Additional file 1: of A method for sensitivity analysis to assess the effects of measurement error in multiple exposure variables using external validation data

Fisher-z transformation formula for generating validity coefficient, SAS macro for implementing the methods, simulation details and results using the methods shown in this work. (DOCX 222 kb

The variance-mean relation for Leafy vegetable intake.

<p>The graph shows a least squares regression line fitted to the scatterplots of the logarithm of center-specific standard deviation versus logarithm of center-specific mean of the consumed amount of leafy vegetables for those who reported consumption on the 24HDR in the EPIC Study, 1992–2000. The approximately linear regression line suggests a variance that increases with the mean.</p

Linearity assessment in the Cox proportional hazards model for Leafy vegetables.

<p>The graph shows a smoothed curve fitted to the scatterplots of log hazard ratio estimate of leafy vegetable intake on all-cause mortality in each DQ category versus DQ category-specific median intake. The approximately linear downward trend suggests a possible linear relation and a beneficial effect of vegetable intake on the risk of all-cause mortality.</p

The area under the curve (AUC) from ROC curve for consumption probability (Part I), and root mean square error (RMSE) and mean bias for the consumed amount (Part II) of the standard and the reduced forms of two-part regression calibration models with transformed DQ.

a<p>; ^b</p><p>The area under the curve (AUC) from ROC curve for consumption probability (Part I), and root mean square error (RMSE) and mean bias for the consumed amount (Part II) of the standard and the reduced forms of two-part regression calibration models with transformed DQ.</p

The boxplots for the distribution of intake of vegetable subgroups.

<p>The country-specific boxplots show the distribution of the consumed amount for those who reported consumption on the 24-HDR for leafy vegetables (LV), fruiting vegetables (FV) and root vegetable (RV) subgroups in the EPIC study, 1992–2000.</p

Significant covariates (marked ×) in the reduced two-part calibration models, after a backward elimination on each part of the standard two-part regression calibration model with transformed DQ and with other covariates selected using the standard way of variable inclusion.

<p>EPIC Study, 1992–2000.</p><p>Q^t is a transformed DQ; Part I, refers to consumption probability part of the two-part calibration model; Part II, refers to consumed amount part of the two-part calibration model;</p><p>*refers to an interaction term.</p><p>Significant covariates (marked ×) in the reduced two-part calibration models, after a backward elimination on each part of the standard two-part regression calibration model with transformed DQ and with other covariates selected using the standard way of variable inclusion.</p

The empirical logit graph for Leafy vegetable intake.

<p>The graph shows loess curves fitted to 1) the scatterplots for the empirical logit (dotted line) and 2) the mean of the predicted logit from a logistic model with log-transformed DQ (thick line) against the DQ category-specific means for leafy vegetable intake in the EPIC Study, 1992–2000. The similarity in the two logit curves suggests that a log- transformed DQ is appropriate for the consumption probability part of the two-part calibration model.</p

Log hazard ratio estimate (standard error) per 100 g usual intake of each of the three vegetable subgroups, calibrated with each of the three forms of regression calibration models in their reduced and standard forms.

<p>s.e^a is the standard error (×10⁻²) for that does not account for the uncertainty in the calibration; s.e^b is the standard error (×10⁻²) that accounts for the uncertainty in the calibration; s.e ratio^c is the ratio of s.e^b to s.e^a.</p><p>Log hazard ratio estimate (standard error) per 100 g usual intake of each of the three vegetable subgroups, calibrated with each of the three forms of regression calibration models in their reduced and standard forms.</p

Additional file 3: of Identifying and correcting epigenetics measurements for systematic sources of variation

Figure S3. Quantile-quantile (QQ) plots for CpG site-specific analysis with respect to smoking using standard adjustment (a), residuals (b), ComBat (c) and SVA (d) correcting methods for the M values. The inflation factor λ is defined as the ratio of the median of the observed log10 transformed p values from the CpG site-specific analysis and the median of the expected log10 transformed p values. (PDF 110 kb

Additional file 2: of Identifying and correcting epigenetics measurements for systematic sources of variation

Figure S2. Quantile-quantile (QQ) plots for CpG site-specific analysis with respect to smoking using standard adjustment (a), residuals (b), ComBat (c) and SVA (d) correcting methods for the β values. The inflation factor λ is defined as the ratio of the median of the observed log10 transformed p values from the CpG site-specific analysis and the median of the expected log10 transformed p values. (PDF 110 kb