Estimating a time-to-event distribution from right-truncated data in an epidemic: A review of methods

Time-to-event data are right-truncated if only individuals who have experienced the event by a certain time can be included in the sample. For example, we may be interested in estimating the distribution of time from onset of disease symptoms to death and only have data on individuals who have died. This may be the case, for example, at the beginning of an epidemic. Right truncation causes the distribution of times to event in the sample to be biased towards shorter times compared to the population distribution, and appropriate statistical methods should be used to account for this bias. This article is a review of such methods, particularly in the context of an infectious disease epidemic, like COVID-19. We consider methods for estimating the marginal time-to-event distribution, and compare their efficiencies. (Non-)identifiability of the distribution is an important issue with right-truncated data, particularly at the beginning of an epidemic, and this is discussed in detail. We also review methods for estimating the effects of covariates on the time to event. An illustration of the application of many of these methods is provided, using data on individuals who had died with coronavirus disease by 5 April 2020.

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Estimation of a treatment policy estimand for time to event data using data collected post discontinuation of randomised treatment

Pharmaceutical Statistics ◽

10.1002/pst.2189 ◽

2022 ◽

Author(s):

Benjamin Hartley ◽

Thomas Drury ◽

Sally Lettis ◽

Bhabita Mayer ◽

Oliver N. Keene ◽

...

Keyword(s):

Event Data ◽

Time To Event ◽

Treatment Policy ◽

Time To Event Data ◽

Using Data

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Impact of limited sample size and follow-up on single event survival extrapolation for health technology assessment: a simulation study

BMC Medical Research Methodology ◽

10.1186/s12874-021-01468-7 ◽

2021 ◽

Vol 21 (1) ◽

Author(s):

Jaclyn M. Beca ◽

Kelvin K. W. Chan ◽

David M. J. Naimark ◽

Petros Pechlivanoglou

Keyword(s):

Sample Size ◽

Time Horizon ◽

Goodness Of Fit ◽

Decision Models ◽

Small Samples ◽

Event Data ◽

Time To Event ◽

Time To Event Data ◽

Event Distribution

Abstract Introduction Extrapolation of time-to-event data from clinical trials is commonly used in decision models for health technology assessment (HTA). The objective of this study was to assess performance of standard parametric survival analysis techniques for extrapolation of time-to-event data for a single event from clinical trials with limited data due to small samples or short follow-up. Methods Simulated populations with 50,000 individuals were generated with an exponential hazard rate for the event of interest. A scenario consisted of 5000 repetitions with six sample size groups (30–500 patients) artificially censored after every 10% of events observed. Goodness-of-fit statistics (AIC, BIC) were used to determine the best-fitting among standard parametric distributions (exponential, Weibull, log-normal, log-logistic, generalized gamma, Gompertz). Median survival, one-year survival probability, time horizon (1% survival time, or 99th percentile of survival distribution) and restricted mean survival time (RMST) were compared to population values to assess coverage and error (e.g., mean absolute percentage error). Results The true exponential distribution was correctly identified using goodness-of-fit according to BIC more frequently compared to AIC (average 92% vs 68%). Under-coverage and large errors were observed for all outcomes when distributions were specified by AIC and for time horizon and RMST with BIC. Error in point estimates were found to be strongly associated with sample size and completeness of follow-up. Small samples produced larger average error, even with complete follow-up, than large samples with short follow-up. Correctly specifying the event distribution reduced magnitude of error in larger samples but not in smaller samples. Conclusions Limited clinical data from small samples, or short follow-up of large samples, produce large error in estimates relevant to HTA regardless of whether the correct distribution is specified. The associated uncertainty in estimated parameters may not capture the true population values. Decision models that base lifetime time horizon on the model’s extrapolated output are not likely to reliably estimate mean survival or its uncertainty. For data with an exponential event distribution, BIC more reliably identified the true distribution than AIC. These findings have important implications for health decision modelling and HTA of novel therapies seeking approval with limited evidence.

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Prognostic review and time-to-event data meta-analysis of low skeletal muscle mass in patients with peripheral arterial disease of the lower limbs undergoing revascularization

International Angiology ◽

10.23736/s0392-9590.19.04248-2 ◽

2020 ◽

Vol 39 (1) ◽

Author(s):

Madeleine Sharpe ◽

Emeka Okoye ◽

George A. Antoniou

Keyword(s):

Skeletal Muscle ◽

Peripheral Arterial Disease ◽

Skeletal Muscle Mass ◽

Meta Analysis ◽

Arterial Disease ◽

Lower Limbs ◽

Event Data ◽

Time To Event ◽

Time To Event Data ◽

Peripheral Arterial

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Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data

Statistical Methods in Medical Research ◽

10.1177/09622802211002868 ◽

2021 ◽

pp. 096228022110028

Author(s):

T Baghfalaki ◽

M Ganjali

Keyword(s):

Linear Model ◽

Joint Modeling ◽

Partially Linear Model ◽

Event Data ◽

Time To Event ◽

Data Set ◽

Partially Linear ◽

Time To Event Data ◽

Count Response ◽

Approximate Bayesian

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.

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Mitigation of biases in estimating hazard ratios under non-sensitive and non-specific observation of outcomes–applications to influenza vaccine effectiveness

Emerging Themes in Epidemiology ◽

10.1186/s12982-020-00091-z ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Ulrike Baum ◽

Sangita Kulathinal ◽

Kari Auranen

Keyword(s):

False Positive ◽

False Positive Rate ◽

Vaccine Effectiveness ◽

Partial Likelihood ◽

Event Data ◽

Time To Event ◽

Positive Events ◽

Time To Event Data ◽

Hazard Ratios ◽

Positive Rate

Abstract Background Non-sensitive and non-specific observation of outcomes in time-to-event data affects event counts as well as the risk sets, thus, biasing the estimation of hazard ratios. We investigate how imperfect observation of incident events affects the estimation of vaccine effectiveness based on hazard ratios. Methods Imperfect time-to-event data contain two classes of events: a portion of the true events of interest; and false-positive events mistakenly recorded as events of interest. We develop an estimation method utilising a weighted partial likelihood and probabilistic deletion of false-positive events and assuming the sensitivity and the false-positive rate are known. The performance of the method is evaluated using simulated and Finnish register data. Results The novel method enables unbiased semiparametric estimation of hazard ratios from imperfect time-to-event data. False-positive rates that are small can be approximated to be zero without inducing bias. The method is robust to misspecification of the sensitivity as long as the ratio of the sensitivity in the vaccinated and the unvaccinated is specified correctly and the cumulative risk of the true event is small. Conclusions The weighted partial likelihood can be used to adjust for outcome measurement errors in the estimation of hazard ratios and effectiveness but requires specifying the sensitivity and the false-positive rate. In absence of exact information about these parameters, the method works as a tool for assessing the potential magnitude of bias given a range of likely parameter values.

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