IV.5.1 Analytic design
Analyses were performed separately in men and women. Initial analyses examined the demographic characteristics o f participants in the exposure groups, defined by the presence and persistence o f psychological distress between Phases 1 and 3. Participants with validated CHD events at each baseline were excluded from analyses, and analyses were restricted to those included in the relevant distress groups.
The first stage o f longitudinal analysis, again from both the Phase 1 and Phase 3 baselines, analysed CHD events to the end of Phase 5 in relation to the distress groups. Follow-up from the Phase 1 baseline was divided into two periods to assess short and long-term effects.
Analyses o f potential mediating or confounding variables, such as health behaviours, CHD risk factors, other psychosocial risk factors, were as follows: -
a. described its relation to distress group, adjusting for age.
b. described its relation to future CHD events, restricting analyses to those included in distress groups, including survival curves, log rank tests, assessment of the proportionality assumption and the best fit of the data.
c. assessed its impact on the distress: CHD association when entered into models as covariates.
d. stratified the distress: CHD association by differing levels o f the variable to look for possible effect-modifications by covariates.
Associations between factor scores o f the GHQ-30 and the persistence o f distress were assessed, and factor scores were used as exposure groups in relation to future CHD events.
IV.5.2 Statistical methods
Statistical analyses were performed using SAS v 6.12 and v8.04 computer software (SAS, Cary, NC: USA). Significance tests for differences between exposure groups used the never group as the reference group. Age adjustment for categorical baseline variables was by direct standardisation, using the whole sample as the standard population, with age divided into four five-year age groups. Continuous variables were age-adjusted using the proc GLM procedure, with age group entered as three categorical, dummy variables into the model. Continuous variables were examined, using the proc univariate procedure to test normality o f distribution, using graphical methods, in addition to skewness (results summarised in Appendix II). Where appropriate, variables were log-transformed and log values used in all analyses. All the biochemical variables, except HDL, were used as log- transformed variables. Quintiles and tertiles were produced, within sexes, across the whole Whitehall II population, using the logged variable where appropriate.
Using the proc lifetest procedure (product-limit method), the CHD survival data were described graphically including graphs o f the survival (without CHD event) function against time; negative log survival function (an estimate o f the cumulative hazard function) against time; and the log negative log o f the survival function against log time. Differences in the survival function, compared to the never group, were evaluated using the log-rank test.
Analyses of CHD events used Cox’s proportional hazard model to estimate effect size and to adjust for multiple variables ’ . This model relies on the assumption that the hazard between the baseline and exposed group is constant over time i.e. that the risk associated with a given exposure does not alter over the period o f follow-up. This proportional hazards assum ption for the exposure variables (distress groups) and main confounders
time-dependent variable and by examination o f the Schoenfeld residual against time The best fit o f data for continuous covariates, was assessed by constructing models with data entered as a continuous variable and divided into tertiles or quintiles and entered both categorically and as a linear variable. Models were compared by examining partial log- likelihood scores and by looking at plots of beta against the midpoints o f categories, to assess whether the relationship with CHD event was linear. Distress groups, age and other non-ordered categorical variables were entered into models using dummy variables. Where continuous variables were used, hazard ratios were expressed for one standard deviation (SD) increase, based on SD o f variable within sexes. The factor scores all had a SD of approximately 1, so for these variables HR’s are expressed for one unit increase.
Inclusion o f covariates in the final fully adjusted models was based on the strength of association between each covariate with either distress or CHD endpoints as well as the effect o f adjustment for covariate on the psychological distress: CHD association, so that all important predictors were included even if there was little or no association with distress. Stepwise selection (entry criterion p=0.10) was also used to construct models within all potential covariates available for inclusion. Those models are not deigned to control for confounding but are useful to confirm that important covariates have not been excluded^^^. Interactions between distress and covariates were tested by comparing models with distress variables and covariates with models including interaction terms for different distress groups. For continuous covariates, the quintile or tertiles were used, entered as a linear variable. Significance assessed by the difference in the partial log likelihood scores between models and the p values for the interaction terms.
Multiple imputation procedures were used in some analyses to allow for missing levels of covariates, using the proc MI and proc Mlanalyze procedures in SAS v8.04. Five imputed datasets were created (proc MI) and used in proc phreg models and the results combined (proc Mlanalyze). These adjusted models were compared with the age adjusted models in the full dataset. Complete subject analyses in the group with the covariate were also performed, and the effect o f adjustment for the covariates in this reduced sample compared with the effect seen in the imputation models.
IV.5.3 Power calculations
Power calculations were performed, within sexes and separately for the Phase 1 and Phase 3 baselines, to assess the size o f exposure group that would be required to detect effect sizes o f 3, 2 and 1.5. It was assumed that the never group would be used as the comparison, non-exposed group.
Analyses used Statcalc sample size for cohort studies in Epi Info 2000 (CDC, Atlanta, GA: USA). The following assumptions were made:
a) Estimates o f disease in the unexposed group occurrence were based on the risk o f all CHD events in whole population, expressed as percentage o f those at beginning of follow-up period (Table IV.2).
b) The ratio of non-exposed to exposed participants was set at 3:1. c) 95% confidence and 80% power were set.
Results are shown in Table IV.4 and indicate, for example, that to detect an increased relative risk o f 1.5 in men from the Phase 1 baseline, 600 men would be required in the exposure group. Dividing the distress exposure groups into strata by other covariates was part o f the analysis plan, which would have implications for power. Assuming a covariate was divided into tertiles, resulting in approximately 200 exposed men in each stratum, a relative risk o f 2 would be detectable within each stratum.
Figure IV .l WHITEHALL II STUDY