# Presentation: 444576

## Surrogate Endpoints for Hepatitis B Trials

- Greg Soon, Ph.D
- Rafia Bhore, Ph.D.
- Division of Biometrics III/Antiviral

**8/7/2002 AC**

**Notes:**
I am Greg Soon, Statistical Team leader for Anti-viral.

This talk will examine the feasibility of replacing biopsy by several outcome variables and use them as primary efficacy measures. That is, to find surrogate endpoints for biopsy

This is a joint work with Dr. Bhore

## Potential Surrogate Endpoints

- Knodell Score (Biopsy, Histology)
- ALT, HBV DNA
- Proportion < threshold
- Change from Baseline
- End of treatment
- Time to suppression
- Duration of suppression
- Time to virologic failure
- DAVG or Average change over time
- Others
- HBeAg, HBeAb, HBsAg, HBsAb
- Composition of the above

**Notes:**
What are the potential replacement measures for biopsy? The measures could be ALT, viral load, and various serologic marks. Different metrics of the same measure could be used, like change from baseline, duration of suppression, etc. 

In this talk liver biopsy will be measured by necro-inflammatory component of the Knodell score, or Knodell score in short.

## Data Source: EpivirHBV Submission

**Notes:**
The analyses will be based on two NDA submissions, one from adefovir submission that was discussed yesterday, and the other NDA is for epivirHBV submission that was reviewed here in 1998.

The Epivir submission had 4 studies with a total of 5 different treatment arms. The four studies are Studies NUCA3010, NUCAB3011, NUCB3009, and NUCB3010. I will also refer them as US Study, IFN-NR Study, Asian Study and Active Control Study. The five treatment groups are placebo, lamivudine 100mg, lamivudine 25mg, lamivudine 100mg in combination with IFN, and IFN alone. Patients on placebo or lamivudine arms were treated for 52 weeks, patients on the two IFN regimens were treated for 24 weeks with 28 weeks no treatment follow-up.

A total of 901 patients enrolled in these four studies had baseline biopsy, Missing biopsy rate at Week 52 ranges from 10 to 21%, average is 16%.

## Data Source: Adefovir Submission

**Notes:**
The two adefovir studies are study 437 and study 438. 437 enrolled e-antigen positive patients, 438 enrolled e-antigen negative patients. There are three study arms: placebo, adefovir 10mg, and adefovir 30mg.

The duration of these two trials are slightly shorter. They are 48 weeks compared to 52 weeks for epivir trials. For convenience I will consider all trials as one year trials.

The biopsy missing rate in these two studies were much lower. Of the 672 patients enrolled that had baseline biopsy, 8% were missing Year 1 biopsy.

Together these two submissions studies 1573 patients, of them 1372 had both baseline and Year 1 biopsy. An additional 17 patients had either missing ALT or HBV DNA at baseline or Year 1. Therefore a total of 1355 patients had both baseline and year 1 biopsy, ALT and HBV DNA. These 1355 subjects will constitute the analysis dataset for this validation

## HBV DNA Assays

- Lamivudine trials used Abbott Hybridization assay, which has a lower limit of approximately 500,000 copies/mL
- Limiting ability to differentiate patient responses on viral load
- Converted to copies/mL for this presentation
- Adefovir Trials used PCR assay that has a lower limit of 400 copies/mL

**Notes:**
Adefovir trials and epivir trials used different assay to measure viral loads. Epivir trials used hybridization assay that has a lower assay limit in the magnitude of 500,000 copies/mL, in contrast adefovir trials used PCR assay which has a lower limit of 400 copies/mL. A lot of patients went below assay limit in epivir trials, and the assay was not able to differentiate these patients in their HBV DNA response. This will be a limiting factor for the analysis.

## Overview

- Summary of Efficacy
- Patient-level Correlation
- Trial-level Correlation
- Proportion of Treatment Effect Explained (PTE)
- Summary

**Notes:**
The talk will be divided into 5 sections. 

First I will summarize efficacy and describe variability
Secondly I will examine the correlations with Knodell score, to see how well can various potential surrogate endpoints predict Knodell score.
Then I will go through two validation approaches. The first one is trial-level correlation, which is a meta-analysis examining the correlation of treatment effects. The second approach is through a concept called proportion of treatment effects explained, or in short PTE. PTE attempts to describe how much of the total treatment effect is mediated through surrogate endpoint.

Finally I will provide a brief summary

## Overview

- Summary of Efficacy
- Patient-level Correlation
- Trial-level Correlation
- Proportion of Treatment Effect Explained (PTE)
- Summary

**Notes:**
Now I will describe efficacy. I will go over several endpoints in detail. These endpoints are Knodell score, ALT, HBV DNA and e antigen status

Remember the analysis dataset does not include all patients enrolled, so the numbers will be different from what you may have seen before.

## Change of Knodell Score vs Baseline

**Notes:**
I will describe the efficacy on Knodell score first. Change from baseline will be compared between treatment groups, and its relationship with baseline Knodell score will also be examined.

## Convention

- White for placebo arms
- Yellow for LAM 100mg or ADV 10mg
- Orange for LAM 25mg or ADV 30mg
- Red for IFN + LAM 100mg
- Green for IFN alone

**Notes:**
This is the color scheme I will be using throughout this presentation. White color will be used for placebo arms in both NDAs, Yellow will be either lamivudine 100mg or adefovir 10mg, these are the doses chosen for marketing. Orange will be for lamivudine 25mg or adefovir 30mg. Red for lamivudine in combination with IFN, and blue for IFN alone

## Slide 10

**Notes:**
This plots baseline Knodell score vs. change of Knodell score for study 438, this is the study that enrolled only e antigen negative patients.

The x-axis is the baseline Knodell score, the y-axis is the change of Knodell score. The change is Year 1 Knodell score minus baseline, so negative changes represent improvement.

Knodell score ranges from 0 to 18, as we can see approximately from x-axis. Patients who have a baseline Knodell score close to 0 will not be able to demonstrate much improvement while patients with baseline biopsy close to 18 could not demonstrate much worsening. The two dashed white lines represents the limit for a patient’s improvement or worsening.

The solod white and yellow lines are smooth splines to capture the average trend.

We can see several things from this graph,
first we see that the yellow line, which is adefovir 10 mg, lies consistently below the solid white line, which is placebo arm, indicating a treatment effect. We also see the gap between the two lines are roughly the same, indicating the size of improvement is not influenced by baseline Knodell score.
Second we see a negative correlation between the baseline and change for each treatment arm. Patients with high baseline Knodell score improved more in both arms compared to patients with low baseline score.
Thirdly, we see the outcome is highly variable, even after adjust for baseline score. The range for variation is about 10 points.

## Slide 11

**Notes:**
This is the same plot for the e antigen positive population in study 437. The orange line is for adefovir 30mg. Again, we see a constant separation of the yellow and orange curve from the white line, we see a negative correlation, and we see variation of Knodell score of similar magnitude.

## Slide 12

**Notes:**
This plots the same relationship for the four epivir studies. First focusing on the white and yellow curve, we see patterns in the US study and the Asian study, similar to e antigen study is the last two graphs. The white line and yellow line crosses in the IFN-NR study, however the crossing occurs at the two ends where there are not many points.

The IFN+LAM arm is similar to placebo in the IFN-NR study. In the Active-control study, IFN alone arm appears to be similar to lamivudine 100mg , but lamividine + IFN looks somewhat worse than the other two arms.

All the curves showed negative correlation, and variability similar to the previous two graphs.

## Log10 ALT/ULN Over Time

**Notes:**
Now we move to the second endpoint, that is ALT. We will use log10 transformation to reduce the skewedness of ALT. Further ALT will be in multiples of its ULN for easier interpretation.

## Study 438

**Notes:**
This plots median ALT over time by treatment arms for the e antigen negative study. Xaxis is visit week which ranges from 0 to 48 weeks. yaxis is median log10 ALT/ULN. Zero on y-axis is 1xULN, 0.2 means 1.6xULN, 0.4 is 2.5xULN, -0.2 is about 0.6xULN

The bars at each vist represent 95% CI for the median. We see a clear separation of the two arms from Week 4 till Week 48.

## Study 437

**Notes:**
The plot for e antigen study showed similar separation of adefovir 10mg and 30mg from placebo arm.

## LAM Studies

**Notes:**
This combines all lamivudine data. Again, the lamividine 100mg vs placebo comparison is similar to adefovir studies.Interferon arms fluctuates, in the end it is close to placebo arms.

The last three slides showed that patients improved more on lamivudine and  adefovir treatments than on placebo, from early visits to Year 1.

The Next two plots will demonstrate the between patients variability at each visit, and variability between visits. I will use adefovir e antigen positive study as an example.

## Study 437

**Notes:**
This is again a plot of the median ALT over time for each treatment group. However, the bars represent 95% confidence interval for actual ALT, not its median. This showed a shift in distribution of ALT at each visit.

## Slide 18

**Notes:**
The next two slides are case studies, to examine how each patient’s ALT changes over time. This is done by picking 15 patients randomly from placebo arm. The next slide will show 15 randomly picked patients from adefovir 10mg.

Of the 15 patients, about 3-5 had sharp rises . Most other patients were stable

## Slide 19

**Notes:**
The next two slides are case studies, to examine how each patient’s ALT changes over time. This is done by picking 15 patients randomly from placebo arm. The next slide will show 15 randomly picked patients from adefovir 10mg.

Of the 15 patients, about 3-5 had sharp rises . Most other patients were stable

## Slide 20

**Notes:**
The next two slides are case studies, to examine how each patient’s ALT changes over time. This is done by picking 15 patients randomly from placebo arm. The next slide will show 15 randomly picked patients from adefovir 10mg.

Of the 15 patients, about 3-5 had sharp rises . Most other patients were stable

## Slide 21

**Notes:**
The next two slides are case studies, to examine how each patient’s ALT changes over time. This is done by picking 15 patients randomly from placebo arm. The next slide will show 15 randomly picked patients from adefovir 10mg.

Of the 15 patients, about 3-5 had sharp rises . Most other patients were stable

## Slide 22

**Notes:**
The next two slides are case studies, to examine how each patient’s ALT changes over time. This is done by picking 15 patients randomly from placebo arm. The next slide will show 15 randomly picked patients from adefovir 10mg.

Of the 15 patients, about 3-5 had sharp rises . Most other patients were stable

## Slide 23

**Notes:**
Of these 15 adefovir 10mg patients, 2-4 had sharp rises.

## Slide 24

**Notes:**
Of these 15 adefovir 10mg patients, 2-4 had sharp rises.

## Log10 HBV DNA Over Time

**Notes:**
The third endpoint is HBV DNA

## Study 438

**Notes:**
In adefovir e antigen negative study, adefovir 10mg is significantly better than placebo quickly after initiation of therapy.

## Study 437

**Notes:**
Note for this endpoint, adefovir 30mg is significantly better than 10mg in the e antigen positive study.

## LAM Studies

**Notes:**
Note lamivudine 100mg and 25mg at the bottom, separated from white placebo arm. IFN-containing regimens were similar to placebo in the end.

## Study 437

**Notes:**
This shows patient to patient variability at each visit.

## Slide 30

**Notes:**
Again, 15 placebo patients were randomly selected for case studies. 4-5 patients had sharp rises in viral load following a drop.

## Slide 31

**Notes:**
Again, 15 placebo patients were randomly selected for case studies. 4-5 patients had sharp rises in viral load following a drop.

## Slide 32

**Notes:**
Again, 15 placebo patients were randomly selected for case studies. 4-5 patients had sharp rises in viral load following a drop.

## Slide 33

**Notes:**
Again, 15 placebo patients were randomly selected for case studies. 4-5 patients had sharp rises in viral load following a drop.

## Slide 34

**Notes:**
Again, 15 placebo patients were randomly selected for case studies. 4-5 patients had sharp rises in viral load following a drop.

## Slide 35

**Notes:**
These 15 adefovir 10mg patients also had rebounds. But the rebound magnitude appears to be smaller than in the placebo arm.

## Slide 36

**Notes:**
These 15 adefovir 10mg patients also had rebounds. But the rebound magnitude appears to be smaller than in the placebo arm.

## HBeAg Loss Over Time

**Notes:**
The last endpoint is HBeAg

## Study 437

**Notes:**
Only adefovir e antigen positive study and lamivudine studies will be presented. The curves represent percent of patients who are e antigen negative at that time.

There is a clear separation  between 30mg and placebo, and 10mg is nearly separated from placebo group. Over time the response increases for all the three arms.

## LAM Studies

**Notes:**
Lamivudine 100mg nearly separates from placebo but not lam25. IFN containing regimens varies over time.

## Transition of HBeAg Status

**Notes:**
This table describes the durability of HBeAg status. 

The two NDAs were combined for this analysis. They were separated into four groups according to treatment.

Let’s go over the placebo group. There are a total of 364 patients in this group. 14% of them became e antigen negative during the 48 week treatment. Of these patients, 37% rebound back to positive status. 26% of them again became negative later, and so on.

For the other three actively treated groups, 26-34% became e antigen negative, of these, 20-28% rebound, of these rebounders, 28-58% resuppress. A few of these will rebound again.

Overall, 1/4 to 1/3 e antigen negatives can not be maintained during the 48 weeks of treatment.

## Overview

- Summary of Efficacy
- Patient-level Correlation
- Trial-level Correlation
- Proportion of Treatment Effect Explained (PTE)
- Summary

**Notes:**
The next topic is on the relationships of endpoints. 

## Lamivudine: HBV DNA vs. Knodell

**Change of Knodell Score**

**Year 1 LOG10 HBV DNA**

**Notes:**
First I will present correlation of HBV DNA vs, Knodell score. The color convention is followed here. HBV DNA will be presented as Year 1 HBV DNA, Knodell will be the change from baseline.

This slide is for lamivudine trials. Each row represents one study. Each box is one treatment group in one study. For example, the first box is placebo arm in the US study, the 2nd row, 2nd box is lamivudine 100mg in the IFN-NR study.

The blue curves in each plot are again smooth splines. 

First, note the effect of the high assay limit. Many patients achieved assay limit and a lot of points clustered at a single line. The data above is relatively sparse, making it more difficuly to discover correlations.

Note all curves have a slightly up trend, but with a lot of noise. Indicating a weak correlation. 

## Lamivudine: HBV DNA vs. Knodell

**Year 1 LOG10 HBV DNA**

**Lamivudine: HBV DNA vs. Knodell**

**Notes:**
These two rows are for the Asain study and the Active-control-study respectively. Again there is slight up trend with a lot of variation, indicating a weak correlation

## Lamivudine: CorrelationYear 1 HBV DNA vs. Knodell Score Change

***: p-value<0.05****	****	******: p-value<0.001**

**Notes:**
This table summarizes the previous two graphs by correlation coefficients. The overall correlation coefficient is about 0.3. The correlation appears to be weaker in Asian study, IFN+LAM arm in IFN-NR study showed a strongly correlation than other treatment groups. 

## Adefovir: HBV DNA vs. Knodell

**Year 1 LOG10 HBV DNA**

**Adefovir: HBV DNA vs. Knodell**

**Notes:**
This set of graphs is for the two adefovir studies. Note the wider range for the xaxis resulting from lower assay limit.

These pictures show a clear up trend that were closer to linear than what we saw for epivir trials. It appears that this trend is true for the whole range of viral load in several plots. Meaning that patients whose viral load were lower at Year 1 are more likely to have better Knodell improvements.

## Adefovir: CorrelationYear 1 HBV DNA vs. Knodell Score Change

***: p-value<0.05****	****	******: p-value<0.001**

**Notes:**
The overall correlation is 0.29, nearly identical to the epivir trials. However, the correlation in e antigen negative study is significantly lower at 0.09.

## Lamivudine: ALT vs. Knodell

**Change of Knodell Score**

**Change of LOG10 ALT**

**Notes:**
Next we study ALT. These correlation appear to be stronger than the ones for HBV DNA. 

## Lamivudine: ALT vs. Knodell

**Change of LOG10 ALT**

**Lamivudine: ALT vs. Knodell**

**Notes:**
Some of these plots suggest a plateau of the correlation between -1 and 0

## Lamivudine: CorrelationALT Change vs. Knodell Score Change

***: p-value<0.05****	****	******: p-value<0.001**

**Notes:**
The overall correlation is 0.43
most of the correlations appear to be consistent within study. Exceptions are the IFN+LAM arm in the IFN-NR study, which showed a much stronger correlation. In Asian study, LAM100 and LAM 25 showed a higher correlation than the placebo group.

## Adefovir: ALT vs. Knodell

**Change of LOG10 ALT**

**Adefovir: ALT vs. Knodell**

**Notes:**
These are for adefovir.

## Adefovir: CorrelationALT Change vs. Knodell Score Change

***: p-value<0.05****	****	******: p-value<0.001**

**Notes:**
The overall correlation is 0.46, very similar to lamivudine trials. Like HBV DNA, e antigen negative study showed a weaker correlation at 0.29, compare to 0.52 for e antigen positive study.

HBeAg status is also associated with change of Knodell score with a correlation coefficient about 0.3.

From these analysis we see HBV DNA, ALT and HBeAg are predictive of change of Knodell score, that is, an improvement in any of these predictors will likely result an average improvement, but the precision for prediction on individual level is very poor.

## DNA, HBeAg & Knodell

**438**

**437 Yr 1 eAg Neg**

**437 Yr 1 eAg +**

**38**
**68**
**62**

**13**
**6**
**17**

**34**
**13**
**21**

**41**
**10**
**16**

**215**
**10**
**53**

## Joint Prediction

**Notes:**
A natural question is that can we improve the precision of prediction by utilizing several predictors simultaneously

## Predicting Change of Knodell

***Excluding adefovir HBeAg negative study**
***stratified by study and treatment**

**Notes:**
In this excecise I incorporated baseline viral load and baseline ALT into the linear model. All the analyses were stratified by study and treatment groups.

First we go through predictors one by one to see how much they add. This is measured by R^2, which describes how much variability in the change of Knodell score is removed when the predictor is used.

As a baseline for these analyses, the baseline ALT and baseline DNA removes 14% of Knodell variation.

Adding baseline Knodell score, the R^2 becomes 47%, confirming the strong correlation we observed at the beginning of the talk.
The other predictors include change of ALT, ....
Change of ALT made the biggest impact, followed by DAVG of ALT at 27%. Year 1 HBV DNA and DAVG DNA comes next at around 20%, followed by nadir e antigen status or Year 1 e antigen status. 

## Slide 55

**Notes:**
Combining change of ALT with other predictors made only marginal improvement. The combination of change of ALT with Year 1 DNA had R^2 at 30%, comparing to 29% using ALT alone. Combining ALT with DAVG DNA produced slightly better prediction at R^2=33%.

Even when 8 predictors are combined, the prediction improved little. 

## Summary

- With near certainty, better response on change of log10 ALT and Year 1 log10 HBV DNA are associated with better Knodell improvement
- The associations are weak to moderate
- Multiple predictors do not improve much on top of ALT

**Notes:**
In summary, with high confidence, HBV DNA, ALT and HBeAg are associated with Knodell score.  However, the strength of association is weak. With ALT somewhat stronger.

Multiple predictors do not improve much upon change of ALT

## Overview

- Summary of Efficacy
- Patient-level Correlation
- Trial-level Correlation
- Proportion of Treatment Effect Explained (PTE)
- Summary

**Notes:**
Now finally validation. The first method I will be talking about is based on trial-level correlation. earlier I talked about correlation between potential surrogates and Knodell score for individual patients in each arm within each study. Instead of individual patients, the basic unit for trial-level correlation will be each trial. 
For each potential surrogate endpoint, for example, viral load, and for each study, we will have a pair of treatment differences between the experimental arm and the control arm, one is treatment difference for Knodell score, the other for treatment difference for surrogate endpoint like viral load. When we have many such pairs from many trials, we can directly study how the treatment effect on surrogate determines the treatment effect on the Knodell score

## Methods

- Studies were divided into smaller trials according to region and ethnic background to increase data points for analysis
- Size of “trials” range from 20 to 70.

**Notes:**
Since the analysis units for this method are clinical trials instead of individual patients, it is important to have many trials to generate sufficient data points for analyses. Unfortunately we only have a total of 6 studies, of which 5 are placebo controlled. Too few for robust analysis.

To get around this limitation, I have divided the six studies into smaller trials mostly according to where the studies were conducted. If the resulting trial is still large, I further divide it according to ethnic background. I end up having about 40 such smaller trials with sample size ranging from 20 to 70.

## HBV DNA vs. Knodell By Trial and Treatment

**Notes:**
First we look at the HBV DNA vs. Knodell score at one year. The plot graphically summarizes the treatment responses in all studies and all treatment arms for viral load and Knodell score. X-axis is treatment response on viral load and Y axis is treatment effect on Knodell score. Each point  represents one arm in one trial. 
Blue points are from adefovir trials while yellow ones are from epivir trials. Capital “A” stands for adefovir 10mg while lower case “a” stands for adefovir 30mg. Capital L stands for LAM100 while lower case “l” stands for Lamivudine 25mg. M stands for LAm100+IFN and F stands for IFN alone.
The size of a letter represents the size of the corresponding trial, so larger trial will have a larger letter.
For example, the capital letter A here (pointer) stands for adefovir 10mg from one of the trial that was part of the adefovir studies. The size of this letter is relatively large so this is from one of the larger trial. This adefovir 10mg arm had a mean viral load of approximately 3.4 logs at Year 1, and the mean Knodell score change is approximately 4 points reduction.

Fist notice the clustering of points according to treatment arms. Adefovir arms are at the lower left corner. Lamivudine arms are right of the adefovir arms, indicating similar response on Knodell score but higher viral load for lamivudine arms. Recall that epivir trials used assay with a much higher lower limit, the viral loads on lamivudine can not go below 5.5, so this difference may just be due to the difference in the assay limit.
The placebo points are scattered at the upper right corner, indicating in general placebo arms are not doing as well in both viral load and Knodell score. IFN-containing regimens are closer to placebo arms.

## ALT  vs. Knodell By Trial and Treatment

**ALT  vs. Knodell By Trial and Treatment**

**Notes:**
This is the same plot but for ALT change. One notable difference from the previous plot is the overlapping of the lamivudine and adefovir responses.

Both graphs show that overall, lamivudine or adefovir arms showed better response in Knodell score, viral load and ALT compared to placebo. IFN containing arms are somewhere in between but closer to placebo.

The next few slides will show directly how the treatment effects, that is, the difference of response between active treatment arms vs. placebo, are correlated.

## HBV DNA vs Knodell: Treatment effects by Trial

**HBV DNA vs Knodell: Treatment effects by Trial**

**R^2=25% (0, 60%)**

**Notes:**
The first two slides are for viral load at the end of one year vs. Knodell score change. In this slide we only show adefovir trials, and the next slide for lamivudine trials. The two drugs were not shown on the same picture because of different assay used.
Each number in this plot stands for one trial, Number 7s in yellow are trials from subdivided from adefovir study 437, 8 is from Study 438. The size of the numbers corresponding to the size of the trial. For example, for the 7 at the lower left corner,  the treatment difference between adefovir and placebo on Year 1 viral load is on axis, about -3.7 logs. The treatment difference for this trial on Knodell score change is about -4.3.
First we note that the treatment effects on viral load ranges from one and half log to 4 and half log, and treatment effects on Knodell score ranges from 1 to 4 and half, all favoring the adefovir arm.
The redline again indicates average effects on Knodell score over effects on Year 1 HBV DNA. The line has a slight up trend, indicating trials with larger treatment differences between adefovir and placebo will also likely have a larger treatment effects on Knodell score. However, this association is not strong. The R-squared is 25%, which is not statistically significantly different from 0.

## HBV DNA vs Knodell: Treatment effects by Trial

**HBV DNA vs Knodell: Treatment effects by Trial**

**R^2=6% (0, 30%)**

**Notes:**
This plot is for lamivudine trials, excluding interferon-containing studies. The R-squared is 6% and not statistically significant.

## ALT vs Knodell: Treatment effects by Trial

**ALT vs Knodell: Treatment effects by Trial**

**R^2=24% (0, 49%)**

**Notes:**
Now we turn to ALT. We no longer have assay limit issue so both the adefovir and lamivudine trials are included. In this plot interferon-containing studies were excluded. Again we see an up trend, suggesting better effects on ALT in a trial is related to better effects on Knodell score. However, the association again is not statistically different from no association.

## ALT vs Knodell: Treatment effects by Trial

**ALT vs Knodell: Treatment effects by Trial**

**R^2=33% (8, 57%)**

**Notes:**
This plot differ from the previous plot only by the points labeled 2 and 4 at the upper right corner. These are interferon-containing trials. These 5 interferon-containing trials had very similar effects on Knodell score, about 0. On the ALT the effects range from about slight worsening to about -0.25 logs reduction in ALT. -0.25 log reduction is about 1 fold reduction.
Even though the effects of these interferon trials varies somewhat on the ALT, neverthless they conform to the trend that smaller effects on ALT corresponding to smaller effects on Knodell score. The R-squared becomes 33% and with a positive lower bound 8%.

So the best number for the association is shown on this slide, with R-squared at 33%. This means that of  the trial to trial variations on the treatment effects on change of Knodell score, by knowing treatment effects on the ALT, we can reduce this variability by 33%. 

So the question is why are we seeing a relatively weak association? What are the factors that influenced this association? I will discuss factors that potentially are partially responsible for what we see here.

## Variability and Correlation

**Notes:**
The first potential factor is within patient variability of the Knodell score. This variability could arise in several ways. If you repeat biopsy on a patient, you could get a different piece of liver that has been affected differently by the disease. Plus the same sample may be read by different readers, or even if the sample is read by the same reader at different times we could end up with different scores. Collectively, within-patient variation measures the variability of doing biopsy two or more times on the same patient at a given time by following the same procedure. 
The total variability in Knodell score we observe arises from both the within patient variability and the variability between patients. For these trials, the total variability as measured by standard deviation is about 3, with adefovir trials having slightly smaller variation. 
Under ideal situations that the biopsy variability is not influenced by the magnitude of the actual biopsy measurement, the relationship can be formulated mathematically. The observed correlation is a function of the true correlation, multiplied by a factor determined by the ratio of within patient variability over the total variability. 
So the question is how much within patient variability exist and how much impact it has on the correlation. Let’s examine some numbers

## Variability and Correlation

**Assume overall SD for Knodell is 3**

**Notes:**
Assume the standard deviation for the Knodell score is 3. Because we have no data to estimate the biopsy variation within a patient,  we looked at a few values. 
The second row shows the case where there is no variability in biopsy within individual patients. In this case the observed and true correlation are the same.
For HBV DNA at Year 1, it is 0.3, for ALT, it is 0.43.
Let’s look at another case, within patient standard deviation is 1.5. This roughly means that if a patient’s true Knodell score is 7, one would have about 2/3 of chance observing a score between 6 and 8, 1/3 chance seeing a score less or equal to 5, or greater  than or equal to 9. In this case the true correlation between DNA and Knodell is 0.35, and 0.5 for ALT vs Knodell
The last case is if one believes the within patient standard deviation of 2.25. Which roughly corresponding to the case where a subject with a true Knodell score of 7 will be told to have a Knodell score of less or equal to 2, or greater than or equal to 12 with 1/3 of times. In this case the DNA correlation is 0.45, ALT is 0.65.

## Impact on relationship among treatment effects

**Notes:**
Now we see weak correlations on individual level, how does it influence trial level correlation?

To fix the idea, let’s imagine that you have followed the same protocol and done a trial 1000 times. Among these 1000 trials how would the surrogate effects correlates with effects on Knodell score?

In reality we can not afford to repeat the same trial 1000 times, instead I will use simulations.

## Replication of a Single Trial

**r1=0.74**
**r0=0.31**
**R=0.56**

**Notes:**
The first study I simulated is the interferon non-responder study. I picked the Lmivudine 100 mg + interferon arm and placebo arm for the comparison. The surrogate endpoint here is ALT. The reason for this particular choice is because different individual correlations in the two arms. The lamivudine+interferon arm had a correlation of 0.74, the placebo arm had a correlation of 0.31.

The plots shows what would happen if you do this study 1000 times. Each point is one such study, x-axis is the treatment effect on ALT and y-axis is the treatment effect on Knodell score. The correlation of the two treatment effects is about 0.56, somewhere in between of the two individual correlations.

By the way, the R-squared for this plot is about 30%.

## Replication of a Single Trial

**r1=0.50**
**r0=0.47**
**R=0.44**

**Notes:**
This simulates the adefovir HBeAg positive study, adefovir 10mg vs placebo. Here the correlation of ALT and Knodell score in the two arms are similar at around 0.5. Again, the trial-level correlation based on replicating this adefovir trial is 0.44, similar to individual level.

These two simulations show that if the trials are similar, likely replication of a single trial, then the trial level correlation will be similar to individual level correlation

## Other considerations

- Variations in trial results are desirable for the trial-level correlation validation method. Two trials of different effect sizes are more useful than two trials of similar effect size

**Notes:**
The effects size of lamivudine and adefovir vs. placebo trials are fairly similar, therefore it would be difficult to have trial level correlation much higher than individual level correlation

## Overview

- Summary of Efficacy
- Patient-level Correlation
- Trial-level Correlation
- Proportion of Treatment Effect Explained (PTE)
- Summary

**Notes:**
The second concept for validation of endpoint is proportion of treatment effects explained. Or briefly PTE. This method has a longer history and has been used in HIV trials.

## Proportion of Treatment Effect Explained

- Attempts to determine, of the total effect size observed for the Knodell score in each trial, how much can be attributed to the effect on the potential surrogate?
- Linear regression model to determine how much effect remain when there is no effects on surrogate
- The remainder portion of the treatment effect is considered mediated through surrogate
- Long used but also widely debated

**Notes:**
Contrary to trial-level correlation, which utilize many trials for analysis. PTE can be computed for each trial.
In the PTE analysis, the overall treatment effect on Knodell score is decomposed into two component, the component that was not predicted by the surrogate endpoint, and the component that is regarded as due to effect on surrogate. This decomposition relies on modeling, typically linear model for continuous data. The PTE is the ratio of the effect sue to surrogate over the over effect on Knodell score. That is, it measures what percent of the overall effect is due to the presence of an effect on surrogate. Ideally this value should be 1, and it would imply that all treatment effect on Knodell is mediated through the surrogate.
This method has been long used but has also been widely debated.

## PTE: HBV DNA vs Knodell

**Notes:**
This table shows the PTE for Year 1 HBV DNA as surrogate for the change of Knodell score.

The first 3 columns are drug name, study name and treatment comparison studied. The last two columns list the PTE and its 95% confidence interval.

Let’s go over the e antigen negative study first, it is in red.
The PTE for the comparison here is 15%, which is statistically not significantly different from 0. Therefore we are not certain if treatment effect on Year 1 viral load is responsible for any of the treatment effects on Knodell score. In this study.

The other studies are in e antigen positive population. The comparisons in white do not involve interferons. The PTEs for the two comparisons in adefovir are 65 and 78% respectively. With lower bounds at 41 and 49%, respectively, suggesting at least a portion of the effects on surrogate is mediated through viral load.

Moving on to epivir trials. The PTEs are 33, 37, 40 and 48% in the 4 comparisons in white. Those are comparisons do not involve interferon. The lower bounds of the 95% confidence interval ranges from 6 to 22%, supporting the statement that at least some of the effects on Knodell is mediated through Year 1 viral load. At the same time we see the upper bound for the first 3 PTEs are <100%, suggesting there are unexplained effects left from viral load.
All the PTEs involving interferon have extremely wide confidence interval, therefore it is impossible to draw any conclusions. This is primarily due to lack of efficacy in these comparisons.

## PTE: ALT vs Knodell

**Notes:**
Next we turn to Change of ALT on log10 scale. The pattern is similar to HBV DNA. 
Again, for e antigen negative adefovir study, the PTE is relatively low at 17%, but with a positive lower bound. All the white comparisons are positive and with positive lower bound, suggesting ALT is responsible for some of the effects on Knodell score. However, most of the upper bounds are less than 100% so ALT do nopt drive all the benefits.

## Overview

- Summary of Efficacy
- Patient-level Correlation
- Trial-level Correlation
- Proportion of Treatment Effect Explained (PTE)
- Summary

**Notes:**
Finally, a summary of the presentation

## Summary

- Treatment effects and variability for HBV DNA, ALT, HBeAg and Knodell score.
- Baseline Knodell correlates with change
- Effects over time for HBV DNA, ALT, and HBeAg
- Both ALT and HBV DNA are variable over time

## Summary

- Weak individual level correlation with Change of Knodell score
- Year 1 HBV DNA, r = 0.3
- Change of ALT, r = 0.45
- Not much improvement with multiple predictors

## Summary

- Weak Trial-level correlation
- Biopsy variability may reduce individual correlation
- Trial level correlation will be similar to individual level correlation if trials are similar
- Adefovir and Epivir trial results are somewhat similar in effect sizes

## Summary

- PTE for Year 1 HBV DNA and Change of ALT
- For baseline HBeAg negative study, both HBV DNA and ALT have low PTE
- For baseline HBeAg + Study, PTE are somewhat consistent in adefovir or lamivudine vs placebo comparisons
- Interferon-containing comparisons are not informative

## END