1. Discussion: Week 7
Phillip Keung

2. Background
Primary biliary cirrhosis of the liver (PBC) is a rare but fatal chronic liver disease of unknown cause, with a prevalence of about 50-cases-per-million population. The primary pathologic event appears to be the destruction of interlobular bile ducts, which may be mediated by immunologic mechanisms. The data are important in two respects. First, controlled clinical trials are difficult to complete in rare diseases, and this case series of patients uniformly diagnosed, treated, and followed is the largest existing for PBC. Second, the data present an opportunity to study the natural history of disease.

3. Background
Between January, 1974 and May, 1984, the Mayo Clinic conducted a double-blinded randomized trial for primary biliary cirrhosis (PBC), comparing the drug D-penicillamine (DPCA) with a placebo. There were 424 patients who met the eligibility criteria seen at the Clinic while the trial was open for patient registration. Both the treating physician and the patient agreed to participate in the randomized trial in 312 of the 424 cases. The date of randomization and a large number of clinical, biomedical, serologic, and histologic parameters were recorded for each of the 312 clinical trial patients. Disease and survival status as of July 1986, were recorded for as many patients as possible. By that date, 125 of the 312 patients had died, with only 11 deaths not attributable to PBC. Eight patients had been lost to follow-up, and 19 had undergone liver transplantation.

4. Agenda 1. Discuss the scientific objectives of analysis.
2. Discuss the measurements.
3. Summarize the univariate distribution of each variable (focus on "Mayo Model" predictors)
4. Compare the covariates for the two treatment arms. (focus on "Mayo Model" predictors)
5. For the DPCA treatment analysis formulate the scientific question in terms of a statistical hypothesis and discuss analysis plans (primary analysis and adjusted analysis).

5. Scientific Objectives
Basically, we want to look at the effect of DPCA treatment on mortality
Who should be included in the analysis? What kind of mortality? More on that later
Outcome: time to event (death) for each patient
Note that some patients left the study or did not die during the course of the study (i.e. some survival times were censored)
Hence, we do not observe the actual time of death for everyone
Need to deal with this partially observed data using survival analysis techniques

6. Censoring
Models that we use generally assume that censoring is completely random
Here, ‘completely random’ means that censoring occurs independently of patient characteristics, including survival time
Is this true? 3 sources of censoring here:
Patient left study after receiving a liver transplant: not independent, since sicker patients would tend to get transplants
Patient was lost to follow-up: plausibly independent
Administrative (i.e. patient still alive at end of study): independent
We will analyze the data as though everyone were censored completely at random

7. A Priori Knowledge Confounding? Effect Modification?
Randomized trial, so no confounding on average
Possible confounders would be balanced between treatment arms (if well randomized)
Effect Modification?
No compelling a priori reason to investigate

8. Definitions What should the outcome be? Death or death due to PBC?
We might want to only consider deaths due to PBC, but what about deaths due to side effects of treatment?
In practice, exact cause of death can be difficult to identify
Should patients be analyzed on an intent-to-treat (ITT) or per-protocol (PP) basis?
ITT: analyze as though patient is on treatment even if non-compliant
PP: analyze only those patients who adhered to treatment protocols

9. ITT vs PP ITT generally preferred for clinical trials
It’s conservative, since keeping people who were not compliant in the treatment group will dilute the treatment effect
Preserves randomization
Excluding non-compliant patients would change the composition of the treatment arms

10. Measurement Issues Variables
Demographic: age, sex
Clinical: Ascites, hepatomegaly, spiders, edema
Biochemical: bilirubin, albumin, urine copper, alkaline phosphatase, SGOT, cholesterol, triglycerides
Histology: stage
Measured at registration and non-invasive (except stage)

11. Mayo Model
Considered age, edema, log(bilirubin), log(albumin) and log(prothrombin) in Mayo model
Will discuss various models for adjusting for these variables next week

12. Note the -9’s in chol and plate; those are missing values
Dataset Summary
. summarize
Variable | Obs Mean Std. Dev Min Max
time |
status |
age |
albu |
alkphos |
ascites |
bili |
chol |
edema |
edemaTx |
hepmeg |
plate |
proth |
sex |
sgot |
spiders |
trigly |
copper |
logalb |
logbil |
logpro |
Note the -9’s in chol and plate; those are missing values

13. Variables

14. Missing Data
Can recode missing values so that Stata knows that they are missing, instead of treating them as -9’s: replace chol = . if chol == -9 replace plate = . if plate == -9

15. Univariate Analysis
tab stage stage | Freq. Percent Cum | | | | Total | tab treat treat | Freq. Percent Cum. 1 | | tab edemaTx edemaTx | Freq. Percent Cum. 0 | | |

16. Univariate Analysis
. summarize logalb Variable | Obs Mean Std. Dev. Min Max logalb | centile logalb, centile( ) -- Binom. Interp. -- Variable | Obs Percentile Centile [95% Conf. Interval] logalb | | | | | summarize logbil logbil |

17. Univariate Analysis
. centile logbil, centile( ) -- Binom. Interp. -- Variable | Obs Percentile Centile [95% Conf. Interval] logbil | | | | | summarize logpro Variable | Obs Mean Std. Dev. Min Max logpro | centile logpro, centile( ) logpro | | | | |

18. Univariate Analysis
. summarize age Variable | Obs Mean Std. Dev. Min Max age | centile age, centile( ) -- Binom. Interp. -- Variable | Obs Percentile Centile [95% Conf. Interval] age | | | | |

19. Univariate Analysis by Arm
. table treat, c(mean age sd age n age) treat | mean(age) sd(age) N(age) | | table treat, c(mean logalb sd logalb n logalb) treat | mean(logalb) sd(logalb) N(logalb) | | table treat, c(mean logpro sd logpro n logpro) treat | mean(logpro) sd(logpro) N(logpro) 1 | |

20. Univariate Analysis by Arm
. table treat, c(mean logbil sd logbil n logbil) treat | mean(logbil) sd(logbil) N(logbil) | | tabu treat stage, col | stage treat | | Total | | 158 | | | | 154 | | Total | | 312 | |

21. Univariate Analysis by Arm
. tabu treat edemaTx, col | edemaTx treat | | Total | | 158 | | | | 154 | | Total | | 312 | |

22. Hypothesis Testing
H0: Survival distributions for treatment and placebo arms are the same
Ha: Survival distributions for treatment and placebo arms are not the same
More on how exactly we test these hypotheses next week

23. Possible Analyses
Form Kaplan-Meier estimates of survival distributions for treatment and placebo groups
Use log-rank test to test whether the 2 survival curves are significantly different
Use Cox regression to examine treatment effect after adjusting for variables of interest
Interpretation of Cox regression coefficients as hazard ratios (i.e. risk of death is x times higher in treatment group versus control group, etc.)

24. Questions?