Counting Process Approach Research Articles

Quantile regression based on the counting process approach under dependent truncated data

This paper focuses on analysing dependent truncated data. To address this, we draw inspiration from some literatures and employ the Archimedean copula model to establish a correlation between the truncation time and the survival time. Building on this, we refer to the U-statistics and the copula-graphic method to estimate the association parameter and the survival function. Subsequently, we proceed to build a quantile regression model and develop an estimation procedure for the quantile regression parameters using the counting process method. To further validate the efficacy of our approach, we conduct simulation experiments with specific settings of quantiles and correlations. In conclusion, we apply our method to analyse two datasets: one pertaining to HIV transfusion infections and the other related to retirement centres.

Time variation of high-risk groups for liver function deteriorations within fluctuating long-term liver function after hepatic radiotherapy in patients with hepatocellular carcinoma

PurposeThe purpose of this study is to find essential risk factors associated with liver function (LF) deteriorations within fluctuating long-term LF and their time-varying effects in patients with hepatocellular carcinoma (HCC) receiving hepatic radiotherapy and to identify high-risk groups for adverse LF deteriorations and their changes over time in facilitating the prevention of hepatic decompensation and the improvement of survival.Materials and methodsA total of 133 HCC patients treated by hepatic radiotherapy were enrolled. A study design was conducted to convert posttreatment long-term LF with fluctuating levels over time to recurrent LF events using defined upgrades in a grading scale. The hazard ratios (HR) of pretreatment biochemical, demographic, clinical, and dosimetric factors in developing posttreatment LF events were estimated using the Cox model. Methodologies of the counting process approach, robust variance estimation, goodness-of-fit testing based on the Schoenfeld residuals, and time-dependent covariates in survival analysis were employed to handle the correlation within subjects and evaluate the time-varying effects during long-term follow-up.ResultsBaseline LF score before radiotherapy and gender were significant factors. Initial HR in developing LF events was 1.17 (95% CI 1.11–1.23; P < 0.001) for each increase of baseline LF score and kept almost constant over time (HR, 1.00; 95% CI 1.00–1.01; P = 0.065). However, no difference was observed regarding initial hazards for gender (HR, 1.00; 95% CI 0.64–1.56; P = 0.994), but the hazard for women got higher monthly over time compared with men (HR, 1.04; 95% CI 1.01–1.07; P = 0.006).ConclusionsHigh-risk groups for adverse LF deteriorations after hepatic radiotherapy may change over time. Patients with poor baseline LF are vulnerable from the beginning. Women require prevention strategies and careful monitoring for deteriorations at a later stage.

SURVIVAL ANALYSIS FOR RECURRENT EVENT DATA USING COUNTING PROCESS APPROACH: APPLICATION TO DIABETICS

Survival analysis is a branch of statistics for analyzing the duration of time until one or more events occur. Time to recurrence of diabetics including survival data. Diabetes can’t be cured but it can be controlled. Diabetics who don’t maintain their health and lifestyle will experience recurrence. Factors thought to influence the recurrence of diabetics are internal factors such as genetics and external factors such as lifestyle. The recurrence time of an object includes recurrent events because each object can experience the same recurrent event during the follow-up. One of the analysis to determine factors that are thought to influence the recurrence time of diabetics is survival analysis. Survival data can be modeled into a regression model if the survival time of an object is influenced by other factors. One of the regression models for survival data is Cox regression. One of the Cox regression models for recurrent event data is the AG model which uses a counting process approach. This study used data on the recurrence of diabetics at MH Thamrin Cileungsi Hospital. Based on data analysis, factors that influence the recurrence of diabetics are age, gender, and type of complication.

ANALISIS SURVIVAL PADA DATA KEJADIAN BERULANG MENGGUNAKAN PENDEKATAN COUNTING PROCESS

Asthma is a disorder that attacks the respiratory tract and causes bronchial hyperactivity to various stimuli characterized by recurrent episodic symptoms such as wheezing, coughing, shortness of breath, and heaviness in the chest. Asthma sufferers will experience exacerbations, namely episodes of asthma recurrence which gradually worsens progressively accompanied by the same symptoms. The length of time a person experiences an exacerbation can be influenced by various factors. To analyze this, the Cox regression model can be used which is within the scope of survival analysis where time is the dependent variable. In the survival analysis, asthma exacerbations were identical/recurrent events where the individual experienced the event more than once during the study. If the survival data contains identical/recurrent events, the analysis uses a counting process approach. Counting Process is an approach used to deal with survival data with identical recurrent events, meaning that recurrences are caused by the same thing, which in this case is the narrowing of the bronchioles in asthmatics. The purpose of this study was to determine the factors that cause asthma exacerbations by using a counting process approach as a data treatment for recurrent events at Diponegoro National Hospital. Based on the results of the analysis, the factors that influence the length of time a patient experiences an exacerbation are the age, gender, and type of cases

Shared Frailty Model for Recurrent Event Competing Risks Data Using Averaged Counting Process Approach

Shared Frailty Model for Recurrent Event Competing Risks Data Using Averaged Counting Process Approach

Parameter Estimation for Additive Hazard Model Recurrent Event Using Counting Process Approach

The Cox regression model is widely used for survival data analysis. The Cox model requires a proportional hazard. If the proportional hazard assumption is doubtful, then the additive hazard model can be used, where the covariates act in an additively to the baseline hazard function. If the observed survival time is more than once for one individual during the observation, it is called a recurrent event. The additive hazard model measures risk difference to the effect of a covariate in absolutely, while the proportional hazards model measure hazard ratio in relatively. The risk coefficients estimation in the additive hazard model mimics the multiplicative hazard model, using partial likelihood methods. The derivation of these estimators, outlined in the technical notes, is based on the counting process approach. The counting process approach was first developed by Aalen on 1975 which combines elements of stochastic integration, martingale theory and counting process theory. The method is applied to study about the effect of supplementation on infant growth and development. Based on the processing results, the factors that affect the growth and development of the infant are gender, treatment and mother's education.

Confirmatory adaptive group sequential designs for single-arm phase II studies with multiple time-to-event endpoints.

Existing methods concerning the assessment of long-term survival outcomes in one-armed trials are commonly restricted to one primary endpoint. Corresponding adaptive designs suffer from limitations regarding the use of information from other endpoints in interim design changes. Here we provide adaptive group sequential one-sample tests for testing hypotheses on the multivariate survival distribution derived from multi-state models, while making provision for data-dependent design modifications based on all involved time-to-event endpoints. We explicitly elaborate application of the methodology to one-sample tests for the joint distribution of (i) progression-free survival (PFS) and overall survival (OS) in the context of an illness-death model, and (ii) time to toxicity and time to progression while accounting for death as a competing event. Large sample distributions are derived using a counting process approach. Small sample properties are studied by simulation. An already established multi-state model for non-small cell lung cancer is used to illustrate the adaptiveprocedure.

4180 CD4 count is a prognostic marker in persons living with HIV and non-small cell lung cancer in the Bronx

OBJECTIVES/GOALS: There is a high burden of lung cancer in persons living with HIV (PLWH). The role that HIV status, by levels of immune function and viral load, has on survival from lung cancer is not fully understood. The study’s objectives were to assess 1) the association of HIV with survival in non-small cell lung cancer (NSCLC) and 2) prognostic factors in PLWH with NSCLC. METHODS/STUDY POPULATION: Participants were from a cohort of lung cancer patients diagnosed between 2004-2017 in the Bronx, NY, with vital status ascertainment at least annually. We compared survival from NSCLC diagnosis between HIV-negative patients (HIV-, N = 2881) and PLWH (N = 88), using Cox regression, accounting for clinical and sociodemographic factors including smoking status. In three separate comparisons to HIV-, PLWH were dichotomized by CD4 count (&lt;200 vs. ≥200 cells/μL), CD4/CD8 ratio (median, &lt;0.43 vs. ≥0.43) and HIV viral load (VL) suppression (&lt;75 vs. ≥75 copies/mL). In PLWH only, we assessed the relationships of CD4 count, CD4/CD8 ratio, and VL at diagnosis with survival adjusting for age, sex, and cancer stage. CD4 count and CD4/CD8 ratio were also examined as time-varying variables using a counting process approach. RESULTS/ANTICIPATED RESULTS: PLWH were younger (median 56 years, IQR 51-52 vs. 68, IQR 60-76) and more likely to be current smokers (58% vs. 37%) at diagnosis than HIV- patients. Median survival was lower in PLWH [1.1 years, 95% confidence interval (95%CI): 0.6-1.3] than in HIV- [1.6 (1.5-1.7)]. Survival comparing PLWH with higher CD4/CD8 to HIV- was similar [hazard ratio (HR), 95%CI: 0.63 (0.37-1.07)], but those with lower CD4/CD8 experienced worse survival (HR = 1.74, 95%CI: 1.07-3.89). Among PLWH, having a CD4 count &lt; 200 cells/μL was associated with over twice the risk of death compared to those with CD4 ≥ 200 cells/μL (HR = 2.37, 95%CI: 1.14-4.92). VL and CD4/CD8 ratio were not associated with survival. Lower time-updated CD4 count was also associated with worse survival (HR = 2.19 for CD4 &lt;200 vs. &gt;200 cells/μL, 95%CI: 1.16-4.13). DISCUSSION/SIGNIFICANCE OF IMPACT: Among persons with NSCLC, CD4/CD8 ratio nearest diagnosis was shown to distinguish mortality risk in PLWH compared with HIV- patients. In addition, PLWH with low CD4 had worse prognosis than PLWH who had higher CD4 counts. These results suggest HIV immune status to be an essential component influencing survival in lung cancer.

A Counting Process Approach for Trend Assessment of Drought Condition

This paper discusses some methodological aspects of the historical analysis of drought, particularly the trend assessment. The Standardized Evapotranspiration Index (SPEI) is widely used as a measure of drought condition. Since different SPEI thresholds allow classifying the risk into moderate, severe, and extreme, the drought occurrence becomes a counting process. In this framework, would a statistical trend test based on a Non-Homogeneous Poisson Process (NHPP) give a similar result of the nonparametric Mann–Kendall (M-K) test? In this paper, we demonstrate that the NHPP approach is able to characterize the information given by the classical M-K approach in term of drought risk classes. Furthermore, we show how it can be used to reinforce the framework of drought trend analysis in combination with a standard non-parametric approach. At a global scale, we find that: (1) areas under increasing risk of drought identified by the NHPP approach are considerably larger in comparison to those identified by M-K; and (2) the results of the two tests are different during crucial periods such as hydrological droughts in winter and spring.

URINARY INCONTINENCE AND DEPRESSION: A LONGITUDINAL ANALYSIS IN MALES

Introduction Urinary incontinence (UI) is a prevalent problem in retirement-aged males that has long been suspected to have significant social consequences. UI has been demonstrated as a significant risk factor for developing depression in retirement-aged females, but this association has been relatively unexplored in males of the same age group. Methods Study Design and Setting: A secondary data analysis was performed on the Health and Retirement Study cohort, a study of adults 51-61 years at recruitment when the first wave was assembled in 1992; all participants were followed up every two years. Information on UI is available from 1996 onwards. Data from biennial follow up of men from 1996 until 2014 was used. Men with probable depression at baseline were excluded from analysis. Variables The outcome of interest was probable depression, defined as a score of ≥3 on the 8-item Center for Epidemiologic Studies-Depression scale. UI was defined based on questions about experience of urine loss. Statistical Analysis Data was then analyzed using a time-dependent recurrent event survival analysis by Cox regression employing the counting process approach. Hazard estimates were adjusted for demographic, psychosocial and health status variables found to confound the association between UI and the outcome of interest. In the final multiple-failures-per-subject model, all variables were treated as time-dependent with the exception of race and ethnicity. As a test of our methodology, we ran the previously described analysis using a female sample and were able to replicate a previously reported association between UI and developing depression. Results Our final model included 8,897 men. Notable baseline characteristics of the study population include 8% of men reporting incontinence in the past year. Additionally, 0.6% were living in a nursing home at entry into the study. A history of psychiatric disease was reported by 7%. Time-dependent recurrent event survival analysis by Cox regression employing the counting process approach yielded an unadjusted hazard ratio of 1.9 (95% CI: 1.7, 2.0). Adjusting for these confounders in a time-dependent fashion yielded a hazard ratio of 1.3, (95% CI: 1.1, 1.4). Conclusions Urinary incontinence is positively associated with incident depression in previously non-depressed retirement-age men. Increased awareness on the part of treating physicians to the benefit of patient's psychosocial welfare is warranted. Limitations included using surrogate probable depression using CES-D score over three instead of clinical diagnosis and many participants were excluded based on incomplete data. Additionally, urinary incontinence was assessed based on previous 12 months, whereas depression only based on the previous week making a temporal interaction more difficult to assess. This research was funded by Not applicable PDF: http://submissions.mirasmart.com/Verify/AAGP2019/Original/AAGP2019-000481/AAGP2019-000481_Fig1.pdf

The Cumulative Incidence of Self-Reported Suicide-Related Thoughts and Attempts in Young Canadians.

To estimate the cumulative incidence of self-reported suicide-related thoughts (SRTs) and suicide attempts (SAs) in males and females from 11 to 25 years of age in Canada. A cohort study was conducted by linking cycles 2 to 8 from the National Longitudinal Survey of Children and Youth, a representative survey of Canadians aged 11 to 25 years conducted from 1996 to 2009. The 11- to 25-year cumulative incidence of self-reported SRTs and SAs (with suicidal intent) was estimated in males and females using a novel application of a counting process approach to account for discontinuous risk intervals between survey cycles. The risk of SRTs was 29% (95% confidence interval [CI], 26% to 31%) in females and 19% (95% CI, 16% to 23%) in males. The risk of SAs was 16% (95% CI, 14% to 19%) in females and 7% (95% CI, 6% to 8%) in males. Over 70% of SRTs and SAs first occur between 11 and 16 years of age and 30% between 11 and 13 years of age, respectively. The risk of SRTs and SAs is high in young Canadians, with most events first occurring in early to mid-adolescence and possibly earlier. Females are at a higher risk compared to males. This research underscores the need for better longitudinal surveillance of SRTs and SAs in the population. A counting process framework could be useful for future research using existing longitudinal surveys suffering from design limitations relating to gaps in respondent follow-up. Furthermore, these findings have implications for younger SRT and SA risk management by clinicians and earlier implementation of suicide prevention programs.

Mixture regression models for the gap time distributions and illness-death processes.

The aim of this study is to provide an analysis of gap event times under the illness-death model, where some subjects experience "illness" before "death" and others experience only "death." Which event is more likely to occur first and how the duration of the "illness" influences the "death" event are of interest. Because the occurrence of the second event is subject to dependent censoring, it can lead to bias in the estimation of model parameters. In this work, we generalize the semiparametric mixture models for competing risks data to accommodate the subsequent event and use a copula function to model the dependent structure between the successive events. Under the proposed method, the survival function of the censoring time does not need to be estimated when developing the inference procedure. We incorporate the cause-specific hazard functions with the counting process approach and derive a consistent estimation using the nonparametric maximum likelihood method. Simulations are conducted to demonstrate the performance of the proposed analysis, and its application in a clinical study on chronic myeloid leukemia is reported to illustrate its utility.

Varying postresection lactate dehydrogenase with overall survival of early stage pancreatic cancer patients

Several previously published studies revealed a hazardous role of pretreatment lactate dehydrogenase (LDH) in survival of advanced or metastatic pancreatic cancer (PC) patients. Nevertheless, in early stage PC patients who are eligible for curative resection, the prognostic role of postresection LDH has never been discussed. In this study, we aimed to explore the prognostic significance of varying postresection LDH among early stage PC patients. In total, 80 PC patients who received curative resection were retrospectively selected from a population-based electronic inpatients database which originated from Shanghai, China. A dynamic survival analysis method, counting process approach in combination with the multiple failure-time Cox model, was applied to evaluate the association between postresection LDH and OS. The multiple failure-time Cox model found that age, resection modality, and postresection LDH were significantly associated with OS: an elevated LDH (defined as > 250 U/L) was related to 2.93 (95% CI: 1.26–6.79) folds of death hazard. Further analysis disclosed an identifiable dose–response association between LDH and OS: compared with LDH≤155 U/L, the HRs for 155 U/L < LDH < 196 U/L, and LDH≥196 U/L were 2.07 (95% CI: 0.88–4.88) and 3.15 (95% CI: 1.30–7.59), respectively. Our study results suggest that postresection LDH is a prominent prognostic factor in this group of early stage PC patients. Maintaining normally ranged LDH after resection might bring about survival benefit in early stage PC patients.

Quantile regression based on counting process approach under semi-competing risks data

In this paper, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. The estimation of quantile regression parameters for the non-terminal event is complicated. We cannot make inference on the non-terminal event without extra assumptions. Thus, we handle this problem by assuming that the joint distribution of the terminal event and the non-terminal event follows a parametric copula model with unspecified marginal distributions. We use the stochastic property of the martingale method to estimate the quantile regression parameters under semi-competing risks data. We also prove the large sample properties of the proposed estimator, and introduce a model diagnostic approach to check model adequacy. From simulation results, it shows that the proposed estimator performs well. For illustration, we apply our proposed approach to analyze a real data.

Kinetics of postdiagnosis platelet count with overall survival of pancreatic cancer: a counting process approach.

The association between long‐term variation of postdiagnosis platelets and survival of pancreatic cancer (PC) has never been discussed by using dynamic survival analysis method. In this retrospective study, we analyzed 311 histologically confirmed PC patients identified from a mega population‐based electronic inpatients database from 2012 to 2013 in China. Counting process approach was applied to restructure the original survival data, the association between post‐diagnosis platelet count and overall survival (OS) of PC was evaluated by multiple failure‐time Cox proportional hazards model. After counting process adjustment, multiple failure‐time Cox proportional hazards model revealed that, regardless of the treatment modalities PC patients received, postdiagnosis thrombocytopenia was prominently associated with OS, compared with PC patients with normally ranged platelet count, the HRs ranged from 2.04 (95% CI: 1.14–3.67) to 10.82 (95% CI: 2.63–44.54), and this inverse association was robust based on further sensitivity analysis. On the contrary, the association between thrombocytosis and OS of PC tended to be inconclusive. Our findings suggested that postdiagnosis thrombocytopenia was associated with significantly compromised survival among PC patients from this large retrospective cohort. Underlying mechanisms behind this association should be further investigated.

The Impact of Media Reporting on the Emergence of Charcoal Burning Suicide in Taiwan

We investigated the association of the intensity of newspaper reporting of charcoal burning suicide with the incidence of such deaths in Taiwan during 1998–2002. A counting process approach was used to estimate the incidence of suicides and intensity of news reporting. Conditional Poisson generalized linear autoregressive models were performed to assess the association of the intensity of newspaper reporting of charcoal burning and non-charcoal burning suicides with the actual number of charcoal burning and non-charcoal burning suicides the following day. We found that increases in the reporting of charcoal burning suicide were associated with increases in the incidence of charcoal burning suicide on the following day, with each reported charcoal burning news item being associated with a 16% increase in next day charcoal burning suicide (p<.0001). However, the reporting of other methods of suicide was not related to their incidence. We conclude that extensive media reporting of charcoal burning suicides appears to have contributed to the rapid rise in the incidence of the novel method in Taiwan during the initial stage of the suicide epidemic. Regulating media reporting of novel suicide methods may prevent an epidemic spread of such new methods.

Additive hazards models for gap time data with multiple causes

Recurrent event data with multiple causes are often observed in biomedical studies. The additive hazards model describes a different aspect of the association between covariates and the failure time than does the proportional hazards model. In this paper, we introduce additive hazards models for the analysis of gap time data of recurrent events with multiple causes. We estimate the regression parameter vector and cumulative baseline cause specific hazard rate function using counting process approach. Asymptotic properties of the estimators are studied. The proposed model is applied to the kidney dialysis data given in Lawless (2003). A simulation study is carried out to assess the performance of the estimates.

Optimal periodic condition inspection and replacement policy for a binary monotone system using a counting process approach

This paper considers a binary monotone system consisting of n components. The system failure process is given by a counting process whose intensity at all times is adapted to information about the system state and at periodic inspection times it is adapted also to information about the component states and their underlying conditions. A parametric policy is introduced prescribing replacement of the entire system either when it enters the failed state, which is observed immediately, or when upon an inspection the intensity is found to have reached a predefined threshold. Costs are associated with inspections, replacements, and system failures, and the periodic inspection interval and intensity threshold that jointly minimize the expected long run cost per unit of time are determined. A numerical example is also included.

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Permutation methods in relative risk regression models

In this paper, we develop a weighted permutation (WP) method to construct confidence intervals for regression parameters in relative risk regression models. The WP method is a generalized permutation approach. It constructs a resampled history which mimics the observed history for individuals under study. Inference procedures are based on studentized score statistics that are insensitive to the forms of the relative risk function. This makes the WP method appealing in the general framework of the relative risk regression model. First-order accuracy of the WP method is established using counting process approach with a partial likelihood filtration. A simulation study indicates that the method typically improves accuracy over asymptotic confidence intervals.