| Figure 4.1 |
Density and cumulative distribution functions |
| Figure 4.2 |
Symmetric continuous distribution |
| Figure 4.3 |
Bimodal distribution |
| Figure 4.4 |
Count variable with clumping at zero |
| Figure 4.5 |
Ordinal variable with strange distribution |
| Figure 4.6 |
Continuous distribution with clumping at the end |
| Figure 4.7 |
Spaghetti plot |
| Figure 4.8 |
Frequency dot chart |
| Figure 4.9 |
Dot chart for categorical demographic variables, stratified by treatment and region |
| Figure 4.10 |
Dot chart showing proportion of subjects having adverse events by treatment, sorted by risk difference, produced by the R greport package. See test.Rnw here |
| ?fig-descript-ph |
Scatterplot of one measurement mode against another |
| Figure 4.13 |
Hexagonal binning replacing scatterplot for large \(n\) |
| Figure 4.14 |
Binned points (2500 total bins) with frequency counts shown as color and transparency level |
| Figure 4.15 |
Empirical cumulative distribution functions |
| Figure 4.16 |
Box plots for glycohemoglobin |
| Figure 4.17 |
Schematic for extended box plot |
| Figure 4.18 |
Extended box plots |
| Figure 4.19 |
Interactive extended box plot |
| Figure 4.20 |
One-half violin plots for longitudinal data, stratified by treatment. Density estimates for groups with insufficient sample sizes are faded. Density plots are back-to-back for treatment A and B. Points are treatment medians. When the black vertical line does not touch the two medians, the medians are significantly different at the \(\alpha=0.05\) level. Graphic was produced by the R greport package. |
| Figure 4.21 |
Moving upper quartile and Gini mean difference for HbA\(_{\mathrm 1c}\) |
| Figure 4.22 |
Moving \(Q_3\) vs. age with extended box plot and histogram |
| Figure 4.23 |
Showing group means and differences |
| Figure 4.24 |
Bar plot with error bars—“dynamite plot” |
| Figure 4.25 |
Dot plot with superimposed box plots |
| Figure 4.26 |
Jittered raw data and violin plots with median indicated by blue + |
| Figure 4.27 |
Single-axis nomogram |
| Figure 4.28 |
Partial effects in NHANES HbA\(_{1c}\) model |
| Figure 4.29 |
Partial effects chart for transformed glycohemoglobin |
| Figure 4.30 |
Nomogram for predicting median HbA\(_{1c}\) |
| Figure 4.31 |
Estimated median survival time for critically ill adults |
| Figure 4.32 |
Probability of hemorrhagic stroke vs. blood pressures |
| Figure 5.1 |
\(t\) distribution for varying d.f. |
| Figure 5.2 |
Posterior distributions for \(\mu\) and \(\sigma\) using a normal model. |
| Figure 5.3 |
Posterior distributions for \(\mu, \sigma, \nu\) for a \(t_{\nu}\) data model |
| Figure 5.4 |
Effect of discounting by a skeptical prior |
| Figure 5.5 |
Prior and posterior distributions for unknown probability of heads |
| Figure 5.6 |
Half-widths of 0.95 credible intervals for \(p\) using a flat prior |
| Figure 5.7 |
Multiplicative margin of error in estimating odds when \(n=384\) and the margin of error in estimating the absolute probability is \(\leq 0.05\). |
| Figure 5.8 |
Two-sample parallel group RCT |
| Figure 5.9 |
Stratified ECDFs for checking \(t\)-test assumptions |
| Figure 5.10 |
Margin of error in estimating \(\sigma\) |
| Figure 5.11 |
Data and box plots for paired data |
| Figure 6.1 |
Multiplicative margin of error for odds ratios |
| Figure 6.2 |
The logistic function |
| Figure 6.3 |
Posterior distribution of odds ratio |
| Figure 7.1 |
Fecal calprotectin by severity |
| Figure 7.2 |
Ranks of calprotectin |
| Figure 7.3 |
Wilcoxon \(P\)-value vs. hypothesized difference. |
| Figure 7.4 |
Bootstrapped differences in medians |
| Figure 7.5 |
Checking Wilcoxon assumption |
| Figure 7.6 |
Checking \(t\)-test assumption |
| Figure 7.7 |
logit ECDF plots for checking the PO assumption (parallelism) in the 2-factor problem |
| Figure 7.8 |
Relationship between odds ratio and assumed mean in the experimental arm |
| Figure 7.9 |
Departure from normality induced by assuming proportional odds |
| Figure 7.10 |
Assessing normality of experimental arm |
| Figure 7.11 |
Discrete distribution for the experimental arm |
| Figure 7.12 |
Margin of error for an ECDF based on Kolmogorov-Smirnov critical values |
| Figure 8.1 |
Example correlation coefficients |
| Figure 8.2 |
Multiple datasets having same Pearson \(r\) |
| Figure 8.3 |
Bland-Altman plot for 2 pH measurements |
| Figure 8.4 |
Difference in pH by time of day |
| Figure 8.5 |
Margin of error for estimating correlation coefficient |
| Figure 8.6 |
Sample size required to ensure a high probability of the sample correlation coefficient being in the right direction |
| Figure 8.7 |
Probability of having the correct sign on \(r\) as a function of \(n\) and true correlation \(\rho\) |
| Figure 8.8 |
loess nonparametric smoother for glucose ratio |
| Figure 8.9 |
Example of super smoother |
| Figure 8.10 |
Moving statistics for glucose ratio |
| Figure 8.11 |
Moving proportions |
| Figure 8.12 |
Moving 6m and 12m mortality estimates |
| Figure 10.1 |
Sample of \(n=100\) points with a linear regression line |
| Figure 10.2 |
Two types of confidence bands |
| Figure 10.3 |
Four examples of residual plots |
| Figure 10.4 |
Harm of percentiling BMI in a regression model |
| Figure 10.5 |
What are quintile numbers modeling? |
| Figure 10.6 |
Assumptions for two predictors |
| ?fig-reg-olslead |
Mean maxfwt by information-losing lead exposure groups |
| Figure 11.1 |
Age of first walking |
| Figure 13.1 |
Distribution of baseline risk in GUSTO-I |
| Figure 13.2 |
A display of an interaction between treatment, extent of disease, and calendar year of start of treatment (Califf et al. (1989)) |
| Figure 13.3 |
Estimates from model with age \(\times\) treatment interaction |
| Figure 13.4 |
Effects of predictors in Cox model |
| Figure 13.5 |
Estimates from a Cox model allowing treatment to interact with both age and sex |
| Figure 13.6 |
Absolute risk increase as a function of risk |
| Figure 13.7 |
Absolute risk reduction by background risk and interacting factor |
| Figure 13.8 |
Absolute benefit vs. baseline risk |
| Figure 13.9 |
GUSTO-I nomogram |
| Figure 13.10 |
Baseline risk, hazard ratio, and absolute effect |
| Figure 13.11 |
Distribution of cost per life saved in GUSTO–I |
| Figure 14.1 |
\(\beta\)-TG levels by diabetic status |
| Figure 14.2 |
8w vs. baseline Hamilton-D depression scores along with loess nonparametric smoothers by treatment |
| Figure 14.3 |
Change from baseline at 8w vs. baseline Hamilton-D depression scores and loess nonparametric smoothers by treatment |
| Figure 14.4 |
Estimated mean Hamilton-D score at 8w using the proportional odds model, allowing for nonlinear and interaction effects. The fitted spline function does more smoothing than the earlier loess estimates. |
| Figure 14.5 |
Estimated treatment difference in mean Ham-D allowing for interaction, thus allowing for non-constant differences. Keep in mind the slight evidence for non-constancy (interaction). |
| ?fig-change-suppcr |
Hospital death as a function of creatinine |
| Figure 14.8 |
Baseball batting averages and regression to the mean |
| Figure 15.1 |
Spaghetti plots for isoproterenol data |
| Figure 15.2 |
AUC by curve fitting and by trapezoidal rule |
| Figure 15.3 |
Mean blood flow by race |
| Figure 15.4 |
Residual plot for generalized least squares fit on untransformed fbf |
| Figure 15.5 |
Checking assumptions of GLS model |
| ?fig-serial-blrm |
MCMC diagnostics |
| Figure 15.10 |
Posterior mean logit |
| Figure 15.11 |
Posterior mean for mean blood flow |
| Figure 18.1 |
Risk of pneumonia with two predictors |
| Figure 18.2 |
Two kinds of thresholds |
| Figure 18.3 |
Thresholds in cardiac biomarkers |
| Figure 18.4 |
Power loss from dichotomizing the response variable |
| Figure 18.5 |
Continuous PSA vs. risk |
| Figure 18.6 |
Prognostic spectrum from various models |
| Figure 19.1 |
Nomogram for estimating P(significant coronary disease) |
| Figure 19.2 |
Nomogram for estimating probability of meningitis |
| Figure 19.3 |
Proportional odds ordinal logistic model for ordinal diagnostic classes from Brazer et al. (1991) |
| Figure 19.4 |
Pre vs. post-test probability |
| Figure 19.5 |
Relative effect of total cholesterol for age 40 and 70; Data from Duke Cardiovascular Disease Databank, \(n=2258\) |
| Figure 19.6 |
Diagnostic Utility of Cholesterol for Diagnosing Significant CAD. Curves are 0.1 and 0.9 quantiles from quantile regression using restricted cubic splines |
| Figure 20.1 |
Average of maximum absolute correlation coefficients |