‘Modeling and Analysis of Competing Risks Data’

there has been much research on analyzing various forms of competing risks data. Nevertheless, there are several occasions in survival studies, where the existing models and methodologies are inadequate for the analysis competing risks data. ldentifiabilty problem and various types of and censoring induce more complications in the analysis of competing risks data than in classical survival analysis. Parametric models are not adequate for the analysis of competing risks data since the assumptions about the underlying lifetime distributions may not hold well. Motivated by this, in the present study. we develop some new inference procedures, which are completely distribution free for the analysis of competing risks data.

Longitudinal outcomes of high-risk human papillomavirus (HPV) infections as competing-risks events following cervical HPV test at baseline visit in the *NIS-LAMS** cohort

Background: The complex natural history of human papillomavirus (HPV) infections following a single HPV test can be modeled as competing-risks events (i.e., no-, transient- or persistent infection) in a longitudinal setting. The covariates associated with these compet ng events have not been previously assessed using competing-risks regression models. Objectives: To gain further insights in the outcomes of cervical HPV infections, we used univariate- and multivariate competing-risks regression models to assess the covariaies associated with these competing events. Study Design and Methods: Covariates associated with three competing outcomes (no-, transient- or persistent HR-HPV infection) were analysed in a sub-cohort of 1,865 women prospectively followed-up in the NIS (n = 3,187) and LAMS Study (n = 12,114). Results: In multivariate competing-risks models (with two other outcomes as competing events), permanently HR-HPV negative outcome was significantly predicted only by the clearance of ASCUS+Pap during FU, while three independent covariates predicted transient HR-HPV infections: i) number of recent (< 12 months) sexual partners (risk increased), ii) previous Pap screening history (protective), and history of previous CIN (increased risk). The two most powerful predictors of persistent HR-HPV infections were persistent ASCUS+Pap (risk increased), and previous Pap screening history (protective). In pair-wise comparisons, number of recent sexual partners and previous CIN history increase the probability of transient HR-HPV infection against the HR-HPV negative competing event, while previous Pap screening history is protective. Persistent ASCUS+Pap during FU and no previous Pap screening history are significantly associated with the persistent HR-HPV outcome (compared both with i) always negative, and ii) transient events), whereas multiparity is protective. Conclusions: Different covariates are associated with the three main outcomes of cervical HPV infections. The most significant covariates of each competing events are probably distinct enough to enable constructing of a risk-profile for each main outcome.

Covariates of high-risk human papillomavirus (HPV) infections are distinct for incident CIN1, CIN2 and CIN3 as disclosed by competing-risks regression models

Background: In addition to the oncogenic human papillomavirus (HPV), several cofactors are needed in cervical carcinogenesis, but whether the HPV covariates associated with incident i) CIN1 are different from those of incident ii) CIN2 and iii) CIN3 needs further assessment. Objectives: To gain further insights into the true biological differences between CIN1, CIN2 and CIN3, we assessed HPV covariates associated with incident CIN1, CIN2, and CIN3. Study Design and Methods: HPV covariates associated with progression to CIN1, CIN2 and CIN3 were analysed in the combined cohort of the NIS (n = 3,187) and LAMS study (n = 12,114), using competing-risks regression models (in panel data) for baseline HR-HPV-positive women (n = 1,105), who represent a sub-cohort of all 1,865 women prospectively followed-up in these two studies. Results: Altogether, 90 (4.8%), 39 (2.1%) and 14 (1.4%) cases progressed to CIN1, CIN2, and CIN3, respectively. Among these baseline HR-HPV-positive women, the risk profiles of incident GIN I, CIN2 and CIN3 were unique in that completely different HPV covariates were associated with progression to CIN1, CIN2 and CIN3, irrespective which categories (non-progression, CIN1, CIN2, CIN3 or all) were used as competing-risks events in univariate and multivariate models. Conclusions: These data confirm our previous analysis based on multinomial regression models implicating that distinct covariates of HR-HPV are associated with progression to CIN1, CIN2 and CIN3. This emphasises true biological differences between the three grades of GIN, which revisits the concept of combining CIN2 with CIN3 or with CIN1 in histological classification or used as a common end-point, e.g., in HPV vaccine trials.

Multilevel competing risk models to evaluate the risk of nosocomial infection

Introduction Risk factor analyses for nosocomial infections (NIs) are complex. First, due to competing events for NI, the association between risk factors of NI as measured using hazard rates may not coincide with the association using cumulative probability (risk). Second, patients from the same intensive care unit (ICU) who share the same environmental exposure are likely to be more similar with regard to risk factors predisposing to a NI than patients from different ICUs. We aimed to develop an analytical approach to account for both features and to use it to evaluate associations between patient- and ICU-level characteristics with both rates of NI and competing risks and with the cumulative probability of infection. Methods We considered a multicenter database of 159 intensive care units containing 109,216 admissions (813,739 admission-days) from the Spanish HELICS-ENVIN ICU network. We analyzed the data using two models: an etiologic model (rate based) and a predictive model (risk based). In both models, random effects (shared frailties) were introduced to assess heterogeneity. Death and discharge without NI are treated as competing events for NI. Results There was a large heterogeneity across ICUs in NI hazard rates, which remained after accounting for multilevel risk factors, meaning that there are remaining unobserved ICU-specific factors that influence NI occurrence. Heterogeneity across ICUs in terms of cumulative probability of NI was even more pronounced. Several risk factors had markedly different associations in the rate-based and risk-based models. For some, the associations differed in magnitude. For example, high Acute Physiology and Chronic Health Evaluation II (APACHE II) scores were associated with modest increases in the rate of nosocomial bacteremia, but large increases in the risk. Others differed in sign, for example respiratory vs cardiovascular diagnostic categories were associated with a reduced rate of nosocomial bacteremia, but an increased risk. Conclusions A combination of competing risks and multilevel models is required to understand direct and indirect risk factors for NI and distinguish patient-level from ICU-level factors.

Nonparametric Estimation of Survivor Function in Bivariate Competing Risk Models’

So far, in the bivariate set up, the analysis of lifetime (failure time) data with multiple causes of failure is done by treating each cause of failure separately. with failures from other causes considered as independent censoring. This approach is unrealistic in many situations. For example, in the analysis of mortality data on married couples one would be interested to compare the hazards for the same cause of death as well as to check whether death due to one cause is more important for the partners’ risk of death from other causes. In reliability analysis. one often has systems with more than one component and many systems. subsystems and components have more than one cause of failure. Design of high-reliability systems generally requires that the individual system components have extremely high reliability even after long periods of time. Knowledge of the failure behaviour of a component can lead to savings in its cost of production and maintenance and. in some cases, to the preservation of human life. For the purpose of improving reliability. it is necessary to identify the cause of failure down to the component level. By treating each cause of failure separately with failures from other causes considered as independent censoring, the analysis of lifetime data would be incomplete. Motivated by this. we introduce a new approach for the analysis of bivariate competing risk data using the bivariate vector hazard rate of Johnson and Kotz (1975).

Competing regression models for longitudinal data

The choice of an appropriate family of linear models for the analysis of longitudinal data is often a matter of concern for practitioners. To attenuate such difficulties, we discuss some issues that emerge when analyzing this type of data via a practical example involving pretestposttest longitudinal data. In particular, we consider log-normal linear mixed models (LNLMM), generalized linear mixed models (GLMM), and models based on generalized estimating equations (GEE). We show how some special features of the data, like a nonconstant coefficient of variation, may be handled in the three approaches and evaluate their performance with respect to the magnitude of standard errors of interpretable and comparable parameters. We also show how different diagnostic tools may be employed to identify outliers and comment on available software. We conclude by noting that the results are similar, but that GEE-based models may be preferable when the goal is to compare the marginal expected responses.

Impact of age and comorbidities on long-term survival of patients with high-risk prostate cancer treated with radical prostatectomy: a multi-institutional competing-risks analysis

Survival after surgical treatment using competing-risk analysis has been previously examined in patients with prostate cancer (PCa). However, the combined effect of age and comorbidities has not been assessed in patients with high-risk PCa who might have heterogeneous rates of competing mortality despite the presence of aggressive disease.

Semiparametric Methods for Semi-competing Risks Problem with Censoring and Truncation

Studies of chronic life-threatening diseases often involve both mortality and morbidity. In observational studies, the data may also be subject to administrative left truncation and right censoring. Since mortality and morbidity may be correlated and mortality may censor morbidity, the Lynden-Bell estimator for left truncated and right censored data may be biased for estimating the marginal survival function of the non-terminal event. We propose a semiparametric estimator for this survival function based on a joint model for the two time-to-event variables, which utilizes the gamma frailty specification in the region of the observable data. Firstly, we develop a novel estimator for the gamma frailty parameter under left truncation. Using this estimator, we then derive a closed form estimator for the marginal distribution of the non-terminal event. The large sample properties of the estimators are established via asymptotic theory. The methodology performs well with moderate sample sizes, both in simulations and in an analysis of data from a diabetes registry.

The Impact of income support programs on transitions to employment

The income support programs are created with the purpose of fighting both, the poverty trap and the inactivity trap. The balance between both is fragile and hard to find. Thus, the goal of this work is to contribute to solve this issue by finding how income support programs, particularly the Portuguese RSI, affect transitions to employment. This is made through duration analysis, namely using Cox and Competing Risks models. A particular feature is introduced in this work as it incorporates the possibility of Defective Risks. The estimated hazard elasticity with respect to the amount of RSI received for individuals who move to employment is -0,41. More than a half of RSI receivers stays for more than a year and the probability of never leaving to employment is 44%. The results appear to indicate that RSI has affected negatively transitions to employment.

Modelling and Analysis of Recurrent Event Data with Multiple Causes

This thesis Entitled “modelling and analysis of recurrent event data with multiple causes.Survival data is a term used for describing data that measures the time to occurrence of an event.In survival studies, the time to occurrence of an event is generally referred to as lifetime.Recurrent event data are commonly encountered in longitudinal studies when individuals are followed to observe the repeated occurrences of certain events. In many practical situations, individuals under study are exposed to the failure due to more than one causes and the eventual failure can be attributed to exactly one of these causes.The proposed model was useful in real life situations to study the effect of covariates on recurrences of certain events due to different causes.In Chapter 3, an additive hazards model for gap time distributions of recurrent event data with multiple causes was introduced. The parameter estimation and asymptotic properties were discussed .In Chapter 4, a shared frailty model for the analysis of bivariate competing risks data was presented and the estimation procedures for shared gamma frailty model, without covariates and with covariates, using EM algorithm were discussed. In Chapter 6, two nonparametric estimators for bivariate survivor function of paired recurrent event data were developed. The asymptotic properties of the estimators were studied. The proposed estimators were applied to a real life data set. Simulation studies were carried out to find the efficiency of the proposed estimators.

Interpreting and comparing risks in the presence of competing events

Competing events are common in medical research. Ignoring them in the statistical analysis can easily lead to flawed results and conclusions. This article uses a real dataset and a simple simulation to show how standard analysis fails and how such data should be analysed

Unemployment Duration: Competing and Defective Risks

This paper examines the determinants of unemployment duration in a competing risks framework with two destination states: inactivity and employment. The innovation is the recognition of defective risks. A polynomial hazard function is used to differentiate between two possible sources of infinite durations. The first is produced by a random process of unlucky draws, the second by workers rejecting a destination state. The evidence favors the mover-stayer model over the search model. Refinement of the former approach, using a more flexible baseline hazard function, produces a robust and more convincing explanation for positive and zero transition rates out of unemployment.