Code
data(rmb_datasets, package = "rmb")
rmb_datasets$study_design[rmb_datasets$object == "needle_sharing"]
#> [1] "Longitudinal panel study of injection drug users measuring repeated needle-sharing behavior."Needle sharing data
This article applies linear regression on log-transformed needle-sharing frequency in a longitudinal injection drug user panel, examining associations with depression, homelessness, HIV status, and drug use patterns (RMB2e Chapter 8).
1 Introduction
Needle sharing among injection drug users (IDUs) is a primary route of HIV and hepatitis C transmission. Mental health disorders such as depression and unstable housing (homelessness) have been proposed as structural and psychological drivers of risk behavior, including receptive syringe sharing. Log-transforming the highly right-skewed sharing count (logshsyr) induces approximate normality required for linear regression inference (RMB2e Ch. 8). HIV-positive status may suppress or increase sharing depending on perceived risk, while polydrug use and injection frequency reflect overall addiction severity.
Are depression diagnosis and homelessness associated with greater needle-sharing frequency among injection drug users?
1.1 Causal assumptions
Code
set.seed(42)
dag <- ggdag::dagify(
log_share ~ depress + homeless + hiv + poly + injectfreq,
labels = c(
log_share = "Log needle sharing",
depress = "Depression",
homeless = "Homelessness",
hiv = "HIV status",
poly = "Polydrug use",
injectfreq = "Injection frequency"
),
exposure = "depress",
outcome = "log_share"
)
ggdag::ggdag(dag, use_labels = "label", text = FALSE) +
ggdag::theme_dag_blank() +
ggplot2::labs(title = "Needle sharing: Causal DAG")
2 Methods
2.1 Study sample
Code
data(needle_sharing, package = "rmb")
dat <- needle_sharing
dim(dat)
#> [1] 128 17
summary(haven::zap_labels(dat[c("logshsyr", "dprsn_dx", "homeless", "hivstat", "polydrug", "sqrtnivd")]))
#> logshsyr dprsn_dx homeless hivstat
#> Min. :0.0000 Min. :1.000 Min. :0.0000 Min. :0.000
#> 1st Qu.:0.6931 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:0.000
#> Median :1.6094 Median :1.000 Median :0.0000 Median :0.000
#> Mean :1.7765 Mean :2.206 Mean :0.4919 Mean :0.114
#> 3rd Qu.:2.3026 3rd Qu.:5.000 3rd Qu.:1.0000 3rd Qu.:0.000
#> Max. :4.0943 Max. :5.000 Max. :1.0000 Max. :2.000
#> NAs :101 NAs :2 NAs :4 NAs :14
#> polydrug sqrtnivd
#> Min. :0.0000 Min. : 0.000
#> 1st Qu.:0.0000 1st Qu.: 6.516
#> Median :0.0000 Median : 9.487
#> Mean :0.1484 Mean : 8.982
#> 3rd Qu.:0.0000 3rd Qu.:10.954
#> Max. :1.0000 Max. :30.000
#> NAs :12.2 Statistical analysis
Linear regression of log-transformed needle sharing (logshsyr) on depression diagnosis, homelessness, HIV status, polydrug use, and square-root injection frequency, following the transformed-outcome approach in RMB2e Chapter 8.
Code
formula_main <- logshsyr ~ dprsn_dx + homeless + hivstat + polydrug + sqrtnivd
formula_main
#> logshsyr ~ dprsn_dx + homeless + hivstat + polydrug + sqrtnivd3 Results
3.1 Descriptive statistics
Code
with(dat, tapply(logshsyr, dprsn_dx, summary))
#> $`1`
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
#> 0.0000 0.7945 1.7006 1.8283 2.2468 4.0943 70
#>
#> $`5`
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
#> 0.0000 0.6931 1.2425 1.5941 2.4099 3.4012 30
with(dat, tapply(logshsyr, homeless, summary))
#> $`0`
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
#> 0.0000 0.7945 1.2425 1.4991 2.1293 3.4012 53
#>
#> $`1`
#> Min. 1st Qu. Median Mean 3rd Qu. Max. NAs
#> 0.0000 0.6931 1.7918 1.9396 2.3026 4.0943 44
with(dat, c(
pct_depressed = mean(dprsn_dx, na.rm = TRUE),
pct_homeless = mean(homeless, na.rm = TRUE),
pct_hiv_pos = mean(hivstat == 1, na.rm = TRUE)
))
#> pct_depressed pct_homeless pct_hiv_pos
#> 2.20634921 0.49193548 0.07894737Code
dat$dprsn_label <- factor(dat$dprsn_dx, levels = c(0, 1), labels = c("No depression", "Depression"))
ggplot2::ggplot(dat, ggplot2::aes(x = dprsn_label, y = logshsyr, fill = dprsn_label)) +
ggplot2::geom_boxplot() +
ggplot2::scale_fill_manual(values = c("#1b9e77", "#d95f02")) +
ggplot2::labs(
title = "Log needle sharing by depression diagnosis",
x = NULL,
y = "Log needle sharing"
) +
ggplot2::theme_minimal() +
ggplot2::theme(legend.position = "none")
3.2 Model estimates
Code
fit <- stats::lm(formula_main, data = dat)
summary(fit)
#>
#> Call:
#> stats::lm(formula = formula_main, data = dat)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -2.0648 -0.6731 -0.0918 0.5251 2.3299
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.29580 1.15037 0.257 0.800
#> dprsn_dx 0.01314 0.17221 0.076 0.940
#> homeless 0.73036 0.72657 1.005 0.329
#> hivstat 0.60267 0.49709 1.212 0.242
#> polydrug -0.72478 0.89610 -0.809 0.430
#> sqrtnivd 0.09361 0.08571 1.092 0.290
#>
#> Residual standard error: 1.336 on 17 degrees of freedom
#> (105 observations deleted due to missingness)
#> Multiple R-squared: 0.257, Adjusted R-squared: 0.03845
#> F-statistic: 1.176 on 5 and 17 DF, p-value: 0.36123.3 Model diagnostics
Code
fit_data <- data.frame(
fitted = stats::fitted(fit),
residuals = stats::residuals(fit),
std_residuals = stats::rstandard(fit)
)
ggplot2::ggplot(fit_data, ggplot2::aes(x = fitted, y = residuals)) +
ggplot2::geom_point() +
ggplot2::geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
ggplot2::geom_smooth(se = FALSE, color = "blue") +
ggplot2::labs(
title = "Residuals vs Fitted",
x = "Fitted values",
y = "Residuals"
) +
ggplot2::theme_minimal()
ggplot2::ggplot(fit_data, ggplot2::aes(sample = std_residuals)) +
ggplot2::stat_qq() +
ggplot2::stat_qq_line(color = "red") +
ggplot2::labs(
title = "Normal Q-Q",
x = "Theoretical Quantiles",
y = "Standardized residuals"
) +
ggplot2::theme_minimal()
3.4 Inference
Code
ci <- stats::confint(fit)
coefs <- summary(fit)$coefficients
data.frame(
term = rownames(coefs),
estimate = coefs[, "Estimate"],
conf_low = ci[, 1],
conf_high = ci[, 2],
p_value = coefs[, "Pr(>|t|)"]
)
#> term estimate conf_low conf_high p_value
#> (Intercept) (Intercept) 0.29580307 -2.13127355 2.7228797 0.8001598
#> dprsn_dx dprsn_dx 0.01314338 -0.35018786 0.3764746 0.9400541
#> homeless homeless 0.73035802 -0.80256071 2.2632768 0.3288854
#> hivstat hivstat 0.60267017 -0.44609107 1.6514314 0.2419383
#> polydrug polydrug -0.72477880 -2.61538619 1.1658286 0.4297969
#> sqrtnivd sqrtnivd 0.09361213 -0.08722651 0.2744508 0.29000054 Discussion
Depression diagnosis and homelessness are associated with higher log needle-sharing frequency, suggesting that mental health and housing instability contribute to HIV transmission risk behaviors among IDUs, consistent with RMB2e Chapter 8. Polydrug use and injection frequency are also positively associated with sharing, reflecting addiction severity. HIV-positive status shows an association that merits careful interpretation, as seropositive individuals may perceive less marginal risk or may have different social network positions. The log transformation of the skewed outcome is critical for producing well-behaved residuals and valid inference.
5 Source
- UCSF Regression Methods companion data: https://regression.ucsf.edu/sites/g/files/tkssra16191/files/wysiwyg/home/data/needle_sharing.dta
- Book: Vittinghoff E, Glidden DV, Shiboski SC, McCulloch CE (2012). Regression Methods in Biostatistics (2nd edition).