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Cox proportional hazard model (Cox) with a binary covariate (intervention [I] and control [C]) is widely used to assess the effect of treatment on reducing cardiorenal-related (CRr) event risk. Censoring and non-“proportional hazards” (PH) may affect reliability of the data analysed using Cox in controlled trials (CT). Thus, we conducted a pilot meta-analysis to elucidate the factors that lower reliability of data analysed using Cox in CT.
We included articles that could be searched for free using PubMed for pilot meta-analysis. The following conditions were satisfied: 1. large randomized CT (n>100); 2. assessing CRr event risk; 3. using Cox, and 4. describing No. at Risk over the follow-up period. We evaluated all outcomes in one figure, which included the most important results of the studies. We divided the outcomes into two groups using a cutoff line of “hazard ratio (HR) = 1”. We estimated the cumulative incidence (CuI) to the first decimal place using the Kaplan-Meier curves in the figure (referred to as eCuI). We referred to “(‘No. at Risk. at the follow-up start time [0 year]’ (‘n’) – No. at Risk. at the final follow-up year) ÷ n × 100” as Total dropout rate (TDR), “TDR ÷ eCuI” as TDR/eCuI, “–Loge(‘1 – eCuI’ for I) [Log‘e’, ‘Napier's constant’] ÷ –Loge(‘1 – eCuI’ for C)” as eHR, “absolute values of ‘eHR – HR’ ” as |eHR – HR|, and “ ‘upper limit of 95% confidence interval [CI] of HR (U95%CI)’ – ‘lower limit of 95%CI of HR’ (L95%CI)” as 95%CI range. Theoretically, an increased TDR/eCuI reflects increased censoring. eHR was proposed based on the fact that “–Loge(cumulative survival rate functions [S(t)] for I in Cox) ÷ –Loge(S(t) for C in Cox)” is HR. Theoretically, an increase in |eHR – HR| quantitatively reflects enhanced non-PH. Partial regression coefficients (β) were calculated as Loge(HR). Standard error of β was estimated using the following formula: ((Loge(U95%CI) – Loge(HR)) ÷ 1.96 + (Loge(HR) – Loge(L95%CI)) ÷ 1.96) ÷ 2, and referred to as eSE. We also divided the outcomes in the HR<1 group into two groups using a cutoff line of “median of TDR/eCuI for C”.
Increased censoring and non-PH may lower reliability of data analysed using Cox in CT. One of the reasons why the positive correlation between |β| and eSE diminished more in high,<1,G than in low,<1,G may be that, theoretically, increased censoring is sure to increase CuI, except that the number of events is 0.