Survival Analysis and Prognostic Modeling
in Lung Cancer
Author: Amira Mandour
Biostatistician | Clinical Trials & Statistical Modeling
Expert
2023-01-03
Introduction:
The goal of this study, is to investigate the survival
outcomes of patients with advanced lung cancer. Using
Kaplan-Meier survival analysis, we aim to evaluate how clinical
factors such as age, sex, performance status, and weight loss influence
patient survival times. By understanding these relationships, we seek to
identify key prognostic factors that may guide clinical decision-making
and improve patient outcomes in lung cancer care.
Data:
This study is a clinical trial of lung cancer patients. The dataset
includes:
Survival Time: Time from diagnosis to death (or
censoring).
Censoring Status: Whether the patient was
censored (1 = event occurred, 0 = censored).
Clinical Covariates: Age, sex, ECOG performance
status (0, 1, 2, 3), weight loss (percentage), smoking status, and tumor
stage.
Methodology:
Kaplan-Meier Survival Analysis: We performed
Kaplan-Meier survival analysis to estimate survival curves for different
groups based on clinical variables. The log-rank test
was used to compare survival between groups (e.g., male vs. female).
Cox Proportional Hazards Model: To investigate the
effect of clinical covariates on survival, a Cox proportional hazards
regression model was built. Hazard ratios (HR) and 95% confidence
intervals (CI) were calculated for each covariate.
Testing the Proportional Hazards Assumption: The
proportional hazards assumption was assessed using Schoenfeld residuals.
Covariates that violated the assumption were identified, and
stratification was applied where necessary.
Stratified Cox Model: In response to the violations
of the proportional hazards assumption, we applied a stratified Cox
model for covariates with significant violations, such as Karnofsky
scores (both physician and patient assessments).
Post-Hoc Analysis of Gender Differences: We
performed a subgroup analysis by gender to explore survival differences
between male and female patients. The stratified Cox model was also
applied to assess the influence of gender on survival while accounting
for other covariates.
Statistical Analysis:
The Kaplan-Meier survival curve shown here illustrates the overall
survival experience of the study cohort. The curve represents the
proportion of patients surviving over time, with survival probability
(in percentage) plotted against time in days. As expected, the survival
probability decreases over time, reflecting the typical course of
advanced lung cancer. The median survival time in this
study is approximately 310 days, indicating that 50% of
the patients survived beyond this point.(Figure 1)
Table 1. Kaplan–Meier Estimates of Survival by
Sex
| Male |
138 |
112 |
270 |
212 |
310 |
| Female |
90 |
53 |
426 |
348 |
550 |
Table 1. The Kaplan–Meier survival estimates are
presented in Table 1, summarizing the survival outcomes by sex. The
table compares the median survival times and the event rates (percentage
of deaths) for males and females in the study.
Males (n = 138) had a median survival time of 270 days (95%
CI: 212–310), with 112 events (deaths), which corresponds to an event
rate of 81.2%. This indicates that 81.2% of male patients in the cohort
experienced the event (death) by the end of the study period.
Females (n = 90) had a significantly longer median survival
time of 426 days (95% CI: 348–550), with 53 events (deaths), yielding an
event rate of 58.9%. This means that 58.9% of female patients in the
cohort experienced the event.
The findings from this Kaplan–Meier analysis indicate that gender is
an important factor in determining survival outcomes. Females in this
cohort had both a longer median survival time and a lower event rate,
suggesting that gender-related factors could play a role in influencing
prognosis.
Survival Test Results:
|
Table 2. Survival Test Results:
|
|
Log-Rank Test Results
|
|
Group
|
N.Freq
|
Observed
|
Expected
|
Test.Statistic..O.E..2.E
|
Variance..O.E..2.V
|
|
Males
|
138
|
112
|
91.5817390295728
|
4.55227631047547
|
40.3714339796426
|
|
Females
|
90
|
53
|
73.4182609704272
|
5.67849708704487
|
40.3714339796427
|
|
Chi-squared
|
|
|
|
0.00131116452035549
|
p = 0.00131
|
The log-rank test was conducted to compare the
survival distributions between male and female patients in the lung
cancer cohort. The test revealed a statistically significant difference
in survival between the two groups, with a chi-square statistic of 10.3
(degrees of freedom = 1) and a p-value of 0.001.(Table
2.)
Male Patients (n = 138): Of the 138 male patients,
112 observed events (deaths) were recorded, compared to an expected 91.6
events. This resulted in a test statistic contribution of 4.55.
Female Patients (n = 90): Among 90 female patients,
53 deaths were observed, with an expected number of 73.4 events,
contributing 5.68 to the test statistic.
The p-value of 0.001 indicates that the survival distributions
between males and females differ significantly. Specifically, females
demonstrated significantly better survival compared to males in this
cohort. These findings are consistent with existing literature
suggesting that female patients with lung cancer tend to have better
survival outcomes than male patients, possibly due to biological,
treatment-related, or other gender-related factors.
Progression Free Survival:
The Kaplan-Meier curve for Progression-Free Survival (PFS) was
calculated for the cohort. The median PFS for the study population was
approximately 348 days, indicating that half of the patients in the
study experienced disease progression or death within this time
frame.
Kaplan-Meier Curves for OS and PFS by Sex:
Survival curves were generated for both Overall Survival (OS) and
Progression-Free Survival (PFS), stratified by sex (male vs. female).
The goal was to assess whether there are any significant differences in
survival outcomes based on gender.
Overall Survival (OS)
The Kaplan-Meier curve for Overall Survival (OS) stratified by sex
demonstrates distinct survival patterns for males and females in this
cohort. The male survival curve consistently shows a lower survival
probability across the study period compared to the female survival
curve. Females have a longer median survival time, reflecting a better
overall prognosis in this cohort.
Progression-Free Survival (PFS) Stratified by
Sex
The Kaplan-Meier survival curves for Progression-Free Survival (PFS)
were generated stratified by sex to explore potential differences in
survival outcomes between males and females in the cohort. The survival
curves for males and females are shown below, and the corresponding
median PFS for each group is provided.
Median PFS for males: The median PFS for males was
approximately 329 days, indicating that half of the male patients in the
cohort remained progression-free for 329 days or longer before
experiencing disease progression or death.
Median PFS for females: The median PFS for females
was approximately 356 days, indicating that half of the female patients
in the cohort remained progression-free for 356 days or longer.
The Kaplan-Meier curves reveal that females tend to have a longer
progression-free survival compared to males, with the female cohort
maintaining a higher probability of being progression-free at later time
points. This suggests that females experience a slower rate of disease
progression compared to males.
The median PFS for females is slightly higher than the median PFS for
males, suggesting that female patients may benefit from a longer time
without disease progression, which could be attributed to biological
factors such as genetic differences or hormonal influences on disease
progression and treatment response.
Cox Proportional Hazards Regression Model
A Cox proportional hazards regression model was
fitted to assess the impact of various clinical and demographic factors
on survival in lung cancer patients. The following variables were
included in the model: Age, ECOG performance
status (ph.ecog), Karnofsky performance score
(ph.karno), and patient Karnofsky score
(pat.karno).
Model Results:
Table 3. Cox Model for Survival Outcomes: A Multivariable Analysis of Lung Cancer Prognostic Factors
| Characteristic |
Hazard Ratio (HR) |
95% CI |
P value |
| Sex |
0.57 |
0.41, 0.80 |
0.001 |
| Age (years) |
1.01 |
0.99, 1.03 |
0.2 |
| ECOG performance status |
1.76 |
1.22, 2.54 |
0.002 |
| Physician Karnofsky score |
1.02 |
1.00, 1.04 |
0.11 |
| Patient Karnofsky score |
0.99 |
0.98, 1.00 |
0.14 |
Age: The hazard ratio (HR) for
age was 1.0108 (95% CI: 0.9922
- 1.030, p = 0.257), suggesting that for each
additional year of age, the risk of death increases by approximately
1.08%. However, the effect of age on survival was not
statistically significant (p > 0.05), indicating
that age is not a strong predictor of survival in this cohort.
Sex was found to be significantly associated
with overall survival. The estimated hazard ratio (HR)
for sex was 0.570 (95% CI: 0.408 - 0.797, p = 0.001),
indicating that females have a significantly lower risk of death
compared to males.
Specifically, the hazard ratio (HR) of 0.570 means that, holding
all other variables constant, females have approximately 43% lower risk
of death than males (1 - 0.570 = 0.430). This is a statistically
significant finding (p < 0.01), suggesting that sex is an important
prognostic factor for overall survival.
ECOG Performance Status (ph.ecog): The HR for
ECOG performance status was 1.6373
(95% CI: 1.1359 - 2.360, p = 0.0082),
indicating that each increase in the ECOG score (which represents
worsening performance status) is associated with a 63.7%
increase in the risk of death. This result was statistically
significant (p < 0.01), suggesting that ECOG
performance status is a key determinant of survival in this
patient population.
Karnofsky Performance Score (ph.karno): The HR
for Karnofsky performance score was
1.0129 (95% CI: 0.9931 - 1.033, p =
0.20326), indicating a slight increase in the risk of
death with each unit increase in the Karnofsky score. However, this
effect was not statistically significant (p > 0.05),
suggesting that Karnofsky performance score does not significantly
affect survival in this model.
Patient Karnofsky Score (pat.karno): The HR for
patient Karnofsky score was 0.9893
(95% CI: 0.9764 - 1.002, p = 0.10625),
indicating a small decrease in the risk of death with higher scores.
While this effect was negative, it was not statistically significant
(p > 0.05), and hence does not appear to have a
meaningful influence on survival in this analysis.
Overall Model Fit and Significance:
The likelihood ratio test (p =
3e-04), Wald test (p =
1e-04), and score test (p =
1e-04) all indicate that the model is statistically
significant overall, suggesting that at least one of the covariates
included in the model (age, ECOG, Karnofsky scores) is significantly
associated with survival.
The concordance index (C-index) was
0.63 (SE = 0.024), indicating that the
model has moderate discriminatory ability in predicting
patient survival outcomes. A C-index of 0.63 suggests that the model can
somewhat distinguish between patients who will experience the event
(death) and those who will survive, but the model’s discriminatory power
could be improved.
Evaluation of Proportional Hazards Assumption:
The proportional hazards assumption (PHA) was evaluated for the
variables included in the Cox proportional hazards regression model
using Schoenfeld residuals. The results of the Schoenfeld residuals test
for each covariate, as well as the global test, are summarized
below.(Table 4)
Table 4. Schoenfeld Residuals Test for Proportional Hazards
Assumption
|
Covariate
|
Chi-Square
|
df
|
p-value
|
|
Sex
|
1.704
|
1
|
0.19
|
|
Age
|
0.001
|
1
|
0.97
|
|
ECOG Performance Status
|
2.040
|
1
|
0.15
|
|
Physician Karnofsky Score (ph.karno)
|
5.411
|
1
|
0.02
|
|
Patient Karnofsky Score (pat.karno)
|
4.737
|
1
|
0.03
|
|
Global Test
|
9.229
|
5
|
0.10
|
Global Test (p = 0.10): The global test p-value
of 0.10 indicates that, overall, there is no significant evidence of a
violation of the proportional hazards assumption for the full model.
This suggests that, collectively, the effect of all covariates on the
hazard of the event does not vary significantly over time.
Sex (p = 0.19): The p-value for sex is 0.19,
which is above the 0.05 threshold. Therefore, there is no evidence to
suggest that the proportional hazards assumption is violated for sex,
meaning the effect of sex on the hazard of death is constant over
time.
Age (p = 0.97): The p-value for age is 0.97,
indicating that there is no significant violation of the proportional
hazards assumption for age. The effect of age on the risk of death does
not change over time in this model.
ECOG Performance Status (p = 0.15): The p-value
for ECOG performance status is 0.15, suggesting that there is no
significant violation of the proportional hazards assumption for ECOG.
This implies that the effect of ECOG performance status on survival is
constant over time.
Physician Karnofsky Score (ph.karno, p = 0.02):
The p-value for physician Karnofsky score is 0.02, which is below 0.05,
indicating that the proportional hazards assumption is violated for this
covariate. This suggests that the effect of the physician-reported
Karnofsky score on the risk of death changes over time.
Patient Karnofsky Score (pat.karno, p = 0.03):
The p-value for patient Karnofsky score is 0.03, which is also below
0.05, indicating a violation of the proportional hazards assumption for
this variable. Similar to physician Karnofsky score, the effect of
patient-reported Karnofsky score on survival is not constant over
time.
The proportional hazards assumption was satisfied for most variables
in the model, as indicated by the p-values of sex, age, and ECOG
performance status, which were all greater than 0.05. However, there is
evidence of a violation of the proportional hazards assumption for
physician Karnofsky score (ph.karno) and patient Karnofsky score
(pat.karno) (p-values 0.02 and 0.03, respectively). These findings
suggest that the effects of these two variables on survival may change
over time, and further analysis, such as including time-varying
covariates for these variables, may be required.
Schoenfeld Residuals for Assessing the Proportional Hazards
Assumption:
We fitted a Cox proportional hazards regression
model to assess the impact of clinical variables on survival,
stratifying by Physician Karnofsky Score (ph.karno) and
Patient Karnofsky Score (pat.karno) to account for
potential violations of the proportional hazards assumption for these
variables.
Key Results:
| Table 5. Cox Proportional Hazards Regression Model (Stratified) Results
After Addressing Proportional Hazards Violations |
| Covariate |
Coefficient (ß) |
Hazard Ratio (HR) |
Confidence Interval
|
p-value |
| 95% CI (Lower) |
95% CI (Upper) |
| Sex |
−0.638 |
0.528 |
0.356 |
0.784 |
0.002 |
| Age |
0.015 |
1.016 |
0.993 |
1.038 |
0.171 |
| ph.ecog |
0.329 |
1.389 |
0.852 |
2.265 |
0.188 |
Sex: The hazard ratio for
sex is 0.528 (95% CI: 0.356,
0.784), indicating that female patients have a significantly
lower risk of the event compared to male patients. This effect is
statistically significant with a p-value of 0.00151.
The negative coefficient for sex suggests that being
female is associated with a decreased risk of the
event.
Age: The hazard ratio for
age is 1.015 (95% CI: 0.993,
1.038), which suggests a slight increase in the hazard for each
additional year of age. However, this effect is not statistically
significant (p = 0.17061), implying that age does not
have a significant impact on survival in this cohort.
ECOG Performance Status: The hazard
ratio for ECOG performance status (ph.ecog) is
1.389 (95% CI: 0.852, 2.265),
suggesting that worse performance status is associated with a higher
risk of the event. However, the p-value of 0.18790
indicates that this result is not statistically significant, and the
effect of ECOG status may not be meaningful after adjustment for other
covariates.
Model Evaluation:
Concordance Index (C-index): The
C-index for this model is 0.597, which
suggests that the model has moderate discriminatory ability, meaning it
has a fair capacity to rank survival times accurately.
Likelihood Ratio Test: The likelihood
ratio test (p = 0.002) indicates that the
model is statistically significant overall.
Wald Test: The Wald test (p =
0.003) also suggests that the model provides a good fit
to the data.
Score (Logrank) Test: The logrank
test (p = 0.003) further supports the
statistical significance of the model, indicating that the covariates
collectively have a significant effect on survival.
Conclusion:
In this analysis, the survival distributions for both overall
survival (OS) and progression-free survival (PFS) were examined. The
Kaplan-Meier curves demonstrate expected survival patterns in advanced
lung cancer, with the female cohort exhibiting better survival outcomes
compared to males. These findings were statistically supported by the
log-rank test, which indicated a significant difference between the
survival curves of males and females.
Further analysis using Cox proportional hazards regression identified
ECOG performance status and gender as significant predictors of
survival, consistent with prior studies that have emphasized the
importance of functional status in lung cancer prognosis.