This is an excellent plan for analyzing your prospective cohort data! Analyzing a 10,000-participant, 15-year follow-up study on diet and cardiovascular disease (CVD) requires careful statistical methods. Here's a detailed guide for each of your requested tasks, emphasizing best practices and relevant considerations.

First, let's assume you have your data structured appropriately. For each participant, you should have:

• ID: Unique participant identifier.


• Diet_Exposure: Your primary exposure variable (e.g., intake of a specific food group, dietary pattern score, nutrient intake). This can be continuous or categorized (e.g., quintiles, tertiles, predefined categories like "high," "medium," "low").


• TimetoCVD_Event: Time from baseline to CVD event (diagnosis of myocardial infarction, stroke, heart failure, etc.) or censoring.


• CVDEventStatus: Binary indicator (1 if CVD event occurred, 0 if censored).


• Age_Baseline: Age at the start of follow-up.


• Sex: Male/Female.


• SmokingStatusBaseline: (e.g., Never, Former, Current).


• BMI_Baseline: Body Mass Index at baseline.


• Other potential confounders/covariates you might consider.

0. Initial Data Exploration & Cleaning (Pre-analysis Steps)

Before diving into the requested analyses, ensure your data is clean and understood:

• Check Data Types: Ensure variables are correctly coded (e.g., numeric for age/BMI, factor for sex/smoking, logical/binary for event status).


• Descriptive Statistics: Summarize all variables (means, standard deviations for continuous; frequencies for categorical).


• Distribution Check: Look at the distribution of continuous variables (histograms, box plots).


• Outcome Definition: Clearly define what constitutes a "CVD event" and ensure consistent coding.


• Time Variable: Ensure TimetoCVD_Event is in a consistent unit (e.g., years, months) and that it's accurately calculated (time from baseline to event/censoring).


• Censoring: Understand the reasons for censoring (end of study, death from non-CVD causes, withdrawal).

1. Calculate Incidence Rates by Exposure Groups

Incidence rate (often called incidence density or person-time rate) is the number of new cases of disease per unit of person-time at risk.

Steps:

• Define Exposure Groups: Categorize your Diet_Exposure variable into meaningful groups (e.g., quintiles, tertiles, or clinically relevant thresholds). Choose a reference group for comparison.


• Calculate Person-Time at Risk: For each participant, this is their TimetoCVD_Event. Sum this time for all participants within each exposure group.


• Count Events: Count the number of CVDEventStatus = 1 within each exposure group.


• Calculate Rate:

• Often reported per 1,000 or 10,000 person-years for easier interpretation.

library(survival)
# Assuming your data frame is named 'my_data'
# And you've created a categorical diet variable 'Diet_Group'
# Calculate person-time and events by group
incidence_summary <- my_data %>%
  group_by(Diet_Group) %>%
  summarise(
    n_events = sum(CVD_Event_Status == 1),
    person_years = sum(Time_to_CVD_Event),
    incidence_rate_per_1000_py = (n_events / person_years) * 1000
  )
print(incidence_summary)

2. Estimate Relative Risks (RR) and Hazard Ratios (HR)

In a time-to-event analysis for a cohort study, Hazard Ratios (HR) are generally preferred over Relative Risks (RR) because they account for varying follow-up times and censoring. RR can be calculated from cumulative incidence (risk) at a specific time point, but HR is more robust for the entire follow-up period.

Hazard Ratio (HR) - Univariate Cox Regression

This estimates the instantaneous rate of an event in the exposed group relative to the unexposed group, while accounting for time.

Steps:

• Define Reference Group: Choose one Diet_Exposure group as your reference (e.g., the lowest quintile, "healthy" group).


• Fit Univariate Cox Model: Use your TimetoCVDEvent and CVDEventStatus as the survival outcome and DietExposure (as a categorical variable) as the predictor.

Software (R Example):

# Fit a univariate Cox Proportional Hazards model
# Ensure Diet_Group is a factor with a specified reference level
my_data$Diet_Group <- relevel(as.factor(my_data$Diet_Group), ref = "Quintile 1")
univariate_cox_model <- coxph(Surv(Time_to_CVD_Event, CVD_Event_Status) ~ Diet_Group, data = my_data)
summary(univariate_cox_model)
# Extract HR and 95% CI
exp(coef(univariate_cox_model))      # HRs
exp(confint(univariate_cox_model))  # 95% CIs

3. Adjust for Confounders using Cox Regression

This is a multivariate Cox Proportional Hazards model where you include your Diet_Exposure along with the specified confounders.

Confounders to Adjust For: AgeBaseline, Sex, SmokingStatusBaseline, BMIBaseline.

Considerations:

• Continuous vs. Categorical Confounders:


• AgeBaseline and BMIBaseline are typically continuous. You can include them as such, assuming a linear relationship with the log hazard. If you suspect non-linearity, consider categorizing them (e.g., quartiles for BMI) or using more advanced methods like restricted cubic splines (see Section 5).


• Sex and SmokingStatusBaseline should be treated as categorical/factor variables.


• Interactions: Initially, don't include interaction terms unless you have a strong a priori hypothesis (e.g., the effect of diet differs significantly by sex).


• Model Selection: For confounders identified a priori based on subject matter knowledge (like age, sex, smoking, BMI for CVD), it's best to include them all in the model, rather than using stepwise selection (which can be unstable).

• Fit Multivariate Cox Model: Include Diet_Exposure and all confounders.

Software (R Example):

# Ensure all confounders are appropriately coded (factors for categorical, numeric for continuous)
# For example, Smoking_Status_Baseline might be:
# my_data$Smoking_Status_Baseline <- relevel(as.factor(my_data$Smoking_Status_Baseline), ref = "Never Smoker")
adjusted_cox_model <- coxph(Surv(Time_to_CVD_Event, CVD_Event_Status) ~ Diet_Group + Age_Baseline + Sex + Smoking_Status_Baseline + BMI_Baseline, data = my_data)
summary(adjusted_cox_model)
# Extract adjusted HR and 95% CI
exp(coef(adjusted_cox_model))      # Adjusted HRs
exp(confint(adjusted_cox_model))  # 95% CIs

4. Test Proportional Hazards (PH) Assumption

The Cox model assumes that the hazard ratio between any two groups remains constant over time. This is the proportional hazards assumption. If it's violated, the single HR estimate can be misleading.

Methods to Test PH Assumption:

• Schoenfeld Residuals Test (Statistical): This is the most common statistical test. It tests the correlation between Schoenfeld residuals and time (or a function of time) for each covariate in the model. A non-significant p-value (typically > 0.05) suggests the assumption holds.


• Interpretation: A significant p-value for a specific covariate (or the global test) indicates a violation for that covariate.


• Graphical Methods:


• Plot of Schoenfeld Residuals: Plotting scaled Schoenfeld residuals against time for each covariate. If the assumption holds, the smoothed mean of residuals should be a flat line around zero.


• Log-Log Survival Plots: Plot log(-log(survival_probability)) against log(time) for different exposure groups. Parallel curves suggest proportionality. This is useful for categorical covariates.

• Stratified Cox Model: If the PH assumption is violated for a categorical variable (e.g., Sex), you can stratify the model by that variable. This allows the baseline hazard to vary across strata but assumes proportionality within each stratum for other covariates.


• Time-Dependent Covariates: If the effect of a covariate changes over time, you can model it as a time-dependent covariate. This is more complex and might involve splitting follow-up time.


• Interaction with Time: Include an interaction term between the problematic covariate and time in the model.


• Different Survival Model: Consider alternative models like accelerated failure time (AFT) models, which make different assumptions.


• Report Time-Varying HRs: If the effect changes over time, report HRs for different time intervals.

# Test PH assumption for the adjusted model
ph_test <- cox.zph(adjusted_cox_model)
print(ph_test)
# Graphical assessment for individual covariates (e.g., Diet_Group)
plot(ph_test, resid = TRUE, se = TRUE, main = "Schoenfeld Residuals vs. Time for Diet_Group")
# For log-log plots (useful for categorical variables, e.g., Diet_Group)
# Note: This is a visual inspection, not a formal test.
plot(survfit(Surv(Time_to_CVD_Event, CVD_Event_Status) ~ Diet_Group, data = my_data),
     fun = "cloglog", col = 1:nlevels(my_data$Diet_Group),
     main = "Log-Log Survival Plot by Diet Group", xlab = "Log(Time)", ylab = "Log(-Log(Survival))")
legend("bottomleft", legend = levels(my_data$Diet_Group), col = 1:nlevels(my_data$Diet_Group), lty = 1)

5. Assess Dose-Response Relationships

This investigates if there's a graded relationship between increasing (or decreasing) levels of diet exposure and CVD risk.

Methods:

• Categorical Exposure with Trend Test:


• Treat your Diet_Exposure categories (e.g., quintiles 1-5) as an ordinal variable in the Cox model. This assigns a linear score to each category.


• The p-value for this variable tests for a linear trend across the categories.


• Caveat: Assumes the step between categories is equidistant in terms of effect, which might not be true.


• Continuous Exposure in Cox Model:


• If your Diet_Exposure variable is continuous (e.g., a dietary score, gram intake), you can include it directly in the Cox model.


• Caveat: Assumes a linear relationship between the continuous exposure and the log hazard of CVD.


• Interpretation: HR per unit increase in the continuous variable.


• Restricted Cubic Splines (RCS):


• Recommended for flexibility: RCS allows you to model non-linear relationships without making strong a priori assumptions about the functional form. It fits smooth curves to the data.


• You define a number of "knots" (usually 3-5) where the spline segments join.


• Interpretation: You'll typically plot the predicted HR (with CIs) across the range of the exposure. The overall p-value for the spline terms tests for any association, and a p-value for the non-linear terms tests specifically for non-linearity.

library(rms) # For restricted cubic splines
# Method 1: Trend test using ordered factor (after adjusted_cox_model)
# Assuming Diet_Group is an ordered factor:
my_data$Diet_Group_Ordered <- as.ordered(my_data$Diet_Group)
trend_cox_model <- coxph(Surv(Time_to_CVD_Event, CVD_Event_Status) ~ Diet_Group_Ordered + Age_Baseline + Sex + Smoking_Status_Baseline + BMI_Baseline, data = my_data)
summary(trend_cox_model) # Look at the p-value for Diet_Group_Ordered
# Method 2: Continuous Exposure (if Diet_Exposure is numeric)
# If your original Diet_Exposure is continuous, e.g., 'Diet_Score_Continuous'
continuous_cox_model <- coxph(Surv(Time_to_CVD_Event, CVD_Event_Status) ~ Diet_Score_Continuous + Age_Baseline + Sex + Smoking_Status_Baseline + BMI_Baseline, data = my_data)
summary(continuous_cox_model)
# Method 3: Restricted Cubic Splines (RCS) for a continuous exposure
# Requires the 'rms' package. Let's assume 'Diet_Score_Continuous' is your continuous exposure.
# Adjust number of knots (e.g., 3, 4, or 5) based on literature/data distribution.
ddist <- datadist(my_data)
ddist <- updata(ddist, Diet_Score_Continuous)
options(datadist = 'ddist')
rcs_model <- cph(Surv(Time_to_CVD_Event, CVD_Event_Status) ~ rcs(Diet_Score_Continuous, 4) + Age_Baseline + Sex + Smoking_Status_Baseline + BMI_Baseline, data = my_data, x=TRUE, y=TRUE)
print(rcs_model) # Look for p-value for overall effect and non-linear effect
# Plot the spline effect
plot(Predict(rcs_model, Diet_Score_Continuous, fun = exp), conf.int = TRUE,
     ylab = "Adjusted HR (95% CI)", xlab = "Diet Score (Continuous)",
     main = "Dose-Response Relationship of Diet Score with CVD Risk")

6. Handle Missing Data Appropriately

Missing data is a common issue in cohort studies and can lead to biased results and reduced statistical power if not handled correctly.

Steps:

• Assess Missingness:


• Quantity: Percentage of missing values for each variable (colSums(is.na(my_data))).


• Pattern: Are values missing completely at random (MCAR), missing at random (MAR), or missing not at random (MNAR)?


• MCAR: Missingness is unrelated to any variable (observed or unobserved).


• MAR: Missingness is related to observed variables but not the unobserved value itself. (e.g., older people are more likely to miss BMI measurements, but among people of the same age, missing BMI is random).


• MNAR: Missingness is related to the unobserved value itself. (e.g., people with very high BMI are more likely to refuse measurement). This is the most problematic.


• Visualize missingness patterns (e.g., naniar package in R, missingno in Python).


• Choose a Strategy (from generally least to most preferred/robust):


• Complete Case Analysis (CCA) / Listwise Deletion:


• Method: Exclude any participant with missing data on any variable in your model.


• Pros: Simple, no imputation needed.


• Cons: Reduces sample size and statistical power. Leads to biased estimates if data are not MCAR. This is often the default behavior of statistical software for regression.


• Recommendation: Only acceptable if very little data (e.g., < 5%) is missing and MCAR.


• Mean/Median Imputation:


• Method: Replace missing values with the mean (for continuous) or median (for skewed continuous) of the observed values for that variable.


• Cons: Underestimates variance, distorts relationships between variables, biases estimates.


• Recommendation: Generally NOT recommended for inferential statistics.


• Last Observation Carried Forward (LOCF) / Baseline Imputation:


• Method: Replace missing follow-up values with the last observed value (LOCF) or with the baseline value (if only missing at follow-up).


• Cons: Can be very misleading, especially if the variable changes over time (e.g., BMI).


• Recommendation: NOT recommended for primary analysis.


• Multiple Imputation by Chained Equations (MICE):


• Method: This is the preferred method for MAR data.


• It creates several (e.g., 5-20) imputed datasets, where missing values are predicted using the observed relationships between all variables in your dataset.


• You run your analysis (e.g., Cox regression) on each imputed dataset.


• The results from these analyses are then pooled using Rubin's rules to get a single, robust estimate and confidence interval. This accounts for the uncertainty due to imputation.


• Pros: Produces unbiased estimates under MAR, maintains statistical power, correctly estimates standard errors.


• Cons: More complex to implement.


• Recommendation: Strongly recommended if you have missing data and believe it is MAR.

library(mice)
library(miceadds) # For pooling coxph models
# 1. Create a data frame with variables to be used in imputation
# Include all variables that will be in your analytical model, plus any auxiliary variables
# that might help predict missingness or be correlated with missing variables.
vars_for_imputation <- my_data %>%
  select(Time_to_CVD_Event, CVD_Event_Status, Diet_Group, Age_Baseline, Sex, Smoking_Status_Baseline, BMI_Baseline, # ... other relevant variables)
# 2. Perform multiple imputation
# 'm' is the number of imputed datasets to create (usually 5-20)
# 'method' specifies the imputation method for each variable type (e.g., 'pmm' for numeric)
# You might need to specify methods per variable, especially for categorical ones.
# For factors: method = "polyreg" or "logreg"
imputed_data <- mice(vars_for_imputation, m = 10, seed = 123)
# 3. Analyze each imputed dataset and pool results
# Define the model to run on each imputed dataset
my_model_formula <- Surv(Time_to_CVD_Event, CVD_Event_Status) ~ Diet_Group + Age_Baseline + Sex + Smoking_Status_Baseline + BMI_Baseline
# Fit Cox model to each imputed dataset
fits <- with(imputed_data, coxph(my_model_formula))
# Pool the results
pooled_results <- pool(fits)
summary(pooled_results, exponentiate = TRUE) # exponentiate=TRUE gives HRs

7. Report per STROBE Guidelines

The STROBE (STrengthening the Reporting of OBservational studies in Epidemiology) statement provides a checklist of 22 items that should be addressed in articles reporting observational studies. Adhering to these guidelines ensures transparency, completeness, and helps readers critically appraise your study.

Key STROBE elements to specifically consider for your analysis:

• Title and Abstract: Clearly state study design (prospective cohort), population, exposure, outcome, main findings (adjusted HRs, CIs).


• Introduction:


• Background/Rationale: Why is this study important? What gaps does it fill?


• Objectives: State your specific aims, including assessing incidence, HRs, confounding, dose-response.


• Methods:


• Study Design: Prospective cohort, 10,000 participants, 15-year follow-up.


• Setting: Where and when was the study conducted?


• Participants: Eligibility criteria, recruitment process, sample size.


• Variables:


• Exposure: Detailed definition of Diet_Exposure (how measured, categorized, reference group).


• Outcome: Detailed definition of CVDEventStatus (endpoints included, diagnostic criteria).


• Confounders: Definitions and measurement of Age, Sex, Smoking, BMI.


• Data Sources/Measurement: How were diet, CVD, and confounders measured? Validity/reliability of methods.


• Bias: Discuss potential sources of bias (selection, information, confounding) and how they were addressed.


• Study Size: Justification for 10,000 participants (power calculation if applicable).


• Quantitative Variables: How continuous variables (age, BMI, diet score) were handled (continuous, categories, splines).


• Statistical Methods:


• Describe incidence rate calculation.


• Specify use of Cox Proportional Hazards regression for HRs.


• List all variables included in the adjusted model.


• Explain how the Proportional Hazards assumption was tested and handled.


• Detail the method for assessing dose-response (e.g., continuous, categorical trend, RCS).


• Crucially: Clearly describe your missing data handling strategy (e.g., "Missing data for X variables were handled using multiple imputation by chained equations (MICE) with 10 imputed datasets. Results were pooled using Rubin's rules."). If CCA was used, acknowledge its limitations.


• State level of significance (e.g., p<0.05).


• Results:


• Participants: Flow diagram (if applicable), number included in analysis, reasons for exclusion/missing data. Baseline characteristics by Diet_Exposure groups (Table 1).


• Descriptive Data: Number of CVD events, total person-years.


• Outcome Data:


• Incidence Rates: Report per Diet_Exposure group (Table or text).


• Unadjusted HRs: For Diet_Exposure (Table).


• Adjusted HRs: For Diet_Exposure and listed confounders, along with 95% CIs and p-values (Table 2). Clearly state the reference group.


• Proportional Hazards Assumption: Report results of the test (e.g., "The proportional hazards assumption was assessed using Schoenfeld residuals and was deemed satisfactory (p > 0.05 for all covariates)."). If violated, explain how you addressed it.


• Dose-Response: Present findings (e.g., "A significant linear trend was observed..." or "Restricted cubic splines revealed a non-linear association..."). Include a figure if using splines.


• Missing Data: Report the extent of missingness for key variables.


• Sensitivity Analyses: If you performed any (e.g., using different confounder adjustments, excluding early events, different imputation methods), report those results.


• Discussion:


• Key Findings: Summarize the main results, particularly the adjusted HRs and dose-response.


• Strengths & Limitations: Discuss study strengths (prospective design, large sample, long follow-up, comprehensive adjustment, appropriate missing data handling) and limitations (e.g., reliance on self-reported diet, residual confounding, unmeasured confounders, generalizability). Acknowledge any limitations related to missing data or PH assumption violations.


• Interpretation: Put your findings in context of existing literature.


• Generalizability: Discuss applicability to other populations.


• Funding: State sources of funding and role of funders.

This comprehensive plan should guide you through a robust and transparent analysis of your cohort data. Good luck!