The mean change in DAS28 from baseline to 6 months, estimated from the MI dataset, was -1.36 units (SE 0.05, negative change indicated reduction in score). The linear regression model explained approximately 27% of the
variance in change in DAS28 (equivalent to the R-square value of the complete case model) and the coefficient corresponding to the constant in this model indicated that the mean change in DAS28 after 6 months, for YEAR B, female, RF and ACPA negative patients with 0 to 35 minutes baseline EMS and mean values of symptom duration, baseline DAS28, pain and fatigue VAS (hereafter referred to as the ‘baseline patient’) was close to this value, at -1.37 (SE 0.13, p<0.0001). The results of the linear regression analysis are shown in Table 4-2. The model suggested that YEAR C patients saw a 0.21 unit greater drop in DAS28 after 6 months than those in YEAR B (SE 0.09, p0.026). Male gender was also a significant predictor of greater reduction in disease activity: on average, DAS28 reduced by 0.19 units more in males than females after 6 months (SE 0.09, p=0.032). Baseline fatigue VAS was an independently statistically significant predictor, not only of change in DAS28 after 6 months, but in all models of change in DAS28 and HAQ-DI: there was less reduction in disease activity and disability with greater baseline fatigue. Each cm of
baseline fatigue VAS predicted a 0.05 unit less reduction in DAS28 at 6 months (SE 0.02, p=0.007, Table 4-2). As expected, higher baseline DAS28 was associated with greater subsequent fall in DAS28 (probably because the higher the initial recorded DAS28, the greater the possible decline after 6 and 12 months). There were no significant interactions between YEAR cohort and the other independent variables, indicating that the effects of the variables in the model were valid for both YEAR B and YEAR C patients. The Wald tests for significance of the overall effect of the interaction between EMS categories and YEAR cohort confirmed that these were non-significant (F statistic 0.53,
degrees of freedom, df 252, p 0.6606) and therefore, the interactions between YEAR cohort and EMS categories were not retained in the final model.
156
Table 4-2 Predictors of change in disease activity from baseline to six months in Yorkshire Early Arthritis Register
Predictor
Multiple imputation analysis
N=1416
Complete case analysis N=530 Coefficient (β) SE p Coefficient (β) SE p YEAR C -0.21 0.09 0.026 -0.02 0.13 0.903 Male gender -0.19 0.09 0.032 -0.23 0.13 0.082 Age* -0.02 0.03 0.457 -0.06 0.05 0.199 SD (months) 0.00 0.01 0.924 0.01 0.01 0.640 RF positive 0.13 0.13 0.299 0.17 0.16 0.295 ACPA positive 0.22 0.15 0.139 0.27 0.15 0.079 Pain VAS 0.02 0.02 0.471 0.00 0.03 0.954 Fatigue VAS 0.05 0.02 0.001 0.06 0.02 0.007 EMS 40-75 minutes 0.03 0.12 0.824 0.03 0.17 0.840 90-210 minutes 0.00 0.12 0.974 0.08 0.18 0.673 ≥220 minutes -0.21 0.12 0.107 -0.28 0.21 0.172 DAS28 -0.67 0.04 <0.0001 -0.64 0.06 <0.0001 Constant -1.37 0.13 <0.0001 -1.52 0.19 <0.0001
Results of linear regression analysis using centred continuous independent variables (value of independent variable -mean of that variable). Outcome variable was change in DAS28 after 6 months (DAS28 at 6 months – baseline DAS28).
Statistically significant (p<0.05) coefficients are highlighted in bold. *Age was entered into the model (as age in years)/10.
For EMS, the referent category was 0-35 minutes. Independent variables were measured at baseline.
ACPA, anti-citrullinated peptide antibodies; DAS28, disease activity score from counts of 28 joints; EMS, early morning stiffness duration; N, number (of cases); p, probability (statistical significance); RF, rheumatoid factor; SD, symptom duration; SE, standard error; VAS, visual analogue score (measured in centimetres); YEAR, Yorkshire Early Arthritis Register.
157
The results of the MI model were compared to those of a complete case model, as unexplained inconsistencies may indicate errors in the imputation process (as described in Chapter 2, 2.5.5.2). This revealed that regression coefficients and SE were similar between the 2 analyses, with slightly smaller SE in the MI model. As in the MI analysis, the Wald test indicated that the interaction effect between cohort and categories of EMS duration was non-significant in this model (F statistic 1.32, 506 df, p = 0.2647). Smaller SEs may have been obtained owing to the greater number of cases included in the MI model. The greatest difference between coefficients was found corresponding to the effects of YEAR C cohort, which was greater in the MI analysis (-0.21), compared to the complete case analysis (-0.02, Table 4-2). However, this difference of 0.19 units of DAS28 was small.
Fit of the linear regression model was checked as described in Chapter 2, 2.5.4.1, by assessing the distribution of the standardised residual values (where residuals were the difference between the value of the actual outcome variable and that predicted by the model and the standardised residual is the value of the actual residual, divided by its SE) and examining the residual versus fitted values plot, which is shown in Figure 4-1. This revealed that the variance of residual values was not dependent on the outcome variable (that is, the
assumption of homoscedasticity was met). The histogram in Figure 4-2 shows normally distributed residuals, with a mean of approximately zero. The values of the standardised residuals were all within the range -3.3 to 3.3, suggesting that there were no outliers.
158
Figure 4-1 Residual versus fittted scatterplot for the linear regression model of change in Disease Activity Score using counts of 28 joints (DAS28) after 6 months for participants of Yorkshire Early Arthritis Register
Residual values represented the difference between observed change in DAS28 and change in DAS28 predicted by the model, whilst fitted values are those predicted by the model.
Figure 4-2 Histogram to show distribution of residuals from the linear regression analysis of change in Disease Activity Score using counts of 28 joints (DAS28) after 6 months in Yorkshire Early Arthritis Register Residual values represent the difference between actual change in DAS28 and change in DAS28 predicted by the model.
Range of standardised residual values (equal to actual residual divided by its standard error): -2.33 to 2.81. -4 -2 0 2 4 Re sid u a ls -4 -3 -2 -1 0 1 Fitted values 0 .1 .2 .3 .4 .5 De n sity -2 -1 0 1 2 3 Standardized residuals
159