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Table 2 Results from simulations without covariates. Naive and regression calibrated effect estimates in linear regression with error-prone exposure X, analysing (A) dummy variables, comparing 5th vs. 1st quintile, (B) quintile numbers, and (C) median values within quintile groups. Results from analysis with continuous exposure is included for comparison. We have X and Y ~ N (0,1) and the error U ~ N (0, ), where is chosen such that the reliability ratio λ is either 0.8, 0.5 or 0.2. The results are obtained via simulation, where the correlation ρ XY between continuous X and Y is set to either 0.7 or 0.2. The true effects are indicated. For the cases marked 'k constant', each individual is measured twice. For the cases marked 'k not constant', the replication pattern is 5 measurements on a random 20% subset of individuals and 1 measurement on the rest. Standard errors for the corrected cases are bootstrapped.

From: Regression analysis with categorized regression calibrated exposure: some interesting findings

     k constant   k not constant  
ρ XY model true coef λ naive coef (SE) RC coef (SE) naive coef (SE) RC coef (SE)
    0.8 0.62 (0.003) 0.70 (0.002) 0.58 (0.003) 0.70 (0.003)
  cont 0.70 0.5 0.47 (0.003) 0.70 (0.004) 0.38 (0.002) 0.70 (0.005)
    0.2 0.23 (0.002) 0.69 (0.010) 0.16 (0.002) 0.69 (0.011)
    0.8 1.85 (0.010) 1.85 (0.008) 1.77 (0.010) 1.77 (0.008)
  A 1.96 0.5 1.61 (0.010) 1.61 (0.009) 1.45 (0.010) 1.47 (0.009)
    0.2 1.14 (0.010) 1.14 (0.008) 0.93 (0.010) 1.00 (0.010)
0.7        
    0.8 0.44 (0.002) 0.44 (0.002) 0.42 (0.002) 0.42 (0.002)
  B 0.47 0.5 0.38 (0.002) 0.38 (0.002) 0.35 (0.002) 0.35 (0.002)
    0.2 0.27 (0.002) 0.27 (0.002) 0.23 (0.002) 0.24 (0.002)
    0.8 0.68 (0.003) 0.76 (0.003) 0.62 (0.003) 0.76 (0.003)
  C 0.76 0.5 0.51 (0.003) 0.76 (0.005) 0.42 (0.003) 0.76 (0.006)
    0.2 0.25 (0.002) 0.75 (0.011) 0.18 (0.002) 0.77 (0.013)
    0.8 0.18 (0.003) 0.20 (0.003) 0.17 (0.003) 0.21 (0.003)
  cont 0.20 0.5 0.13 (0.003) 0.20 (0.004) 0.11 (0.002) 0.20 (0.004)
    0.2 0.07 (0.002) 0.20 (0.006) 0.04 (0.002) 0.19 (0.006)
    0.8 0.52 (0.010) 0.52 (0.010) 0.53 (0.010) 0.52 (0.010)
  A 0.56 0.5 0.45 (0.010) 0.45 (0.010) 0.41 (0.010) 0.42 (0.010)
    0.2 0.32 (0.010) 0.32 (0.010) 0.25 (0.010) 0.27 (0.009)
0.2        
    0.8 0.13 (0.002) 0.13 (0.002) 0.12 (0.002) 0.12 (0.002)
  B 0.13 0.5 0.11 (0.002) 0.11 (0.002) 0.10 (0.002) 0.10 (0.002)
    0.2 0.08 (0.002) 0.08 (0.002) 0.06 (0.002) 0.06 (0.002)
    0.8 0.19 (0.003) 0.22 (0.004) 0.18 (0.003) 0.22 (0.004)
  C 0.22 0.5 0.14 (0.003) 0.21 (0.005) 0.12 (0.003) 0.22 (0.005)
    0.2 0.07 (0.002) 0.22 (0.007) 0.05 (0.002) 0.21 (0.007)