Impact of missing data due to drop‐outs on estimators for rates of change in longitudinal studies: a simulation study

Abstract

Many cohort studies and clinical trials are designed to compare rates of change over time in one or more disease markers in several groups. One major problem in such longitudinal studies is missing data due to patient drop-out. The bias and efficiency of six different methods to estimate rates of changes in longitudinal studies with incomplete observations were compared: generalized estimating equation estimates (GEE) proposed by Liang and Zeger (1986); unweighted average of ordinary least squares (OLSE) of individual rates of change (UWLS); weighted average of OLSE (WLS); conditional linear model estimates (CLE), a covariate type estimates proposed by Wu and Bailey (1989); random effect (RE), and joint multivariate RE (JMRE) estimates. The latter method combines a linear RE model for the underlying pattern of the marker with a log-normal survival model for informative drop-out process. The performance of these methods in the presence of missing data completely at random (MCAR), at random (MAR) and non-ignorable (NIM) were compared in simulation studies. Data for the disease marker were generated under the linear random effects model with parameter values derived from realistic examples in HIV infection. Rates of drop-out, assumed to increase over time, were allowed to be independent of marker values or to depend either only on previous marker values or on both previous and current marker values. Under MACR all six methods yielded unbiased estimates of both group mean rates and between-group difference. However, the cross-sectional view of the data in the GEE method resulted in seriously biased estimates under MAR and NIM drop-out process. The bias in the estimates ranged from 30 per cent to 50 per cent. The degree of bias in the GEE estimates increases with the severity of non-randomness and with the proportion of MAR data. Under MCAR and MAR all the other five methods performed relatively well. RE and JMRE estimates were more efficient(that is, had smaller variance) than UWLS, WLS and CL estimates. Under NIM, WLS and particularly RE estimates tended to underestimate the average rate of marker change (bias approximately 10 per cent). Under NIM, UWLS, CL and JMRE performed better in terms of bias (3-5 per cent) with the JMRE giving the most efficient estimates. Given that markers are key variables related to disease progression, missing marker data are likely to be at least MAR. Thus, the GEE method may not be appropriate for analysing such longitudinal marker data. The potential biases due to incomplete data require greater recognition in reports of longitudinal studies. Sensitivity analyses to assess the effect of drop-outs on inferences about the target parameters are important.

The analysis of incomplete cost data due to dropout

“…Several papers present tailor made methods, pertinent only to the type of data under study (see for instance [22][23][24]). Another category of methods that was excluded were the generalised linear mixed models (GLMM) and its variants generalised estimating equation (GEE) and pattern-mixture models [25][26][27]. Mixed models are generalisations of the general linear model (i.e.…”

A comment on analyzing addictive behaviors over time

“…It is not unusual to observe differential rates of missing data between intervention and control conditions, which could positively bias results toward the intervention (to the extent that missingness is related to the observed outcomes). Indeed, simulation studies have shown that ordinary GEE can yield badly biased estimates (e.g., 30%-50% bias) when the missing data are generated under a MAR process (Touloumi, Babiker, Pocock, & Darbyshire, 2001). Examining missing data patterns and testing assumptions of the missing data mechanisms is vital for the selection of an appropriate analytic technique to address missing data and minimize bias (Houck et al, 2004;Yang & Shoptaw, 2005).…”

Short-term Hormone Therapy with Transdermal Estradiol Improves Cognition for Postmenopausal Women with Alzheimer's Disease: Results of a Randomized Controlled Trial

“…Sensitivity analyses evaluate potential bias caused by missing values in follow-up measures to ensure peak sensitivity at all time points [52, 53] and reliability at time points where attrition is less than 30%. Sensitivity analyses are typically conducted to assess the effect of dropouts on inferences about the target parameters, and are particularly important when the treatment arms are unequal [53].…”

“…Sensitivity analyses evaluate potential bias caused by missing values in follow-up measures to ensure peak sensitivity at all time points [52, 53] and reliability at time points where attrition is less than 30%. Sensitivity analyses are typically conducted to assess the effect of dropouts on inferences about the target parameters, and are particularly important when the treatment arms are unequal [53]. Although there are no clear guidelines regarding the acceptable amount of missing data in a clinical trial (or any longitudinal study), values ranging from 60%–80% as minimum acceptable follow-up rates have been proposed [54–56].…”