The statistical power of regional association analysis with weighted FLM on the familial data with effect modeled as |<i>β</i>_<i>j</i>| = log(<i>s</i>)|log₁₀(MAF_<i>j</i>)|/2 and all causal variants having MAFs ≤ 0.03.

<p>Proportion of causal variants is the proportion of all rare variants (MAF ≤ 0.03) within the region (all rare variants = 100%). B—B-spline basis functions; F—Fourier basis functions; (1, 1)—the unweighted model; (0.5, 0.5)—the weighted model with <i>a</i>₁ = <i>a</i>₂ = 0.5; (1, 25)—the weighted model with <i>a</i>₁ = 1 and <i>a</i>₂ = 25.</p

Weights calculated as Beta(MAF; <i>a</i>₁, <i>a</i>₂) for three weighting modes.

<p>Numbers in parentheses are the values of the beta function parameters <i>a</i>₁ and <i>a</i>₂.</p

Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 95% with a four-week recall period.

<p>Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 95% with a four-week recall period.</p

Distribution of cases of “true pneumonia” (true disease) according to caregiver report of “suspected pneumonia” (reported symptoms) and true disease status.

<p>Cell <i>a</i> represents children with “true pneumonia” (true positives) whose caregiver gave a report of “suspected pneumonia” (test positive). Cell <i>b</i> represents children without pneumonia (true negatives) whose caregiver gave a report of “suspected pneumonia” (test positive). Cell <i>c</i> represents children with “true pneumonia” (true positives) whose caregiver did not give a report of “suspected pneumonia” (test negative). Cell <i>d</i> represents children without pneumonia (true negatives) whose caregiver did not give a report of “suspected pneumonia” (test negative).</p

Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 95%.

<p>Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 95%.</p

Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 95% with an eight-week recall period.

<p>Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 95% with an eight-week recall period.</p

Additional file 1: of Pneumonia hospitalisations in Scotland following the introduction of pneumococcal conjugate vaccination in young children

Pneumonia hospitalisations in Scotland following the introduction of pneumococcal conjugate vaccination in young children. (DOCX 114 kb

Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 99%.

<p>Distribution of cases of “true pneumonia” according to caregiver report of “suspected pneumonia” (test) and true disease status when test sensitivity is 80% and specificity is 99%.</p

Graphical representation of the basic model: <i>y</i> – outcome (colorectal cancer, CRC); <i>x</i> – true concentration of the biomarker, 25-OHD; <i>xt</i> – measured concentration of the biomarker, 25-OHD; <i>g</i> – a vector of predictor variables: age, sex, smoking, BMI, physical activity, family history, NSAIDs intake, socioeconomic status, total caloric intake, alcohol intake, consumption of red meat, dietary vitamin D intake and SNPs associated with CRC or 25-OHD; <i>z</i> – unmeasured, hidden confounders.

<p>Link <i>u</i> represents the effect of predictor variables on 25-OHD, <i>w</i> is the effect of 25-OHD on CRC, <i>wg</i> is the effect of predictor variables on the CRC, <i>v</i> is the effect of unmeasured confounders on the 25-OHD and <i>wz</i> is the effect of unmeasured confounders on colorectal cancer.</p

Characteristics of ORCADES Study participants (n = 1972).

<p>Characteristics of ORCADES Study participants (n = 1972).</p