Midpoint Imputation Research Articles

Left, Right, Midpoint and Random Point Imputation Techniques for Weibull Regression Model with Right and Interval-Censored Data”

The research explores several imputation techniques, namely left, right, midpoint and random imputations for the MLE of the Weibull regression model with covariate for uncensored, right, and interval-censored data. A simulation study is conducted to obtain the parameter estimates of the model with different imputation techniques, sample sizes, and censoring proportions and its performance are evaluated using bias, standard error (SE), and root mean square error (RMSE). The simulation result indicates that midpoint imputation technique outperformed other techniques based on the lowest RMSE values. Finally, the model was fit to diabetic nephropathy data were fitted to the model using selected imputation techniques. The result concluded that the Weibull regression model may provide a good fit to the data and that the covariate, gender has a significant effect on the survival time of patient kidneys.

Improvement of Midpoint Imputation for Estimation of Median Survival Time for Interval-Censored Time-to-Event Data.

Progression-free survival (PFS) is used to evaluate treatment effects in cancer clinical trials. Disease progression (DP) in patients is typically determined by radiological testing at several scheduled tumor-assessment time points. This produces a discrepancy between the true progression time and the observed progression time. When the observed progression time is considered as the true progression time, a positively biased PFS is obtained for some patients, and the estimated survival function derived by the Kaplan-Meier method is also biased. While the midpoint imputation method is available and replaces interval-censored data with midpoint data, it unrealistically assumes that several DPs occur at the same time point when several DPs are observed within the same tumor-assessment interval. We enhanced the midpoint imputation method by replacing interval-censored data with equally spaced timepoint data based on the number of observed interval-censored data within the same tumor-assessment interval. The root mean square error of the median of the enhanced method is almost always smaller than that of the midpoint imputation regardless of the tumor-assessment frequency. The coverage probability of the enhanced method is close to the nominal confidence level of 95% in most scenarios. We believe that the enhanced method, which builds upon the midpoint imputation method, is more effective than the midpoint imputation method itself.

Socioeconomic inequalities in type 2 diabetes and job demands/control/support - The Maastricht Study

Abstract Background Low socioeconomic position (SEP) is an important determinant of Type 2 Diabetes Mellitus (T2DM). Adverse environments in the exposome might be involved; however, the environmental factors are under-studied compared to lifestyle. We explored low job control, high job demands, and low job support as pathways between SEP and T2DM. Methods Cross-sectional and longitudinal data from 8,090 participants of The Maastricht Study were used. Prevalent T2DM was measured by an oral glucose tolerance test and incident T2DM was self-reported in annual follow-up questionnaires. SEP was operationalized by baseline measures of education, occupation, and income. The work stressors were measured by questionnaires at baseline. For Cox regression, the survival time was computed by midpoint imputation. The associations of SEP, job demands, control, and support with T2DM were examined as well as the mediating role of the work stressors by using a counterfactual framework. Results 2.8% (N = 172) of the participants without T2DM at baseline reported incident T2DM. People with lower SEP were more likely to report T2DM during the follow-up course (e.g.; education HR = 2.21, 95%CI: 1.53-3.20) and more often had prevalent T2DM. Low job control was associated with prevalent T2DM (OR = 1.44 95%CI: 1.25-1.67), but not with incident T2DM. Job control explained 7.23% of the relationship between income and prevalent T2DM. Job demand suppressed the relationship of education (3.65%) and occupation (3.72%) with prevalent T2DM. Conclusions Our findings provide modest evidence for environmental injustice in T2DM exposome. The substantial higher risks of diabetes in low SEP is to a small extent explained by lower control at work. Furthermore, by having lower psychosocial job demands, they are protected against T2DM. Key messages • Job demands and control play a role in SEP and prevalent T2DM relationship. • Work stressors might not be a major target for tackling socioeconomic inequalities in type 2 diabetes.

Modeling lifetime of parallel components system with covariate, right and interval censored data

This research aims to model the lifetime of parallel components system with covariates, right, and interval censored data. The lifetimes of the components are assumed to follow the exponential distribution, with constant failure rates. A simulation study is conducted to assess the performance of the maximum likelihood estimates, without and with midpoint imputation method at various sample sizes, censoring proportions, and number of components in the system. The combination which produces the best parameter estimates is then identified by comparing the bias, standard error and root mean square error of these estimates. The simulation results indicate that the midpoint imputation method produces more efficient and accurate parameter estimates with smaller bias, standard error and root mean square error. Also, in general, better estimates are obtained at low censoring levels, large sample sizes, and a high number of parallel components in the system. The proposed model is then fitted to a modified real data of diabetic retinopathy patients. Following that, the non-parametric log-rank test and Wald hypothesis test are carried out to check the significance of the covariate, age in the model. The results show that the model fits the data rather well and the age of patients has no significant effect on the survival time of the patients’ eyes.

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

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.

Incidence rate estimation, periodic testing and the limitations of the mid-point imputation approach.

BackgroundIt is common to use the mid-point between the latest-negative and earliest-positive test dates as the date of the infection event. However, the accuracy of the mid-point method has yet to be systematically quantified for incidence studies once participants start to miss their scheduled test dates.MethodsWe used a simulation-based approach to generate an infectious disease epidemic for an incidence cohort with a high (80–100%), moderate (60–79.9%), low (40–59.9%) and poor (30–39.9%) testing rate. Next, we imputed a mid-point and random-point value between the participant’s latest-negative and earliest-positive test dates. We then compared the incidence rate derived from these imputed values with the true incidence rate generated from the simulation model.ResultsThe mid-point incidence rate estimates erroneously declined towards the end of the observation period once the testing rate dropped below 80%. This decline was in error of approximately 9%, 27% and 41% for a moderate, low and poor testing rate, respectively. The random-point method did not introduce any systematic bias in the incidence rate estimate, even for testing rates as low as 30%.ConclusionsThe mid-point assumption of the infection date is unjustified and should not be used to calculate the incidence rate once participants start to miss the scheduled test dates. Under these conditions, we show an artefactual decline in the incidence rate towards the end of the observation period. Alternatively, the single random-point method is straightforward to implement and produces estimates very close to the true incidence rate.

A Logspline Estimation for a Linear Regression Model with an Interval-Censored Continuous Covariate

The study of a linear regression model with an interval-censored covariate, which was motivated by an acquired immunodeficiency syndrome (AIDS) clinical trial, was first proposed by Gómez et al. They developed a likelihood approach, together with a two-step conditional algorithm, to estimate the regression coefficients in the model. However, their method is inapplicable when the interval-censored covariate is continuous. In this article, we propose a novel and fast method to treat the continuous interval-censored covariate. By using logspline density estimation, we impute the interval-censored covariate with a conditional expectation. Then, the ordinary least-squares method is applied to the linear regression model with the imputed covariate. To assess the performance of the proposed method, we compare our imputation with the midpoint imputation and the semiparametric hierarchical method via simulations. Furthermore, an application to the AIDS clinical trial is presented.

OP0068 Rheumatoid Arthritis Atlantoaxoidal Subluxation in Biological Era

BackgroundRheumatoid arthritis (RA) is a chronic, systemic inflammatory disease that affects synovial joints. Cervical spine damage, due to rheumatoid inflammation, may produces atlantoaxial subluxation that can produce severe neurological symptoms....

Local regression when the responses are Interval-Censored

Conditional expectation imputation and local-likelihood methods are contrasted with a midpoint imputation method for bivariate regression involving interval-censored responses. Although the methods can be extended in principle to higher order polynomials, our focus is on the local constant case. Comparisons are based on simulations of data scattered about three target functions with normally distributed errors. Two censoring mechanisms are considered: the first is analogous to current-status data in which monitoring times occur according to a homogeneous Poisson process; the second is analogous to a coarsening mechanism such as would arise when the response values are binned. We find that, according to a pointwise MSE criterion, no method dominates any other when interval sizes are fixed, but when the intervals have a variable width, the local-likelihood method often performs better than the other methods, and midpoint imputation performs the worst. Several illustrative examples are presented.

Simple parametric survival analysis with anonymized register data: A cohort study with truncated and interval censored event and censoring times

BackgroundTo preserve patient anonymity, health register data may be provided as binned data only. Here we consider as example, how to estimate mean survival time after a diagnosis of metastatic colorectal cancer from Norwegian register data on time to death or censoring binned into 30 day intervals. All events occurring in the first three months (90 days) after diagnosis were removed to achieve comparability with a clinical trial. The aim of the paper is to develop and implement a simple, and yet flexible method for analyzing such interval censored and truncated data.MethodsConsidering interval censoring a missing data problem, we implement a simple multiple imputation strategy that allows flexible sensitivity analyses with respect to the shape of the censoring distribution. To allow identification of appropriate parametric models, a χ2-goodness-of-fit test--also imputation based--is derived and supplemented with diagnostic plots. Uncertainty estimates for mean survival times are obtained via a simulation strategy. The validity and statistical efficiency of the proposed method for varying interval lengths is investigated in a simulation study and compared with simpler alternatives.ResultsMean survival times estimated from the register data ranged from 1.2 (SE = 0.09) to 3.2 (0.31) years depending on period of diagnosis and choice of parametric model. The shape of the censoring distribution within intervals did generally not influence results, whereas the choice of parametric model did, even when different models fit the data equally well. In simulation studies both simple midpoint imputation and multiple imputation yielded nearly unbiased analyses (relative biases of -0.6% to 9.4%) and confidence intervals with near-nominal coverage probabilities (93.4% to 95.7%) for censoring intervals shorter than six months. For 12 month censoring intervals, multiple imputation provided better protection against bias, and coverage probabilities closer to nominal values than simple midpoint imputation.ConclusionBinning of event and censoring times should be considered a viable strategy for anonymizing register data on survival times, as they may be readily analyzed with methods based on multiple imputation.

Estimation of colorectal adenoma recurrence with dependent censoring

BackgroundDue to early colonoscopy for some participants, interval-censored observations can be introduced into the data of a colorectal polyp prevention trial. The censoring could be dependent of risk of recurrence if the reasons of having early colonoscopy are associated with recurrence. This can complicate estimation of the recurrence rate.MethodsWe propose to use midpoint imputation to convert interval-censored data problems to right censored data problems. To adjust for potential dependent censoring, we use information from auxiliary variables to define risk groups to perform the weighted Kaplan-Meier estimation to the midpoint imputed data. The risk groups are defined using two risk scores derived from two working proportional hazards models with the auxiliary variables as the covariates. One is for the recurrence time and the other is for the censoring time. The method described here is explored by simulation and illustrated with an example from a colorectal polyp prevention trial.ResultsWe first show that midpoint imputation under an assumption of independent censoring will produce an unbiased estimate of recurrence rate at the end of the trial, which is often the main interest of a colorectal polyp prevention trial, and then show in simulations that the weighted Kaplan-Meier method using the information from auxiliary variables based on the midpoint imputed data can improve efficiency in a situation with independent censoring and reduce bias in a situation with dependent censoring compared to the conventional methods, while estimating the recurrence rate at the end of the trial.ConclusionThe research in this paper uses midpoint imputation to handle interval-censored observations and then uses the information from auxiliary variables to adjust for dependent censoring by incorporating them into the weighted Kaplan-Meier estimation. This approach can handle a situation with multiple auxiliary variables by deriving two risk scores from two working PH models. Although the idea of this approach might appear simple, the results do show that the weighted Kaplan-Meier approach can gain efficiency and reduce bias due to dependent censoring.

Analysis of Colorectal Adenoma Recurrence Data Subject to Informative Censoring

The treatment effect of a colorectal polyp prevention trial is often evaluated from the colorectal adenoma recurrence status at the end of the trial. However, early colonoscopy from some participants complicates estimation of the final study end recurrence rate. The early colonoscopy could be informative of status of recurrence and induce informative differential follow-up into the data. In this article, we use midpoint imputation to handle interval-censored observations. We then apply a weighted Kaplan-Meier method to the imputed data to adjust for potential informative differential follow-up, while estimating the recurrence rate at the end of the trial. In addition, we modify the weighted Kaplan-Meier method to handle a situation with multiple prognostic covariates by deriving a risk score of recurrence from a working logistic regression model and then use the risk score to define risk groups to perform weighted Kaplan-Meier estimation. We argue that midpoint imputation will produce an unbiased estimate of recurrence rate at the end of the trial under an assumption that censoring only depends on the status of early colonoscopy. The method described here is illustrated with an example from a colon polyp prevention study.

Nonparametric Estimation of the Joint Distribution of a Survival Time Subject to Interval Censoring and a Continuous Mark Variable

This article considers three nonparametric estimators of the joint distribution function for a survival time and a continuous mark variable when the survival time is interval censored and the mark variable may be missing for interval-censored observations. Finite and large sample properties are described for the nonparametric maximum likelihood estimator (NPMLE) as well as estimators based on midpoint imputation (MIDMLE) and coarsening the mark variable (CMLE). The estimators are compared using data from a simulation study and a recent phase III HIV vaccine efficacy trial where the survival time is the time from enrollment to infection and the mark variable is the genetic distance from the infecting HIV sequence to the HIV sequence in the vaccine. Theoretical and empirical evidence are presented indicating the NPMLE and MIDMLE are inconsistent. Conversely, the CMLE is shown to be consistent in general and thus is preferred.

Behavior of the Kaplan-Meier Estimator for Deterministic Imputations to Interval-Censored Data and the Turnbull Estimator

Despite the fact that the left-point imputation for the interval-censored data produces shorter individual survival time than the right-point imputation, we observe that the Kaplan-Meier estimator based on the left-point imputation can sometimes produce greater survival rate than the right-point imputation during certain period of time interval. In practice, if the exact date of occurrence is not known due to interval-censoring, the date of examination when the event was observed is most often recorded as though the exact time of event (right-point imputation). Therefore, we investigated behavior of the deterministic imputations for the Kaplan-Meier estimator and compared with the Turnbull estimator (1976), a standard analysis of interval-censored data, by simulation. The mid-point imputation is shown to have smallest mean squared errors at most range of time under moderate to small censoring for all hazard rates investigated here, although ad hoc estimators of SE underestimate true SE. Under heavy censoring, either the right-, mid-or left-point imputations are shown to have smallest mean squared errors over certain periods. The right-point imputation (KMR) may be acceptable with large percent right-censored under increasing hazard. On the other hand, the Turnbull estimator (TB) is usually not shown to have smallest mean squared errors. We find a systematic bias of TB at tail similar to that of KMR.

A Markov Chain Monte Carlo EM Algorithm for Analyzing Interval-Censored Data under the Cox Proportional Hazards Model

This paper proposes a Monte Carlo EM (MCEM) algorithm for fitting the proportional hazards model for interval-censored failure-time data. The algorithm generates orderings of the failures from their probability distribution under the model. We maximize the average of the log-likelihoods from these completed data sets to obtain updated parameter estimates. As with the standard Cox model, this algorithm does not require the estimation of the baseline hazard function. The performance of the algorithm is evaluated using simulations, and the method is applied to data from AIDS and cancer studies. Our results indicate that our method produced more precise and unbiased estimates than methods of right and midpoint imputation.

Effects of mid-point imputation on the analysis of doubly censored data.

Doubly censored data arise in some cohort studies of the AIDS incubation period because the time of infection may be known only up to an interval defined by two successive screening tests for HIV antibody. A simple analytic approach is to impute the infection time by the mid-point of the interval and then apply standard survival techniques for right censored data. The objective of this paper is to investigate the statistical properties of such a mid-point imputation approach. We investigated the asymptotic bias of the Kaplan-Meier estimate, coverage probabilities of associated confidence intervals, bias in hazard ratio, and the size of the logrank test. We show that the statistical properties of mid-point imputation depend strongly on the underlying distributions of infection times and the incubation periods, and the width of the interval between screening tests. In the absence of treatment, the median incubation period of HIV infection is approximately 10 years, and we conclude that, for this situation, mid-point imputation is a reasonable procedure for interval widths of 2 years or less.