Group Name: Stat Attack
- Jigar Rambhiya
- Sumit Patil
- Aarchi Rastogi
A pharmaceutical company conducted a single-arm clinical trial to assess the efficacy of their drug on 200 lung cancer patients. The primary endpoint of interest was the 24-month event-free survival rate. A patient was defined to have experienced an event only if disease progression occurred or death was recorded.
The standard of care for this diagnosis was widely assumed to have a 24-month event-free survival rate of 50%. The trial began on 01 Jan 2020, and patients were recruited over a period of 24 months. The final analysis was conducted with a data cut-off date of 01 Jan 2024.
Two exercises were solved as part of this project:
Exercise 1: Determine whether the study drug's 24-month event-free survival rate is significantly better than the 50% standard of care, using real trial data.
Exercise 2: Simulate a future single-arm trial for liver cancer patients using the same drug, where the standard of care has a 24-month survival rate of 40% and the drug is expected to achieve 60%. Estimate the probability that the trial will successfully demonstrate the drug's superiority.
The dataset contains records for 200 patients with the following variables:
| Variable | Description |
|---|---|
| subject_id | Unique identifier for each patient |
| recruitment_date | Date patient was enrolled in the trial |
| event_or_withdrawal_date | Date of event or withdrawal (blank if neither occurred) |
| reason | Reason for trial discontinuation (blank if completed or lost to follow-up) |
Data Processing:
- Calculated follow-up duration in months from recruitment date to event or withdrawal date
- Missing end dates were treated as censored observations
- Withdrawal of consent cases were also treated as censored
- Created binary indicators for event status and 24-month outcome
Statistical Method: Kaplan-Meier Survival Analysis
The Kaplan-Meier estimator was chosen because:
- It is a non-parametric method requiring no distributional assumptions
- It correctly handles right-censored observations
- It estimates survival probability at each event time point
Confidence intervals were constructed using Greenwood's formula.
Hypothesis:
- H₀: S(24) = 0.50 (drug survival rate equals standard of care)
- H₁: S(24) > 0.50 (drug survival rate is better)
- Significance level: α = 0.05
- Decision rule: Reject H₀ if lower bound of 95% CI > 0.50
Trial Assumptions:
- Sample size: 200 patients
- Recruitment period: 24 months
- Final analysis: 48 months after trial start
- Standard of care 24-month survival: 40%
- Expected drug 24-month survival: 60%
- Annual dropout rate: 5%
Simulation Steps:
- Patient entry times simulated from Uniform(0, 24) distribution
- Event times simulated from Exponential distribution with rate λ = -log(0.60)/24
- Dropout times simulated from Exponential distribution with rate λ = 0.05/12
- Administrative censoring applied at 48 months
- Observed time = minimum of event time, dropout time, and administrative censoring time
- Kaplan-Meier used to estimate 24-month survival probability
- H₀ rejected if lower bound of one-sided 95% CI > 0.40
- Process repeated 5000 times to estimate probability of success
| Metric | Value |
|---|---|
| 24-Month Event-Free Survival Rate | 75% |
| 95% Confidence Interval | (69%, 81%) |
| Decision | H₀ Rejected |
Since the lower bound of the confidence interval (69%) is greater than 50%, we conclude that the study drug's 24-month event-free survival rate is significantly better than the standard of care.
In simple terms: 3 out of 4 patients on the study drug were free from disease progression or death at the 24-month mark, compared to only 1 in 2 patients on the standard treatment. This improvement is statistically significant.
| Metric | Value |
|---|---|
| Total Simulations | 5,000 |
| Successful Rejections of H₀ | 4,998 |
| Failed Rejections | 2 |
| Observed Probability of Success | 99.96% |
| Statistical Power | ~100% |
In simple terms: When we simulated the liver cancer trial 5,000 times under the assumption that the drug truly works as expected, the trial successfully detected the drug's benefit in virtually every single run. This means the planned study design is extremely well-powered and very likely to succeed.
- Language: R
- Libraries:
survival,survminer,lubridate,readr
├── R_codes.R # Full analysis and simulation code
├── Dataset.csv # Trial data for 200 patients
├── Report.pdf # Detailed written report
└── README.md # Project documentation
- Kaplan-Meier Estimator — Non-parametric method to estimate survival probability over time
- Greenwood's Formula — Used to compute variance of the Kaplan-Meier estimate for confidence interval construction
- Right Censoring — Occurs when the event has not been observed by the end of the study period
- Monte Carlo Simulation — Repeated random sampling to estimate the probability of a real-world outcome
- Exponential Distribution — Used to model time-to-event and dropout times due to its constant hazard rate property
This project was submitted as part of the NMIMS Hackathon 2026 (Hack-A-Stat). The problem statement and dataset were provided by the hackathon organizers.