The impact of missing data on analyses of a time-dependent exposure in a longitudinal cohort: a simulation study

Development of a long-term time-weighted exposure metric that accounts for missing data in the Seychelles Child Development Study

In many studies of the health effects of toxicants, exposure is measured once even though exposure may be continuous. However, some studies collect repeated measurements on participants over an extended time with the goal of determining a long-term metric that captures the average or cumulative exposure. This can be challenging, especially when exposure is measured at irregular intervals and has some missing values. Here we describe a method for determining a measure of long-term exposure using data on postnatal mercury (Hg) from the Seychelles Child Development Study (SCDS) Main Cohort as a model. In this cohort (n = 779), we incorporate postnatal Hg values that were measured on most study participants at seven ages, three between 6 months and 5.5 years ("childhood"), and an additional four between 17 and 24 years ("early adulthood"). We develop time-weighted measures of average exposure during the childhood and the early adulthood periods and compare the strengths and weaknesses of our metric to two standard measures: overall average and cumulative exposure. We account for missing values through an imputation method that uses information about age- and sex-specific Hg means and the participant's Hg values at similar ages to estimate subject-specific missing Hg values. We compare our method to the implicit imputation assumed by these two standard methods, and to Fully Conditional Specification (FCS), an alternative method of imputing missing data. To determine the accuracy of our imputation method we use data from participants with no missing Hg values in the relevant time window. The imputed values from our proposed method are substantially closer to the observed values on average than the average or cumulative exposure, while also performing slightly better than FCS. In conclusion, time-weighted long-term exposure appears to offer advantages over cumulative exposure in longitudinal studies with repeated measures where the follow-up period for a toxicant is similar for all participants. Additionally, our method to impute missing values maximizes the number of participants for whom the overall exposure metric can be calculated and should provide a more accurate long-term exposure metric than standard methods when exposure has missing values. Our method is applicable to any study of long-term toxicant effects when longitudinal exposure measurements are available but have missing values.

Multiple imputation methods for handling missing values in longitudinal studies with sampling weights: Comparison of methods implemented in Stata

Many analyses of longitudinal cohorts require incorporating sampling weights to account for unequal sampling probabilities of participants, as well as the use of multiple imputation (MI) for dealing with missing data. However, there is no guidance on how MI and sampling weights should be implemented together. We simulated a target population based on the Australian Bureau of Statistics Estimated Resident Population and drew 1000 random samples dependent on three design variables to mimic the Longitudinal Study of Australian Children. The target analysis was the weighted prevalence of overweight/obesity over childhood. We evaluated the performance of several MI approaches available in Stata, based on multivariate normal imputation (MVNI), fully conditional specification (FCS) and twofold FCS: a weighted imputation model, imputing missing data separately for each quintile sampling weight grouping, including the design stratum indicator in the imputation model, and using sampling weights as a covariate in the imputation model. Approaches based on available cases and inverse probability weighting (IPW), with time-varying weights, were also compared. We observed severe issues of convergence with FCS and twofold FCS. All MVNI-based approaches performed similarly, producing minimal bias and nominal coverage, except for when imputation was conducted separately for each quintile sampling weight group. IPW performed equally as well as MVNI-based approaches in terms of bias, however, was less precise. In similar longitudinal studies, we recommend using MVNI with the design stratum as a covariate in the imputation model. If this is unknown, including the sampling weight as a covariate is an appropriate alternative.

Multiple imputation methods for handling missing values in a longitudinal categorical variable with restrictions on transitions over time: a simulation study

Background

Longitudinal categorical variables are sometimes restricted in terms of how individuals transition between categories over time. For example, with a time-dependent measure of smoking categorised as never-smoker, ex-smoker, and current-smoker, current-smokers or ex-smokers cannot transition to a never-smoker at a subsequent wave. These longitudinal variables often contain missing values, however, there is little guidance on whether these restrictions need to be accommodated when using multiple imputation methods. Multiply imputing such missing values, ignoring the restrictions, could lead to implausible transitions.

Methods

We designed a simulation study based on the Longitudinal Study of Australian Children, where the target analysis was the association between (incomplete) maternal smoking and childhood obesity. We set varying proportions of data on maternal smoking to missing completely at random or missing at random. We compared the performance of fully conditional specification with multinomial and ordinal logistic imputation, and predictive mean matching, two-fold fully conditional specification, indicator based imputation under multivariate normal imputation with projected distance-based rounding, and continuous imputation under multivariate normal imputation with calibration, where each of these multiple imputation methods were applied, accounting for the restrictions using a semi-deterministic imputation procedure.

Results

Overall, we observed reduced bias when applying multiple imputation methods with restrictions, and fully conditional specification with predictive mean matching performed the best. Applying fully conditional specification and two-fold fully conditional specification for imputing nominal variables based on multinomial logistic regression had severe convergence issues. Both imputation methods under multivariate normal imputation produced biased estimates when restrictions were not accommodated, however, we observed substantial reductions in bias when restrictions were applied with continuous imputation under multivariate normal imputation with calibration.

Conclusion

In a similar longitudinal setting we recommend the use of fully conditional specification with predictive mean matching, with restrictions applied during the imputation stage.

Electronic supplementary material

The online version of this article (10.1186/s12874-018-0653-0) contains supplementary material, which is available to authorized users.

A comparison of multiple imputation methods for handling missing values in longitudinal data in the presence of a time-varying covariate with a non-linear association with time: a simulation study

Background

Missing data is a common problem in epidemiological studies, and is particularly prominent in longitudinal data, which involve multiple waves of data collection. Traditional multiple imputation (MI) methods (fully conditional specification (FCS) and multivariate normal imputation (MVNI)) treat repeated measurements of the same time-dependent variable as just another ‘distinct’ variable for imputation and therefore do not make the most of the longitudinal structure of the data. Only a few studies have explored extensions to the standard approaches to account for the temporal structure of longitudinal data. One suggestion is the two-fold fully conditional specification (two-fold FCS) algorithm, which restricts the imputation of a time-dependent variable to time blocks where the imputation model includes measurements taken at the specified and adjacent times. To date, no study has investigated the performance of two-fold FCS and standard MI methods for handling missing data in a time-varying covariate with a non-linear trajectory over time – a commonly encountered scenario in epidemiological studies.

Methods

We simulated 1000 datasets of 5000 individuals based on the Longitudinal Study of Australian Children (LSAC). Three missing data mechanisms: missing completely at random (MCAR), and a weak and a strong missing at random (MAR) scenarios were used to impose missingness on body mass index (BMI) for age z-scores; a continuous time-varying exposure variable with a non-linear trajectory over time. We evaluated the performance of FCS, MVNI, and two-fold FCS for handling up to 50% of missing data when assessing the association between childhood obesity and sleep problems.

Results

The standard two-fold FCS produced slightly more biased and less precise estimates than FCS and MVNI. We observed slight improvements in bias and precision when using a time window width of two for the two-fold FCS algorithm compared to the standard width of one.

Conclusion

We recommend the use of FCS or MVNI in a similar longitudinal setting, and when encountering convergence issues due to a large number of time points or variables with missing values, the two-fold FCS with exploration of a suitable time window.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-017-0372-y) contains supplementary material, which is available to authorized users.

Drug Burden Index and change in cognition over time in community-dwelling older men: the CHAMP study

OBJECTIVE

Anticholinergic and sedative medications are associated with acute cognitive impairment, but the long-term impact on change in cognition is unclear. This study investigated the effect of anticholinergic and sedative medications, quantified using the Drug Burden Index (DBI), on change in cognition over time in community-dwelling older men.

METHODS

This was a prospective cohort study of men aged ≥70 years in Sydney, Australia. DBI was assessed at baseline, 2, and 5 years. Cognitive performance was assessed using the Mini-Mental State Exam (MMSE) at each wave. Logistic quantile mixed-effects modelling was used to assess the adjusted effect of DBI on the median MMSE-time profile. Analyses were restricted to men with English-speaking backgrounds (n = 1059, 862, and 611 at baseline, 2, and 5 years).

RESULTS

Overall, 292 (27.7%), 258 (29.9%), and 189 (31.3%) men used anticholinergic or sedative medications at baseline, 2, and 5 years. There was a concave relationship between MMSE and time, where higher DBI corresponded to lower MMSE scores (coefficient: -0.161; 95% CI: -0.250 to -0.071) but not acceleration of declining MMSE over time.

CONCLUSIONS

Exposure to anticholinergic and sedative medications is associated with a small impairment in cognitive performance but not decline in cognition over time. KEY MESSAGES Exposure to anticholinergic and sedative medications, quantified using the Drug Burden Index, is associated with small cross-sectional impairments in cognitive performance. There was no evidence that exposure to anticholinergic and sedative medications is associated with accelerating decline in cognitive performance over a 5-year follow-up. Older people taking anticholinergic and sedative medications may derive immediate but small benefits in cognitive performance from clinical medication reviews to minimize or cease prescribing of these medications.

Breast Cancer and Modifiable Lifestyle Factors in Argentinean Women: Addressing Missing Data in a Case-Control Study

A number of studies have evidenced the effect of modifiable lifestyle factors such as diet, breastfeeding and nutritional status on breast cancer risk. However, none have addressed the missing data problem in nutritional epidemiologic research in South America. Missing data is a frequent problem in breast cancer studies and epidemiological settings in general. Estimates of effect obtained from these studies may be biased, if no appropriate method for handling missing data is applied. We performed Multiple Imputation for missing values on covariates in a breast cancer case-control study of Córdoba (Argentina) to optimize risk estimates. Data was obtained from a breast cancer case control study from 2008 to 2015 (318 cases, 526 controls). Complete case analysis and multiple imputation using chained equations were the methods applied to estimate the effects of a Traditional dietary pattern and other recognized factors associated with breast cancer. Physical activity and socioeconomic status were imputed. Logistic regression models were performed. When complete case analysis was performed only 31% of women were considered. Although a positive association of Traditional dietary pattern and breast cancer was observed from both approaches (complete case analysis OR=1.3, 95%CI=1.0-1.7; multiple imputation OR=1.4, 95%CI=1.2-1.7), effects of other covariates, like BMI and breastfeeding, were only identified when multiple imputation was considered. A Traditional dietary pattern, BMI and breastfeeding are associated with the occurrence of breast cancer in this Argentinean population when multiple imputation is appropriately performed. Multiple Imputation is suggested in Latin America’s epidemiologic studies to optimize effect estimates in the future.

Effects of Changes in Number of Medications and Drug Burden Index Exposure on Transitions Between Frailty States and Death: The Concord Health and Ageing in Men Project Cohort Study

OBJECTIVES

To investigate the effects of number of medications and Drug Burden Index (DBI) on transitions between frailty stages and death in community-dwelling older men.

DESIGN

Cohort study.

SETTING

Sydney, Australia.

PARTICIPANTS

Community-dwelling men aged 70 and older (N=1,705).

MEASUREMENTS

Self-reported questionnaires and clinic visits were conducted at baseline and 2 and 5 years. Frailty was assessed at all three waves according to the modified Fried frailty phenotype. The total number of regular prescription medications and DBI (a measure of exposure to sedative and anticholinergic medications) were calculated over the three waves. Data on mortality over 9 years were obtained. Multistate modeling was used to characterize the transitions across three frailty states (robust, prefrail, frail) and death.

RESULTS

Each additional medication was associated with a 22% greater risk of transitioning from the robust state to death (adjusted 95% confidence interval (CI)=1.06-1.41). Every unit increase in DBI was associated with a 73% greater risk of transitioning from the robust state to the prefrail state (adjusted 95% CI=1.30-2.31) and a 2.75 times greater risk of transitioning from the robust state to death (adjusted 95% CI=1.60-4.75). There was no evidence of an adjusted association between total number of medications or DBI and the other transitions.

CONCLUSION

Although the possibility of confounding by indication cannot be excluded, additional medications were associated with greater risk of mortality in robust community-dwelling older men. Greater DBI was also associated with greater risk of death and transitioning from the robust state to the prefrail state.

Quantification of the smoking-associated cancer risk with rate advancement periods: meta-analysis of individual participant data from cohorts of the CHANCES consortium

BACKGROUND

Smoking is the most important individual risk factor for many cancer sites but its association with breast and prostate cancer is not entirely clear. Rate advancement periods (RAPs) may enhance communication of smoking related risk to the general population. Thus, we estimated RAPs for the association of smoking exposure (smoking status, time since smoking cessation, smoking intensity, and duration) with total and site-specific (lung, breast, colorectal, prostate, gastric, head and neck, and pancreatic) cancer incidence and mortality.

METHODS

This is a meta-analysis of 19 population-based prospective cohort studies with individual participant data for 897,021 European and American adults. For each cohort we calculated hazard ratios (HRs) for the association of smoking exposure with cancer outcomes using Cox regression adjusted for a common set of the most important potential confounding variables. RAPs (in years) were calculated as the ratio of the logarithms of the HRs for a given smoking exposure variable and age. Meta-analyses were employed to summarize cohort-specific HRs and RAPs.

RESULTS

Overall, 140,205 subjects had a first incident cancer, and 53,164 died from cancer, during an average follow-up of 12 years. Current smoking advanced the overall risk of developing and dying from cancer by eight and ten years, respectively, compared with never smokers. The greatest advancements in cancer risk and mortality were seen for lung cancer and the least for breast cancer. Smoking cessation was statistically significantly associated with delays in the risk of cancer development and mortality compared with continued smoking.

CONCLUSIONS

This investigation shows that smoking, even among older adults, considerably advances, and cessation delays, the risk of developing and dying from cancer. These findings may be helpful in more effectively communicating the harmful effects of smoking and the beneficial effect of smoking cessation.

Change in weight and waist circumference and risk of colorectal cancer: results from the Melbourne Collaborative Cohort Study

BACKGROUND

Studies reporting the association between change in weight or body mass index during midlife and risk of colorectal cancer have found inconsistent results, and only one study to date has reported the association between change in waist circumference (a measure of central adiposity) and risk of colorectal cancer.

METHODS

We investigated the association between risk of colorectal cancer and changes in directly measured waist circumference and weight from baseline (1990-1994) to wave 2 (2003-2007). Cox regression, with age as the time metric and follow-up starting at wave 2, adjusted for covariates selected from a causal model, was used to estimate the Hazard Ratios (HRs) and 95 % Confidence Intervals (CIs) for the change in waist circumference and weight in relation to risk of colorectal cancer.

RESULTS

A total of 373 cases of colorectal cancer were diagnosed during an average 9 years of follow-up of 20,605 participants. Increases in waist circumference and weight were not associated with the risk of colorectal cancer (HR per 5 cm increase in waist circumference = 1.02; 95 % CI: 0.95, 1.10; HR per 5 kg increase in weight = 0.93; 0.85, 1.02). For individuals with a waist circumference at baseline that was less than the sex-specific mean value there was a slight increased risk of colorectal cancer associated with a 5 cm increase in waist circumference at wave 2 (HR = 1.08; 0.97, 1.21).

CONCLUSION

Increases in waist circumference and weight during midlife do not appear to be associated with the risk of colorectal cancer.

Are trajectories of self-regulation abilities from ages 2-3 to 6-7 associated with academic achievement in the early school years?

BACKGROUND

The aim of this study was to estimate the association between two key aspects of self-regulation, 'task attentiveness' and 'emotional regulation' assessed from ages 2-3 to 6-7 years, and academic achievement when children were aged 6-7 years.

METHODS

Participants (n = 3410) were children in the Longitudinal Study of Australian Children. Parents rated children's task attentiveness and emotional regulation abilities when children were aged 2-3, 4-5 and 6-7. Academic achievement was assessed using the Academic Rating Scale completed by teachers. Linear regression models were used to estimate the association between developmental trajectories (i.e. rate of change per year) of task attentiveness and emotional regulation, and academic achievement at 6-7 years.

RESULTS

Improvements in task attentiveness between 2-3 and 6-7 years, adjusted for baseline levels of task attentiveness, child and family confounders, and children's receptive vocabulary and non-verbal reasoning skills at age 6-7 were associated with greater teacher-rated literacy [B = 0.05, 95% confidence interval (CI) = 0.04-0.06] and maths achievement (B = 0.04, 95% CI = 0.03-0.06) at 6-7 years. Improvements in emotional regulation, adjusting for baseline levels and covariates, were also associated with better teacher-rated literacy (B = 0.02, 95% CI = 0.01-0.04) but not with maths achievement (B = 0.01, 95% CI = -0.01-0.02) at 6-7 years. For literacy, improvements in task attentiveness had a stronger association with achievement at 6-7 years than improvements in emotional regulation.

CONCLUSIONS

Our study shows that improved trajectories of task attentiveness from ages 2-3 to 6-7 years are associated with improved literacy and maths achievement during the early school years. Trajectories of improving emotional regulation showed smaller effects on academic outcomes. Results suggest that interventions that improve task attentiveness when children are aged 2-3 to 6-7 years have the potential to improve literacy and maths achievement during the early school years.

Using decision trees to understand structure in missing data

OBJECTIVES

Demonstrate the application of decision trees--classification and regression trees (CARTs), and their cousins, boosted regression trees (BRTs)--to understand structure in missing data.

SETTING

Data taken from employees at 3 different industrial sites in Australia.

PARTICIPANTS

7915 observations were included.

MATERIALS AND METHODS

The approach was evaluated using an occupational health data set comprising results of questionnaires, medical tests and environmental monitoring. Statistical methods included standard statistical tests and the 'rpart' and 'gbm' packages for CART and BRT analyses, respectively, from the statistical software 'R'. A simulation study was conducted to explore the capability of decision tree models in describing data with missingness artificially introduced.

RESULTS

CART and BRT models were effective in highlighting a missingness structure in the data, related to the type of data (medical or environmental), the site in which it was collected, the number of visits, and the presence of extreme values. The simulation study revealed that CART models were able to identify variables and values responsible for inducing missingness. There was greater variation in variable importance for unstructured as compared to structured missingness.

DISCUSSION

Both CART and BRT models were effective in describing structural missingness in data. CART models may be preferred over BRT models for exploratory analysis of missing data, and selecting variables important for predicting missingness. BRT models can show how values of other variables influence missingness, which may prove useful for researchers.

CONCLUSIONS

Researchers are encouraged to use CART and BRT models to explore and understand missing data.

Change in body size and mortality: results from the Melbourne collaborative cohort study

BACKGROUND

The association between change in weight or body mass index, and mortality is widely reported, however, both measures fail to account for fat distribution. Change in waist circumference, a measure of central adiposity, in relation to mortality has not been studied extensively.

METHODS

We investigated the association between mortality and changes in directly measured waist circumference, hips circumference and weight from baseline (1990-1994) to wave 2 (2003-2007) in a prospective cohort study of people aged 40-69 years at baseline. Cox regression, with age as the time metric and follow-up starting at wave 2, adjusted for confounding variables, was used to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) for change in body size in relation to mortality from all causes, cardiovascular disease and cancer.

RESULTS

There were 1465 deaths (109 cancer, 242 cardiovascular disease) identified during an average 7.7 years of follow-up from 21 298 participants. Compared to minimal increase in body size, loss of waist circumference (HR: 1.26; 95% CI: 1.09-1.47), weight (1.80; 1.54-2.11), or hips circumference (1.35; 1.15-1.57) were associated with an increased risk of all-cause mortality, particularly for older adults. Weight loss was associated with cardiovascular disease mortality (2.40; 1.57-3.65) but change in body size was not associated with obesity-related cancer mortality.

CONCLUSION

This study confirms the association between weight loss and increased mortality from all-causes for older adults. Based on evidence from observational cohort studies, weight stability may be the recommended option for most adults, especially older adults.

Introduction to multiple imputation for dealing with missing data

Missing data are common in both observational and experimental studies. Multiple imputation (MI) is a two-stage approach where missing values are imputed a number of times using a statistical model based on the available data and then inference is combined across the completed datasets. This approach is becoming increasingly popular for handling missing data. In this paper, we introduce the method of MI, as well as a discussion surrounding when MI can be a useful method for handling missing data and the drawbacks of this approach. We illustrate MI when exploring the association between current asthma status and forced expiratory volume in 1 s after adjustment for potential confounders using data from a population-based longitudinal cohort study.