List of Abbreviations
2) Stability of sleep clusters over time
This sub-study examined exactly the same UKHLS participants over two discrete time points (i.e. using data they provided at Wave 1 and again at Wave 4). The aim was to assess whether the same (number and classification of) sleep clusters would be generated using LCA on data from the same participants (regardless of any changes in the membership of individuals to any given sleep cluster) over time.
2.5.2.4 LCA power assessment
During the literature searches conducted in the course of the present thesis, no appropriate “rule of thumb” emerged for conducting LCA power estimation, although several authors have made related recommendations. One of these suggested that there should, ideally, be 10-15 observations per parameter, which implies that in the present thesis’ LCA analyses, at least 210 to 315 participants would be required for the 21 discrete sleep parameters assessed using the UKHLS sleep module (i.e. those that were used in generating the latent sleep models; Comrey and Lee, 1992). An alternative recommendation was that no latent class analysis should be conducted on samples smaller than 100 participants (Gorsuch,1983, Kline,1979); while a sample of 1000 participants was felt sufficient to generate ‘excellent’ analytical power (Comrey and Lee, 1992). Likewise, a sample of 200-250 was felt to afford ‘fair’ estimation power (Comrey and Lee, 1992, Cattell, 1978, Guilford, 1954). Meanwhile, on the basis of several Monto Carlo studies simulations, some authors suggest that a larger sample size can be required when the aim of the LCA analyses is to detect small-sized clusters or a larger number of clusters, and when larger numbers of indicators with limited variability across the sample are used (Dziak et al., 2014, Tein et al., 2013, Nylund et al., 2007). As such, all of these (somewhat eclectic) recommendations suggest that the analyses undertaken for this part of the present thesis had ample
power, since the UKHLS dataset drew on a population-based study with a very large sample size (>50,000 households) – a sample that was more than large and variable enough to ensure a sufficient level of power to estimate cluster-based classifications using LCA analysis.
2.5.3 The treatment of missing data
Prior to the exclusion of missing data, these data were examined for the “missing at random” assumption. Missing completely at random means that the missing data do not systematically differ from the observed data, since the cause of missingness is unrelated to the data (van Buuren, 2012). However, missing completely at random is extremely difficult to assess, thus a broader assumption ‒ missing at random ‒ was examined instead (Van Buuren, 2012, Cattle et al., 2011). The missing at random assumption means that any possible systematic difference between the missing data and the observed data could be explained by differences in the characteristics of the observed data (Van Buuren, 2012, Sterne at al., 2009). For example, missing blood pressure measurements might be lower than reported blood pressure measurements but only because women in their very early pregnancy may be more likely to have missing blood pressure measurements (Sterne at al., 2009). It was important to assess the “missing not at random” assumption, as this would bias the estimates generated by analyses in which variables and/or participants were excluded on the basis of missing data (Allison, 2002). Missing not at random simply means that the missing data are systematically different from the observed data for reasons that can not be explained by the observed characteristics of the data (Van Buuren, 2012, Cattle et al., 2011). For instance, participants with low socioeconomic status might avoid reporting their income because of their hidden worries (Cattle et al., 2011) or pregnant women with GHTN might not attend their antenatal care clinic because they have headache (Sterne et al., 2009).
In the present thesis, it was originally considered worthwhile using multiple imputation to deal with missing data, since multiple imputation is considered superior to all other method for treating missing data (Van Buuren, 2012, Rubin, 2004). However, rather than imputing values for missing data, the variables and/or participants with any missing data were instead simply excluded (i.e.listwise deletion) – a technique that deals with missingness but only at the risk of creating biased analytical samples, and decreasing the statistical power of the sample available for analysis. However, this approach (variable or participant deletion) may still be superior to most other imputation techniques (particularly simple ones), as it is capable of generating a
sample on which an unbiased estimate can be calculated provided the “missing at random” assumption can be upheld (Allison, 2002). That said, multiple imputation (a complex, multistage imputation method, recommended by many authors including Rubin, 1996), would not have biased the estimate, and would have improved the standard error of the estimate and preserved the power of the analyses (Van Buuren, 2012, Rubin, 2004). However, Sterne et al. (2009) have pointed out that a lack of experience in multiple imputation can often generate misleading results and incorrect conclusions (Sterne et al., 2009). In the event, multiple imputations could not be used to address problems with missing data in the UKHLS dataset due to computational limitations, many of which resulted from the sheer size and complexity of the UKHLS dataset (i.e. a very large dataset containing some variables with a very large number of response categories). On the other hand, the power of the analyses in the Scott/Ciantar study would have remained severely underpowered even were multiple imputation to have been applied. Likewise, the number of auxiliary variables (i.e.
variables which are included in the imputation model but not in the main regression model of the analysis; Thoemmes and Rose, 2014, Little and Rubin, 2002) required to impute values for missing sleep and medical variables with sufficient certainty were severely limited by the small number of such variables with complete data (i.e. n=108) – a substantive problem given a minimum of 10 participants per variable were required for inclusion in the imputation model and given that the number of auxiliary variables included should not be more than one third of the cases with complete data (i.e. all participants excluding those with missing data, Hardt et al., 2012).
Finally, some of the variables that would have been important to include in any imputation models (particularly those required to impute missing sleep and/or pregnancy outcome data) were unavailable within either of the two datasets: in the UKHLS there was insufficient information on pregnancy-related variables (e.g.
gestational age and BMI) to use as predictors in the imputation model; whilst in the Scott/Ciantar study there were insufficient sociodemographic and psychological measures to include in the imputation model for missing sleep variables. Multiple imputation would nonetheless remain an aspiration for future research in this field (see Discussion, Chapter 7), not least because most of the studies reviewed in the present thesis appeared to have avoided using multiple imputation and instead chose to delete cases with (any, relevant) missing data. That said, the best solution to the challenge of missing data is to avoid this during data collection, or by including more cases and variables so that these are available to inform subsequent multiple imputation (e.g.
larger studies with data on a greater variety of sociodemographic and medical-related variables, and with better data quality/completeness).
2.6 Conclusion
The present chapter aimed to briefly describe the rationale behind the samples, data and analytical techniques used in the analytical chapters that follow. These involved two principal, advanced statistical techniques (latent class analysis, or LCA; and multivariable logistic regression) the latter informed by recent advances in causal inference techniques (particularly the use of directed acyclic graphs, or DAGs, to identify suitable covariate adjustment sets for inclusion in multivariable statistical models). Some of these methods were used in the systematic review and meta-analyses undertaken in Chapter 3, which helped to strengthen the choice of analytical methods in the present thesis. Further detail on many of the methodological decisions made when planning and conducting the present thesis can be found in the Appendix – detail collated therein to ensure that the remainder of the thesis was clear and easy to read and assimilate.