Statistics of clinical trials - Calculation of tumor trial endpoint

1. summary

Clinical trial end point （End Point） Serve different research purposes . In the development of traditional cancer drugs , The purpose of early clinical trials is to evaluate the safety and bioactivity of drugs , If the tumor shrinks . Later efficacy studies usually evaluate whether the drug can provide clinical benefits , Such as prolonged survival or improved symptoms .

2. Definition of efficacy indicators ：

2.1 Time - Event type indicators ：

Total survival time (Overall Survival ,OS)： The time from the randomization to the death of the patient due to any cause .

Disease free survival (Disease－Free Survival ,DFS)： The time between the start of randomization and the occurrence of tumor recurrence or death from any cause . Although in most cases of adjuvant therapy , Overall survival remains a traditional endpoint , However, when the survival time is prolonged and it is unrealistic to choose the survival time as the end point of the clinical trial ,DFS It can be used as an important endpoint .

Progression free survival (Progression-Free Survival ,PFS)：PFS It is defined as the time between the start of randomization and the occurrence of objective tumor progression or death .

Time of disease progression (Time to Progression ,TTP)：TTP It is defined as the time between the start of randomization and the occurrence of objective tumor progression .TTP Not including death .

Treatment failure time (Time to Treatment Failure ,TTF)： That is, from randomization to whatever reason （ Including disease progression 、 Treat toxicity and death ） The time between the termination of treatment .

2.2 Rate index ：

Objective response rate (Objective Response Rate ,ORR)（ Some call the overall response rate ）： It refers to the proportion of patients whose tumor volume reduces to a predetermined value and can maintain the minimum time limit . The objective response rate is generally defined as the sum of complete response and partial response .

Overall response rate （ORR）： Complete remission was achieved at least once after treatment （CR） Or partial relief （PR） Proportion of patients .

Disease control rate （DCR）： Complete remission was achieved at least once after treatment （CR）、 Partial remission （PR） Or the lesion is stable （SD） Proportion of patients .

3. Calculation of efficacy index

3.1 Time - Event type

3.1.1 SAS Calculation ：

Calculate the time of disease progression in different groups （TTP） And progression free survival （PFS）, use Kaplan-Meier Method for descriptive statistics , use Greenwood Methods calculate the standard error , And provide 95% confidence interval , Draw a survival curve . use log-rank Test and compare whether there are differences in survival curves between different treatment groups .

Some raw data ：

Raw data

I can send the original version by private mail Excel data , Also used R Language to download the original lung data .

3.1.2 SAS code：

*
 Input ：
Lung For the data set （ contain subjid Subjects 、time Time to live 、status state ）
 The survival rate per survival time is calculated = Number of deaths at this time point / Number of survivors at the beginning of this time point .
         What is deleted at this time point is not death , But the next point in time counts as death , Not included in the denominator calculated at the next time point .
        
 Output ：
1. use ci Draw a survival curve .
2.lpgrank Tested p Values in the equivalence and group check form .
3. Median survival time and CI stay lung_3.;


proc lifetest data=lung outsurv=ci method=km atrisk conftype=log;
time time*status(1);
strata /group=sex test=(logrank);
ods output productLimitEstimates=lung_2 quartiles=lung_3;
run;

*code explain ：
proc lifetest: Call the survival analysis process step .
data=lung： Input lung Data sets .
outsurv=ci： Output ci Data sheet （ See the screenshot below ）.
method=km： draw Kaplan-Meier curve .
atrisk ： Output lung_2 Of NumberAtRisk Number of people at risk （ The denominator ）,ObservedEvents Number of people who have reached the end event .
time*status(1)： Time to live * state （ Delete logo ）.
test=(logrank)： use logrank Test method .
ods output： Output two data sets lung_2,lung_3（ See below .）
;

CI surface

Lung_2 surface

Lung_3 surface

Survival curve

3.1.2 The calculation principle is as follows ：

set up t_{1}< t_{2}<t_{3}<t_{4}<....<t{_k},： Indicates the occurrence of the event k Some time ;

n_{j}： It means the moment tj The number of survivors before ;

d_{j}： Express t_{j} Events happen all the time （ Reach the end point ） The number of people , Syncopation s_{j}=n_{j}-d_{j};

Then the survival distribution function （SDF） as follows ：

\hat{S}\left ( t_{j} \right )=\prod_{i=1}^{j}(1-\frac{d_{k}}{n_{k}})

The standard error is （Greenwood Law ）：

\hat{\sigma}( \hat{S}\left ( t_{j} \right ))=\hat{S}\left ( t_{j} \right )\sqrt{\sum_{k=1}^{j}\frac{d_{k}}{n_{k}s_{k}}}

95% The confidence interval is , The first way （Kalbfleisch&Prentice 1980.,excel Not calculated yet ）：

\hat{S}\left ( t_{j} \right )^{exp(\pm 1.96s)}\\ s=\hat{\sigma}( \hat{S}\left ( t_{j} \right ))/(\hat{S}\left ( t_{j} \right )*ln(\hat{S}\left ( t_{j} \right )))

95% The confidence interval is , The second way （SAS Calculation method ）：

\hat{S}\left ( t_{j} \right ) \pm 1.96 \hat{\sigma} (\hat{S}\left ( t_{j} \right ))

But I can get it by private letter excel Calculation file .

The test of two survival curves （logrank Law ）:

H0： Two groups of individuals at any point in time , There was no difference in survival rate .

H1： Two groups of individuals at any point in time , Survival rates vary .

Group	Number of events reaching the destination	Number of surviving individuals	Number of risk individuals ( total )
Group A	daj	saj=naj-daj	naj
Group B	dbj	sbj=nbj-dbj	nbj
total	dj	sj	nj

List all the time points , Calculate the actual frequency and theoretical frequency at each time point , structure x^2 statistic

\sum_{i=1}^{k}(Q_{A}-E_{A})/E_{A}+\sum_{i=1}^{k}(Q_{B}-E_{B})/E_{B}

You can calculate p value . May refer to https://zhuanlan.zhihu.com/p/392104512?ivk_sa=1024320u.

Risk ratio （hazard ratio,HR） The calculation of ：

HR=\frac{Q_{A}/E_{A}}{Q_{B}/E_{B}}

3.2 Rate index sas Calculation

Calculate groups ORR、DCR And 95% confidence interval , use Fisher Exact test for comparison .（ If the real world studies , At the same time, the method of propensity score matching , After correcting the baseline, use Fisher Exact test for comparison .）

sas The code is as follows :

*
 Input ：
rr For the data set （ contain SUBJID Subject number 、ARM Group 、ORR Whether to achieve ORR）

 Output ：
OneWayFreqs: Single factor frequency 
Binomial: Binomial ratio 
BinomialTest: Binomial proportional test 
 Single group rate and 95CI In the binomial scale .

;

ods output Binomial= Binomial;
proc freq data=rr;
by arm;
table ORR/binomial alpha=0.05;
run;

4. Some considerations about deletion

event / Delete	event / Reason for deletion	classification
event	progress	progress
event	Death	Death
event	There was no baseline imaging	There was no baseline imaging
Delete	A new anti-tumor treatment was started before the event	Start new anti-tumor therapy
Delete	The date of the event is more than two evaluation cycles from the date of the last imaging examination	Missing two consecutive imaging examinations
Delete	There was no efficacy evaluation or the results of efficacy evaluation were NE	There was no efficacy evaluation after taking the medicine
Delete	No incident occurred , And the subjects were still taking the medicine	Continue to treat
Delete	No incident occurred , And the subjects have been out of the group	Lost visit

Treatment of deletion in calculating survival rate ： What is deleted at this time point is not death , But the next point in time counts as death , Not included in the denominator calculated at the next time point . Specific to see excel Calculation of survival rate in the table .

5. reference

1.CDE. Guidelines for endpoint technology in clinical trials of antineoplastic drugs .

2.CDE. Technical guidelines for clinical data collection of anti-tumor drug marketing application .

3.CDE. Technical guidelines for clinical trials of antineoplastic drugs .

4. Zha Zha Dong's wechat official account .https://mp.weixin.qq.com/s/U8lxK9EmitQmb3wr_FNVRA.

5. CHENFENG et al . Clinical trial statistics .

6. Knowing that Wang buliuxing .https://zhuanlan.zhihu.com/p/392104512?ivk_sa=1024320u.