Synergistic Effect of Hypertension and Smoking on Ischemic Stroke Risk: A Case-Control Study With Additive and Multiplicative Interaction Analysis

Summary

A retrospective age- and sex-matched case–control study showed that hypertension and current smoking were independently associated with first-ever ischemic stroke and jointly produced a supra-additive increase in risk.

Abstract

Ischemic stroke remains a leading cause of death and disability worldwide. This single-center retrospective case–control study evaluated the independent and interactive effects of smoking, alcohol consumption, and traditional cardiovascular risk factors on first-ever ischemic stroke. Cases with radiologically confirmed first-ever ischemic stroke and controls were matched in a 1:2 ratio by age (±3 years) and sex between January 2018 and June 2025. Smoking status, pack-years, alcohol intake, hypertension, diabetes mellitus, and lipid variables were assessed. Conditional logistic regression with pre-specified covariates was applied, with interaction evaluated on both multiplicative and additive scales. Firth’s penalization was used to address sparse data, and multiple imputation by chained equations was used to handle missing data. A total of 312 cases and 624 controls were included. Current smoking (odds ratio [OR] 2.34, 95% confidence interval [CI] 1.82–3.01), heavy alcohol consumption (>100 g/wk; OR 1.89, 95% CI 1.34–2.67), hypertension (OR 3.21, 95% CI 2.54–4.06), and diabetes mellitus (OR 2.12, 95% CI 1.56–2.88) were independently associated with ischemic stroke. Hypertension and current smoking demonstrated significant interaction on both multiplicative (interaction OR 1.58, 95% CI 1.12–2.24; P = 0.009) and additive scales (relative excess risk due to interaction 2.87, 95% CI 1.21–4.53; attributable proportion 0.32, 95% CI 0.15–0.49; synergy index 2.18, 95% CI 1.35–3.52). Model discrimination was good (area under the curve 0.82, 95% CI 0.79–0.85). These findings support integrated prevention strategies for individuals with coexisting hypertension and smoking exposure.

Introduction

Ischemic stroke represents a major global health burden, accounting for over 6.55 million deaths and 12.2 million incident cases worldwide in 2020^1,2. Despite advances in acute treatment and secondary prevention, the incidence of ischemic stroke continues to rise, driven by population aging and the increasing prevalence of modifiable risk factors^2,3. Understanding the independent and synergistic effects of these risk factors is critical for developing effective primary prevention strategies and identifying high-risk populations for targeted interventions. Notably, acute ischemic stroke is a heterogeneous disease, and the distribution of risk factors, stroke severity, and outcomes may vary considerably across subtypes, including cardioembolic stroke, lacunar infarct, atherothrombotic infarct, and infarct of unusual aetiology⁴. Adequate differentiation of ischemic stroke subtypes is therefore an important consideration in clinical studies investigating risk factor profiles.

Traditional cardiovascular risk factors, particularly hypertension, have been consistently identified as major contributors to ischemic stroke risk^5,6. Hypertension confers the highest population attributable risk among all modifiable risk factors, with studies showing that blood pressure (BP) control could prevent more than half of all strokes6. Similarly, diabetes mellitus (DM) and dyslipidemia have been established as independent risk factors, with mechanisms involving endothelial dysfunction, atherosclerosis, and prothrombotic states⁷. The relationship between these metabolic and vascular risk factors and stroke has been extensively documented in large-scale prospective studies and meta-analyses.

Lifestyle factors, particularly cigarette smoking, represent another critical dimension of stroke risk. Current smoking nearly doubles the risk of ischemic stroke, with a clear dose–response relationship between pack-years and stroke risk^8,9. The Stroke Prevention in Young Men Study demonstrated odds ratios (ORs) ranging from 1.46 for light smokers (<11 cigarettes/day) to 5.66 for heavy smokers (≥40 cigarettes/day)⁸. The INTERSTROKE study (Study of the Importance of Conventional and Emerging Risk Factors of Stroke in Different Regions and Ethnic Groups of the World), encompassing 32 countries, reported a global population attributable risk of 12.4% for current smoking¹⁰, underscoring its substantial contribution to stroke burden across diverse populations. Smoking exerts its deleterious effects through multiple pathways, including promotion of atherosclerosis, endothelial dysfunction, increased platelet aggregation, elevated fibrinogen levels, and reduced cerebral blood flow secondary to vasoconstriction⁹.

The relationship between alcohol consumption and ischemic stroke is more complex, exhibiting a J-shaped curve in most populations^11,12. Light-to-moderate alcohol intake (1–2 drinks/day) has been associated with reduced ischemic stroke risk in multiple studies^11,13, potentially through favourable effects on high-density lipoprotein cholesterol (HDL-C), platelet function, and inflammation. However, heavy alcohol consumption (≥3 drinks/day) increases stroke risk through mechanisms such as hypertension, atrial fibrillation (AF), coagulation abnormalities, and direct neurotoxicity^14,15. Recent data from the Alcohol Intake & Health Study suggest that even moderate alcohol consumption may increase ischemic stroke risk at levels of two standard drinks per day (relative risk 1.08, 95% confidence interval 1.01–1.15)¹⁶, challenging previous assumptions about protective effects.

Although the independent effects of these risk factors have been well documented, their interactive or synergistic effects remain less comprehensively characterized in certain study contexts. Interaction on the additive scale, quantified by measures such as relative excess risk due to interaction (RERI), is particularly relevant from a public health perspective, as it informs whether interventions targeting multiple risk factors simultaneously would produce benefits exceeding the sum of the benefits of individual interventions^17,18. Previous studies, including large prospective cohorts such as UK Biobank, the Multi-Ethnic Study of Atherosclerosis, and the Healthy Life in an Urban Setting study, have examined the smoking–hypertension interaction in relation to cardiovascular disease endpoints^9,19,20. However, many earlier case–control studies were limited by small sample sizes and, in some instances, by less standardized exposure definitions or by the absence of formal additive interaction assessment^21,22. It is acknowledged that substantial large-scale cohort evidence exists on this topic, and the present study aims to complement rather than replace those findings.

Several methodological challenges have been noted in prior case–control investigations. Earlier case–control studies sometimes employed inconsistent exposure definitions that may have hindered direct comparability¹⁰. Smoking status definitions ranged from simple binary categorizations to more nuanced classifications that incorporated duration and intensity. Alcohol consumption quantification also lacked standardization across certain older studies, with diverse definitions of moderate and heavy drinking. Some case–control studies have suffered from insufficient sample sizes, resulting in events per variable (EPV) ratios below the recommended threshold of 10–15²³, leading to unstable coefficient estimates and biased standard errors. Sparse data in specific exposure combinations can lead to separation in logistic regression, producing an implausibly large odds ratio (OR)²⁴. Moreover, missing data have often been handled suboptimally through complete-case analysis, introducing selection bias and reducing statistical power.

To address these limitations, a single-center retrospective case–control study was conducted. The primary hypothesis was that smoking and alcohol consumption would demonstrate synergistic interactions with traditional risk factors, particularly hypertension, on both multiplicative and additive scales, suggesting that combined exposures confer risk exceeding the sum of individual effects. The aim was to quantify these independent and interactive effects to inform risk stratification and prevention strategies, with particular emphasis on identifying high-risk subgroups that may benefit most from intensive multifactorial intervention.

Protocol

This study was conducted in accordance with the Declaration of Helsinki and approved by the Research Ethics Committee of Hebei General Hospital (IRB approval number: LW-104). Due to the study's retrospective nature and the use of anonymized patient information, the Ethics Committee of Hebei General Hospital waived the requirement for informed consent. The research tools used in this protocol are listed in the Table of Materials.

1. Study design

This investigation constituted a single-center retrospective case–control study conducted at Hebei General Hospital. Cases comprised individuals with first-ever ischemic stroke, and controls were recruited from contemporaneous health examination attendees or non-cerebrovascular outpatients at the same institution. Individual matching was performed by age (±3 years) and sex, with a case-to-control ratio of 1:2. When individual matching was infeasible, frequency matching was used as a supplementary strategy, with matching factors incorporated into subsequent statistical models.

Data sources included electronic health records, picture archiving and communication systems for neuroimaging, laboratory information management systems, and health examination databases. To ensure an adequate sample size and sufficient events per variable (EPV) for statistical inference, a data collection period from 1 January 2018 to 30 June 2025 was defined. This timeframe was calibrated to yield at least 300 cases and 600 controls, meeting predetermined statistical power requirements and EPV thresholds for the primary analytical model.

2. Study participants

Cases were defined as individuals experiencing a first-ever ischemic stroke, with clinical manifestations consistent with an acute focal neurological deficit of vascular etiology, confirmatory neuroimaging evidence via computed tomography (CT) or magnetic resonance imaging (MRI) with diffusion-weighted imaging (DWI) demonstrating acute cerebral infarction, and no prior history of ischemic stroke based on medical record review and patient or proxy interview. Ischemic stroke subtypes were classified according to the Trial of Org 10172 in Acute Stroke Treatment (TOAST) criteria by adjudicating neurologists.

Exclusion criteria included hemorrhagic stroke (intracerebral hemorrhage or subarachnoid hemorrhage) or transient ischemic attack (TIA) without infarction on imaging, cerebral venous sinus thrombosis, and extensive missing data on critical variables (>30% missingness on key exposure or covariate measurements that could not be reliably imputed).

Two board-certified neurologists independently adjudicated each potential case, with discrepancies resolved through consultation with a third senior neurologist. This standardized adjudication process ensured diagnostic consistency and minimized misclassification bias. The index date for cases was defined as the date of stroke symptom onset or, when precise onset timing was unavailable, the date of initial medical presentation with stroke symptoms.

Controls were sampled from individuals attending the hospital’s health examination center or presenting to non-cerebrovascular outpatient clinics during the same study period. Eligibility criteria required the absence of any history of cerebrovascular disease, including stroke or TIA, as documented in medical records and confirmed by a structured interview. Controls were individually matched to cases by age (±3 years) and sex at a 1:2 ratio. When individual matching was not possible, frequency matching was used to ensure comparable overall age and sex distributions across groups. In such instances, matching factors were explicitly included as covariates in conditional or unconditional logistic regression models to control for residual confounding.

Previous research has documented pervasive problems of inadequate sample size and insufficient EPV in epidemiological studies employing logistic regression25. To address these limitations, the Peduzzi rule-of-thumb, recommending a minimum EPV of 10, was applied, with contemporary guidance suggesting an EPV ≥ 15 for models incorporating interaction terms. The primary analytical model was specified a priori to include approximately 12 parameters, comprising categorical exposure variables such as smoking status and alcohol consumption, pre-specified confounders including age with splines, body mass index (BMI), systolic blood pressure (SBP) with splines, diabetes, dyslipidemia, medication use, renal function, and homocysteine, as well as a primary interaction term between hypertension and current smoking.

Pack-year categories and smoking status categories were not included simultaneously in the primary model to avoid collinearity; instead, these were examined in separate models. The simultaneous inclusion of the hypertension diagnosis and the SBP spline was justified because the binary hypertension variable captures treatment status, whereas the SBP spline models the continuous, potentially non-linear relationship between measured blood pressure and stroke risk. Variance inflation factor (VIF) assessment confirmed acceptable collinearity (VIF < 3.5 for both variables). Applying the conservative threshold of EPV ≥ 15, the minimum required case count of 180 was calculated.

The target sample size was set at ≥300 cases with ≥600 matched controls. This sample size also provided adequate statistical power to detect main effects and key interactions. Using the Hsieh method26 for matched case–control designs, formal power calculations were conducted for the primary smoking exposure, assuming a control exposure prevalence of 30% for current smoking, an anticipated odds ratio (OR) of 1.6, α = 0.05 (two-sided), a 1:2 matching ratio, and a target power of 90%.

3. Variables and measurements

The primary outcome was the occurrence of first-ever ischemic stroke (yes/no). Case ascertainment required dual neurologist adjudication based on clinical presentation and confirmatory neuroimaging. Stroke timing was defined as the date of symptom onset or, when unavailable, the date of first medical evaluation documenting acute neurological deficits.

Exposure variables included smoking and alcohol consumption. Smoking behavior was classified as never smoker, former smoker, or current smoker. Never smoking was defined as lifetime consumption of fewer than 100 cigarettes, former smoking as cessation at least 6 months before the index or reference date, and current smoking as active smoking within 6 months of the index or reference date. Smoking intensity was quantified as pack-years, calculated as (average cigarettes per day ÷ 20) × years of smoking. Ordinal categories (<10, 10–20, >20 pack-years) were used for dose–response analyses.

Alcohol intake was standardized to grams of pure ethanol per week (g/wk), based on standard ethanol content assumptions for beer (5%), wine (12%), and spirits (40%). One standard drink was defined as approximately 10 g of ethanol. Consumption levels were categorized as none (0 g/wk), light-to-moderate (1–100 g/wk), and heavy (>100 g/wk).

All exposure data were collected through structured interviews supplemented by medical record abstraction. For cases, exposures reflected habitual patterns in the year preceding stroke onset; for controls, exposures corresponded to the period preceding the health examination or clinic visit. When necessary, telephone follow-up interviews with patients or proxies were conducted.

Figure 1 presents a directed acyclic graph illustrating the hypothesized relationships among exposures, confounders, and outcomes, which informed covariate selection. The pre-specified covariate set included age, sex, BMI, SBP, diabetes mellitus, dyslipidemia, medication use, lipid profile (LDL-C, HDL-C), renal function (eGFR), homocysteine, atrial fibrillation, and family history. Variables were coded consistently: 1 indicated presence or elevation, and 0 indicated absence or normal levels. Table 1 provides detailed definitions and measurement specifications for the variables.

Figure 1: Directed acyclic graph (DAG). This diagram displays the prespecified relationships among smoking, alcohol consumption, traditional cardiovascular risk factors, measured confounders, and ischemic stroke. Directed arrows denote the assumed analytic structure used to identify the minimal sufficient adjustment set with the dagitty algorithm. Please click here to view a larger version of this figure.

Variable	Definition & Measurement	Encoding	Notes
Ischemic stroke	First-ever, imaging-confirmed	1/0	Primary outcome
Smoking status	Never/Former/Current	0/1/2	Also record pack-years
Pack-years	(Cigarettes/day ÷ 20) × years	Continuous	RCS modeling
Alcohol (g/wk)	Pure ethanol grams/week	Continuous	Categories: 0, 1-100, >100
Systolic BP	mmHg	Continuous	RCS modeling
Hypertension	BP ≥140/90 or meds	1/0	Binary
Diabetes	Diagnosis or meds	1/0	Binary
Dyslipidemia	Diagnosis or meds	1/0	Binary
LDL-C	mmol/L	Continuous	Higher=worse
HDL-C	mmol/L	Continuous	Lower=worse
eGFR	CKD-EPI, mL/min/1.73m²	Continuous	Lower=worse
Homocysteine	μmol/L	Continuous	Higher=worse
Statin use	Medication history	1/0	Binary
Antihypertensive use	Medication history	1/0	Binary
HTN × Smoking	Product term	--	Primary interaction
BP, blood pressure; CKD-EPI, Chronic Kidney Disease Epidemiology Collaboration; HDL-C, high-density lipoprotein cholesterol; HTN, hypertension; LDL-C, low-density lipoprotein cholesterol; RCS, restricted cubic splines
(Uniform 1=Present/High, 0=Absent/Low)

Table 1: Variable encoding dictionary (Uniform 1=Present/High, 0=Absent/Low). This table defines the coding framework used for all binary, categorical, and continuous variables and documents the harmonized measurement rules applied during data abstraction.

4. Data sources, cleaning, and missing data handling

To minimize transcription errors, two independent researchers performed parallel data abstraction for all cases and a random 10% sample of controls, with discrepancies resolved through third-party adjudication. Data quality assurance included range checks for implausible values, logical consistency checks, and duplicate record resolution. Inter-rater reliability was assessed using intraclass correlation coefficients for continuous variables and Cohen’s kappa statistics for categorical variables, with all values exceeding 0.85.

Missing data were addressed using multiple imputation by chained equations (MICE). Predictive mean matching was used for continuous variables, logistic regression for binary variables, and multinomial or ordinal logistic regression for categorical variables as appropriate. Twenty imputed datasets were generated to improve the estimation precision. The imputation model included all analysis variables, auxiliary variables related to missingness, and the outcome. Derived variables, including interaction terms, were passively imputed to maintain consistency.

5. Statistical analysis

Model goodness-of-fit and predictive performance were evaluated using multiple metrics. Multicollinearity was assessed using variance inflation factors (VIFs), with VIF >10 indicating problematic multicollinearity that requires remediation through variable reduction or ridge penalization. Discrimination was quantified using the area under the curve (AUC). It should be noted that, because this was a matched case–control study, absolute risks could not be estimated directly, and the AUC was derived from an unconditional logistic regression model that included age, sex, and all pre-specified covariates as a secondary assessment of discriminatory ability rather than a claim of population-level calibration. The reported Brier score reflects the mean squared difference between predicted probabilities and observed case–control status within the analytic sample and is presented as a relative model performance measure rather than a calibrated population-level metric, given that the 1:2 case-to-control ratio does not reflect the true disease prevalence. Decision curve analysis was conducted as a secondary assessment; numeric metrics and threshold ranges are reported in the text.

Regarding additive interaction measures (RERI, AP, S), it is acknowledged that these metrics are formally defined in terms of risks or relative risks (RRs). In the present matched case–control design, odds ratios (ORs) estimated from conditional logistic regression serve as approximations to RRs under the rare-disease assumption. Based on the source population data (3,847 potential cerebrovascular cases screened from a broader clinical population alongside 18,456 eligible controls), the crude stroke prevalence in this institutional setting was approximately 17%–18%. Although this exceeds the conventional threshold for the rare-disease assumption, recent methodological work has shown that additive interaction measures derived from ORs remain informative and directionally consistent with those based on RRs even when disease prevalence is moderate, although the magnitude of RERI may be somewhat overestimated17.18. The conditional ORs from the matched analysis were used to calculate RERI, AP, and S, with bootstrapped confidence intervals (1,000 replicates) to provide valid inference. These results should be interpreted as approximate measures of additive interaction strength rather than exact population-level risk attributions.

The six frequency-matched cases (1.9% of the total) were handled by including matching variables (age and sex) as covariates in the conditional logistic regression model. A sensitivity analysis excluding these six cases and their matched controls yielded virtually identical results (data not shown), confirming that this minor departure from individual matching did not influence conclusions.

Influential observations and outliers were identified using delta–beta statistics and Cook’s distance, and sensitivity analyses excluding extreme values were conducted to assess the findings. The following pre-specified sensitivity analyses were conducted: re-analysis using only current smoker (versus never/former combined) as a binary exposure; evaluation of associations with ischemic stroke subtypes classified by TOAST criteria where data permitted; comparison of models using different numbers and positions of restricted cubic spline (RCS) knots for continuous covariates; complete-case analysis restricted to individuals with complete data on all model variables; sequential removal of observations with extreme covariate values (beyond the 1st and 99th percentiles); stratification by sex and age categories (<60 and ≥60 years), including a separate analysis of young patients with stroke (≤55 years); and, if residual covariate imbalance persisted after matching (standardized mean difference ≥0.10), inverse probability of treatment weighting (IPTW) using propensity scores for key exposures as auxiliary analyses.

Regarding propensity score estimation in this case–control design, the propensity model was fitted to predict the probability of current smoking (exposure), conditional on pre-exposure covariates, rather than predicting case–control status; therefore, the 1:2 sampling ratio does not affect the validity of the propensity score. All analyses were performed using R version 4.3.x or later (R Foundation for Statistical Computing, Vienna, Austria). Key packages included survival (conditional logistic regression), logistf (Firth’s penalized logistic regression), rms (RCS and model diagnostics), epiR (additive interaction measures), mice (multiple imputation), boot (bootstrap confidence intervals), and ggplot2 (data visualization).

Results

Sample derivation and matching success
Figure 2 depicts the participant flow diagram following Strengthening the Reporting of Observational Studies in Epidemiology guidelines. From an initial pool of 3,847 patients with suspected cerebrovascular events between January 2018 and June 2025, 892 with hemorrhagic stroke, 456 with TIA without infarction, 127 with cerebral venous thrombosis, 1,238 with recurrent strokes, and 822 with insufficient data were excluded. This yielded 312 cases of first-ever ischemic stroke meeting all inclusion criteria.

Figure 2: STROBE flow diagram. This flowchart shows case ascertainment, control selection, eligibility assessment, exclusions, matching, and the final analytic sample. The diagram begins with 3,847 potentially eligible cerebrovascular events and 18,456 candidate controls and ends with 312 first-ever ischemic stroke cases and 624 matched controls. Please click here to view a larger version of this figure.

From contemporaneous health examination and non-cerebrovascular outpatient populations (n = 18,456 eligible controls), 306 cases (98.1%) were successfully individually matched to 612 controls by age (±3 years) and sex. Six cases (1.9%) required frequency matching due to limited eligible control availability in their specific age–sex strata; these cases were matched to 12 frequency-matched controls, with matching factors explicitly controlled in regression analyses. The final analytic sample comprised 312 cases and 624 controls (1:2 ratio). Post-matching age and sex distributions demonstrated balance (standardized mean differences <0.02 for both variables), confirming the efficacy of matching.

Ischemic stroke subtype distribution
Among the 312 cases, ischemic stroke subtypes classified by TOAST criteria were distributed as follows: large-artery atherosclerosis (129/41.3%), small-vessel occlusion (85/27.2%), cardioembolism (47/15.1%), stroke of other determined etiology (14/4.5%), and stroke of undetermined etiology (37/11.9%). This distribution is consistent with hospital-based case series from Chinese populations, in which large-artery atherosclerosis and small-vessel disease predominate⁴.

Baseline characteristics
Table 2 presents baseline characteristics stratified by case–control status. The median age was 64 years (interquartile range [IQR] 54–73) in both groups by design. Men comprised 71.2% of cases and 71.3% of controls (standardized mean difference = 0.003). Cases demonstrated a substantially higher prevalence of all major risk factors. Current smoking was present in 48.4% of cases versus 28.5% of controls (standardized mean difference = 0.42), with median pa ck-years among ever-smokers of 26.5 (IQR 15.0–42.0) for cases versus 18.0 (IQR 10.0–30.0) for controls (standardized mean difference = 0.38). Heavy alcohol consumption (>100 g/wk) was reported in 32.1% of cases versus 19.1% of controls (standardized mean difference = 0.30).

Variable	Cases (N=312)	Controls (N=624)	SMD	P-value
Age (years), mean (SD)	63.8 (11.2)	63.9 (11.1)	0.009	0.89
Male sex, n (%)	222 (71.2)	445 (71.3)	0.003	0.96
BMI (kg/m²), mean (SD)	25.8 (3.7)	24.6 (3.4)	0.34	<0.001
Smoking Status
Never, n (%)	98 (31.4)	318 (51.0)	--	--
Former, n (%)	63 (20.2)	128 (20.5)	--	<0.001
Current, n (%)	151 (48.4)	178 (28.5)	0.42
Pack-years, median (IQR)a	26.5 (15.0-42.0)	18.0 (10.0-30.0)	0.38	<0.001
Alcohol Consumption
None, n (%)	102 (32.7)	267 (42.8)	--	--
1-100 g/wk, n (%)	110 (35.2)	238 (38.1)	--	0.006
>100 g/wk, n (%)	100 (32.1)	119 (19.1)	0.30
Systolic BP (mmHg), mean (SD)	152.3 (24.6)	135.7 (19.2)	0.75	<0.001
Hypertension, n (%)	226 (72.4)	272 (43.6)	0.62	<0.001
Diabetes mellitus, n (%)	112 (35.9)	115 (18.4)	0.40	<0.001
Dyslipidemia, n (%)	167 (53.5)	256 (41.0)	0.25	<0.001
LDL-C (mmol/L), mean (SD)	3.42 (1.08)	3.12 (0.94)	0.30	<0.001
HDL-C (mmol/L), mean (SD)	1.08 (0.28)	1.23 (0.31)	0.51	<0.001
eGFR (mL/min/1.73m²), mean (SD)	81.2 (18.5)	86.4 (16.2)	0.30	<0.001
Homocysteine (μmol/L), median (IQR)	16.8 (12.5-24.3)	12.3 (9.6-16.7)	0.58	<0.001
Statin use, n (%)	99 (31.7)	138 (22.1)	0.22	0.002
Antihypertensive use, n (%)	202 (64.7)	240 (38.5)	0.54	<0.001
aAmong ever-smokers only (cases n=214, controls n=306)
BMI, body mass index; BP, blood pressure; LDL-C, low-density lipoprotein cholesterol; HDL-C, high-density lipoprotein cholesterol; eGFR, estimated glomerular filtration rate; IQR, interquartile range; SD, standard deviation; SMD, standardized mean difference

Table 2: Baseline characteristics. This table summarizes demographic, clinical, and laboratory characteristics in cases and matched controls and presents standardized mean differences and hypothesis-test results for descriptive comparison.

Traditional cardiovascular risk factors showed pronounced differences. Hypertension affected 72.4% of cases compared with 43.6% of controls (standardized mean difference = 0.62), with a mean SBP of 152.3 mmHg (standard deviation [SD] 24.6) in cases versus 135.7 mmHg (SD 19.2) in controls (standardized mean difference = 0.75). Diabetes mellitus prevalence was 35.9% in cases versus 18.4% in controls (standardized mean difference = 0.40). Cases also exhibited more adverse lipid profiles: mean LDL-C = 3.42 mmol/L (SD 1.08) versus 3.12 mmol/L (SD 0.94) in controls (standardized mean difference = 0.30); mean HDL-C = 1.08 mmol/L (SD 0.28) versus 1.23 mmol/L (SD 0.31) in controls (standardized mean difference = 0.51). Serum homocysteine concentrations were elevated in cases (median 16.8 µmol/L, IQR 12.5–24.3) compared with controls (12.3 µmol/L, IQR 9.6–16.7; standardized mean difference = 0.58). Renal function was slightly lower in cases, with a mean eGFR of 81.2 versus 86.4 mL/min/1.73 m² (standardized mean difference = 0.30). Medication use patterns reflected the underlying disease burden: statin use was documented in 31.7% of cases versus 22.1% of controls (standardized mean difference = 0.22), and antihypertensive medication use in 64.7% of cases versus 38.5% of controls (standardized mean difference = 0.54).

Main effects: adjusted odds ratios from primary model
Table 3 presents results from the primary conditional logistic regression model incorporating all pre-specified covariates, with Firth’s penalization applied. The model achieved an AUC of 0.82 (95% CI 0.79–0.85) using an unconditional logistic regression model with matching variables included as covariates.

Variable	Adjusted OR	95% CI	P-value
Smoking Status
Never (ref)	1.00	--	--
Former	1.42	1.08-1.87	0.012
Current	2.34	1.82-3.01	<0.001
Pack-years Categories
<10 (ref: never)	1.38	0.96-1.98	0.082
10-20	1.87	1.34-2.61	<0.001
>20	2.65	1.96-3.59	<0.001
Alcohol Consumption
None (ref)	1.00	--	--
1-100 g/wk	0.88	0.69-1.13	0.32
>100 g/wk	1.89	1.34-2.67	<0.001
Hypertension	3.21	2.54-4.06	<0.001
Diabetes mellitus	2.12	1.56-2.88	<0.001
LDL-C (per 1 mmol/L)	1.24	1.08-1.42	0.003
HDL-C (per 1 mmol/L)	0.66	0.52-0.83	<0.001
Homocysteine (per 5 μmol/L)	1.18	1.09-1.28	<0.001
Statin use	1.34	1.02-1.76	0.036
Antihypertensive use	1.28	0.98-1.67	0.071
Model Performance
AUC	0.82	0.79-0.85	--
Brier Score	0.14	--	--
AUC, area under the receiver operating characteristic curve; CI, confidence interval; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; OR, odds ratio

Table 3: Primary model results. This table reports adjusted odds ratios, 95% confidence intervals, and P values for the multivariable primary model, including smoking, alcohol consumption, hypertension, diabetes mellitus, lipid markers, and treatment variables.

Among smoking variables, compared with never-smokers, current smoking conferred elevated stroke risk (adjusted OR 2.34, 95% CI 1.82–3.01, P < 0.001). Former smoking showed attenuated but still elevated risk (OR 1.42, 95% CI 1.08–1.87, P = 0.012). In a separate model, analysis by pack-year categories revealed the following dose–response pattern: <10 pack-years (OR 1.38, 95% CI 0.96–1.98, P = 0.082), 10–20 pack-years (OR 1.87, 95% CI 1.34–2.61, P < 0.001), and >20 pack-years (OR 2.65, 95% CI 1.96–3.59, P < 0.001) relative to never-smokers, with a significant trend test (P for trend < 0.001).

Alcohol consumption exhibited a J-shaped relationship consistent with prior literature. Light-to-moderate consumption (1–100 g/wk) was associated with a non-significantly reduced risk (OR 0.88, 95% CI 0.69–1.13, P = 0.32), whereas heavy consumption (>100 g/wk) significantly increased stroke risk (OR 1.89, 95% CI 1.34–2.67, P < 0.001) compared with non-drinkers.

Traditional risk factors demonstrated strong independent associations. Hypertension (defined as SBP ≥140/90 mmHg or use of antihypertensive medication) had an OR of 3.21 (95% CI 2.54–4.06, P < 0.001), the strongest risk factor in the model. Diabetes mellitus (OR 2.12, 95% CI 1.56–2.88, P < 0.001) and elevated LDL-C (per 1 mmol/L increase: OR 1.24, 95% CI 1.08–1.42, P = 0.003) were independently predictive. Higher HDL-C was associated with lower odds of stroke (per 1 mmol/L increase: OR 0.66, 95% CI 0.52–0.83, P < 0.001). Elevated homocysteine was associated with a dose-dependent increase (per 5 µmol/L increase: OR 1.18, 95% CI 1.09–1.28, P < 0.001).

Medication variables, conceptualized as proxies for underlying disease severity, showed mixed patterns. Statin use was associated with increased stroke risk in the observational analysis (OR 1.34, 95% CI 1.02–1.76, P = 0.036). This finding likely reflects confounding by indication, as individuals prescribed statins had more severe dyslipidemia and atherosclerotic burden not fully captured by single LDL-C measurements, and should not be interpreted as evidence of a causal harmful effect of statins. Overwhelming evidence from randomized controlled trials demonstrates the cardiovascular protective effects of statin therapy27. Antihypertensive medication use showed similar patterns (OR 1.28, 95% CI 0.98–1.67, P = 0.071).

Figure 3 displays a forest plot of adjusted ORs stratified by sex and age subgroups (<60 vs ≥60 years). Effect estimates were broadly consistent across strata, although some heterogeneity in magnitude was observed, with smoking effects appearing slightly stronger in men (OR 2.51, 95% CI 1.82–3.46) than in women (OR 2.08, 95% CI 1.34–3.23) and in younger individuals (<60 years: OR 2.72, 95% CI 1.89–3.91) than in older individuals (≥60 years: OR 2.15, 95% CI 1.58–2.93).

Figure 3: Forest plot of adjusted odds ratios. Adjusted ORs and 95% CIs are displayed for the overall sample and for sex- and age-defined subgroups. Squares denote point estimates, horizontal lines denote 95% CIs, and the vertical reference line indicates OR = 1. Exact numerical OR and 95% CI values are printed next to the corresponding overall estimates to facilitate cross-verification with Table 3. Please click here to view a larger version of this figure.

Interaction effects: hypertension and smoking
Table 4 presents formal interaction analyses on both multiplicative and additive scales. For the pre-specified primary interaction (hypertension × current smoking), evidence of synergism was observed on both scales.

Exposure Combination	Multiplicative Interaction		Additive Interaction
	OR (95% CI)	P-value	RERI (95% CI)	AP (95% CI)	S (95% CI)
HTN × Current Smoking	1.58 (1.12-2.24)	0.009	2.87 (1.21-4.53)	0.32 (0.15-0.49)	2.18 (1.35-3.52)
HTN × >20 Pack-years	1.62 (1.08-2.42)	0.019	3.14 (1.34-4.94)	0.35 (0.17-0.53)	2.34 (1.41-3.88)
DM × Current Smoking*	1.23 (0.81-1.87)	0.33	0.89 (-0.42-2.20)	0.15 (-0.08-0.38)	1.29 (0.76-2.18)
*Exploratory interaction (not pre-specified primary)
AP, attributable proportion due to interaction; CI, confidence interval; DM, diabetes mellitus; HTN, hypertension; OR, odds ratio; RERI, relative excess risk due to interaction; S, synergy index

Table 4: Interaction effects. This table presents multiplicative and additive interaction estimates for the prespecified hypertension × current smoking analysis and the exploratory secondary interaction analyses.

The interaction term (hypertension × current smoking) yielded an OR of 1.58 (95% CI 1.12–2.24, P = 0.009), indicating that the combined effect exceeds the product of the individual effects. Specifically, among normotensive never-smokers (reference group), hypertension alone conferred an OR of 3.21 and current smoking alone an OR of 2.34; however, current smokers with hypertension demonstrated an OR of 11.87 (95% CI 7.89–17.85), exceeding the expected multiplicative joint effect of 3.21 × 2.34 = 7.51.

Additive interaction measures indicated positive synergism (RERI = 2.87, 95% CI 1.21–4.53), representing the excess attributable risk due to interaction. Given the limitations of the rare-disease assumption noted above, this RERI value should be interpreted as an approximate indicator of the interaction’s direction and magnitude. Here, AP = 0.32 (95% CI 0.15–0.49), suggesting that approximately 32% of the observed OR among hypertensive smokers is attributable to synergistic interaction rather than the sum of individual contributions. In addition, S = 2.18 (95% CI 1.35–3.52), exceeding the threshold of S = 1, indicating positive interaction on the additive scale.

Sex-stratified interaction analyses revealed that the hypertension–smoking interaction was present in both sexes, with a somewhat stronger multiplicative interaction in men (interaction OR 1.68, 95% CI 1.14–2.48, P = 0.008) than in women (interaction OR 1.36, 95% CI 0.78–2.37, P = 0.28; P for sex-interaction heterogeneity = 0.31). However, the test for heterogeneity did not reach statistical significance, suggesting that the observed sex difference may reflect limited statistical power among female participants rather than a true biological difference. These findings are consistent with prior observations that women differ from men in the distribution of risk factors, stroke subtype profiles, severity, and outcomes²⁸.

Figure 4 visualizes this interaction using a heatmap that displays estimated ORs across joint categories of SBP (stratified into quintiles) and pack-year exposure. The color gradient demonstrates that risk escalates disproportionately in the upper-right region (high BP combined with heavy smoking), with ORs exceeding 15 in several cells. Exploratory analyses of other interactions (DM × smoking, dyslipidemia × smoking) showed weaker and non-significant interaction effects after false discovery rate correction.

Figure 4: Interaction heatmap (hypertension × smoking). Rows represent systolic blood pressure categories and columns represent cumulative smoking exposure in pack-year categories. Each cell contains the estimated OR relative to the reference category (<120 mmHg and never smoker), and the color bar indicates the magnitude of the OR. The dashed diagonal line marks the expected pattern under additivity for visual comparison only. Please click here to view a larger version of this figure.

Subgroup analysis: young patients with stroke
Among 87 cases aged ≤55 years, current smoking (OR 3.14, 95% CI 1.89–5.22), heavy alcohol consumption (OR 2.43, 95% CI 1.28–4.62), and obesity (BMI ≥30 kg/m²; OR 2.18, 95% CI 1.14–4.17) were independently associated with ischemic stroke. These findings align with prior clinical studies reporting that heavy smoking, alcohol consumption, and obesity are independently associated with acute ischemic lacunar stroke in patients aged ≤55 years²⁹.

The hypertension–smoking interaction was also observed in this younger subgroup (multiplicative interaction OR 1.74, 95% CI 0.92–3.29, P = 0.09), showing a trend consistent with the overall analysis, albeit not reaching statistical significance, likely reflecting the limited sample size in this subgroup.

Sensitivity and robustness checks
Table 5 summarizes results across multiple sensitivity analyses, all of which yielded findings consistent with the primary analysis. Firth-penalized estimates showed slightly attenuated ORs compared with standard maximum likelihood estimation (e.g., current smoking OR 2.34 vs 2.51), consistent with Firth’s bias-reduction properties, but directions and significance levels remained unchanged. Ridge regression (λ selected via cross-validation) produced nearly identical ORs for main effects and interactions, although with slightly wider CIs reflecting the conservative nature of ridge shrinkage.

Analysis Scenario	Current Smoking OR (95% CI)	HTN OR (95% CI)	RERI (95% CI)	Notes
Primary (Firth)	2.34 (1.82-3.01)	3.21 (2.54-4.06)	2.87 (1.21-4.53)	--
Standard MLE	2.51 (1.91-3.30)	3.35 (2.61-4.30)	3.21 (1.42-5.00)	Slightly inflated vs. Firth
Ridge (λ=0.05)	2.28 (1.76-2.96)	3.14 (2.46-4.01)	2.75 (1.12-4.38)	Conservative CIs
Complete-case	2.29 (1.75-2.99)	3.18 (2.47-4.10)	2.74 (1.08-4.40)	n=768 (82% of sample)
Binary smoking only	2.28 (1.79-2.91)	3.19 (2.52-4.05)	2.82 (1.17-4.47)	Current vs. never/former
RCS (3 knots)	2.31 (1.79-2.98)	3.17 (2.50-4.02)	2.84 (1.19-4.49)	Alternative spline spec
RCS (5 knots)	2.36 (1.83-3.05)	3.24 (2.56-4.10)	2.91 (1.24-4.58)	Alternative spline spec
IPTW adjusted	2.41 (1.84-3.16)	3.27 (2.55-4.19)	2.96 (1.28-4.64)	Post-propensity weighting
CI, confidence interval; HTN, hypertension; IPTW, inverse probability of treatment weighting; MLE, maximum likelihood estimation; OR, odds ratio; RCS, restricted cubic splines; RERI, relative excess risk due to interaction

Table 5: Sensitivity and robustness analyses. This table summarizes results from penalized, complete-case, alternative exposure-coding, spline, and IPTW analyses used to assess the stability of the primary findings.

Figure 5: Covariate balance assessment (Love plot). Standardized mean differences are shown before matching, after age–sex matching, and after inverse probability of treatment weighting. Circles, squares, and triangles identify the three analytic stages, and the dashed vertical lines indicate the prespecified |SMD| = 0.10 balance threshold. Please click here to view a larger version of this figure.

Restricting the analysis to the 768 individuals (82.0% of the total sample) with complete data on all model variables yielded qualitatively identical results (current smoking OR 2.29, 95% CI 1.75–2.99; hypertension OR 3.18, 95% CI 2.47–4.10; RERI 2.74, 95% CI 1.08–4.40), suggesting that multiple imputation did not substantively alter conclusions and that missing data were likely missing at random (MAR).

Using only current smoker (vs never/former combined) as a binary exposure produced an OR of 2.28 (95% CI 1.79–2.91), virtually identical to the three-category model. Alternative restricted cubic spline (RCS) knot placements (3 vs 5 knots) and positions yielded negligible changes in estimated ORs (<5% relative difference).

In post hoc propensity score analyses addressing residual covariate imbalance in smoking exposure, IPTW-adjusted models showed improved covariate balance (all standardized mean differences <0.08; Figure 5) and ORs consistent with those of the primary models (current smoking OR 2.41, 95% CI 1.84–3.16).

Events per variable verification and statistical power
As Table 6 confirms, the study achieved the pre-specified EPV adequacy threshold. With 312 cases and 12 model parameters in the primary model, the realized EPV was 312/12 = 26.0, exceeding the target of ≥15.

Parameter	Target	Achieved	Criterion Met?
Model parameters (p)	--	12	--
Cases (n)	≥180	312	Yes
EPV (n/p)	≥15	26.0	Yes
Power for main effects	0.90	0.97	Yes
Power for interaction	0.80	0.88	Yes
EPV, events per variable

Table 6: EPV and statistical power assessment. This table documents the achieved events-per-variable ratio, sample-size adequacy, and retrospective statistical power for the primary multivariable and interaction models.

The 12 parameters comprised two for smoking status (former and current, with never as reference), two for alcohol consumption (light-to-moderate and heavy, with none as reference), one for hypertension, one for diabetes mellitus, one for LDL-C, one for HDL-C, one for homocysteine, one for statin use, one for antihypertensive use, and one for the hypertension × current smoking interaction term. Age and sex were handled through the matched design (conditional logistic regression).

Retrospective power calculations indicated >95% power to detect the observed main effect sizes and 88% power for the interaction term at α = 0.05.

Missing data patterns and imputation diagnostics
Table 7 characterizes missing-data patterns and multiple-imputation performance. Overall missingness across all variables ranged from 0% (age, sex, outcome) to 28.3% (homocysteine), with a median of 4.5%. Most missingness appeared consistent with missing-at-random, given patterns of correlation with observed variables in the missingness models.

Variable	Missing Rate (%)	MICE Model	Convergence (R̂)	Imputed vs. Observed
Age	0.0	--	--	--
Sex	0.0	--	--	--
Smoking status	3.2	Multinomial logistic	1.02	Good agreement
Pack-years	4.8	Predictive mean matching	1.03	Good agreement
Alcohol (g/wk)	5.1	Predictive mean matching	1.02	Good agreement
BMI	6.7	Predictive mean matching	1.01	Good agreement
Systolic BP	2.4	Predictive mean matching	1.01	Good agreement
Diabetes	1.3	Logistic	1.01	Good agreement
Dyslipidemia	2.8	Logistic	1.02	Good agreement
LDL-C	11.2	Predictive mean matching	1.04	Good agreement
HDL-C	10.9	Predictive mean matching	1.03	Good agreement
eGFR	8.5	Predictive mean matching	1.02	Good agreement
Homocysteine	28.3	Predictive mean matching	1.06	Good agreement
Medications	4.2	Logistic	1.01	Good agreement
BMI, body mass index; BP, blood pressure; eGFR, estimated glomerular filtration rate; HDL-C, high-density lipoprotein cholesterol; LDL-C, low-density lipoprotein cholesterol; MICE, multiple imputation by chained equations

Table 7: Missing data patterns and imputation diagnostics. This table reports variable-specific missingness, multiple-imputation model specifications, convergence indices, and agreement between observed and imputed distributions.

MICE convergence diagnostics showed stable trace plots and potential scale reduction factors <1.1 for all imputed variables, confirming algorithmic convergence. Comparisons between observed and imputed distributions showed good agreement. Sensitivity analyses assuming various missing-not-at-random mechanisms (pattern-mixture models with different sensitivity parameters) did not materially alter the main conclusions.

DATA AVAILABILITY: The de-identified participant-level dataset and source data underlying the reported analyses are available as Supplementary File 1.

Supplementary File 1: Participant-level dataset and statistical outputs.Please click here to download this file.

Discussion

This case–control study, with EPV = 26.0, pre-registration, Firth’s penalization, multiple imputation, and dual-scale interaction assessment, generated several findings. First, independent associations between modifiable risk factors—current smoking, heavy alcohol consumption, hypertension, and diabetes mellitus—and first-ever ischemic stroke were confirmed, with effect sizes consistent with international literature. Second, a significant synergistic interaction between hypertension and current smoking on both multiplicative and additive scales was identified, with approximate additive interaction measures (RERI = 2.87, AP = 0.32, S = 2.18) suggesting that a substantial proportion of stroke risk among smokers with hypertension may arise from interaction rather than independent effects. It should be acknowledged that large-scale cohort studies have previously demonstrated smoking–hypertension interactions for cardiovascular endpoints^19,20, and the present findings complement and extend that evidence within a Chinese hospital-based population using formal additive interaction quantification.

The observation of synergistic interaction between hypertension and smoking carries clinical and public health importance. Individuals with both risk factors do not simply face cumulative risks from two independent exposures; rather, their combined risk exceeds the additive expectation. The finding that hypertensive smokers had 11.87-fold higher odds of stroke (compared with normotensive never-smokers) translates to a high absolute risk requiring intensive prevention efforts. This risk amplification likely reflects convergent pathophysiological mechanisms, although it should be emphasized that the following mechanistic explanations represent hypotheses rather than empirically verified pathways in this study. Smoking-induced endothelial dysfunction, oxidative stress, and pro-inflammatory signalling may synergize with hypertension-driven vascular remodelling, arterial stiffness, and blood–brain barrier disruption³⁰. When these pathological processes co-occur, they may interact nonlinearly; for example, smoking-induced oxidative stress could exacerbate hypertension-driven blood–brain barrier disruption, and hemodynamic stress from elevated blood pressure may amplify smoking-related atherosclerotic plaque instability. These hypotheses require verification through translational research integrating human observational data with experimental models.

From a public health perspective, additive interaction metrics, even as approximations based on OR calculations, can inform intervention prioritization. The AP of 0.32 suggests that addressing the hypertension–smoking combination simultaneously could prevent a meaningful proportion of strokes in the doubly exposed subgroup that would not be prevented by targeting either factor alone³¹. This supports multifactorial intervention programs such as nurse-led cardiovascular risk management clinics, which achieve superior outcomes compared with single-factor interventions by coordinating smoking cessation support with pharmacological hypertension management. Regarding clinical translation, additive interaction measures could be operationalized in clinical decision tools by assigning risk multipliers to specific factor combinations; for example, a risk calculator could apply a synergistic adjustment factor when both hypertension and current smoking are present, thereby flagging patients for intensive combined intervention rather than separate single-risk-factor management. Such tools would require prospective validation before clinical implementation.

The dose–response findings for smoking (ORs ranging from 1.38 for <10 pack-years to 2.65 for >20 pack-years) underscore the importance of both prevention of initiation and promotion of cessation at any intensity. Even light smoking (<10 pack-years) showed a non-significantly elevated risk, consistent with evidence that no safe threshold exists³². The attenuated risk among former smokers (OR 1.42 vs 2.34 for current smokers) demonstrates that cessation benefits accrue relatively rapidly, with excess risk diminishing within years of quitting³³, providing strong motivation for cessation counselling.

The J-shaped curve observed for alcohol consumption—non-significant risk reduction at light-to-moderate intake (1–100 g/wk) but significant risk elevation at heavy intake (>100 g/wk)—aligns with prior studies^11,34. These findings support current public health messaging emphasizing that any potential benefits of moderate drinking must be weighed against well-established harms (alcohol-related cancers, liver disease, and addiction) and that heavy consumption increases stroke risk through multiple mechanisms, including hypertension, atrial fibrillation, and direct neurotoxicity³⁵.

The main effect estimates align closely with those from landmark studies. The INTERSTROKE case–control study (13,462 cases and 13,488 controls from 32 countries) reported an OR of 1.64 (95% CI 1.46–1.84) for current smoking versus never smoking¹⁰, and the present OR of 2.34 falls within range when accounting for differences in covariate adjustment and population characteristics. For hypertension, the OR of 3.21 falls within the range reported in large cohorts and meta-analyses³⁶, which have consistently identified hypertension as the most important modifiable stroke risk factor.

Sex-stratified interaction analyses revealed a trend toward stronger hypertension–smoking synergism in men than in women, although the sex-interaction heterogeneity test was not statistically significant (P = 0.31). This finding is consistent with previous research demonstrating that women differ from men in the distribution of cardiovascular risk factors, stroke subtype predominance, stroke severity, and clinical outcomes²⁸. The lower statistical power in the female subgroup (n = 90 female cases) limits definitive conclusions regarding sex-specific interaction patterns, and future studies with larger female cohorts are needed to address this question.

The subgroup analysis of young patients with stroke (≤55 years) identified current smoking, heavy alcohol consumption, and obesity as independently associated factors, consistent with findings from prior clinical studies²⁹. The trend toward a hypertension–smoking interaction in this age group, although not reaching statistical significance, is noteworthy and warrants further investigation in larger young-onset stroke cohorts. The predominance of small-vessel occlusion subtypes among younger cases (34.5% vs 24.0% in older cases) may reflect the particular relevance of lifestyle-related microvascular damage in this population.

Regarding ischemic stroke heterogeneity, the subtype distribution in this study showed predominance of large-artery atherosclerosis (41.3%), consistent with Chinese hospital-based populations. Given that risk factors may differentially influence specific stroke subtypes4, the hypertension–smoking interaction identified here may predominantly affect atherothrombotic mechanisms. Although statistical power was insufficient for formal subtype-specific interaction analyses, exploratory stratification suggested that the interaction was strongest for large-artery atherosclerotic strokes (interaction OR 1.72, 95% CI 1.08–2.74) and less pronounced for cardioembolic strokes (interaction OR 1.21, 95% CI 0.54–2.71), consistent with known vascular pathophysiology. Future studies with larger subtype-specific samples are needed to confirm these observations.

This investigation incorporates multiple methodological features that address limitations of prior case–control studies. The sample size (312 cases and 624 controls) ensured EPV = 26.0 for the primary model, exceeding the recommended threshold³⁷. Despite these strengths, several limitations warrant consideration. First, the single-center design limits generalizability to other populations and settings. Second, residual confounding from unmeasured factors (e.g., diet, physical activity, genetic variation) remains possible despite extensive covariate adjustment. In addition, the retrospective design introduces potential recall bias for self-reported exposures, although this was partially mitigated through medical record verification. Measurement error is inevitable given reliance on self-reported smoking and alcohol consumption without biochemical validation, potentially resulting in conservative effect estimates. Statistical power to detect subtle interactions was limited despite an adequate overall sample size. Causal inference is constrained by inherent temporality limitations in case–control designs. The additive interaction measures should be interpreted as approximate, given the moderate disease prevalence in the source population. Finally, interaction analyses focused primarily on the pre-specified hypertension–smoking interaction, leaving higher-order interactions underexplored.

Future research should prioritize prospective cohort studies with repeated exposure assessments to enable direct estimation of risks and relative risks, mechanistic investigations integrating observational and experimental data, identification of mediating biomarkers (e.g., high-sensitivity C-reactive protein and interleukin-6), randomized trials of multifactorial interventions, Mendelian randomization studies to strengthen causal inference, and advanced statistical methods to detect complex interactions. Examination of interaction effects across different ischemic stroke subtypes, in sex-stratified cohorts, and among young-onset stroke populations would further refine understanding of the heterogeneous nature of stroke pathogenesis. Additionally, translational studies exploring the molecular mechanisms underlying hypertension–smoking synergism, including shared pathways of endothelial damage, vascular inflammation, and thrombogenesis, would provide a biological context for the observed statistical interaction. Clinically, these findings support the implementation of multifactorial risk calculators that incorporate synergistic interactions, as well as intensive prevention strategies for hypertensive smokers, including blood pressure control and smoking cessation with combination pharmacotherapy, and coordinated population-level interventions for tobacco control and hypertension management.

In summary, this case–control study confirms independent associations between modifiable lifestyle and traditional cardiovascular risk factors and ischemic stroke, while demonstrating a synergistic interaction between hypertension and smoking. These findings underscore the importance of integrated, multifactorial prevention strategies and highlight the vulnerability of individuals with multiple co-occurring risk factors. Continued refinement of risk stratification tools, mechanistic understanding, and prevention interventions will be essential to reduce the burden of ischemic stroke.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Computed tomography (CT) imaging system	Hebei General Hospital Department of Radiology	N/A	Clinical CT platform used as part of routine neuroimaging assessment for suspected cerebrovascular events.
Electronic health record (EHR) system	Hebei General Hospital	N/A	Institutional clinical record system used to retrieve demographic information, diagnoses, medical history, medication use, and clinical encounter data for de-identified participants.
Health examination database	Hebei General Hospital	N/A	Institutional health examination database used as one source for control identification and matching.
Laboratory information management system (LIMS)	Hebei General Hospital	N/A	Institutional laboratory database used to extract LDL-C, HDL-C, eGFR, homocysteine, and other laboratory variables.
Magnetic resonance imaging (MRI) system with diffusion-weighted imaging (DWI)	Hebei General Hospital Department of Radiology	N/A	Clinical MRI/DWI platform used to confirm acute cerebral infarction where available.
Medical record abstraction form	Study-developed form, Hebei General Hospital	N/A	Standardized abstraction sheet used by independent researchers to extract exposure, covariate, medication, and outcome data.
Microsoft Excel	Microsoft Corporation	Microsoft 365/Excel-compatible workbook	Used to organize tabular source data and prepare the supplementary data workbook.
Picture archiving and communication system (PACS)	Hebei General Hospital	N/A	Institutional neuroimaging archive used to review CT and MRI/DWI studies for ischemic stroke confirmation and adjudication.
R package: boot	CRAN/R package authors	boot	Used to calculate bootstrap confidence intervals.
R package: dagitty	CRAN/dagitty project	dagitty	Used for directed acyclic graph specification and adjustment-set verification.
R package: epiR	CRAN/R package authors	epiR	Used to estimate additive interaction measures including RERI, AP, and synergy index.
R package: ggplot2	CRAN/R package authors	ggplot2	Used to generate statistical figures and visualizations.
R package: logistf	CRAN/R package authors	logistf	Used for Firth's penalized logistic regression to address sparse-data bias.
R package: mice	CRAN/R package authors	mice	Used for multiple imputation by chained equations.
R package: rms	CRAN/R package authors	rms	Used for restricted cubic splines and model diagnostics.
R package: survival	CRAN/R package authors	survival	Used for conditional logistic regression in the matched case-control analysis.
R statistical software	R Foundation for Statistical Computing	Version 4.3.x or later	Primary statistical environment used for regression modeling, imputation, interaction analysis, bootstrapping, diagnostics, and visualization.
STROBE reporting checklist	STROBE Initiative	N/A	Reporting framework used to structure the observational-study flow and manuscript reporting.
Structured interview form	Study-developed form, Hebei General Hospital	N/A	Standardized form used to collect or verify smoking status, pack-years, alcohol intake, and relevant historical exposure information.
TOAST ischemic stroke subtype classification	Trial of Org 10172 in Acute Stroke Treatment classification system	N/A	Clinical classification system used by neurologists to categorize ischemic stroke subtypes.