Semiparametric models for cumulative incidence functions

In analyses of time-to-failure data with competing risks, cumulative incidence functions may be used to estimate the time-dependent cumulative probability of failure due to specific causes. These functions are commonly estimated using nonparametric methods, but in cases where events due to the cause of primary interest are infrequent relative to other modes of failure, nonparametric methods may result in rather imprecise estimates for the corresponding subdistribution. In such cases, it may be possible to model the cause-specific hazard of primary interest parametrically, while accounting for the other modes of failure using nonparametric estimators. The cumulative incidence estimators so obtained are simple to compute and are considerably more efficient than the usual nonparametric estimator, particularly with regard to interpolation of cumulative incidence at early or intermediate time points within the range of data used to fit the function. More surprisingly, they are often nearly as efficient as fully parametric estimators. We illustrate the utility of this approach in the analysis of patients treated for early stage breast cancer.     

Marginal Models for Clustered Time‐to‐Event Data with Competing Risks Using Pseudovalues

Summary Many time‐to‐event studies are complicated by the presence of competing risks and by nesting of individuals within a cluster, such as patients in the same center in a multicenter study. Several methods have been proposed for modeling the cumulative incidence function with independent observations. However, when subjects are clustered, one needs to account for the presence of a cluster effect either through frailty modeling of the hazard or subdistribution hazard, or by adjusting for the within‐cluster correlation in a marginal model. We propose a method for modeling the marginal cumulative incidence function directly. We compute leave‐one‐out pseudo‐observations from the cumulative incidence function at several time points. These are used in a generalized estimating equation to model the marginal cumulative incidence curve, and obtain consistent estimates of the model parameters. A sandwich variance estimator is derived to adjust for the within‐cluster correlation. The method is easy to implement using standard software once the pseudovalues are obtained, and is a generalization of several existing models. Simulation studies show that the method works well to adjust the SE for the within‐cluster correlation. We illustrate the method on a dataset looking at outcomes after bone marrow transplantation.     

Regression modeling of competing risks data based on pseudovalues of the cumulative incidence function

Typically, regression models for competing risks outcomes are based on proportional hazards models for the crude hazard rates. These estimates often do not agree with impressions drawn from plots of cumulative incidence functions for each level of a risk factor. We present a technique which models the cumulative incidence functions directly. The method is based on the pseudovalues from a jackknife statistic constructed from the cumulative incidence curve. These pseudovalues are used in a generalized estimating equation to obtain estimates of model parameters. We study the properties of this estimator and apply the technique to a study of the effect of alternative donors on relapse for patients given a bone marrow transplant for leukemia.     

Confidence bands for cumulative incidence curves under the additive risk model

In the context of competing risks, the cumulative incidence function is often used to summarize the cause-specific failure-time data. As an alternative to the proportional hazards model, the additive risk model is used to investigate covariate effects by specifying that the subject-specific hazard function is the sum of a baseline hazard function and a regression function of covariates. Based on such a formulation, we present an approach to constructing simultaneous confidence intervals for the cause-specific cumulative incidence function of patients with given risk factors. A melanoma data set is used for the purpose of illustration.     

Omnibus tests for comparison of competing risks with adjustment for covariate effects

This article develops omnibus tests for comparing cause-specific hazard rates and cumulative incidence functions at specified covariate levels. Confidence bands for the difference and the ratio of two conditional cumulative incidence functions are also constructed. The omnibus test is formulated in terms of a test process given by a weighted difference of estimates of cumulative cause-specific hazard rates under Cox proportional hazards models. A simulation procedure is devised for sampling from the null distribution of the test process, leading to graphical and numerical technques for detecting significant differences in the risks. The approach is applied to a cohort study of type-specific HIV infection rates.     

Changes in Risk of Immediate Adverse Reactions to Iodinated Contrast Media by Repeated Administrations in Patients with Hepatocellular Carcinoma

Background

To elucidate whether repeated exposures to iodinated contrast media increase the risk of adverse reaction.

Materials and Methods

We retrospectively reviewed 1,861 patients with hepatocellular carcinoma who visited authors’ institution, a tertiary referral center, between 2004 and 2008. We analyzed cumulative probability of adverse reactions and risk factors. We categorized all symptoms into hypersensitivity reactions, physiologic reactions, and other reactions, according to the American College of Radiology guidelines, and evaluated each category as an event. We estimated the association between hazard for adverse reactions and the number of cumulative exposures to contrast media. We also evaluated subsequent contrast media injections and adverse reactions.

Results

There were 23,684 contrast media injections in 1,729 patients. One hundred and thirty-two patients were excluded because they were given no contrast media during the study period. Adverse reactions occurred in 196 (0.83%) patients. The cumulative incidence at 10^th, 20^th, and 30^th examination was 7.9%, 15.2%, and 24.1%, respectively. Presence of renal impairment was found to be one of risk factors for adverse reactions. The estimated hazard of overall adverse reaction gradually decreased until around 10^th exposure and rose with subsequent exposures. The estimated hazard of hypersensitivity showed V-shaped change with cumulative number of exposures. The estimated hazard of physiologic reaction had a tendency toward decreasing and that of other reaction had a tendency toward increasing. Second adverse reaction was more severe than the initial in only one among 130 patients receiving subsequent injections.

Conclusion

Repeated exposures to iodinated contrast media increase the risk of adverse reaction.     

Cause‐Specific Cumulative Incidence Estimation and the Fine and Gray Model Under Both Left Truncation and Right Censoring

Summary The standard estimator for the cause‐specific cumulative incidence function in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is a weighted empirical cumulative distribution function and the other a product‐limit estimator. This equivalence suggests an alternative view of the analysis of time‐to‐event data with left truncation and right censoring: individuals who are still at risk or experienced an earlier competing event receive weights from the censoring and truncation mechanisms. As a consequence, inference on the cumulative scale can be performed using weighted versions of standard procedures. This holds for estimation of the cause‐specific cumulative incidence function as well as for estimation of the regression parameters in the Fine and Gray proportional subdistribution hazards model. We show that, with the appropriate filtration, a martingale property holds that allows deriving asymptotic results for the proportional subdistribution hazards model in the same way as for the standard Cox proportional hazards model. Estimation of the cause‐specific cumulative incidence function and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time‐dependent weights. We show the implementation in the R statistical package. The proportional subdistribution hazards model is used to investigate the effect of calendar period as a deterministic external time varying covariate, which can be seen as a special case of left truncation, on AIDS related and non‐AIDS related cumulative mortality.     

Multiple imputation methods for inference on cumulative incidence with missing cause of failure

Analysis of cumulative incidence (sometimes called absolute risk or crude risk) can be difficult if the cause of failure is missing for some subjects. Assuming missingness is random conditional on the observed data, we develop asymptotic theory for multiple imputation methods to estimate cumulative incidence. Covariates affect cause-specific hazards in our model, and we assume that separate proportional hazards models hold for each cause-specific hazard. Simulation studies show that procedures based on asymptotic theory have near nominal operating characteristics in cohorts of 200 and 400 subjects, both for cumulative incidence and for prediction error. The methods are illustrated with data on survival after breast cancer, obtained from the National Surgical Adjuvant Breast and Bowel Project (NSABP).     

Estimation of separable direct and indirect effects in continuous time

Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular, estimands on the hazard scale, such as ratios of cause-specific or subdistribution hazards, are fundamentally hard to interpret causally. Estimands on the risk scale, such as contrasts of cumulative incidence functions, do have a clear causal interpretation, but they only capture the total effect of the treatment on the event of interest; that is, effects both through and outside of the competing event. To disentangle causal treatment effects on the event of interest and competing events, the separable direct and indirect effects were recently introduced. Here we provide new results on the estimation of direct and indirect separable effects in continuous time. In particular, we derive the nonparametric influence function in continuous time and use it to construct an estimator that has certain robustness properties. We also propose a simple estimator based on semiparametric models for the two cause-specific hazard functions. We describe the asymptotic properties of these estimators and present results from simulation studies, suggesting that the estimators behave satisfactorily in finite samples. Finally, we reanalyze the prostate cancer trial from Stensrud et al. (2020).     

A nonproportional hazards Weibull accelerated failure time regression model

We present a study of risk factors measured in mean before age 50 and subsequent incidence of heart disease over 32 years of follow-up. The data are from the Framingham Heart Study. The standard accelerated failure time model assumes the logarithm of time until an event has a constant dispersion parameter and a location parameter that is a linear function of covariates. Parameters are estimated by maximum likelihood. We reject a standard Weibull model for these data in favor of a model with the dispersion parameter depending on the location parameter. This model suggests that the cumulative hazard ratio for two individuals shrinks towards unity over the follow-up period. Thus, not only the standard Weibull, but also the semiparametric proportional hazards (Cox) model is inadequate for this data. The model improvement appears particularly valuable when estimating the difference in predicted outcome probabilities for two individuals.     

The age-specific cumulative incidence of infection with pandemic influenza H1N1 2009 was similar in various countries prior to vaccination

Background

During the influenza pandemic of 2009 estimates of symptomatic and asymptomatic infection were needed to guide vaccination policies and inform other control measures. Serological studies are the most reliable way to measure influenza infection independent of symptoms. We reviewed all published serological studies that estimated the cumulative incidence of infection with pandemic influenza H1N1 2009 prior to the initiation of population-based vaccination against the pandemic strain.

Methodology and Principal Findings

We searched for studies that estimated the cumulative incidence of pandemic influenza infection in the wider community. We excluded studies that did not include both pre- and post-pandemic serological sampling and studies that included response to vaccination. We identified 47 potentially eligible studies and included 12 of them in the review. Where there had been a significant first wave, the cumulative incidence of pandemic influenza infection was reported in the range 16%–28% in pre-school aged children, 34%–43% in school aged children and 12%–15% in young adults. Only 2%–3% of older adults were infected. The proportion of the entire population infected ranged from 11%–18%. We re-estimated the cumulative incidence to account for the small proportion of infections that may not have been detected by serology, and performed direct age-standardisation to the study population. For those countries where it could be calculated, this suggested a population cumulative incidence in the range 11%–21%.

Conclusions and Significance

Around the world, the cumulative incidence of infection (which is higher than the cumulative incidence of clinical disease) was below that anticipated prior to the pandemic. Serological studies need to be routine in order to be sufficiently timely to provide support for decisions about vaccination.     

Bayesian modeling of time-varying and waning exposure effects

In epidemiologic studies, there is often interest in assessing the association between exposure history and disease incidence. For many diseases, incidence may depend not only on cumulative exposure, but also on the ages at which exposure occurred. This article proposes a flexible Bayesian approach for modeling age-varying and waning exposure effects. The Cox model is generalized to allow the hazard of disease to depend on an integral, across the exposed ages, of a piecewise polynomial function of age, multiplied by an exponential decay term. Linearity properties of the model facilitate posterior computation via a Gibbs sampler, which generalizes previous algorithms for Cox regression with time-dependent covariates. The approach is illustrated by an application to the study of protective effects of breastfeeding on incidence of childhood asthma.     

Nonparametric association analysis of bivariate left‐truncated competing risks data

We develop time‐varying association analyses for onset ages of two lung infections to address the statistical challenges in utilizing registry data where onset ages are left‐truncated by ages of entry and competing‐risk censored by deaths. Two types of association estimators are proposed based on conditional cause‐specific hazard function and cumulative incidence function that are adapted from unconditional quantities to handle left truncation. Asymptotic properties of the estimators are established by using the empirical process techniques. Our simulation study shows that the estimators perform well with moderate sample sizes. We apply our methods to the Cystic Fibrosis Foundation Registry data to study the relationship between onset ages of Pseudomonas aeruginosa and Staphylococcus aureus infections.     

Climate change and livestock parasites: integrated management of sheep blowfly strike in a warmer environment

The incidence of parasite‐mediated livestock disease is the result of a complex interaction of factors such as parasite and host abundance, host susceptibility, climate and, critically, farmer husbandry and intervention strategies, all of which change seasonally in space and time. Given the complexity of the interacting factors, the effects of environment changes on disease incidence are hard to predict, as accordingly are the optimal husbandry responses required to ameliorate any effects. Here a model system is used to explore these issues. Cutaneous myiasis (blowfly strike) is common disease of livestock and would be expected to be highly sensitive to even small changes in climate; it provides a good model for highlighting the problems inherent in attempting to predict the effect of climate change on livestock disease incidence. For this, a stochastic simulation model is used to examine the changes in the seasonal incidence of ovine cutaneous myiasis on farms in the United Kingdom and the likely effects of changes in husbandry and control strategies. The simulations show that the range of elevated temperatures predicted by current climate change scenarios result in an elongated blowfly season with earlier spring emergence and a higher cumulative incidence of strike. Overall, higher temperatures increased strike incidence disproportionately in ewes in early summer, but had relatively less direct effect on the pattern of lamb strike incidence; a +3 °C increase in average temperature approximately doubles the cumulative incidence of strike in lambs but results in four times more strikes in ewes. A range of strike management options is examined and the models show that changes in husbandry practices are also likely to have an important effect in reducing early season ewe strike incidences. The simulations suggest that integrated changes in husbandry practices are likely to be able to manage expected increases in strike, given the range of climate changes currently predicted.     

The effect of treatment delay on time-to-recovery in the presence of unobserved heterogeneity

We study the effect of delaying treatment in the presence of (unobserved) heterogeneity. In a homogeneous population and assuming a proportional treatment effect, a treatment delay period will result in notably lower cumulative recovery percentages. We show in theoretical scenarios using frailty models that if the population is heterogeneous, the effect of a delay period is much smaller. This can be explained by the selection process that is induced by the frailty. Patient groups that start treatment later have already undergone more selection. The marginal hazard ratio for the treatment will act differently in such a more homogeneous patient group. We further discuss modeling approaches for estimating the effect of treatment delay in the presence of heterogeneity, and compare their performance in a simulation study. The conventional Cox model that fails to account for heterogeneity overestimates the effect of treatment delay. Including interaction terms between treatment and starting time of treatment or between treatment and follow up time gave no improvement. Estimating a frailty term can improve the estimation, but is sensitive to misspecification of the frailty distribution. Therefore, multiple frailty distributions should be used and the results should be compared using the Akaike Information Criterion. Non-parametric estimation of the cumulative recovery percentages can be considered if the dataset contains sufficient long term follow up for each of the delay strategies. The methods are demonstrated on a motivating application evaluating the effect of delaying the start of treatment with assisted reproductive techniques on time-to-pregnancy in couples with unexplained subfertility.     

Estimating the cumulative incidence of SARS-CoV-2 with imperfect serological tests: Exploiting cutoff-free approaches

Large-scale serological testing in the population is essential to determine the true extent of the current SARS-CoV-2 pandemic. Serological tests measure antibody responses against pathogens and use predefined cutoff levels that dichotomize the quantitative test measures into sero-positives and negatives and use this as a proxy for past infection. With the imperfect assays that are currently available to test for past SARS-CoV-2 infection, the fraction of seropositive individuals in serosurveys is a biased estimator of the cumulative incidence and is usually corrected to account for the sensitivity and specificity. Here we use an inference method—referred to as mixture-model approach—for the estimation of the cumulative incidence that does not require to define cutoffs by integrating the quantitative test measures directly into the statistical inference procedure. We confirm that the mixture model outperforms the methods based on cutoffs, leading to less bias and error in estimates of the cumulative incidence. We illustrate how the mixture model can be used to optimize the design of serosurveys with imperfect serological tests. We also provide guidance on the number of control and case sera that are required to quantify the test’s ambiguity sufficiently to enable the reliable estimation of the cumulative incidence. Lastly, we show how this approach can be used to estimate the cumulative incidence of classes of infections with an unknown distribution of quantitative test measures. This is a very promising application of the mixture-model approach that could identify the elusive fraction of asymptomatic SARS-CoV-2 infections. An R-package implementing the inference methods used in this paper is provided. Our study advocates using serological tests without cutoffs, especially if they are used to determine parameters characterizing populations rather than individuals. This approach circumvents some of the shortcomings of cutoff-based methods at exactly the low cumulative incidence levels and test accuracies that we are currently facing in SARS-CoV-2 serosurveys.     

The impact of under and over-recording of cancer on death certificates in a competing risks analysis: A simulation study

Background: With linked register and cause of death data becoming more accessible than ever, competing risks methodology is being increasingly used as a way of obtaining “real world” probabilities of death broken down by specific causes. It is important, in terms of the validity of these studies, to have accurate cause of death information. However, it is well documented that cause of death information taken from death certificates is often lacking in accuracy and completeness. Methods: We assess through use of a simulation study the effect of under and over-recording of cancer on death certificates in a competing risks analysis consisting of three competing causes of death: cancer, heart disease and other causes. Using realistic levels of misclassification, we consider 24 scenarios and examine the bias in the cause-specific hazard ratios and the cumulative incidence function. Results: The bias in the cumulative incidence function was highest in the oldest age group reaching values as high as 2.6 percentage units for the “good” cancer prognosis scenario and 9.7 percentage units for the “poor” prognosis scenario. Conclusion: The bias resulting from the chosen levels of misclassification in this study accentuate concerns that unreliable cause of death information may be providing misleading results. The results of this simulation study convey an important message to applied epidemiological researchers.     

Increased Risk of Acute Pancreatitis in Patients with Rheumatoid Arthritis: A Population-Based Cohort Study

The study was conducted to determine whether patients with rheumatoid arthritis (RA) are at increased risk of acute pancreatitis compared with those without RA and to determine if the risk of acute pancreatitis varied by anti-RA drug use. We used the large population-based dataset from the National Health Insurance (NHI) program in Taiwan to conduct a retrospective cohort study. Patients newly diagnosed with RA between 2000 and 2011 were referred to as the RA group. The comparator non-RA group was matched with propensity score, using age and sex, in the same time period. We presented the incidence density by 100,000 person-years. The propensity score and all variables were analyzed in fully adjusted Cox proportional hazard regression. The cumulative incidence of acute pancreatitis was assessed by Kaplan-Meier analysis, with significance based on the log-rank test. From claims data of one million enrollees randomly sampled from the Taiwan NHI database, 29,755 adults with RA were identified and 119,020 non- RA persons were matched as a comparison group. The RA cohort had higher incidence density of acute pancreatitis (185.7 versus 119.0 per 100,000 person-years) than the non-RA cohort. The adjusted hazard ratio (HR) was 1.62 (95% CI [confidence interval] 1.43–1.83) for patients with RA to develop acute pancreatitis. Oral corticosteroid use decreased the risk of acute pancreatitis (adjusted HR 0.83, 95% CI 0.73–0.94) but without a dose-dependent effect. Current use of disease modifying anti-rheumatic drugs or tumor necrosis factor blockers did not decrease the risk of acute pancreatitis. In conclusion, patients with RA are at an elevated risk of acute pancreatitis. Use of oral corticosteroids may reduce the risk of acute pancreatitis.     

Long-term effect of interferon plus ribavirin on hepatitis B surface antigen seroclearance in patients dually infected with hepatitis B and C viruses

Background

Interferon-α/ribavirin combination therapy might promote hepatitis B surface antigen (HBsAg) seroclearance in patients dually infected with hepatitis B and C viruses (HBV/HCV), but the long-term effect remains unclear. We aimed to investigate the rate of and the factors associated with HBsAg seroclearance during long-term follow-up after interferon-α/ribavirin combination therapy in HBV/HCV dually-infected patients.

Methodology/Principal Findings

Eighty-one patients who received interferon-α/ribavirin combination therapy for 24 weeks with a follow-up period of >24 weeks were enrolled. HBV serological markers and HBV DNA were determined every 6 months. Early and late HBsAg seroclearance were defined as HBsAg loss in less or more than 6 months after end-of-treatment, respectively. Fifteen (18.5%) patients had HBsAg seroclearance during a mean follow-up period of 3.4 (0.5–5.1) years. The 5-year cumulative incidence was 25.6%. Baseline cirrhosis and HBV DNA negativity 1 year after end-of-treatment were independently predictive of HBsAg seroclearance with an odds ratio (OR), 95% confidence intervals (CI) of 16.6, 1.8–153 and 9.2, 1.4–62.1, respectively, by Cox regression hazard analysis. Four patients developed early and 11 developed late HBsAg seroclearance, respectively. Cox regression hazard analysis showed no factor was associated with early HBsAg seroclearance, whilst HBV DNA negativity 1 year after end-of-treatment was the only significant factor predicting late HBsAg loss (OR, 43.0; CI, 2.5–745). Five patients had HBsAg seroconversion with a 5-year cumulative incidence of 8.3%. HBV DNA negativity at baseline and one year after EOT had a trend for HBsAg seroconversion. HCV response did not correlate to HBsAg loss.

Conclusions

We demonstrated that interferon-α/ribavirin had long-term effect on HBsAg seroclearance in dually HBV/HCV-infected patients. Baseline cirrhosis and seroclearance of HBV DNA 1 year after end-of-treatment were significant factors associated with HBsAg seroclearance.     

Impact of and Correction for Outcome Misclassification in Cumulative Incidence Estimation

Cohort studies and clinical trials may involve multiple events. When occurrence of one of these events prevents the observance of another, the situation is called “competing risks”. A useful measure in such studies is the cumulative incidence of an event, which is useful in evaluating interventions or assessing disease prognosis. When outcomes in such studies are subject to misclassification, the resulting cumulative incidence estimates may be biased. In this work, we study the mechanism of bias in cumulative incidence estimation due to outcome misclassification. We show that even moderate levels of misclassification can lead to seriously biased estimates in a frequently unpredictable manner. We propose an easy to use estimator for correcting this bias that is uniformly consistent. Extensive simulations suggest that this method leads to unbiased estimates in practical settings. The proposed method is useful, both in settings where misclassification probabilities are known by historical data or can be estimated by other means, and for performing sensitivity analyses when the misclassification probabilities are not precisely known.