Phillip Keung Background Primary biliary cirrhosis of the liver PBC is a rare but fatal chronic liver disease of unknown cause with a prevalence of about 50casespermillion population The primary pathologic event appears to be the destruction of interlobular bile ducts which may be mediate ID: 530647
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Slide1
Discussion: Week 7
Phillip KeungSlide2
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.Slide3
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.Slide4
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). Slide5
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 techniquesSlide6
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 randomSlide7
A Priori Knowledge
Confounding?
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 investigateSlide8
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 protocolsSlide9
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 armsSlide10
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)Slide11
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 weekSlide12
Dataset Summary
. summarize
Variable |
Obs
Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
time | 312 2006.362 1123.281 41 4556
status | 312 .400641 .4908156 0 1
age | 312 50.01901 10.58126 26.2779 78.4394
albu
| 312 3.52 .419892 1.96 4.64
alkphos
| 312 1982.656 2140.389 289 13862.4
ascites | 312 .0769231 .2668974 0 1
bili
| 312 3.25609 4.530315 .3 28
chol
| 312 335.5417 246.3656 -9 1775
edema | 312 .1185897 .3238245 0 1
edemaTx
| 312 .1105769 .2745068 0 1
hepmeg
| 312 .5128205 .5006386 0 1
plate | 312 258.4615 99.77717 -9 563
proth
| 312 10.72564 1.004323 9 17.1
sex | 312 .8846154 .3199988 0 1
sgot
| 312 122.5563 56.69952 26.35 457.25
spiders | 312 .2884615 .4537747 0 1
trigly
| 282 124.7021 65.14864 33 598
copper | 310 97.64839 85.61392 4 588
logalb
| 312 1.250796 .1268699 .6729445 1.534714
logbil
| 312 .575678 1.032173 -1.203973 3.332205
logpro
| 312 2.368609 .0882652 2.197225 2.839078
Note the -9’s in
chol
and plate; those are missing valuesSlide13
VariablesSlide14
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
r
eplace plate = . if plate == -9Slide15
Univariate Analysis
tab stage
stage | Freq. Percent Cum.
------------+-----------------------------------
1 | 16 5.13 5.13
2 | 67 21.47 26.60
3 | 120 38.46 65.06
4 | 109 34.94 100.00
------------+-----------------------------------
Total | 312 100.00
tab treat
treat | Freq. Percent Cum.
------------+-----------------------------------
1 | 158 50.64 50.64
2 | 154 49.36 100.00
------------+-----------------------------------
Total | 312 100.00
tab
edemaTx
edemaTx
| Freq. Percent Cum.
------------+-----------------------------------
0 | 263 84.29 84.29
.5 | 29 9.29 93.59
1 | 20 6.41 100.00
------------+-----------------------------------
Total | 312 100.00Slide16
Univariate Analysis
. summarize
logalb
Variable |
Obs
Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
logalb
| 312 1.250796 .1268699 .6729445 1.534714
. centile
logalb
, centile( 10 25 50 75 90 )
--
Binom
. Interp. --
Variable |
Obs
Percentile Centile [95% Conf. Interval]
-------------+-------------------------------------------------------------
logalb
| 312 10 1.099611 1.063606 1.123247
| 25 1.196948 1.163151 1.20896
| 50 1.266948 1.252763 1.280934
| 75 1.335001 1.319086 1.348073
| 90 1.392274 1.378766 1.408545
. summarize
logbil
Variable |
Obs
Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
logbil
| 312 .575678 1.032173 -1.203973 3.332205Slide17
Univariate Analysis
. centile
logbil
, centile( 10 25 50 75 90 )
--
Binom
. Interp. --
Variable |
Obs
Percentile Centile [95% Conf. Interval]
-------------+-------------------------------------------------------------
logbil
| 312 10 -.6384507 -.6931472 -.5108256
| 25 -.2231435 -.356675 -.1053605
| 50 .2994182 .1823216 .5877866
| 75 1.245516 1.139768 1.504077
| 90 1.983736 1.856298 2.433613
. summarize
logpro
Variable |
Obs
Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
logpro
| 312 2.368609 .0882652 2.197225 2.839078
. centile
logpro
, centile( 10 25 50 75 90 )
--
Binom
. Interp. --
Variable |
Obs
Percentile Centile [95% Conf. Interval]
-------------+-------------------------------------------------------------
logpro
| 312 10 2.272126 2.261763 2.282382
| 25 2.302585 2.292535 2.312536
| 50 2.360854 2.351375 2.360854
| 75 2.406945 2.397895 2.433613
| 90 2.484907 2.459589 2.512189Slide18
Univariate Analysis
. summarize age
Variable |
Obs
Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
age | 312 50.01901 10.58126 26.2779 78.4394
. centile age, centile( 10 25 50 75 90 )
--
Binom
. Interp. --
Variable |
Obs
Percentile Centile [95% Conf. Interval]
-------------+-------------------------------------------------------------
age | 312 10 35.39301 34.00906 37.42523
| 25 42.04582 40.67432 43.93096
| 50 49.79465 48.486 51.84021
| 75 56.75292 55.96312 59.00011
| 90 63.80288 62.37514 67.3416Slide19
Univariate Analysis by Arm
. table treat, c(mean age
sd
age n age)
----------------------------------------------
treat | mean(age)
sd
(age) N(age)
----------+-----------------------------------
1 | 51.41911 11.00716 158
2 | 48.58254 9.957839 154
----------------------------------------------
. table treat, c(mean
logalb
sd
logalb
n
logalb
)
----------------------------------------------------
treat | mean(
logalb
)
sd
(
logalb
) N(
logalb
)
----------+-----------------------------------------
1 | 1.249004 .1323506 158
2 | 1.252634 .1213943 154
----------------------------------------------------
.
. table treat, c(mean
logpro
sd
logpro
n
logpro
)
----------------------------------------------------
treat | mean(
logpro
)
sd
(
logpro
) N(
logpro
)
----------+-----------------------------------------
1 | 2.362828 .077233 158
2 | 2.374541 .0982104 154
----------------------------------------------------Slide20
Univariate Analysis by Arm
. table treat, c(mean
logbil
sd
logbil
n
logbil
)
----------------------------------------------------
treat | mean(
logbil
)
sd
(
logbil
) N(
logbil
)
----------+-----------------------------------------
1 | .5379485 .9652755 158
2 | .6143875 1.0984 154
----------------------------------------------------
.
tabu
treat stage, col
| stage
treat | 1 2 3 4 | Total
-----------+--------------------------------------------+----------
1 | 12 35 56 55 | 158
| 75.00 52.24 46.67 50.46 | 50.64
-----------+--------------------------------------------+----------
2 | 4 32 64 54 | 154
| 25.00 47.76 53.33 49.54 | 49.36
-----------+--------------------------------------------+----------
Total | 16 67 120 109 | 312
| 100.00 100.00 100.00 100.00 | 100.00 Slide21
Univariate Analysis by Arm
.
tabu
treat
edemaTx
, col
|
edemaTx
treat | 0 .5 1 | Total
-----------+---------------------------------+----------
1 | 132 16 10 | 158
| 50.19 55.17 50.00 | 50.64
-----------+---------------------------------+----------
2 | 131 13 10 | 154
| 49.81 44.83 50.00 | 49.36
-----------+---------------------------------+----------
Total | 263 29 20 | 312
| 100.00 100.00 100.00 | 100.00Slide22
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 weekSlide23
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.)Slide24
Questions?