Longitudinal Study Methodologies

Had to share the one prompt that has transformed how I approach AI research. 📌 Save this post. Don’t just ask for point-in-time data like a junior PM. Instead, build in more temporal context through systematic data collection over time. Use this prompt to become a superforecaster with the help of AI. Great for product ideation, competitive research, finance, investing, etc. ⏰⏰⏰⏰⏰⏰⏰⏰⏰⏰⏰⏰ TIME MACHINE PROMPT: Execute longitudinal analysis on [TOPIC]. First, establish baseline parameters: define the standard refresh interval for this domain based on market dynamics (enterprise adoption cycles, regulatory changes, technology maturity curves). For example, AI refresh cycle may be two weeks, clothing may be 3 months, construction may be 2 years. Calculate n=3 data points spanning 2 full cycles. For each time period, collect: (1) quantitative metrics (adoption rates, market share, pricing models), (2) qualitative factors (user sentiment, competitive positioning, external catalysts), (3) ecosystem dependencies (infrastructure requirements, complementary products, capital climate, regulatory environment). Structure output as: Current State Analysis → T-1 Comparative Analysis → T-2 Historical Baseline → Delta Analysis with statistical significance → Trajectory Modeling with confidence intervals across each prediction. Include data sources. ⏰⏰⏰⏰⏰⏰⏰⏰⏰⏰⏰⏰

Standard regression breaks the moment your confounder is affected by prior treatment. And in longitudinal data — HIV therapy, dialysis, statins, ventilator management — that is the default. You measure CD4 at every visit. You adjust for it in a time-varying Cox model. You think you controlled for confounding. For the total causal effect, you likely did not. You may have blocked part of the pathway you are trying to estimate. --- The problem A time-varying covariate can be: → Confounder of future treatment → Mediator of past treatment → Predictor of the outcome Condition on it → bias Ignore it → confounding Standard regression has no clean solution. --- The fix: Marginal Structural Models Do not condition. Weight. 1️⃣ Model treatment over time 2️⃣ Build stabilized IPTW weights 3️⃣ Create a pseudo-population where treatment ⟂ history 4️⃣ Run weighted regression → causal effect --- Assumptions (non-negotiable) ✓ Consistency ✓ Sequential exchangeability ✓ Positivity ✓ No interference If these fail, no method will save you. --- Estimation layer ⚠️ IPTW needs a well-specified treatment model ✓ TMLE is doubly robust --- Bottom line ❌ Time-varying Cox / GEE → biased total effect ✅ MSM + IPTW → recovers causal effect --- This is Post in my Causal Inference Visual Guide series. Previously: KM → PSM → IPW → IV → DiD → RDD → DAGs → TTE → Synthetic Control → MSM ♻️ Repost if this clarified longitudinal confounding 💾 Save for your next study design #CausalInference #MarginalStructuralModels #Epidemiology #Biostatistics #PublicHealth

The document outlines the principles and applications of Linear Mixed Models (LMMs), a statistical approach used to analyze data with both fixed and random effects. Fixed effects represent population-level patterns, while random effects account for individual variability. This dual modeling structure is particularly useful for longitudinal and clustered data. LMMs combine a regression model for the mean response with a covariance model to handle dependencies within subjects. Between-subject variation is captured using random intercepts and slopes, while within-subject variation accounts for repeated measurements over time. Estimation methods such as Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) are employed, with REML offering a correction for fixed effects' degrees of freedom. An example application examines lung function decline in cystic fibrosis patients, exploring differences by gender and genetic factors. The document emphasizes the importance of visualizing trends, identifying systematic effects, and modeling random variation to capture complex data structures. Overall, LMMs provide a robust framework for analyzing hierarchical and repeated measures data. Link: https://lnkd.in/efGZdWfE #statistics

Let's assume that you analyse a longitudinal clinical trial with a binary endpoint. Longitudinal means that observations were made for each study patient multiple times, at subsequent timepoints (study visits). Your goal is to formally compare the fraction (%) of some event between the treatment arms (groups) through a hypothesis test. For example, you may want to compare the % of somehow defined clinical successes between the new investigated treatment and some standard of care. You may also want to adjust these estimates for some numerical covariates, test interactions, and even the within-arm trends of % over time (for "stability"). But the problem is that the % of events is very small at certain timepoints (like 1-5) or even drops to zero over time. / This may happen at any sample size, even for thousands of data - it's all about the population %. Small samples make it just easier to happen. / This creates the problem called a quasi separation (one value, 0 or 1 dominates in the response variable in certain groups) or full separation (all 0 or all 1 in the response variable in certain groups). In other words: - quasi separation = some combination of predictors perfectly predicts the outcome in parts of the data - full separation = a predictor completely determines the outcome (like 0s in group A 1s in group). In either case, the classic logistic regression may either be biased or not converge and you may notice warning or error messages thrown by the estimation procedure like: `iterations limit exceeded` or `fitted probabilities numerically 0 or 1 occurred`. That's because for full separation the Maximum Likelihood Estimation (MLE) fails: the model tries to assign infinite-heading coefficients (log-odds -> ±∞) to match the perfect separation, which leads to non-convergence. For the quasi separation the situation ends up with unstable estimates for the predictors - when you look at the coefficients table, some estimates are infinite (or close to it) or even missing from the printout (depending on the implementation). The corresponding standard errors may be huge. You will notice it for sure! 😎 There are various approaches to this problem, e.g.: ➡️ exact logistic regression ➡️ Firth-penalised logistic regression ➡️ Bayesian logistic regression ➡️ a set of independent exact tests (Fisher, Boschloo, Barnard); they don't allow for interactions and covariate adjustments. Here I will focus on the Firth approach, but in an unusual manner - applied to the GEE estimation, necessary to handle correlated (repeated) responses. The penalisation is applied to the likelihood function, but there's no such thing in GEE, which a semi-parametric method. This is why we call it "Firth-like". / 💡 You might be interested also in a mixed model (GLMM) instead of GEE, but in my field we prefer the marginal rather than conditional approach. / Let me show you an example that may be useful for your work: https://lnkd.in/d2dvq6hB #statistics #datascience

*** Multilevel Modeling *** Multilevel Modeling (MLM)—also known as hierarchical linear modeling or mixed-effects modeling. This technique is invaluable when your data has a nested structure, such as students within classrooms, repeated measures for the same person, or employees within departments. What Is Multilevel Modeling? Multilevel models account for the dependency between observations by modeling random and fixed effects. This is crucial when individuals or observations are grouped (or clustered), and we expect that responses within a group may be more similar to each other than to those in different groups. When to Use MLM Use MLM when your data involves: • Nested structures: Students within schools, patients within hospitals • Repeated measures: Longitudinal studies tracking individuals over time • Variability across groups: You expect slopes or intercepts to differ across units (e.g., teaching style effects differ by school) Steps to Perform Multilevel Modeling 1. Explore the Data Structure• Check for clustering and identify levels (e.g., Level 1: students; Level 2: schools). 2. Fit a Null (Empty) Model• Estimate a model with only the intercept to assess intraclass correlation (ICC), which measures the proportion of variance explained by group-level clustering. 3. Add Level-1 Predictors• These are individual-level variables (e.g., student GPA, age). 4. Add Level-2 Predictors• These represent group-level influences (e.g., school funding, classroom size). 5. Random Intercepts and Slopes• Allow intercepts and/or slopes to vary across groups if needed. This allows for more flexible modeling of heterogeneity. 6. Check Model Fit• To evaluate model adequacy, use AIC, BIC, likelihood ratio tests, and residual plots. 7. Interpret Results• Evaluate fixed effects (average effects across all groups) and random effects (variance across groups). Example Imagine you’re analyzing math scores of students across schools: Student scores are predicted by socioeconomic status (SES), and intercepts and slopes for SES vary by school. --- B. Noted