When we explored the validity of imputations of missing N
When we explored the validity of imputations of missing N-stage or M-stage based on our four clinical assumptions we found the following results. First, 4-year overall survival was very similar for men with a recorded N-stage, but missing M-stage, and corresponding men with recorded M0 (89.5% vs 89.6%). This similarity was observed to such a degree that the patient survival curves for MX and M0 appear as one line. Survival of men with M1 in this cohort was substantially lower at 39.7% (Fig. 1). This pattern was also observed when the analysis was restricted to N0 and N1 disease individually.
Second, for low/intermediate-risk men with missing M-stage and corresponding men with recorded M0, survival was also very similar (92.0% vs 93.1%), and substantially higher than men with recorded M1 (59.2%). Again, this similarity was observed to such a degree that the patient survival curves for MX and M0 appear as one line (Fig. 2a).
Third, the same pattern was seen for low/intermediate-risk men with missing N-stage and corresponding men with recorded N0 (90.9% vs 93.7%), where survival was also much lower for men with N1 (81.4%, Fig. 2b).
Fourth, 4-year survival for high-risk men with missing M-stage was 71.4% which differed substantially from corresponding men with recorded M0 or M1 (84.5% vs 36.7%, Fig. 3). These results support the first three clinical assumptions that:
Adjusted Cox regression, compared to the unadjusted analysis, showed that there was some residual bias when using the first three clinical assumptions as there were significant differences in survival between MX (assumption one and three) or NX (assumption two) compared to either N0 or M0, respectively (HRs and 95% CIs >1) (Table 3). The adjusted model provided further support for assumption two as it Bradykinin (acetate) showed a decrease from an unadjusted HR of 1.50 to an adjusted HR of 1.26, confirming the presence of confounding from other variables.
However, the performance of our clinical assumptions compared to multiple imputation is very similar. For assumptions two and three, survival of NX and MX values imputed to N0 and M0 using multiple imputation were in line with our clinical assumptions given the very similar hazard ratios (Table 3, Table 4). Multiple imputation rarely imputes values to M1 (assumption two) or N1 (assumption three), highlighting that our clinical assumptions are as appropriate as multiple imputation in this setting and both methods perform relatively well for patients in the low/intermediate-risk group. For assumption one, our clinical assumptions were weaker than the method using multiple imputation given the hazard ratios for the MX values imputed to M0 were further away from 0 (HR 1.39 95% 1.27–1.53 vs. HR 1.13 95% CI 1.00–1.28). However multiple imputation was still imperfect as those missing values imputed to M1, rather than M0, were not comparable to the survival of men with M1 (HR 2.53 95% CI 2.07–3.09 vs. 7.11 95% CI 6.71–7.53), a bias which does not affect our clinical assumptions given antibiotics are assumed to be negative (M0).
Funding M.G.P. was partly supported by the NHS National Institute for Health Research through an Academic Clinical Fellowship (ACF-2014-20-002). H.P. was supported by the University College London Hospitals/University College London Comprehensive Biomedical Research Centre. J.v.d.M. was partly supported by the National Institute for Health Research Collaboration for Leadership in Applied Health Research and Care North Thames at Bart’s Health NHS Trust. M.G.P., A.S., T.C., S.C., J.N., A.A., N.W.C., H.P., and J.v.d.M. are members of the Project Team of the National Prostate Cancer Audit (www.npca.org.uk) funded by the Healthcare Quality Improvement Partnership (www.hqip.org.uk). The views expressed in this article are those of the authors and not necessarily those of the NHS, the National Institute for Health Research or the Department of Health and Social Care.