Choice of reference in the evaluation of the day-of-week effect on mortality on hemodialysis
Authors: Hui Zhang, Douglas E. Schaubel, John D. Kalbfleisch, Bruce M. Robinson, Ronald L. Pisoni, Friedrich K. Port, Rajiv Saran
Journal: Kidney International (2012)

To the Editor: Liu and Foley (LF)1.Liu J. Foley R.N. Alternate-day dialysis may be needed for hemodialysis.Kidney Int. 2012; 81: 1055-1057Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar question the methods in our analysis of day-of-week effects.2.Zhang H. Schaubel D.E. Kalbfleisch J.D. et al.Dialysis outcomes and analysis of practice patterns suggests the dialysis schedule affects day-of-week mortality.Kidney Int. 2012; 81: 1108-1115Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar Arguing that mortality on the day following the weekend (day 1) is of primary interest, they present a hypothetical example in which the death rates for days 1–7 are 10, 1, 1, 1, 1, 1, and 1, respectively, and note that the comparison of day 1 with the average of days 2–7 should yield a relative risk (RR) of 10. Our method would compare the log rate for day 1 with the average of the log rates for days 1–7 to obtain an RR=7.2 (not 4.4 as LF have stated), which, they claim, understates the true RR. In fact, the log RR in our analysis is 6/7 times theirs, and hence these two approaches yield the same test statistic and P-value. A weakness in the approach suggested by LF1.Liu J. Foley R.N. Alternate-day dialysis may be needed for hemodialysis.Kidney Int. 2012; 81: 1055-1057Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar is exemplified in Table 1, in which mortality (hypothetical rates) is elevated on day 1 and day 5, and RRs are computed under LF (RRL) and our (RRZ) approaches. As we claim in the preceding paragraph, log RRZ=6/7 × log RRL for each day. When day 1 is compared with day 5, we find RR=10/3.05=3.28, directly from the rates. It is noteworthy that RRZ=exp(1.97–0.79)=3.25 gives the same result except for round-off, whereas RRL=exp(2.30–0.92)=3.97 gives a sizeable overestimate. The lack of self-consistency in the LF1.Liu J. Foley R.N. Alternate-day dialysis may be needed for hemodialysis.Kidney Int. 2012; 81: 1055-1057Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar approach stems from the reference being different for each RR, an issue avoided in our approach.Table 1Rates, log rates, and estimated RRs using the approaches advocated by Zhang et al.,2.Zhang H. Schaubel D.E. Kalbfleisch J.D. et al.Dialysis outcomes and analysis of practice patterns suggests the dialysis schedule affects day-of-week mortality.Kidney Int. 2012; 81: 1108-1115Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar denoted by RRZ and Liu and Foley,1.Liu J. Foley R.N. Alternate-day dialysis may be needed for hemodialysis.Kidney Int. 2012; 81: 1055-1057Abstract Full Text Full Text PDF PubMed Scopus (11) Google Scholar denoted by RRLDayMortality rate (hypothetical)Log (rate)Log RRZLog RRL1D102.301.97aLog RRZ=log(rate)-avg[log(rate)]=2.30-(2.30–0.22…-0.22)/7=1.97; i.e., RRZ=7.2.2.30bLog RRL=log(rate)-avg*[log(rate)]=2.30-(-0.22–0.22…-0.22)/6=2.30; i.e., RRL=10. *Indicates that the average excludes the day of interest. Bold entries are hypothetical, as opposed to empirical, thus precluding statements regarding statistical significance.20.8-0.22-0.55-0.643D0.8-0.22-0.55-0.6440.8-0.22-0.55-0.645D3.051.120.790.9260.8-0.22-0.55-0.6470.8-0.22-0.55-0.64Total17.052.32Average2.440.33Abbreviations: D, dialysis; RR, relative risk.a Log RRZ=log(rate)-avg[log(rate)]=2.30-(2.30–0.22…-0.22)/7=1.97; i.e., RRZ=7.2.b Log RRL=log(rate)-avg*[log(rate)]=2.30-(-0.22–0.22…-0.22)/6=2.30; i.e., RRL=10.*Indicates that the average excludes the day of interest.Bold entries are hypothetical, as opposed to empirical, thus precluding statements regarding statistical significance. Open table in a new tab Abbreviations: D, dialysis; RR, relative risk.