Code
data(rmb_datasets, package = "rmb")
rmb_datasets$study_design[rmb_datasets$object == "esoph"]
#> [1] "Unmatched case-control study of esophageal cancer and alcohol/tobacco exposures in France."Ille-et-Vilaine study data
This article reproduces the Ille-et-Vilaine esophageal cancer case-control analysis from Tuyns et al. (1977), fitting logistic regression for case status on alcohol, tobacco, and age as in RMB2e Chapter 5.
1 Introduction
Esophageal squamous cell carcinoma has historically been associated with heavy alcohol and tobacco use. Tuyns and colleagues (1977) conducted an unmatched case-control study in the Ille-et-Vilaine department of France, recruiting 200 cases and 775 controls to quantify the joint effects of alcohol and tobacco consumption on cancer risk. Because both exposures correlate with age and with each other, confounding-adjusted logistic regression is essential for valid inference (RMB2e Ch. 5).
Is heavy alcohol consumption associated with esophageal cancer after adjustment for tobacco use and age group?
1.1 Causal assumptions
Code
set.seed(42)
dag <- ggdag::dagify(
cancer ~ age + tob + alc,
alc ~ age,
tob ~ age,
labels = c(
cancer = "Esophageal cancer",
age = "Age group",
tob = "Tobacco",
alc = "Alcohol"
),
exposure = "alc",
outcome = "cancer"
)
ggdag::ggdag(dag, use_labels = "label", text = FALSE) +
ggdag::theme_dag_blank() +
ggplot2::labs(title = "Esoph: Causal DAG")
2 Methods
2.1 Study sample
Code
data(esoph, package = "rmb")
dat <- esoph
dim(dat)
#> [1] 975 7
summary(haven::zap_labels(dat[c("case", "age", "agegp", "tob", "tobgp", "alc", "alcgp")]))
#> case age agegp tob
#> Min. :0.0000 Min. :25.00 Min. :1.000 Min. : 0.00
#> 1st Qu.:0.0000 1st Qu.:41.00 1st Qu.:2.000 1st Qu.: 0.00
#> Median :0.0000 Median :52.00 Median :3.000 Median : 7.50
#> Mean :0.2051 Mean :52.23 Mean :3.272 Mean :11.75
#> 3rd Qu.:0.0000 3rd Qu.:63.00 3rd Qu.:4.000 3rd Qu.:17.50
#> Max. :1.0000 Max. :91.00 Max. :6.000 Max. :60.00
#> tobgp alc alcgp
#> Min. :1.000 Min. : 0.00 Min. :1.000
#> 1st Qu.:1.000 1st Qu.: 24.00 1st Qu.:1.000
#> Median :1.000 Median : 45.00 Median :2.000
#> Mean :1.763 Mean : 52.77 Mean :1.855
#> 3rd Qu.:2.000 3rd Qu.: 73.00 3rd Qu.:2.000
#> Max. :4.000 Max. :268.00 Max. :4.0002.2 Statistical analysis
Logistic regression models case status on grouped alcohol consumption (alcgp) adjusted for grouped tobacco consumption (tobgp) and age group (agegp), following the categorical-predictor approach in RMB2e Chapter 5.
Code
formula_main <- case ~ alcgp + tobgp + agegp
formula_main
#> case ~ alcgp + tobgp + agegp3 Results
3.1 Descriptive statistics
Code
with(dat, table(alcgp, case))
#> case
#> alcgp 0 1
#> 1 385 29
#> 2 280 75
#> 3 88 51
#> 4 22 45
with(dat, prop.table(table(alcgp, case), margin = 1))
#> case
#> alcgp 0 1
#> 1 0.92995169 0.07004831
#> 2 0.78873239 0.21126761
#> 3 0.63309353 0.36690647
#> 4 0.32835821 0.67164179
with(dat, table(tobgp, case))
#> case
#> tobgp 0 1
#> 1 448 78
#> 2 178 58
#> 3 98 33
#> 4 51 31Code
alc_rates <- with(dat, tapply(case, alcgp, mean))
alc_df <- data.frame(
alcgp = names(alc_rates),
rate = as.numeric(alc_rates)
)
alc_df$alcgp <- factor(alc_df$alcgp, levels = names(alc_rates))
ggplot2::ggplot(alc_df, ggplot2::aes(x = alcgp, y = rate)) +
ggplot2::geom_col(fill = "#d95f02") +
ggplot2::labs(
title = "Crude case rate by alcohol consumption group",
x = "Alcohol group (gm/day)",
y = "Proportion cases"
) +
ggplot2::theme_minimal()
3.2 Model estimates
Code
fit <- stats::glm(formula_main, data = dat, family = stats::binomial())
summary(fit)
#>
#> Call:
#> stats::glm(formula = formula_main, family = stats::binomial(),
#> data = dat)
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -7.16053 0.50912 -14.065 < 2e-16 ***
#> alcgp 1.09868 0.10303 10.664 < 2e-16 ***
#> tobgp 0.43357 0.09384 4.620 3.83e-06 ***
#> agegp 0.74321 0.08178 9.088 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 989.49 on 974 degrees of freedom
#> Residual deviance: 730.95 on 971 degrees of freedom
#> AIC: 738.95
#>
#> Number of Fisher Scoring iterations: 53.3 Model diagnostics
Code
fit_alc_only <- stats::glm(case ~ alcgp, data = dat, family = stats::binomial())
stats::anova(fit_alc_only, fit, test = "Chisq")
#> Analysis of Deviance Table
#>
#> Model 1: case ~ alcgp
#> Model 2: case ~ alcgp + tobgp + agegp
#> Resid. Df Resid. Dev Df Deviance Pr(>Chi)
#> 1 973 845.72
#> 2 971 730.95 2 114.77 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 13.4 Inference
Code
or <- exp(stats::coef(fit))
ci <- exp(stats::confint(fit))
data.frame(
term = names(or),
odds_ratio = unname(or),
conf_low = ci[, 1],
conf_high = ci[, 2],
p_value = summary(fit)$coefficients[, "Pr(>|z|)"]
)
#> term odds_ratio conf_low conf_high p_value
#> (Intercept) (Intercept) 0.0007766439 0.0002745303 0.002025383 6.270979e-45
#> alcgp alcgp 3.0002047835 2.4619572608 3.689197049 1.497794e-26
#> tobgp tobgp 1.5427575820 1.2840941386 1.856194529 3.831928e-06
#> agegp agegp 2.1026764394 1.7986710045 2.479600792 1.006057e-194 Discussion
Heavy alcohol consumption is strongly associated with esophageal cancer risk after adjustment for tobacco use and age, consistent with the dose-response pattern reported by Tuyns et al. (1977) and discussed in RMB2e Chapter 5. Tobacco consumption and older age are independently associated with elevated odds. The likelihood-ratio test comparing the alcohol-only model to the full model confirms that tobacco and age explain additional variation in case status beyond alcohol alone. These findings underscore the importance of mutual adjustment when exposures are correlated.
5 Source
- Tuyns AJ et al. (1977). Esophageal cancer in Ille-et-Vilaine in relation to levels of alcohol and tobacco consumption. Bull Cancer, 64(1), 45–60.
- UCSF Regression Methods companion data: https://regression.ucsf.edu/sites/g/files/tkssra16191/files/wysiwyg/home/data/esoph.dta
- Book: Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE (2012). Regression Methods in Biostatistics (2nd edition).