Skillintermediate

Outcome Analysis and Statistical Methods Guide

Rigorous outcome analysis is essential for clinical decision support documents. This guide covers survival analysis, response assessment, statistical testing, and data visualization for patient cohort analyses and treatment evaluation.

Claude Code Knowledge Pack7/10/2026

Overview

Outcome Analysis and Statistical Methods Guide

Overview

Survival Analysis

Kaplan-Meier Method

Overview

Non-parametric estimator of survival function from time-to-event data
Handles censored observations (patients alive at last follow-up)
Provides survival probability at each time point
Generates characteristic step-function survival curves

Key Concepts

Censoring

Right censoring: Most common - patient alive at last follow-up or study end
Left censoring: Rare in clinical studies
Interval censoring: Event occurred between two assessment times
Informative vs non-informative: Censoring should be independent of outcome

Survival Function S(t)

S(t) = Probability of surviving beyond time t
S(0) = 1.0 (100% alive at time zero)
S(t) decreases as time increases
Step decreases at each event time

Median Survival

Time point where S(t) = 0.50
50% of patients alive, 50% have had event
Reported with 95% confidence interval
"Not reached (NR)" if fewer than 50% events

Survival Rates at Fixed Time Points

1-year survival rate, 2-year survival rate, 5-year survival rate
Read from K-M curve at specific time point
Report with 95% CI: S(t) ± 1.96 × SE

Calculation Example

Time  Events  At Risk  Survival Probability
0     0       100      1.000
3     2       100      0.980 (98/100)
5     1       95       0.970 (97/100 × 95/98)
8     3       87       0.936 (94/100 × 92/95 × 84/87)
...

Log-Rank Test

Purpose: Compare survival curves between two or more groups

Null Hypothesis: No difference in survival distributions between groups

Test Statistic

Compares observed vs expected events in each group at each time point
Weights all time points equally
Follows chi-square distribution with df = k-1 (k groups)

Reporting

Chi-square statistic, degrees of freedom, p-value
Example: χ² = 6.82, df = 1, p = 0.009
Interpretation: Significant difference in survival curves

Assumptions

Censoring is non-informative and independent
Proportional hazards (constant HR over time)
If non-proportional, consider time-varying effects

Alternatives for Non-Proportional Hazards

Gehan-Breslow test: Weights early events more heavily
Peto-Peto test: Modifies Gehan-Breslow weighting
Restricted mean survival time (RMST): Difference in area under K-M curve

Cox Proportional Hazards Regression

Purpose: Multivariable survival analysis, estimate hazard ratios adjusting for covariates

Model: h(t|X) = h₀(t) × exp(β₁X₁ + β₂X₂ + ... + βₚXₚ)

h(t|X): Hazard rate for individual with covariates X
h₀(t): Baseline hazard function (unspecified)
exp(β): Hazard ratio for one-unit change in covariate

Hazard Ratio Interpretation

HR = 1.0: No effect
HR > 1.0: Increased risk (harmful)
HR < 1.0: Decreased risk (beneficial)
HR = 0.50: 50% reduction in hazard (risk of event)

Example Output

Variable              HR      95% CI         p-value
Treatment (B vs A)    0.62    0.43-0.89      0.010
Age (per 10 years)    1.15    1.02-1.30      0.021
ECOG PS (2 vs 0-1)    1.85    1.21-2.83      0.004
Biomarker+ (vs -)     0.71    0.48-1.05      0.089

Proportional Hazards Assumption

Hazard ratio constant over time
Test: Schoenfeld residuals, log-minus-log plots
Violation: Time-varying effects, consider stratification or time-dependent covariates

Multivariable vs Univariable

Univariable: One covariate at a time, unadjusted HRs
Multivariable: Multiple covariates simultaneously, adjusted HRs
Report both: Univariable for all variables, multivariable for final model

Model Selection

Forward selection: Start with empty model, add significant variables
Backward elimination: Start with all variables, remove non-significant
Clinical judgment: Include known prognostic factors regardless of p-value
Parsimony: Avoid overfitting, rule of thumb 1 variable per 10-15 events

Response Assessment

RECIST v1.1 (Response Evaluation Criteria in Solid Tumors)

Target Lesions

Select up to 5 lesions total (maximum 2 per organ)
Measurable: ≥10 mm longest diameter (≥15 mm for lymph nodes short axis)
Sum of longest diameters (SLD) at baseline

Response Categories

Complete Response (CR)

Disappearance of all target and non-target lesions
Lymph nodes must regress to <10 mm short axis
Confirmation required at ≥4 weeks

Partial Response (PR)

≥30% decrease in SLD from baseline
No new lesions or unequivocal progression of non-target lesions
Confirmation required at ≥4 weeks

Stable Disease (SD)

Neither PR nor PD criteria met
Minimum duration typically 6-8 weeks from baseline

Progressive Disease (PD)

≥20% increase in SLD AND ≥5 mm absolute increase from smallest SLD (nadir)
OR appearance of new lesions
OR unequivocal progression of non-target lesions

Example Calculation

Baseline SLD: 80 mm (4 target lesions)
Week 6 SLD: 52 mm

Percent change: (52 - 80)/80 × 100% = -35%
Classification: Partial Response (≥30% decrease)

Week 12 SLD: 48 mm (nadir)
Week 18 SLD: 62 mm

Percent change from nadir: (62 - 48)/48 × 100% = +29%
Absolute change: 62 - 48 = 14 mm
Classification: Progressive Disease (>20% AND ≥5 mm increase)

iRECIST (Immune RECIST)

Purpose: Account for atypical response patterns with immunotherapy

Modifications from RECIST v1.1

iUPD (Immune Unconfirmed Progressive Disease)

Initial increase in tumor burden or new lesions
Requires confirmation at next assessment (≥4 weeks later)
Continue treatment if clinically stable

iCPD (Immune Confirmed Progressive Disease)

Confirmed progression at repeat imaging
Discontinue immunotherapy

Pseudoprogression

Initial apparent progression followed by response
Mechanism: Immune cell infiltration increases tumor size
Incidence: 5-10% of patients on immunotherapy
Management: Continue treatment if patient clinically stable

New Lesions

Record size and location but continue treatment
Do not automatically classify as PD
Confirm progression if new lesions grow or additional new lesions appear

Other Response Criteria

Lugano Classification (Lymphoma)

PET-based: Deauville 5-point scale
- Score 1-3: Negative (metabolic CR)
- Score 4-5: Positive (residual disease)
CT-based: If PET not available
Bone marrow: Required for staging in some lymphomas

RANO (Response Assessment in Neuro-Oncology)

Glioblastoma-specific: Accounts for pseudoprogression with radiation/temozolomide
Enhancing disease: Bidimensional measurements (product of perpendicular diameters)
Non-enhancing disease: FLAIR changes assessed separately
Corticosteroid dose: Must document, increase may indicate progression

mRECIST (Modified RECIST for HCC)

Viable tumor: Enhancing portion only (arterial phase enhancement)
Necrosis: Non-enhancing areas excluded from measurements
Application: Hepatocellular carcinoma with arterial enhancement

Outcome Metrics

Efficacy Endpoints

Overall Survival (OS)

Definition: Time from randomization/treatment start to death from any cause
Advantages: Objective, not subject to assessment bias, regulatory gold standard
Disadvantages: Requires long follow-up, affected by subsequent therapies
Censoring: Last known alive date
Analysis: Kaplan-Meier, log-rank test, Cox regression

Progression-Free Survival (PFS)

Definition: Time from randomization to progression (RECIST) or death
Advantages: Earlier readout than OS, direct treatment effect
Disadvantages: Requires regular imaging, subject to assessment timing
Censoring: Last tumor assessment without progression
Sensitivity Analysis: Assess impact of censoring assumptions

Objective Response Rate (ORR)

Definition: Proportion of patients achieving CR or PR (best response)
Denominator: Evaluable patients (baseline measurable disease)
Reporting: Percentage with 95% CI (exact binomial method)
Duration: Time from first response to progression (DOR)
Advantage: Binary endpoint, no censoring complications

Disease Control Rate (DCR)

Definition: CR + PR + SD (stable disease ≥6-8 weeks)
Less Stringent: Captures clinical benefit beyond objective response
Reporting: Percentage with 95% CI

Duration of Response (DOR)

Definition: Time from first CR or PR to progression (among responders only)
Population: Subset analysis of responders
Analysis: Kaplan-Meier among responders
Reporting: Median DOR with 95% CI

Time to Treatment Failure (TTF)

Definition: Time from start to discontinuation for any reason (progression, toxicity, death, patient choice)
Advantage: Reflects real-world treatment duration
Components: PFS + toxicity-related discontinuations

Safety Endpoints

Adverse Events (CTCAE v5.0)

Grading

Grade 1: Mild, asymptomatic or mild symptoms, clinical intervention not indicated
Grade 2: Moderate, minimal/local intervention indicated, age-appropriate ADL limitation
Grade 3: Severe or medically significant, not immediately life-threatening, hospitalization/prolongation indicated, disabling, self-care ADL limitation
Grade 4: Life-threatening consequences, urgent intervention indicated
Grade 5: Death related to adverse event

Reporting Standards

Adverse Event Summary Table:

AE Term (MedDRA)        Any Grade, n (%)  Grade 3-4, n (%)  Grade 5, n (%)
                        Trt A    Trt B    Trt A   Trt B     Trt A   Trt B
─────────────────────────────────────────────────────────────────────────
Hematologic
  Anemia                45 (90%) 42 (84%) 8 (16%) 6 (12%)   0       0
  Neutropenia           35 (70%) 38 (76%) 15 (30%) 18 (36%) 0       0
  Thrombocytopenia      28 (56%) 25 (50%) 6 (12%) 4 (8%)    0       0
  Febrile neutropenia   4 (8%)   6 (12%)  4 (8%)  6 (12%)   0       0

Gastrointestinal
  Nausea                42 (84%) 40 (80%) 2 (4%)  1 (2%)    0       0
  Diarrhea              31 (62%) 28 (56%) 5 (10%) 3 (6%)    0       0
  Mucositis             18 (36%) 15 (30%) 3 (6%)  2 (4%)    0       0

Any AE                  50 (100%) 50 (100%) 38 (76%) 35 (70%) 1 (2%) 0

Serious Adverse Events (SAEs)

SAE incidence and type
Relationship to treatment (related vs unrelated)
Outcome (resolved, ongoing, fatal)
Causality assessment (definite, probable, possible, unlikely, unrelated)

Treatment Modifications

Dose reductions: n (%), reason
Dose delays: n (%), duration
Discontinuations: n (%), reason (toxicity vs progression vs other)
Relative dose intensity: (actual dose delivered / planned dose) × 100%

Statistical Analysis Methods

Comparing Continuous Outcomes

Independent Samples t-test

Application: Compare means between two independent groups (normally distributed)
Assumptions: Normal distribution, equal variances (or use Welch's t-test)
Reporting: Mean ± SD for each group, mean difference (95% CI), t-statistic, df, p-value
Example: Mean age 62.3 ± 8.4 vs 58.7 ± 9.1 years, difference 3.6 years (95% CI 0.2-7.0, p=0.038)

Mann-Whitney U Test (Wilcoxon Rank-Sum)

Application: Compare medians between two groups (non-normal distribution)
Non-parametric: No distributional assumptions
Reporting: Median [IQR] for each group, median difference, U-statistic, p-value
Example: Median time to response 6.2 [4.1-8.3] vs 8.5 [5.9-11.2] weeks, p=0.042

ANOVA (Analysis of Variance)

Application: Compare means across three or more groups
Output: F-statistic, p-value (overall test)
Post-hoc: If significant, pairwise comparisons with Tukey or Bonferroni correction
Example: Treatment effect varied by biomarker subgroup (F=4.32, df=2, p=0.016)

Comparing Categorical Outcomes

Chi-Square Test for Independence

Application: Compare proportions between two or more groups
Assumptions: Expected count ≥5 in at least 80% of cells
Reporting: n (%) for each cell, χ², df, p-value
Example: ORR 45% vs 30%, χ²=6.21, df=1, p=0.013

Fisher's Exact Test

Application: 2×2 tables when expected count <5
Exact p-value: No large-sample approximation
Two-sided vs one-sided: Typically report two-sided
Example: SAE rate 3/20 (15%) vs 8/22 (36%), Fisher's exact p=0.083

McNemar's Test

Application: Paired categorical data (before/after, matched pairs)
Example: Response before vs after treatment switch in same patients

Sample Size and Power

Power Analysis Components

Alpha (α): Type I error rate, typically 0.05 (two-sided)
Beta (β): Type II error rate, typically 0.10 or 0.20
Power: 1 - β, typically 0.80 or 0.90 (80-90% power)
Effect size: Expected difference (HR, mean difference, proportion difference)
Sample size: Number of patients or events needed

Survival Study Sample Size

Events-driven: Need sufficient events (deaths, progressions)
Rule of thumb: 80% power requires approximately 165 events for HR=0.70 (α=0.05, two-sided)
Accrual time + follow-up time determines calendar time

Response Rate Study

Example: Detect ORR difference 45% vs 30% (15 percentage points)
- α = 0.05 (two-sided)
- Power = 0.80
- Sample size: n = 94 per group (188 total)
- With 10% dropout: n = 105 per group (210 total)

Data Visualization

Survival Curves

Kaplan-Meier Plot Best Practices

# Key elements for publication-quality survival curve
1. X-axis: Time (months or years), starts at 0
2. Y-axis: Survival probability (0 to 1.0 or 0% to 100%)
3. Step function: Survival curve with steps at event times
4. 95% CI bands: Shaded region around survival curve (optional but recommended)
5. Number at risk table: Below x-axis showing n at risk at time intervals
6. Censoring marks: Vertical tick marks (|) at censored observations
7. Legend: Clearly identify each curve
8. Log-rank p-value: Prominently displayed
9. Median survival: Horizontal line at 0.50, labeled
10. Follow-up: Median follow-up time reported

Number at Risk Table Format

Number at risk
Group A   50    42    35    28    18    10     5
Group B   48    38    29    19    12     6     2
Time      0     6     12    18    24    30    36 (months)

Hazard Ratio Annotation

On plot: HR 0.62 (95% CI 0.43-0.89), p=0.010
Or in caption: Log-rank test p=0.010; Cox model HR=0.62 (95% CI 0.43-0.89)

Waterfall Plots

Purpose: Visualize individual patient responses to treatment

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