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How to Understand Survival Probability Using the Kaplan–Meier Method — and Why Censoring Matters

 Survival analysis is a core component of clinical research, especially in oncology and rare disease trials where time-to-event endpoints such as PFS, OS, or time to loss of ambulation play a central role. Among all methods, the Kaplan–Meier (KM) estimator remains the most widely used tool to calculate and visualize survival probability. However, its interpretation is often misunderstood—particularly when censoring is heavy or uneven across groups. This article provides a clear, practical guide covering: How survival probability is calculated using the KM method How censored observations impact the KM curve and interpretation How to simulate survival data in R and SAS to visualize the effect of censoring 1. How the Kaplan–Meier Method Calculates Survival Probability The Kaplan–Meier (KM) estimator is a nonparametric method to estimate the survival function, S ( t ) S(t) from time-to-event data that may include censoring. KM produces a step function that updates on...
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Prompt Engineering for Chatgpt (5)

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Format of the Game Play Pattern To use this pattern, your prompt should make the following fundamental contextual statements: Create a game for me around X OR we are going to play an X game One or more fundamental rules of the game You will need to replace "X" with an appropriate game topic, such as "math" or "cave exploration game to discover a lost language". You will then need to provide rules for the game, such as "describe what is in the cave and give me a list of actions that I can take" or "ask me questions related to fractions and increase my score every time I get one right." Examples: Create a cave exploration game for me to discover a lost language. Describe where I am in the cave and what I can do. I should discover new words and symbols for the lost civilization in each area of the cave I visit. Each area should also have part of a story that uses the language. I should have to collect all the words and symbols to be able ...
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The difference between MMRM with vs without random effects

  🧠 Short Answer Model Type Random Effect Included? Type of Model Assumes Subject-specific Trajectories? Typical Use MMRM ❌ No Marginal model ❌ No Regulatory trials (e.g. FDA) Linear Mixed Model (LME) ✅ Yes Conditional model ✅ Yes Academic studies, hierarchical modeling 🔍 MMRM = No Random Effects ✅ Standard MMRM (FDA-favored) Marginal model : estimates population-average effects. Uses a repeated statement in SAS (or nlme::gls() in R). Models the within-subject covariance directly (e.g., UN, AR(1), CS). Assumes no subject-specific random intercepts/slopes. ➕ Pros: Very flexible in modeling within-subject correlations . Doesn't assume normally distributed random effects. Performs well under MAR with dropout. Standard in late-phase clinical trials and regulatory submissions . ➖ Cons: Can become unstable with too many timepoints (e.g., unstructured covariance). Cannot model subject-level variation (e.g., random slopes). 📘 Example in ...
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Use FDA Suggestions on Missing Data and Sensitivity Analyses

  The U.S. FDA provides guidance and expectations on how to handle missing data in clinical trials, especially in the context of estimands and sensitivity analyses . Below is a detailed summary based on key regulatory documents and practices. 📘 1. Key FDA Guidance Documents A. FDA (2019): "Estimands and Sensitivity Analyses in Clinical Trials" Focus: Aligning analysis with the trial objective and handling intercurrent events , like treatment discontinuation or dropout. Introduces the estimand framework from ICH E9(R1). Emphasizes sensitivity analysis under plausible MNAR assumptions. 🔗 Link: FDA Estimand Guidance (PDF) 📌 2. FDA Expectations at a Glance Topic FDA View Primary analysis Can assume MAR (e.g., MMRM) if justified Sensitivity analysis Must explore MNAR scenarios (not just MAR) Multiple imputation Acceptable if properly implemented Pattern-mixture models Encouraged as part of sensitivity analyses Reference-based imputation (CIR, J2R) Inc...
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