expected recruitment in 24 months. The study will employ an adaptive increase in sample size and/or minimum follow-up at the Interim analysis when ∼80% of patients have been enrolled. The adaptations utilize extensive simulations to choose a new sample size up to 2500 and new minimal follow-up time up to 36 months that provides a Bayesian predictive power of 85%. Bayesian calculations are based on patient-level information rather than summary statistics therefore enabling more reliable interim decisions. Constant or proportional hazard assumptions are not required for this approach because two separate Piece-wise Constant Hazard Models with Gamma-priors are fitted to the interim data. Bayesian predictive power is then calculated using Monte-Carlo methodology. Via extensive simulations, we have examined the utility of the proposed design for situations with time varying hazards and non-proportional hazards ratio such as situations of delayed treatment effect (Figure) and crossing of survival curves. The heat map of Bayesian predictive power obtained when the interim Kaplan-Meier curves reflected delayed response shows that for this scenario an optimal combination of increased sample size and increased follow-up time would be needed to attain 85% predictive power. Conclusion A proposed adaptive design with sample size and minimum follow-up period adaptation based on Bayesian predictive power at interim looks allows for de-risking the trial of uncertainties regarding effect size in terms of control arm outcome rate, hazard ratio, and recruitment rate. Funding Acknowledgement Type of funding sources: Private company. Main funding source(s): Abiomed, Inc Figure 1

Cox Piecewise Constant Hazard Model with Bayesian Method

Cox PH model is one of the survival models that is widely used for analyzing time-to-event data. Cox PH model consists of two main components, the baseline hazard consisting of time-dependent component; and the exponential function accomodating explanatory variables. The baseline hazard is not estimated in the Cox PH model, thus not accommodating the need for hazard rate estimation. Therefore, in this paper we discuss the estimation of baseline hazard through piecewise constant hazard using Bayesian method. Gamma distribution is assumed for the piecewise constant baseline hazard, and normal distribution is assumed for the regression coefficient. Sampling from the posterior is conducted using Markov chain Monte Carlo through Gibbs sampling. Echocardiogram data containing 106 observations and 6 explanatory variables were used in analysis. The result showed that the baseline hazard functions were estimated and each of parameters in the model is converged as shown by the trace plot and posterior density plot.

Educational inequalities and regional variation in colorectal cancer survival in Finland

BackgroundPrevious studies have reported lower colorectal cancer (CRC) survival in patients with low compared to high educational levels. We investigated the impact of education on CRC survival by using both individual and area-based information on education. MethodsPatients diagnosed with CRC in Finland in 2007–2016 were followed up for death until the end of 2016. Age-standardized relative survival and relative excess risk of death (RER) were estimated by sex using period approach. RERs were adjusted for age, stage at diagnosis, cancer site, urbanity, hospital district and municipality by using Bayesian piecewise constant excess hazard models. Analyses were conducted including individual (basic, secondary, high) and area-based (quartiles Q1-Q4 based on the proportion of population with basic education) education separately as well as both measures in one model. ResultsWe analysed in all 24 462 CRC patients. There was a clear gradient in 5-year relative survival across education groups (men: basic 62 %, secondary 64 %, high 69 %; women: basic 61 %, secondary 67 %, high 71 %). Compared to the basic education group, RER in the high education group was significantly lower. This association was still present after including area-based education in the models (men: RER 0.72, 95 % Confidence interval (CI) 0.64−0.81; women: RER 0.76, 95 % CI 0.59−0.96). Area-based education revealed smaller effect estimates than individual education in CRC survival and no association for men. ConclusionIndividual education information should be preferred over area-based when survival differences are studied by education. Educational differences in CRC survival are still present in Finland.

Outlier robust modeling of survival curves in the presence of potentially time-varying coefficients.

In time to event studies, censoring often occurs and models that take this into account are wide-spread. In the presence of outliers, standard estimators of model parameters may be affected such that results and conclusions are not reliable anymore. This in turn also hampers the detection of these outliers due to masking effects. To cope with outliers when using proportional hazard models, we propose to use the Brier score as a loss function. Since the coefficients often vary over time, we focus on the piecewise constant hazard model, which can flexibly model time-varying coefficients if a large number of cut-points is used. To prevent overfitting, we add a penalty term that potentially shrinks time-varying effects to constant effects. By fitting the coefficients of the piecewise constant hazard model using a penalized Brier score loss, we obtain a robust model that can handle time-varying coefficients. Its good performance is illustrated in a simulation study and using two datasets from practice.

Predicting the duration of sickness absence spells due to back pain: a population-based study from Sweden

ObjectivesWe aimed to develop and validate a prediction model for the duration of sickness absence (SA) spells due to back pain (International Statistical Classification of Diseases and Related Health Problems...

Impact of rates of referral and systemic therapy on 1-year outcomes in metastatic NSCLC: A real-world population based study.

e18238 Background: EGFR/ALK inhibitors and immunotherapy represent promising treatments for metastatic NSCLC, but patients must be referred to a cancer center (CC) to be considered for these treatments. Local referral rates to a CC for advanced pancreatic cancer are only 51%. We hypothesized that rates of referral for stage IV NSCLC are also low, thereby affecting survival. Methods: Using linked data from the provincial cancer registry, oncology specific EMR, administrative claims and vital statistics, we identified all patients diagnosed with stage IV NSCLC from 2009 to 2016 in Alberta, Canada. Demographics, Charlson Comorbidity Index (CCI), method of diagnosis, year of diagnosis and site of metastasis were compared between patients referred vs not referred (NR) to a CC and between those who received systemic therapy (ST) vs those who did not. A multivariable piecewise constant hazard model was constructed to estimate the hazard ratio (HR) of death in the 1st year. Results: We identified 9717 stage IV NSCLC patients among whom 65.8% and 34.2% were diagnosed pre and post 2012. In this cohort, 6907 (71%) were seen at a CC. Factors which predict referral to a cancer center are: dx by cytology (OR 6.81, 95% CI: 5.99-7.75; p &lt; 0.001) or histology (OR 6.29, 95% CI: 5.40-7.34; p &lt; 0.001) vs radiologic dx; Age &lt; 70 (OR 1.87, 95% CI: 1.69-2.07; p &lt; 0.001); dx after 2012 (OR 1.52, 95% Cl 1.36-1.70; p &lt; 0.001) and CCI≤1 (OR 1.50, 95% Cl 1.34-1.68; p &lt; 0.001). ST was administered to 2057(21.2%). Factors that predict ST are: dx by cytology (OR 6.48, 95% CI: 5.18-8.11; p &lt; 0.001) or histology (OR 6.35.18 , 95% CI: 5.02-8.04; p &lt; 0.001); Age &lt; 70 (OR 2.55, 95% Cl 2.33-2.82; p &lt; 0.001); CCI≤1 (OR 1.56, 95% Cl 1.39-1.76; p &lt; 0.001); dx after 2012 (OR 1.28, 95% CI: 1.16-1.41 and female gender (OR 1.18 , 95% CI: 1.07-1.29; p &lt; 0.001; p &lt; 0.001). Within the 1st year post dx, HR for mortality was lower both in patients referred to a CC vs NR (HR 0.3, 95%CI .28-0.31, p &lt; 0.0001) and patients receiving ST vs no ST (HR 0.3, 95% CI .28-0.32, p &lt; 0.0001). Conclusions: Close to 1 in 3 patients with stage IV NSCLC were not referred to a CC even though referral and receipt of ST were associated with a significantly lower risk of death in the 1st year following diagnosis. Clear delineation and wide dissemination of appropriate referral pathways are needed to improve outcomes, especially among older patients.

Casual effect of methotrexate+etanercept/infliximab on survival ofpatients withrheumatoid arthritis.

Background and objectives: Following the discovery of new drugs, physicians and pharmaceutical companies have become interested in examining patients’ mortality and morbidity rates. In this respect, the effects of methotrexate (MTX)+etanercept/infliximab (ETA/INF) therapy on the survival of rheumatoid arthritis patients (RA) were evaluated in this study using marginal structural piecewise constant baseline hazard model.Patients and methods: According to the standard protocol, MTX is considered as the first-line treatment for RA patients. If there is no adequate response to MTX, biologic drugs will be added. To compare the survival rates of RA patients in MTX- and MTX+ETA/INF-treated groups, the piecewise constant baseline hazard model was fitted. Then, due to the existence of the time-dependent confounder (VAS) which was affected by previous treatment, the weight for each person-time was calculated via the inverse probability treatment weighting method. These weights were then used by marginal structural piecewise constant baseline hazard model. Finally, these models were compared.Results: The median (IQR) of the follow-up period in patients receiving MTX+ETN/INF and MTX was 11 (15.25) and 11 (31), respectively, and the 8-year survival rate was reported by 70% versus 68%, respectively. First, the piece-wise constant baseline hazard model was fitted. Fitting the given model showed that MTX+ETA/INF had a significant effect on patients’ survival (HR=0.789, 95% CI [0.634, 0.983]). Second, marginal structural piecewise constant baseline hazard model was fitted. But, the results of this model revealed that MTX+ETA/INF did not have a significant impact on patients’ survival (HR=0.968, 95% CI [0.860, 1.090]).Conclusion: Adjusting the pain score over time as a time-dependent confounder via marginal structural piecewise constant baseline hazard model, it has been demonstrated that MTX+ETA/INF does not have a significant effect on patients’ survival rates. Therefore, a significant difference can be found between survival rates of these groups using longitudinal studies.

Web-based statistical tools for the analysis and design of clinical trials that incorporate historical controls

A collection of web-based statistical tools (http://research.mdacc.tmc.edu/SmeeactWeb/) are described that enable investigators to incorporate historical control data into analysis of randomized clinical trials using Bayesian hierarchical modeling as well as implement adaptive designs that balance posterior effective sample sizes among the study arms and thus maximize power. With balanced allocation guided by “dynamic” Bayesian hierarchical modeling, the design offers the potential to assign more patients to experimental therapies and thereby enhance efficiency while limiting bias and controlling average type I error. The tools effectuate analysis and design for static (non-hierarchical Bayesian analysis) and two types of dynamic (hierarchical Bayesian inference using empirical Bayes and spike-and-slab hyperprior) methods for Gaussian data models, as well as a dynamic method for time-to-failure endpoints based on a piecewise constant hazard model. The site also offers interfaces to facilitate calibration of the model hyperparameters. These allow users to test different parameters in the presence of the historical data on the basis of their resultant frequentist properties, including bias and mean squared error. All calculations are performed on a central computational server. The user may upload data, choose trial settings, run computations in real-time, and review the results using only a web browser. The back-end web module, computation module, and MCMC sampling module are developed in the C#, R, and C++ languages, respectively, and a communication module is also available to ensure the continued connection between the client computer and the back-end server during the Bayesian computations. The statistical tools are described and demonstrated with examples.

Optimal hazard models based on partial information

The proportional hazards (PH), mixture hazards (MH), proportional reversed hazards (PRH), and mixture reversed hazards (MRH) models are widely used in various applications in many fields, but their optimality properties remain unknown. We represent these important reliability models as general escort models and derive them as solutions to several information theoretic formulations. Thus far, the escort models are defined in physics by the normalized powers of one or product of two probability mass or density functions and have been derived in statistics and physics as the solutions to different information formulations. The general escort models introduced in this paper include the escorts of densities, as well as the escorts of survival functions and cumulative distribution functions which represent the hazards models. Moreover, we show that the MH and MRH models are also optimal according to formulations in terms of the mean variation distance. Additional results explore reliability properties of the escort of two densities. A notable property is that the escort of two densities with non-constant hazard rates can be a constant hazard rate model. Another result characterizes the PH model in terms of the survival function of the escort of two densities. Comparisons of the MH, escort of two densities, and the mixture of two distributions are illustrated.

Selection of reference groups in the Life Span Study of atomic bomb survivors.

In cohort studies, unbiased estimation of exposure-outcome associations requires selection of an appropriate reference group of unexposed individuals. We illustrate strategies for analyzing cohort data with multiple potential reference groups. We analyzed the association between radiation exposure and incidence of first primary solid cancer among 105,444 participants of the Life Span Study (Hiroshima and Nagasaki, Japan, 1958-2009). Potential reference groups included zero-dose survivors at different ground distances from the hypocenter (internal) and city residents who were not in either city at the time of the bombings (external). DS02R1 weighted absorbed colon doses were estimated by the DS02 dosimetry system. Piecewise constant hazard models estimated excess relative risks of first primary solid cancer. We focused on sex-averaged excess relative risks and the shape of the dose-response curve. A model with internal standardization provided a sex-averaged excess relative risk of 0.510, 95% confidence interval: (0.414, 0.612) per gray of weighted absorbed colon dose, as well as strong evidence of a curvilinear dose response among males (P=0.008). Selection of not-in-city residents as the reference group resulted in a larger excess relative risk of 0.560, 95% confidence interval: (0.467, 0.657) per gray, and reduced evidence of a curvilinear dose response among males (P=0.042). These differences were particularly apparent at weighted absorbed colon doses <1 gray. In cohort studies, selection of an appropriate reference group requires understanding of the nature of unmeasured confounding to which the results could be sensitive.

869P - Modeling of Tumor Kinetics and Overall Survival to Identify Predictive Factors for Efficacy of Durvalumab in Patients with Urothelial Carcinoma (UC)

Background: Durvalumab is a human mAb that binds to PD-L1 and blocks its interaction with PD-1 and CD80. The objectives of this analysis were to describe the longitudinal tumor size profiles, identify factors predicting tumor growth and regression, and associate tumor kinetics with overall survival (OS). Methods: Longitudinal tumor size and OS data obtained from UC patients (Study 1108; NCT# CD-ON-MEDI4736-1108) who received durvalumab were analyzed using a nonlinear mixed effect model that describe tumor growth, tumor killing, and delay in immune response leading to tumor killing. An OS model was developed by linking model-predicted tumor size over time to survival hazard in a constant hazard model. Potential predictive factors of tumor growth and regression, as well as survival were evaluated in a multivariate covariate analysis in the tumor kinetic and OS model, respectively. Results: Tumor kinetic and OS models adequately described the longitudinal tumor size and survival data from UC patients. The most influential factor associated with more rapid tumor growth was high baseline neutrophil-to-lymphocyte ratio (NLR), while lymph node disease was associated with decreased growth rate. Tumor (TC) or immune cell PD-L1 expression (IC), baseline tumor size and liver metastasis were identified as predictive factors for tumor killing. Simulations showed increased response rates with higher TC and/or IC (by 6/9%, and 18/24%, with 25% and 50% cutoff for TC/IC, respectively). After accounting for tumor response, the risk of death decreased with higher TC/IC and lower baseline hemoglobin and albumin levels, while liver metastasis, lymph node disease, and prior carboplatin treatment were associated with higher risk. Conclusions: Tumor kinetic modeling identified factors that predict tumor growth and shrinkage following durvalumab therapy in UC patients, and permits investigation of predictive biomarker strategies considering confounding factors. Joint modeling that associates predicted tumor kinetics with OS allows model-based extrapolation of missing data and evaluation of other factors influencing OS after accounting for change in tumor size over time. Clinical trial identification: NCT01693562 (September 14, 2012) Legal entity responsible for the study: MedImmune Funding: MedImmune Disclosure: Y. Zheng: Corporate sponsored research: MedImmune, Shareholder: Roche, MedImmune, Employee: MedImmune. X. Jin: Employee MedImmune and shareholder AstraZeneca. R. Narwal: Employee and shareholder MedImmune. C-Y. D Jin: Employee and stock holder of AstraZeneca. A. Gupta: Employment MedImmune, shareholder AstraZeneca + Bristol-Myers Squibb. Y. Ben, P. Mukhopadhyay: Employee and shareholder AstraZeneca. B. Higgs, L. Roskos: Employment MedImmune, shareholder AstraZeneca.

L0 Regularization for the Estimation of Piecewise Constant Hazard Rates in Survival Analysis

In a survival analysis context, we suggest a new method to estimate the piecewise constant hazard rate model. The method provides an automatic procedure to find the number and location of cut points and to estimate the hazard on each cut interval. Estimation is performed through a penalized likelihood using an adaptive ridge procedure. A bootstrap procedure is proposed in order to derive valid statistical inference taking both into account the variability of the estimate and the variability in the choice of the cut points. The new method is applied both to simulated data and to the Mayo Clinic trial on primary biliary cirrhosis. The algorithm implementation is seen to work well and to be of practical relevance.

Artificial Neural Network Model for Predicting Lung Cancer Survival

The object of our present study is to develop a piecewise constant hazard model by using an Artificial Neural Network (ANN) to capture the complex shapes of the hazard functions, which cannot be achieved with conventional survival analysis models like Cox proportional hazard. We propose a more convenient approach to the PEANN created by Fornili et al. to handle a large amount of data. In particular, it provides much better prediction accuracies over both the Poisson regression and generalized estimating equations. This has been demonstrated with lung cancer patient data taken from the Surveillance, Epidemiology and End Results (SEER) program. The quality of the proposed model is evaluated by using several error measurement criteria.

An optimized approach for right atrial flutter ablation: a post hoc analysis of the AURUM 8 study.

Radiofrequency catheter ablation of typical atrial flutter can vary largely in duration from patient to patient. The purpose of this work was to determine optimal combination of ablation settings leading to the highest procedural efficacy. Our retrospective multivariate analysis comprised 448 patients undergoing atrial flutter ablation with nonirrigated 8-mm catheters at 19 clinical centers. Four procedural variables were included in the prognostic model: preset maximum temperature, preset maximum power, catheter-tip material (gold vs. platinum-iridium), and ablation technique (maximum voltage-guided vs. conventional anatomical approach). Univariate and multivariate analyses were performed using the logistic regression (for acute ablation success) and Cox constant proportional hazard models (for cumulative ablation time). Significant multivariate predictors of acute ablation success were a higher preset maximum temperature (odds 1.083 per 1°C, P < 0.05) and gold-tip catheter (odds 2.096, P < 0.05). Predictors of cumulative ablation time were the maximum voltage-guided ablation technique (hazard ratio 1.856, P < 0.001), higher preset maximum temperature (hazard ratio 1.039 per 1°C, P < 0.001), and gold-tip catheter (hazard ratio 1.225, P < 0.05). The combination of optimal settings (70°C, 70W, gold-tip catheter, maximum voltage-guided technique) increased the acute success rate from 91.7% (for the entire study cohort) to 100%, and reduced median cumulative ablation time from 8.3 to 4.3min, median total procedure duration from 76 to 55min, and median fluoroscopy time from 14 to 7min. The combination of maximum voltage-guided gold-tip ablation at 70°C and 70W was associated with 100% ablation success and minimal ablation times for nonirrigated ablation of atrial flutter.

Exploring Parameter Relations for Multi-Stage Models in Stage-Wise Constant and Time Dependent Hazard Rates

Summary Single cohort stage-frequency data are considered when assessing the stage reached by individuals through destructive sampling. For this type of data, when all hazard rates are assumed constant and equal, Laplace transform methods have been applied in the past to estimate the parameters in each stage-duration distribution and the overall hazard rates. If hazard rates are not all equal, estimating stage-duration parameters using Laplace transform methods becomes complex. In this paper, two new models are proposed to estimate stage-dependent maturation parameters using Laplace transform methods where non-trivial hazard rates apply. The first model encompasses hazard rates that are constant within each stage but vary between stages. The second model encompasses time-dependent hazard rates within stages. Moreover, this paper introduces a method for estimating the hazard rate in each stage for the stage-wise constant hazard rates model. This work presents methods that could be used in specific types of laboratory studies, but the main motivation is to explore the relationships between stage maturation parameters that, in future work, could be exploited in applying Bayesian approaches. The application of the methodology in each model is evaluated using simulated data in order to illustrate the structure of these models.