Survival analysis with time-dependent covariates subject to missing data or measurement error: Multiple Imputation for Joint Modeling (MIJM)

Many phenomena in the social or the medical sciences can be described as events, meaning that a qualitative change occurs at some particular point in time. Typical research questions focus on whether, when, and under which circumstances events occur. In the social sciences, discrete-time-to-event models are popular (Discrete-Time Survival Analysis Model, DTSAM). Data analyzed through DTSAMs is in the so-called person-period format. The model is a logistic regression model with the event indicator as the dependent variable. However, like many other statistical applications, the practical analysis of discrete-time survival data is challenged by missing data in one or more covariates. Negative consequences of such missing data range from efficiency losses to bias. A popular approach to circumvent these unwanted effects of missing data is multiple imputation (MI). With multiple imputation, it is crucial to include outcome information in the model for imputing partially observed covariates. Unfortunately, this is not straightforward in case of DTSAM, since we (a) usually have a partly observed (left- or right-censored) outcome, (b) do not have only one outcome variable, but two: the event indicator and the time-to-event and (c) have to decide whether to impute while the data set is still in person format or after transformation in person-period format, especially if we look at time-invariant information. Since there is little guidance on how to incorporate the observed outcome information in the imputation model of missing covariates in discrete-time survival analysis, we explore different approaches using fully conditional specification (FCS) (van Buuren 2006) and the newer substantial model compatible (SMC-) FCS MI (Bartlett et al., 2014). These approaches vary in their complexity with which we incorporate the outcome into the imputation model, the FCS algorithm used, and the data format used during the imputation. We compare the methods using Monte Carlo simulations and provide a practical example using data from the German Family Panel pairfam.We confirm the results by White and Royston (2009) and Beesley et al. (2016) that imputing conditional on the (partly imputed) uncensored time-to-event yields high bias. A compatible imputation model for SMC-FCS MI with data in person-period format proves to be the key to imputations with good performance results under different simulation conditions.

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CONTINUOUSLY RECORDED SUCKLING BEHAVIOUR AND ITS EFFECT ON LACTATIONAL AMENORRHOEA

Journal of Biosocial Science ◽

10.1017/s0021932099002898 ◽

1999 ◽

Vol 31 (3) ◽

pp. 289-310 ◽

Cited By ~ 15

Author(s):

H. WILLIAM TAYLOR ◽

MARGARET VÁZQUEZ-GEFFROY ◽

STEVEN J. SAMUELS ◽

DONNA M. TAYLOR

Keyword(s):

Survival Analysis ◽

New Mexico ◽

Menstrual Cycle ◽

Time Dependent ◽

Rate Of Return ◽

Specific Rate ◽

Mexican Women ◽

New Mexican ◽

Time Dependent Covariates ◽

Ovarian Cyclicity

The hypothesis that the month-specific rate of return to ovarian cyclicity after childbirth is causally related to suckling pattern was tested for a population of New Mexican women recruited within the service area of New Mexico Highlands University and for a nationwide USA subpopulation of women recruited through membership of the Couple to Couple League (CCL). Survival analysis for time-dependent covariates was used, and significant predictors of the first postpartum menses were found. Important differences were detected in the suckling pattern for the two groups and a 5:2 differential was found in their respective rates of menstrual cycle recovery. Although the two groups were comparable perinatally, daily and time-windowed breast-feeding performance fell off at twice the rate for the New Mexico population when contrasted with the CCL sample. For both populations, the introduction of solid feeds was a strong and significant predictor of returning menstrual cyclicity, independent of suckling pattern.

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Joint Modelling Approaches to Survival Analysis via Likelihood-Based Boosting Techniques

Computational and Mathematical Methods in Medicine ◽

10.1155/2021/4384035 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Colin Griesbach ◽

Andreas Groll ◽

Elisabeth Bergherr

Keyword(s):

Survival Analysis ◽

Variable Selection ◽

Time Dependent ◽

Gradient Boosting ◽

Joint Models ◽

Cell Counts ◽

Longitudinal Outcome ◽

Event Times ◽

Time Dependent Covariates ◽

Updating Procedure

Joint models are a powerful class of statistical models which apply to any data where event times are recorded alongside a longitudinal outcome by connecting longitudinal and time-to-event data within a joint likelihood allowing for quantification of the association between the two outcomes without possible bias. In order to make joint models feasible for regularization and variable selection, a statistical boosting algorithm has been proposed, which fits joint models using component-wise gradient boosting techniques. However, these methods have well-known limitations, i.e., they provide no balanced updating procedure for random effects in longitudinal analysis and tend to return biased effect estimation for time-dependent covariates in survival analysis. In this manuscript, we adapt likelihood-based boosting techniques to the framework of joint models and propose a novel algorithm in order to improve inference where gradient boosting has said limitations. The algorithm represents a novel boosting approach allowing for time-dependent covariates in survival analysis and in addition offers variable selection for joint models, which is evaluated via simulations and real world application modelling CD4 cell counts of patients infected with human immunodeficiency virus (HIV). Overall, the method stands out with respect to variable selection properties and represents an accessible way to boosting for time-dependent covariates in survival analysis, which lays a foundation for all kinds of possible extensions.

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Multiple Imputation of Missing Data at Level 2: A Comparison of Fully Conditional and Joint Modeling in Multilevel Designs

Journal of Educational and Behavioral Statistics ◽

10.3102/1076998617738087 ◽

2017 ◽

Vol 43 (3) ◽

pp. 316-353 ◽

Cited By ~ 7

Author(s):

Simon Grund ◽

Oliver Lüdtke ◽

Alexander Robitzsch

Keyword(s):

Missing Data ◽

Multiple Imputation ◽

International Student ◽

Student Assessment ◽

Joint Modeling ◽

Computational Procedure ◽

International Student Assessment ◽

Fully Conditional Specification ◽

Using Data ◽

Level 2

Multiple imputation (MI) can be used to address missing data at Level 2 in multilevel research. In this article, we compare joint modeling (JM) and the fully conditional specification (FCS) of MI as well as different strategies for including auxiliary variables at Level 1 using either their manifest or their latent cluster means. We show with theoretical arguments and computer simulations that (a) an FCS approach that uses latent cluster means is comparable to JM and (b) using manifest cluster means provides similar results except in relatively extreme cases with unbalanced data. We outline a computational procedure for including latent cluster means in an FCS approach using plausible values and provide an example using data from the Programme for International Student Assessment 2012 study.

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Multiple Imputation for Multivariate Missing Data: The Joint Modeling Approach

10.1201/9780429156397-6 ◽

2021 ◽

pp. 143-180

Author(s):

Yulei He ◽

Guangyu Zhang ◽

Chiu-Hsieh Hsu

Keyword(s):

Missing Data ◽

Multiple Imputation ◽

Joint Modeling ◽

Modeling Approach

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Estimating trends in the incidence rate with interval censored data and time-dependent covariates

Statistical Methods in Medical Research ◽

10.1177/0962280219829892 ◽

2019 ◽

Vol 29 (1) ◽

pp. 272-281 ◽

Cited By ~ 2

Author(s):

Alain Vandormael ◽

Frank Tanser ◽

Diego Cuadros ◽

Adrian Dobra

Keyword(s):

Multiple Imputation ◽

Incidence Rate ◽

Censored Data ◽

Transformation Model ◽

Time Dependent ◽

Cumulative Distribution ◽

Interval Censored Data ◽

Interval Censored ◽

Time Dependent Covariates ◽

Imputation Approach

We propose a multiple imputation method for estimating the incidence rate with interval censored data and time-dependent (and/or time-independent) covariates. The method has two stages. First, we use a semi-parametric G-transformation model to estimate the cumulative baseline hazard function and the effects of the time-dependent (and/or time-independent covariates) on the interval censored infection times. Second, we derive the participant's unique cumulative distribution function and impute infection times conditional on the covariate values. To assess performance, we simulated infection times from a Cox proportional hazards model and induced interval censoring by varying the testing rate, e.g., participants test 100%, 75%, 50% of the time, etc. We then compared the incidence rate estimates from our G-imputation approach with single random-point and mid-point imputation. By comparison, our G-imputation approach gave more accurate incidence rate estimates and appropriate standard errors for models with time-independent covariates only, time-dependent covariates only, and a mixture of time-dependent and time-independent covariates across various testing rates. We demonstrate, for the first time, a multiple imputation approach for incidence rate estimation with interval censored data and time-dependent (and/or time-independent) covariates.

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