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Predicted cumulative incidence functions for females aged 20 to 50 years, with CD4 count 120 cells/ μl at ART initiation.
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Background and objective:
Competing risk data are frequently interval-censored in real-world applications, that is, the exact event time is not precisely observed but is only known to lie between two time points such as clinic visits. This type of data requires special handling because the actual event times are unknown. To deal with this problem...
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Context 1
... of 120 cells/ μl at ART initiation, according to age at ART initiation, are depicted in Fig. 3 . Fitting the proportional subdistribution hazards model (i.e. Fine-Gray model) for loss to care and the proportional odds model for death can be performed by setting α 1 = 0 and α 2 = 1 , as ...
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We consider nonparametric and semiparametric resampling of multistate event histories by simulating multistate trajectories from an empirical multivariate hazard measure. One advantage of our approach is that it does not necessarily require individual patient data, but may be based on published information. This is also attractive for both study pl...
Citations
... Specifically, the censoring times may differ per event type: while the time to treatment initiation is censored when a patient leaves AS for another reason, the time to cancer progression for the same patient is censored at the last available biopsy. Li (2016) and Park et al. (2019) extended the likelihood for proportional hazard models for the combination of competing risks and interval censoring, though an adaption in joint models is still missing. ...
Active surveillance (AS), where biopsies are conducted to detect cancer progression, has been acknowledged as an efficient way to reduce the overtreatment of prostate cancer. Most AS cohorts use fixed biopsy schedules for all patients. However, the ideal test frequency remains unknown, and the routine use of such invasive tests burdens the patients. An emerging idea is to generate personalized biopsy schedules based on each patient's progression-specific risk. To achieve that, we propose the interval-censored cause-specific joint model (ICJM), which models the impact of longitudinal biomarkers on cancer progression while considering the competing event of early treatment initiation. The underlying likelihood function incorporates the interval-censoring of cancer progression, the competing risk of treatment, and the uncertainty about whether cancer progression occurred since the last biopsy in patients that are right-censored or experience the competing event. The model can produce patient-specific risk profiles until a horizon time. If the risk exceeds a certain threshold, a biopsy is conducted. The optimal threshold can be chosen by balancing two indicators of the biopsy schedules: the expected number of biopsies and expected delay in detection of cancer progression. A simulation study showed that our personalized schedules could considerably reduce the number of biopsies per patient by more than 50% compared to the fixed schedules, though at the cost of a slightly longer detection delay.
... Women with no visits following delivery were excluded. This analysis was performed using the function ciregic in the R package intccr (57). ...
Medical records of pregnant and postpartum women living with HIV and their infants attending a large referral facility in Kenya from 2015 to 2019 were analyzed to identify characteristics associated with retention in care and viral suppression. Women were stratified based on the timing of HIV care enrollment: known HIV-positive (KHP; enrolled pre-pregnancy) and newly HIV-positive (NHP; enrolled during pregnancy). Associations with retention at 18 months postpartum and viral suppression (< 1000 copies/mL) were determined. Among 856 women (20% NHP), retention was 83% for KHPs and 53% for NHPs. Viral suppression was 88% for KHPs and 93% for NHPs, but 19% of women were missing viral load results. In a competing risk model, viral suppression increased by 18% for each additional year of age but was not associated with other factors. Overall, 1.9% of 698 infants with ≥ 1 HIV test result were HIV-positive. Tailored interventions are needed to promote retention and viral load testing, particularly for NHPs, in the PMTCT continuum.
... The motivation of using two different series is that one can easily rely on the R package intccr (Park et al., 2019) to implement the B-spline modeling of the φ j functions, naturally preserving the nonnegativity and monotonicity. ...
... ciregic, available in the R package intccr(Park et al., 2019). The BP uses fixed knots, once the degree m w and the interval [a e w , b e w ], the support of W e , are determined. ...
In this paper, we consider a class of partially linear transformation models with interval-censored competing risks data. Under a semiparametric generalized odds rate specification for the cause-specific cumulative incidence function, we obtain optimal estimators of the large number of parametric and nonparametric model components via maximizing the likelihood function over a joint B-spline and Bernstein polynomial spanned sieve space. Our specification considers a relatively simpler finite-dimensional parameter space, approximating the infinite-dimensional parameter space as n → ∞, thereby allowing us to study the almost sure consistency, and rate of convergence for all parameters, and the asymptotic distributions and efficiency of the finite-dimensional components. We
study the finite sample performance of our method through simulation studies under a variety of scenarios. Furthermore, we illustrate our methodology via application to a dataset on HIV-infected individuals from sub-Saharan Africa
... To account for competing risks of culling or dead/missing and interval-censored data, the survival analyses used semi-parametric competing risks regression under interval censoring, using the R package 'intccr' and the related methodology [32]. In the present analyses, the two competing events (outcomes) were wastage due to premature culling (c = 1), and wastage due to dead/missing (c = 2), with remaining ewes censored (c = 0). ...
Ewe wastage is the combination of on-farm mortality and premature culling. Internationally, there is limited research on actual wastage incidence and causes in commercial sheep flocks. To the authors’ knowledge, this is the first study that reports both lifetime wastage and detailed annual wastage in a sample of commercial New Zealand flocks. This study utilized data collected from 13,142 ewes from four cohorts on three commercial New Zealand farms (Farm A 2010-born, Farm A 2011-born, Farm B, Farm C), during the period 2011–2017, as they aged from replacement hoggets to 6-year-old ewes (Farm A and Farm B) or 3-year-old ewes (Farm C). Data collection visits occurred at three or four key management times each year, namely pre-mating, pregnancy diagnosis, pre-lambing and weaning. At each visit, body condition score (BCS) was assessed and any ewes that were culled or had died on farm were recorded. As this was a lifetime study, each ewe was assigned an outcome and corresponding ‘exit age’. By the end of the study, all ewes that had exited their respective flocks, were classified as either prematurely culled, or dead/missing, or if still in the flock, as censored, and either the exact date or interval in which they exited the flock was recorded. Semi-parametric competing risk (premature culling vs. dead/missing), interval-censored survival models were developed to: 1. describe the association between hogget reproductive outcomes and risk of subsequent wastage, and 2. assess pre-mating BCS as a predictor of wastage in that production year. Of the 13,142 enrolled ewes, 50.4% exited their respective flocks due to premature culling and 40.0% due to on-farm dead/missing, giving a total of 90.4% that exited due to wastage. Annual mortality incidence ranged from 3.5 to 40.2%. As a hogget, wastage incidence ranged from 7.6 to 45.4%. Pregnancy or rearing a lamb as a hogget did not increase risk of subsequent wastage. In all years, pre-mating BCS was a predictor of ewe wastage, with odds of wastage lower with increasing BCS. Therefore, farmers should focus on improving pre-mating BCS to 3.5/5.0 by assessing ewe BCS at weaning, allowing poorer-BCS ewes to be managed to gain BCS before re-breeding.
... In addition to the MI methods considered, we applied the B-spline sieve semiparametric maximum likelihood approach of Bakoyannis et al (INTCCR) using the "intccr" R package, 46 fitting a proportional subdistribution hazards (Fine and Gray 47 ) model without covariates, because we wanted to compare MI methods with a LB method. We also wanted to test the authors' claim that the INTCCR method's performance was superior to that of Delord and Genin's approach. ...
... We also wanted to test the authors' claim that the INTCCR method's performance was superior to that of Delord and Genin's approach. 46 INTCCR only allows for half-open intervals of the form (L i , R i ], whereas exactly observed times require closed intervals. Therefore, for the exactly observed times in our simulated data, we set the left boundary to be the observed time minus 1 day and the right boundary to be the observed time. ...
In patient follow‐up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as “bounded” or “interval‐censored.” Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood‐based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log‐normal regression with postimputation back‐transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.
... Note that there is another recent package intccr available in R, dealing with interval censored competing risk data, see Park et al. (2019). Similar to the MIICD-package it addresses the regression analysis of the CIF for interval censored competing risk data. ...
... It allows for SH analysis. Park et al. (2019) mention that the variance estimator of the imputation approach used by the MIICD-package is biased if the imputation model is misspecified. Furthermore the intccr-package provides analysis via the proportional odds model. ...
The topic of this thesis is the investigation of hospital acquired infections (HAI) and how to deal with time dependency in this context. When investigating the risk of HAI, researchers face the challenge of competing risks. The complete picture can be illustrated and investigated via an illness-death model. Considering HAI as an outcome, there are two perspectives to distinguish amongst: The clinicians’ and the epidemiologists’ perspective, concerning risk and aetiology of HAI, respectively. A common approach for risk factor analysis of HAI is logistic regression. This is a valid but rather crude approach as time is ignored. This thesis examines the analysis of HAI via logistic regression adjusted for time, either length of stay
(LOS) or time at risk (TAR). Both approaches are attempts to incorporate time dependency. However, clarification is needed about what is modeled and whether this is appropriate. The investigation of adjustment for LOS demonstrates that this approach is not valid. LOS consists of the time before and the time after HAI. Thus, not only effects on the occurrence of HAI impact LOS, but also effects on death and discharge after the infection. A simulation study shows that risk factor analysis via logistic regression adjusted for LOS can result in misleading effect estimates leading to wrong conclusions. Furthermore, adjustment for TAR is investigated. While there are well understood regression models available for investigation
of the cumulative incidence function (CIF), insights are needed in what logistic regression adjusted for TAR models. A simulation study shows, that it is unclear how the results can be translated into a measure modeling the CIF and thus addressing the clinicians’ perspective. Furthermore, the results show that this approach is no measure corresponding to the epidemiologists’ perspective, distinguishing between direct and indirect effects on HAI.
A further challenge arising when investigating HAI are unknown infection times. It may occur that only the infection status and LOS are known, but the time of infection is not. This is an extreme version of interval censoring of time-to-event data. There are tools for interval censored data motivated by studies collecting data at scheduled visit times. Investigation via real and simulated data shows that these methods can be applied in an extreme interval censoring setting. The results for analysis of the clinicians’ and epidemiologists’ perspective are promising when considering HAI as an outcome. Considering HAI as a time-dependent exposure and its burden measured by change in LOS or its effect on the death and discharge hazard, estimates of each transition can be obtained from the existing tools for interval censored data. These estimates can be used for manual calculation of the quantity of interest. The topics covered in this thesis are important in recent hospital epidemiology. There are many settings where time dependency plays an important role but infection times are unknown. For instance, this is also the case when investigating COVID-19.
In conclusion, even with rough data it is worthwhile considering more sophisticated approaches in order to investigate HAI incorporating time. Thus, a better reflection of the reality of HAI development in can be given.
... While we do not intend to compare all the available packages, the new R function allows researchers to compare the results of subhazard regression and marginal hazard regression for their own data. An R package for subhazard regression using interval censored data is only recently developed[44]. ...
For the analysis of competing risks data, three different types of hazard functions have been considered in the literature, namely the cause-specific hazard, the sub-distribution hazard, and the marginal hazard function. Accordingly, medical researchers can fit three different types of the Cox model to estimate the effect of covariates on each of the hazard function. While the relationship between the cause-specific hazard and the sub-distribution hazard has been extensively studied, the relationship to the marginal hazard function has not yet been analyzed due to the difficulties related to non-identifiability. In this paper, we adopt an assumed copula model to deal with the model identifiability issue, making it possible to establish a relationship between the sub-distribution hazard and the marginal hazard function. We then compare the two methods of fitting the Cox model to competing risks data. We also extend our comparative analysis to clustered competing risks data that are frequently used in medical studies. To facilitate the numerical comparison, we implement the computing algorithm for marginal Cox regression with clustered competing risks data in the R joint.Cox package and check its performance via simulations. For illustration, we analyze two survival datasets from lung cancer and bladder cancer patients.
Advances in survival analysis have facilitated unprecedented flexibility in data modeling, yet there remains a lack of tools for graphically illustrating the influence of continuous covariates on predicted survival outcomes. We propose the utilization of a colored contour plot to depict the predicted survival probabilities over time, and provide a Shiny app and R package as implementations of this tool. Our approach is capable of supporting conventional models, including the Cox and Fine-Gray models. However, its capability shines when coupled with cutting-edge machine learning models such as deep neural networks.
Background:
Composite time-to-event endpoints are beneficial for assessing related outcomes jointly in clinical trials, but components of the endpoint may have different censoring mechanisms. For example, in the PRagmatic EValuation of evENTs And Benefits of Lipid-lowering in oldEr adults (PREVENTABLE) trial, the composite outcome contains one endpoint that is right censored (all-cause mortality) and two endpoints that are interval censored (dementia and persistent disability). Although Cox regression is an established method for time-to-event outcomes, it is unclear how models perform under differing component-wise censoring schemes for large clinical trial data. The goal of this article is to conduct a simulation study to investigate the performance of Cox models under different scenarios for composite endpoints with component-wise censoring.
Methods:
We simulated data by varying the strength and direction of the association between treatment and outcome for the two component types, the proportion of events arising from the components of the outcome (right censored and interval censored), and the method for including the interval-censored component in the Cox model (upper value and midpoint of the interval). Under these scenarios, we compared the treatment effect estimate bias, confidence interval coverage, and power.
Results:
Based on the simulation study, Cox models generally have adequate power to achieve statistical significance for comparing treatments for composite outcomes with component-wise censoring. In our simulation study, we did not observe substantive bias for scenarios under the null hypothesis or when the treatment has a similar relative effect on each component outcome. Performance was similar regardless of if the upper value or midpoint of the interval-censored part of the composite outcome was used.
Conclusion:
Cox regression is a suitable method for analysis of clinical trial data with composite time-to-event endpoints subject to different component-wise censoring mechanisms.
Introduction/aims:
Disease progression in myotonic dystrophy (DM) is marked by milestone events, when functional thresholds are crossed. DM type 2 (DM2) is considered less severe than DM type 1 (DM1), but whether this applies uniformly to all features is unknown. We compared the age-dependent risk for milestone events in DM1 and DM2, and tested for associations with age of onset and sex.
Methods:
We studied a large cohort of adult participants in a national registry of DM1 and DM2. Using annual surveys from participants, we ascertained milestone events for motor involvement (use of cane, walker, ankle brace, wheelchair, or ventilatory device), systemic involvement (diabetes, pacemaker, cancer), loss of employment due to DM, and death.
Results:
Mean follow-up of registry participants (DM1 = 929, DM2=222) was 7 years. Disability and motor milestones occurred at earlier ages in DM1 than in DM2. In contrast, the risk of diabetes was higher and tended to occur earlier in DM2 (HR=0.56, p=<0.001). In DM1, the milestone events tended to occur earlier, and life expectancy was reduced, when symptoms began at younger ages. In DM1, men were at greater risk for disability (HR=1.34, p=<0.01), use of ankle braces (HR=1.41, p=0.02), and diabetes (HR=2.2, p=<0.0001), whereas women were at greater risk for using walkers (HR=0.68, p=0.001) or malignancy (0.66, p=<0.01).
Discussion:
Milestone events recorded through registries can be used to assess long-term impact of DM in large cohorts. Except for diabetes, the age-related risk of milestone events is greater in DM1 than in DM2.
