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Table 4 Estimates of ORSCL, ORVF and ORMH (95% CI), and ORMH (2.5–97.5pct): Simulated data (study period = 22 days). Results are shown graphically in Fig. 4

From: A novel weighting method to remove bias from within-subject exposure dependency in case-crossover studies

Days in 1 period 1 day 2 days 3 days 4 days 7 days 11 days
M 21 10 6 4 2 1
One binary exposure variable only       
ORSCL exp(β) 6.02 (4.14–8.75) 5.30 (3.73–7.53) 4.60 (3.27–6.48) 5.23 (3.65–7.50) 6.61 (3.27–13.33) 4.00 (2.45–6.53)
ORVF exp(β) 4.00 (2.58–6.20) 4.00 (2.80–5.71) 4.00 (2.45–6.53) 4.00 (2.45–6.53)
ORMH exp(β) 4.00 (2.93–5.46) 4.00 (2.92–5.48) 4.00 (2.89–5.53) 4.00 (2.87–5.57) 4.00 (2.19–7.29) 4.00 (2.45–6.53)
ORG exp(β) 4.00 (2.85–5.66) 4.00 (2.82–5.60) 4.00 (2.84–5.70) 4.00 (2.82–5.81) 4.00 (2.12–9.00) 4.00 (2.57–6.69)
One binary exposure variable and one binary time-varying confounder       
ORSCL exp(β) 6.35 (4.52–8.91) 5.57 (4.04–7.68) 4.76 (3.49–6.51) 5.29 (3.81–7.35) 6.79 (3.59–12.86) 4.34 (2.76–6.82)
exp(γ) 2.20 (1.60–3.01) 1.78 (1.28–2.48) 1.80 (1.27–2.54) 2.06 (1.39–3.06) 1.91 (1.25–2.91) 1.35 (0.83–2.20)
ORVF exp(β) 4.08 (2.74–6.07) 4.02 (2.90–5.58) 4.02 (2.57–6.29) 4.31 (2.75–6.74)
exp(γ) 2.20 (1.51–3.22) 1.78 (1.20–2.63) 1.83 (1.25–2.67) 2.02 (1.24–3.31) 2.34 (1.43–3.85) 1.94 (1.16–3.24)
ORMH exp(β) 4.16 (3.09–5.61) 4.36 (3.15–6.03) 4.40 (3.11–6.24) 3.54 (2.49–5.04) 4.11 (2.17–7.80) 5.56 (2.73–11.30)
ORG exp(β) 3.96 (2.88–5.46) 4.06 (2.93–5.61) 4.11 (2.97–5.78) 4.00 (2.85–5.67) 4.04 (2.26–8.80) 4.34 (2.86–7.40)
exp(γ) 2.10 (1.53–2.81) 1.77 (1.25–2.47) 1.76 (1.23–2.53) 2.01 (1.39–2.83) 1.90 (1.27–2.86) 1.35 (0.80–2.26)
  1. M is the number of control periods while study period is fixed as 22 days (precisely, study period = Int(22/(M + 1)) *(M + 1)) days)
  2. ORSCL: odds ratio by the standard conditional logistic regression; ORVF: odds ratio by the Vines and Farrington’s method; ORMH: odds ratio by the Mantel-Haenszel method; ORG: odds ratio by the Greenland’s method; 95%CI: 95% confidence interval; 2.5–97.5pct: 2.5 to 97.5 percentiles; exp(β): the estimate for the rate ratio for the exposure; exp(γ): the estimate for the rate ratio for the time-varying confounder