D4 Methods of comparing treatments

Comparing cancer treatments

In section C2 we learned how to interpret survival curves, which indicate the probability of surviving beyond a given period of time from diagnosis of disease.

In this section we will examine data from a study published in 1979, that is conveniently available with R’s survival package.

The citation for the study is

J H Edmonson, T R Fleming, D G Decker, G D Malkasian, E O Jorgensen, J A Jefferies, 
M J Webb, L K Kvols, Cancer Treat Rep . 1979 Feb;63(2):241-7.
Different chemotherapeutic sensitivities and host factors affecting prognosis in 
advanced ovarian carcinoma versus minimal residual disease

The abstract is provided at the end of this vignette.

The data for the ovarian cancer study has the following form:

library(survival)
datatable(ovarian)

The variable description is

Format:

       futime:    survival or censoring time                           
       fustat:    censoring status                                     
       age:       in years                                             
       resid.ds:  residual disease present (1=no,2=yes)                
       rx:        treatment group                                      
       ecog.ps:   ECOG performance status (1 is better, see reference)

We will consider three aspects of interpretation of these data.

Estimation of survival probabilities by treatment group

osurv = Surv(ovarian$futime, ovarian$fustat)
ofit1 = survfit(osurv~ovarian$rx)
plot(ofit1, lty=1:2)
legend(0, .4, lty=1:2, legend=c("cyc 1g/m2", "cyc .5g/m2 + adria"))

Testing for treatment effect

survdiff(osurv~ovarian$rx)

## Call:
## survdiff(formula = osurv ~ ovarian$rx)
## 
##               N Observed Expected (O-E)^2/E (O-E)^2/V
## ovarian$rx=1 13        7     5.23     0.596      1.06
## ovarian$rx=2 13        5     6.77     0.461      1.06
## 
##  Chisq= 1.1  on 1 degrees of freedom, p= 0.3

Modeling the survival curves for the effect of residual disease

We can produce a very compact, two parameter model for the survival distributions for patients with and without residual disease.

summary(survreg(osurv~I(ovarian$resid.ds-1), 
   dist="exponential"))

## 
## Call:
## survreg(formula = osurv ~ I(ovarian$resid.ds - 1), dist = "exponential")
##                          Value Std. Error     z      p
## (Intercept)              7.919      0.577 13.72 <2e-16
## I(ovarian$resid.ds - 1) -1.214      0.667 -1.82  0.069
## 
## Scale fixed at 1 
## 
## Exponential distribution
## Loglik(model)= -96.1   Loglik(intercept only)= -98
##  Chisq= 3.87 on 1 degrees of freedom, p= 0.049 
## Number of Newton-Raphson Iterations: 4 
## n= 26

ofit2 = survfit(osurv~ovarian$resid.ds)
plot(ofit2, lty=1:2)
tim = 1:1200
pp_nores = 1-pexp(1:1200, 1/exp(7.9)) # round parameter value
lines(tim, pp_nores, col="blue")
pp_res = 1-pexp(1:1200, 1/exp(7.9-1.2))
lines(tim, pp_res, col="red")

Exercises

D.4.1 Interpret confidence intervals for the one-year survival probabilities for the two treatments, ignoring the presence or absence of residual disease.

par(mfrow=c(1,2))
with(ovarian[ovarian$rx==1,], plot(survfit(Surv(futime,fustat)~1),conf.int=TRUE))
with(ovarian[ovarian$rx==2,], plot(survfit(Surv(futime,fustat)~1),conf.int=TRUE))

Answers

D.4.1

Abstract of 1979 paper:

Treatment of patients with advanced ovarian carcinoma (stages IIIB and IV) using 
either cyclophosphamide alone (1 g/m2) or cyclophosphamide (500 mg/m2) plus 
adriamycin (40 mg/m2) by iv injection every 3 weeks each produced partial 
regression in approximately one third of the patients. Survival curves and 
time-to-progression curves for the two regimens were nearly identical 
in these patients with advanced disease. These same regimens produced different 
results when used monthly in patients who had minimal residual 
disease (stages II and IIIA). In patients with minimal residual disease 
the therapeutic index of the combination regimen was superior to that of 
cyclophosphamide alone. Prognosis was better overall among patients with 
minimal residual disease than among patients with advanced disease. Within 
the minimal-disease group grossly complete excision of tumor prior to 
chemotherapy was associated with still better prognosis. Among patients 
with advanced disease, prognosis was significantly better for older patients 
despite their generally less favorable performance scores. Much 
of this prognostic superiority appeared to be related to menopausal 
status and presumably to the depletion of endogenous estrogens in the older patients.