Evaluating competing adverse and beneficial outcomes using a mixture model

Competing risk models to evaluate the factors for time to loss to follow-up among tuberculosis patients at Ambo General Hospital

BACKGROUND

A major challenge for most tuberculosis programs is the inability of tuberculosis patients to complete treatment for one reason or another. Failure to complete the treatment contributes to the emergence of multidrug-resistant TB. This study aimed to evaluate the risk factors for time to loss to follow-up treatment by considering death as a competing risk event among tuberculosis patients admitted to directly observed treatment short course at Ambo General Hospital, Ambo, Ethiopia.

METHODS

Data collected from 457 tuberculosis patients from January 2018 to January 2022 were used for the analysis. The cause-specific hazard and sub-distribution hazard models for competing risks were used to model the outcome of interest and to identify the prognostic factors associated to treatment loss to follow-up. Loss to follow-up was used as an outcome measure and death as a competing event.

RESULTS

Of the 457 tuberculosis patients enrolled, 54 (11.8%) were loss to follow-up their treatment and 33 (7.2%) died during the follow up period. The median time of loss to follow-up starting from the date of treatment initiation was 4.2 months. The cause-specific hazard and sub-distribution hazard models revealed that sex, place of residence, HIV status, contact history, age and baseline weights of patients were significant risk factors associated with time to loss to follow-up treatment. The findings showed that the estimates of the covariates effects were different for the cause specific and sub-distribution hazard models. The maximum relative difference observed for the covariate between the cause specific and sub-distribution hazard ratios was 12.2%.

CONCLUSIONS

Patients who were male, rural residents, HIV positive, and aged 41 years or older were at higher risk of loss to follow-up their treatment. This underlines the need that tuberculosis patients, especially those in risk categories, be made aware of the length of the directly observed treatment short course and the effects of discontinuing treatment.

Causal inference in the face of competing events

Purpose of review

Epidemiologists frequently must handle competing events, which prevent the event of interest from occurring. We review considerations for handling competing events when interpreting results causally.

Recent findings

When interpreting statistical associations as causal effects, we recommend following a causal inference "roadmap" as one would in an analysis without competing events. There are, however, special considerations to be made for competing events when choosing the causal estimand that best answers the question of interest, selecting the statistical estimand (e.g. the cause-specific or subdistribution) that will target that causal estimand, and assessing whether causal identification conditions (e.g., conditional exchangeability, positivity, and consistency) have been sufficiently met.

Summary

When doing causal inference in the competing events setting, it is critical to first ascertain the relevant question and the causal estimand that best answers it, with the choice often being between estimands that do and do not eliminate competing events.

Methods of competing risks flexible parametric modeling for estimation of the risk of the first disease among HIV infected men

Background

Patients infected with the Human Immunodeficiency Virus (HIV) are susceptible to many diseases. In these patients, the occurrence of one disease alters the chance of contracting another. Under such circumstances, methods for competing risks are required. Recently, competing risks analyses in the scope of flexible parametric models have risen to address this requirement. These lesser-known analyses have considerable advantages over conventional methods.

Methods

Using data from Multi Centre AIDS Cohort Study (MACS), this paper reviews and applies methods of competing risks flexible parametric models to analyze the risk of the first disease (AIDS or non-AIDS) among HIV-infected patients. We compared two alternative subdistribution hazard flexible parametric models (SDH_FPM1 and SDH_FPM2) with the Fine & Gray model. To make a complete inference, we performed cause-specific hazard flexible parametric models for each event separately as well.

Results

Both SDH_FPM1 and SDH_FPM2 provided consistent results regarding the magnitude of coefficients and risk estimations compared with estimations obtained from the Fine & Gray model, However, competing risks flexible parametric models provided more efficient and smoother estimations for the baseline risks of the first disease. We found that age at HIV diagnosis indirectly affected the risk of AIDS as the first event by increasing the number of patients who experience a non-AIDS disease prior to AIDS among > 40 years. Other significant covariates had direct effects on the risks of AIDS and non-AIDS.

Discussion

The choice of an appropriate model depends on the research goals and computational challenges. The SDH_FPM1 models each event separately and requires calculating censoring weights which is time-consuming. In contrast, SDH_FPM2 models all events simultaneously and is more appropriate for large datasets, however, when the focus is on one particular event SDH_FPM1 is more preferable.

Missingness in the Setting of Competing Risks: from missing values to missing potential outcomes

Purpose of review

The setting of competing risks in which there is an event that precludes the event of interest from occurring is prevalent in epidemiological research. Unless studying all-cause mortality, any study following up individuals is subject to having a competing risk should individuals die during time period that the study covers. While there are prior papers discussing the need for competing risk methods in epidemiologic research, we are not aware of any review that discusses issues of missing data in a competing risk setting.

Recent Findings

We provide an overview of causal inference in competing risks as potential outcomes are missing, provide some strategies in dealing with missing (or misclassified) event type, and missing covariate data in competing risks. The strategies presented are specifically focused on those that may easily be implemented in standard statistical packages. There is ongoing work in terms of causal analyses, dealing with missing event type information, and missing covariate values specific to competing risk analyses.

Summary

Competing events are common in epidemiologic research. While there has been a focus on why one should conduct a proper competing risk analysis, a perhaps unrecognized issue is in terms of missingness. Strategies exist to minimize the impact of missingness in analyses of competing risks.

When to Censor?

Loss to follow-up is an endemic feature of time-to-event analyses that precludes observation of the event of interest. To our knowledge, in typical cohort studies with encounters occurring at regular or irregular intervals, there is no consensus on how to handle person-time between participants' last study encounter and the point at which they meet a definition of loss to follow-up. We demonstrate, using simulation and an example, that when the event of interest is captured outside of a study encounter (e.g., in a registry), person-time should be censored when the study-defined criterion for loss to follow-up is met (e.g., 1 year after last encounter), rather than at the last study encounter. Conversely, when the event of interest must be measured within the context of a study encounter (e.g., a biomarker value), person-time should be censored at the last study encounter. An inappropriate censoring scheme has the potential to result in substantial bias that may not be easily corrected.

Competing risks mixture model for traffic incident duration prediction

Traffic incident duration is known to result from a combination of multiple factors, including covariates such as spatial and temporal characteristics, traffic conditions, and existence of secondary accidents but also the clearance method itself. In this paper, a competing risks mixture model is used to investigate the influence of clearance methods and various covariates on the duration of traffic incidents and predict traffic incident duration. The proposed mixture model considers the uncertainty in any of five clearance methods that occurred. The probability of the clearance method is specified in the mixture by using a multinomial logistic model. Three candidate distributions, namely, generalized gamma, Weibull, and log-logistic are tested to determine the most appropriate probability density function of the parametric survival analysis model. The unobserved heterogeneity is also incorporated into the mixture model in a way that allows parameters to vary across observations based on the three candidate distributions. The methods are illustrated with incident data from Singaporean expressways from January 2010 to December 2011. Regression analysis reveals that the probability of different clearance methods and the duration of traffic incidents are both significantly affected by various factors, such as traffic conditions and incident characteristics. Results show that the proposed mixture model is better than the traditional accelerated failure time model, and it predicts traffic incident duration with reasonable accuracy, as shown by the mean average percent error.

Applying competing risks regression models: an overview

In many clinical research applications the time to occurrence of one event of interest, that may be obscured by another--so called competing--event, is investigated. Specific interventions can only have an effect on the endpoint they address or research questions might focus on risk factors for a certain outcome. Different approaches for the analysis of time-to-event data in the presence of competing risks were introduced in the last decades including some new methodologies, which are not yet frequently used in the analysis of competing risks data. Cause-specific hazard regression, subdistribution hazard regression, mixture models, vertical modelling and the analysis of time-to-event data based on pseudo-observations are described in this article and are applied to a dataset of a cohort study intended to establish risk stratification for cardiac death after myocardial infarction. Data analysts are encouraged to use the appropriate methods for their specific research questions by comparing different regression approaches in the competing risks setting regarding assumptions, methodology and interpretation of the results. Notes on application of the mentioned methods using the statistical software R are presented and extensions to the presented standard methods proposed in statistical literature are mentioned.

Competing risks and the clinical community: irrelevance or ignorance?

Life expectancy has dramatically increased in industrialized nations over the last 200 hundred years. The aging of populations carries over to clinical research and leads to an increasing representation of elderly and multimorbid individuals in study populations. Clinical research in these populations is complicated by the fact that individuals are likely to experience several potential disease endpoints that prevent some disease-specific endpoint of interest from occurrence. Large developments in competing risks methodology have been achieved over the last decades, but we assume that recognition of competing risks in the clinical community is still marginal. It is the aim of this article to address translational aspects of competing risks to the clinical community. We describe clinical populations where competing risks issues may arise. We then discuss the importance of agreement between the competing risks methodology and the study aim, in particular the distinction between etiologic and prognostic research questions. In a review of 50 clinical studies performed in individuals susceptible to competing risks published in high-impact clinical journals, we found competing risks issues in 70% of all articles. Better recognition of issues related to competing risks and of statistical methods that deal with competing risks in accordance with the aim of the study is needed. Copyright © 2011 John Wiley & Sons, Ltd.

Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry

In the analysis of survival data, there are often competing events that preclude an event of interest from occurring. Regression analysis with competing risks is typically undertaken using a cause-specific proportional hazards model. However, modern alternative methods exist for the analysis of the subdistribution hazard with a corresponding subdistribution proportional hazards model. In this paper, we introduce a flexible parametric mixture model as a unifying method to obtain estimates of the cause-specific and subdistribution hazards and hazard-ratio functions. We describe how these estimates can be summarized over time to give a single number comparable to the hazard ratio that is obtained from a corresponding cause-specific or subdistribution proportional hazards model. An application to the Women's Interagency HIV Study is provided to investigate injection drug use and the time to either the initiation of effective antiretroviral therapy, or clinical disease progression as a competing event.

Inference for mutually exclusive competing events through a mixture of generalized gamma distributions

BACKGROUND

Time-to-event data with 2 or more types of endpoints are found in many epidemiologic settings. Instead of treating the times for one of the endpoints as censored observations for the other, we present an alternative approach where we treat competing events as distinct outcomes in a mixture. Our objective was to determine if and how the mixture was modified in response to an intervention.

METHODS

We used a mixture of generalized gamma distributions to concatenate the overall frequency and distribution of the times of 2 competing events commonly observed in critical care trials, namely (1) unassisted breathing followed by discharge home alive and (2) in-hospital death. We applied our proposed methods to data from 2 randomized clinical trials of critically ill patients.

RESULTS

Mechanical ventilation with lower tidal volumes modified the mixture (P = 0.103) when compared with traditional tidal volumes by lowering the overall frequency of death (P = 0.005), rather than through affecting either the distributions of times to unassisted breathing (P = 0.477) or times to death (P = 0.718). Likewise, use of a conservative versus a liberal fluid management modified the mixture (P < 0.001) by achieving earlier times to unassisted breathing (P < 0.001) and not through affecting the overall frequency of death (P = 0.202) or the distribution of times to death (P = 0.693).

CONCLUSIONS

A mixture approach to competing risks provides a means to determine the overall effect of an intervention and insights into how this intervention modifies the components of the mixture.

Competing risk regression models for epidemiologic data

Competing events can preclude the event of interest from occurring in epidemiologic data and can be analyzed by using extensions of survival analysis methods. In this paper, the authors outline 3 regression approaches for estimating 2 key quantities in competing risks analysis: the cause-specific relative hazard ((cs)RH) and the subdistribution relative hazard ((sd)RH). They compare and contrast the structure of the risk sets and the interpretation of parameters obtained with these methods. They also demonstrate the use of these methods with data from the Women's Interagency HIV Study established in 1993, treating time to initiation of highly active antiretroviral therapy or to clinical disease progression as competing events. In our example, women with an injection drug use history were less likely than those without a history of injection drug use to initiate therapy prior to progression to acquired immunodeficiency syndrome or death by both measures of association ((cs)RH = 0.67, 95% confidence interval: 0.57, 0.80 and (sd)RH = 0.60, 95% confidence interval: 0.50, 0.71). Moreover, the relative hazards for disease progression prior to treatment were elevated ((cs)RH = 1.71, 95% confidence interval: 1.37, 2.13 and (sd)RH = 2.01, 95% confidence interval: 1.62, 2.51). Methods for competing risks should be used by epidemiologists, with the choice of method guided by the scientific question.