Aim of the Project- An application of the Kaplan-Meier estimator, Lifetable Analysis and a clinical data, the survival time of 76 breast cancer patients categorized under three different treatments, which is presented with respected lifetables along with survival and hazard function for comparison. Statistical techniques Used- Kaplan-Meier estimator, Lifetable Analysis Software Used- SAS, Excel

1. Survival Report of 76 breast cancer patients under three different treatments
Summary
This review presents an application of the Kaplan-Meier estimator, Lifetable Analysis and a
clinical data, the survival time of 76 breast cancer patients categorized under three different
treatments, which is presented with respected lifetables along with survival and hazard
function for comparison. From various test results it is evident treatment R stands out little
better than the rest although all of the treatments have low survival rate, with less difference in
response among the cancer patients.
Introduction
Survival times are data that measure follow-up time from a defined starting point to the
occurrence of a given event, for example the time from the beginning to the end of a remission
period or the time from the diagnosis of a disease to death. Standard statistical techniques
cannot usually be applied because the underlying distribution is rarely Normal and the data are
often 'censored'. A survival time is described as censored when there is a follow-up time but
the event has not yet occurred or is not known to have occurred. We consider methods for the
analysis of data when the response of interest is the time until some event occurs, such events
are generically referred to as failure. The survival analysis attempts to cover both the
parametric and nonparametric methods, the emphasis is on the more recent nonparametric
developments with applications to medical research.
The data set is follow up to a clinical trial conducted in the early 80’s on 76 breast cancer
patients to investigate three different treatments- Radiotherapyalone (R),Radiotherapyand
Chemotherapy(RC),andChinese traditionalmedicine(CTM). Duringthe tenure of five yearsof the
examination-25patientsreceivedR,27 receivedR&C,andthe other24 receivedCTM.The survival time
(inmonths) isthe time until cosmeticdeteriorationwhichisdeterminedbythe appearance of breast
retraction.
Procedure along with computation, output and pictorial representation
Computational Tables from SAS
Summaryof censoredanduncensoredvalues-
Summary of the Number of Censored and Uncensored Values
Stratumtreatment Total Failed Censored
Percent
Censored
1CTM 24 20 4 16.67
2R 25 18 7 28.00
3RC 27 21 6 22.22
Total 76 59 17 22.37

2. The above table shows the summary of all the censored and uncensored values obtained from
the given data set.
1.Kaplan –Meier Estimate
SAS procedure- For each case in the sample, we define three variables, Time, Status and
Treatment. Let Time denote the survival time (exact or censored), Status be a dummy variable
with Status=0 if Time is censored and 1 otherwise and Treat be a variable with Treat = R if the
patient received Radiotherapy alone, RC if the patient receive Radiotherapy and Chemotherapy
and CTM if the patient received Chinese traditional medicine. The SAS code for procedure
LIFETEST can be used to test the above null hypothesis. We should simply add a STRATA
statement after the Time statement.
We computed and plotted the PLS estimates of S(t) at every time for the R,RC and CTM
groups.
Hence using proc lifetest we acquire the following result. We also include the Survival
distribution function but later on different section.
SAS output-
The following tables are the SAS output of Product Limit (PL) survival estimates under the three
treatment groups CTM, R and RC.
(a) CTM-
Product-Limit Survival Estimates
Time SurvivalFailure Survival Standard Error
Number
Failed
Number
Left
0.0000 1.0000 0 0 0 24
10.0000 0.95830.0417 0.0408 1 23
13.0000 0.91670.0833 0.0564 2 22
14.0000 0.87500.1250 0.0675 3 21
16.0000 0.83330.1667 0.0761 4 20
16.0000* . . . 4 19
18.0000 0.78950.2105 0.0838 5 18
20.0000 0.74560.2544 0.0899 6 17
21.0000 0.70180.2982 0.0947 7 16
27.0000 0.65790.3421 0.0984 8 15
28.0000 . . . 9 14
28.0000 0.57020.4298 0.1030 10 13
28.0000* . . . 10 12
32.0000 0.52270.4773 0.1048 11 11

3. 33.0000 . . . 12 10
33.0000 0.42760.5724 0.1051 13 9
34.0000 0.38010.6199 0.1036 14 8
39.0000* . . . 14 7
41.0000 0.32580.6742 0.1020 15 6
46.0000 0.27150.7285 0.0984 16 5
51.0000 0.21720.7828 0.0925 17 4
52.0000 0.16290.8371 0.0838 18 3
53.0000 0.10860.8914 0.0713 19 2
55.0000* . . . 19 1
57.0000 01.0000 . 20 0
Summary Statistics for Time Variable Time
Quartile Estimates
Percent
Point
Estimate
95% Confidence Interval
Transform [Lower Upper)
75 51.0000LOGLOG 33.000057.0000
50 33.0000LOGLOG 21.000046.0000
25 20.0000LOGLOG 10.000028.0000
Mean
Standard
Error
34.0943 3.2433
(b) R-
Product-Limit Survival Estimates
Time SurvivalFailure Survival Standard Error
Number
Failed
Number
Left
0.0000 1.0000 0 0 0 25
16.0000 0.96000.0400 0.0392 1 24
17.0000* . . . 1 23
18.0000 0.91830.0817 0.0554 2 22
20.0000 0.87650.1235 0.0668 3 21
24.0000 0.83480.1652 0.0755 4 20
25.0000 0.79300.2070 0.0825 5 19
27.0000 . . . 6 18
27.0000 0.70960.2904 0.0925 7 17
29.0000 0.66780.3322 0.0961 8 16
33.0000 0.62610.3739 0.0987 9 15
35.0000 0.58430.4157 0.1006 10 14
36.0000 0.54260.4574 0.1017 11 13
39.0000* . . . 11 12
41.0000 0.49740.5026 0.1028 12 11
44.0000* . . . 12 10

4. 45.0000 0.44770.5523 0.1038 13 9
50.0000 0.39790.6021 0.1035 14 8
52.0000 0.34820.6518 0.1018 15 7
52.0000* . . . 15 6
56.0000 . . . 16 5
56.0000 0.23210.7679 0.0954 17 4
58.0000* . . . 17 3
59.0000 0.15470.8453 0.0896 18 2
60.0000* . . . 18 1
60.0000* . . . 18 0
Summary Statistics for Time Variable Time
Quartile Estimates
Percent
Point
Estimate
95% Confidence Interval
Transform [Lower Upper)
75 56.0000LOGLOG 45.0000 .
50 41.0000LOGLOG 27.000056.0000
25 27.0000LOGLOG 16.000036.0000
Mean
Standard
Error
41.4362 3.1849
(c) RC-
Product-Limit Survival Estimates
Time SurvivalFailure Survival Standard Error
Number
Failed
Number
Left
0.0000 1.0000 0 0 0 27
9.0000 0.96300.0370 0.0363 1 26
11.0000 0.92590.0741 0.0504 2 25
17.0000 . . . 3 24
17.0000 0.85190.1481 0.0684 4 23
19.0000 0.81480.1852 0.0748 5 22
21.0000 0.77780.2222 0.0800 6 21
24.0000 0.74070.2593 0.0843 7 20
25.0000 0.70370.2963 0.0879 8 19
27.0000 0.66670.3333 0.0907 9 18
28.0000 0.62960.3704 0.0929 10 17
28.0000* . . . 10 16
29.0000 0.59030.4097 0.0951 11 15
29.0000* . . . 11 14
30.0000 0.54810.4519 0.0972 12 13

5. 33.0000 0.50600.4940 0.0984 13 12
37.0000 0.46380.5362 0.0989 14 11
39.0000 0.42160.5784 0.0985 15 10
40.0000* . . . 15 9
44.0000 0.37480.6252 0.0980 16 8
46.0000* . . . 16 7
47.0000* . . . 16 6
51.0000 0.31230.6877 0.0996 17 5
52.0000 0.24990.7501 0.0973 18 4
54.0000 0.18740.8126 0.0909 19 3
56.0000 0.12490.8751 0.0792 20 2
58.0000 0.06250.9375 0.0593 21 1
60.0000* . . . 21 0
Summary Statistics for Time Variable Time
Quartile Estimates
Percent
Point
Estimate
95% Confidence Interval
Transform [Lower Upper)
75 52.0000LOGLOG 39.000058.0000
50 37.0000LOGLOG 25.000052.0000
25 24.0000LOGLOG 11.000029.0000
Mean
Standard
Error
36.9469 3.2011
2.Life-table Analysis
SAS Procedure-The SAS procedure for the life-table analysis remains the same but here under
proc lifetest we define the intervals under which we are creating the life-table.
SAS output-
The following tables are the SAS output of life-table analysis under the three treatment groups
CTM,R and RC.
(a) CTM-

6. Life Table Survival Estimates
Interval
Num
ber
Faile
d
Numb
er
Censo
red
Effect
ive
Samp
le
Size
Conditi
onal
Probabi
lity of
Failure
Conditi
onal
Probabi
lity
Standar
d
Error
Survi
val
Fail
ure
Survi
val
Stand
ard
Error
Media
n
Resid
ual
Lifeti
me
Media
n
Stand
ard
Error
Evaluated at the
Midpoint of the Interval
[Low
er,
Upp
er) PDF
PDF
Stand
ard
Error
Hazar
d
Hazar
d
Stand
ard
Error
0 5 0 0 24.0 0 0
1.000
0 0 0
31.75
02
2.704
6 0 . 0 .
5 10 0 0 24.0 0 0
1.000
0 0 0
26.75
02
2.704
6 0 . 0 .
10 15 3 0 24.0 0.1250 0.0675
1.000
0 0 0
21.75
02
2.704
6
0.02
50
0.013
5
0.026
667
0.015
362
15 20 2 1 20.5 0.0976 0.0655
0.875
0
0.12
50
0.067
5
18.40
64
2.560
6
0.01
71
0.011
5
0.020
513
0.014
486
20 25 2 0 18.0 0.1111 0.0741
0.789
6
0.21
04
0.083
7
14.53
75
2.466
0
0.01
75
0.011
8
0.023
529
0.016
609
25 30 3 1 15.5 0.1935 0.1004
0.701
9
0.29
81
0.094
6
17.45
00
8.267
7
0.02
72
0.014
6
0.042
857
0.024
601
30 35 4 0 12.0 0.3333 0.1361
0.566
0
0.43
40
0.103
8
18.75
00
7.577
7
0.03
77
0.016
9 0.08
0.039
192
35 40 0 1 7.5 0 0
0.377
4
0.62
26
0.103
6
17.50
00
2.130
0 0 . 0 .
40 45 1 0 7.0 0.1429 0.1323
0.377
4
0.62
26
0.103
6
12.50
00
2.204
8
0.01
08
0.010
4
0.030
769
0.030
678
45 50 1 0 6.0 0.1667 0.1521
0.323
5
0.67
65
0.101
8
8.333
3
2.041
2
0.01
08
0.010
4
0.036
364
0.036
213
50 55 3 0 5.0 0.6000 0.2191
0.269
5
0.73
05
0.098
1
4.166
7
1.863
4
0.03
23
0.016
7
0.171
429
0.089
424
55 60 1 1 1.5 0.6667 0.3849
0.107
8
0.89
22
0.070
9
3.750
0
3.061
9
0.01
44
0.012
6 0.2
0.173
205
60 . 0 0 0.0 0 0
0.035
9
0.96
41
0.047
8 . . . . . .
(b) R-

7. Life Table Survival Estimates
Interval
Num
ber
Faile
d
Numb
er
Censo
red
Effect
ive
Samp
le
Size
Conditi
onal
Probab
ility of
Failure
Conditi
onal
Probab
ility
Standa
rd
Error
Survi
val
Fail
ure
Survi
val
Stand
ard
Error
Medi
an
Resid
ual
Lifeti
me
Media
n
Stand
ard
Error
Evaluated at the
Midpoint of the Interval
[Low
er,
Upp
er) PDF
PDF
Stand
ard
Error
Hazar
d
Hazar
d
Stand
ard
Error
0 5 0 0 25.0 0 0
1.000
0 0 0
44.23
88
10.65
22 0 . 0 .
5 10 0 0 25.0 0 0
1.000
0 0 0
39.23
88
10.65
22 0 . 0 .
10 15 0 0 25.0 0 0
1.000
0 0 0
34.23
88
10.65
22 0 . 0 .
15 20 2 1 24.5 0.0816 0.0553
1.000
0 0 0
29.23
88
10.76
04
0.01
63
0.011
1
0.017
021
0.012
025
20 25 2 0 22.0 0.0909 0.0613
0.918
4
0.08
16
0.055
3
28.41
59
9.931
8
0.01
67
0.011
3
0.019
048
0.013
453
25 30 4 0 20.0 0.2000 0.0894
0.834
9
0.16
51
0.075
5
26.25
18
4.471
7
0.03
34
0.015
2
0.044
444
0.022
085
30 35 1 0 16.0 0.0625 0.0605
0.667
9
0.33
21
0.096
0
25.14
18
2.256
2
0.00
835
0.008
17
0.012
903
0.012
897
35 40 2 1 14.5 0.1379 0.0906
0.626
2
0.37
38
0.098
7
20.70
59
2.221
9
0.01
73
0.011
7
0.029
63
0.020
894
40 45 1 1 11.5 0.0870 0.0831
0.539
8
0.46
02
0.102
2
16.87
29
2.150
8
0.00
939
0.009
14
0.018
182
0.018
163
45 50 1 0 10.0 0.1000 0.0949
0.492
9
0.50
71
0.103
6
12.50
71
2.105
9
0.00
986
0.009
58
0.021
053
0.021
023
50 55 2 1 8.5 0.2353 0.1455
0.443
6
0.55
64
0.104
3
8.173
1
2.055
8
0.02
09
0.013
8
0.053
333
0.037
376
55 60 3 1 5.5 0.5455 0.2123
0.339
2
0.66
08
0.102
6
4.583
3
1.954
3
0.03
70
0.018
2 0.15
0.080
283
60 . 0 2 1.0 0 0
0.154
2
0.84
58
0.085
8 . . . . . .
(b) RC-

8. Life Table Survival Estimates
Interval
Num
ber
Faile
d
Numb
er
Censo
red
Effect
ive
Samp
le
Size
Conditi
onal
Probab
ility of
Failure
Conditi
onal
Probab
ility
Standa
rd
Error
Survi
val
Fail
ure
Survi
val
Stand
ard
Error
Medi
an
Resid
ual
Lifeti
me
Media
n
Stand
ard
Error
Evaluated at the
Midpoint of the Interval
[Low
er,
Upp
er) PDF
PDF
Stand
ard
Error
Hazar
d
Hazar
d
Stand
ard
Error
0 5 0 0 27.0 0 0
1.000
0 0 0
35.07
50
5.759
1 0 . 0 .
5 10 1 0 27.0 0.0370 0.0363
1.000
0 0 0
30.07
50
5.759
1
0.00
741
0.007
27
0.007
547
0.007
546
10 15 1 0 26.0 0.0385 0.0377
0.963
0
0.03
70
0.036
3
26.18
33
5.651
4
0.00
741
0.007
27
0.007
843
0.007
842
15 20 3 0 25.0 0.1200 0.0650
0.925
9
0.07
41
0.050
4
22.29
17
5.541
7
0.02
22
0.012
1
0.025
532
0.014
711
20 25 2 0 22.0 0.0909 0.0613
0.814
8
0.18
52
0.074
8
21.17
17
9.877
2
0.01
48
0.010
1
0.019
048
0.013
453
25 30 4 2 19.0 0.2105 0.0935
0.740
7
0.25
93
0.084
3
25.09
02
2.273
5
0.03
12
0.014
3
0.047
059
0.023
366
30 35 2 0 14.0 0.1429 0.0935
0.584
8
0.41
52
0.096
1
22.17
65
2.090
9
0.01
67
0.011
3
0.030
769
0.021
693
35 40 2 0 12.0 0.1667 0.1076
0.501
3
0.49
87
0.098
9
18.29
41
1.935
8
0.01
67
0.011
3
0.036
364
0.025
607
40 45 1 1 9.5 0.1053 0.0996
0.417
7
0.58
23
0.098
5
14.41
18
1.813
1
0.00
879
0.008
57
0.022
222
0.022
188
45 50 0 2 7.0 0 0
0.373
7
0.62
63
0.097
4
10.00
00
1.889
8 0 . 0 .
50 55 3 0 6.0 0.5000 0.2041
0.373
7
0.62
63
0.097
4
5.000
0
2.041
2
0.03
74
0.018
1
0.133
333
0.072
577
55 60 2 0 3.0 0.6667 0.2722
0.186
9
0.81
31
0.090
5
3.750
0
2.165
1
0.02
49
0.015
8 0.2
0.122
474
60 . 0 1 0.5 0 0
0.062
3
0.93
77
0.059
1 . . . . . .
Goodness of Fit test
In thissectionwe will performthe goodnessof fittestunder the differentdistributionandwe will select
the appropriate distributionaccordingtothe AICvalue (the lowerthe better).
Conclusion-Fromthe tablesof the SASoutputwe will selectLogNormal distributionasourmodel for
fittingthe data.

9. Detailsof the SASoutputare giveninthe followingmanner-
SAS Output-
Exponential Distribution-
Fit Statistics
-2 Log Likelihood 175.956
AIC (smaller is better) 177.956
AICC (smaller is better)178.010
BIC (smaller is better) 180.287
Analysis of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error95% Confidence LimitsChi-Square Pr > ChiSq
Intercept 1 3.4570 0.1089 3.2436 3.6704 1007.79 <.0001
Scale 0 1.0000 0.0000 1.0000 1.0000
Weibull Scale 1 31.7213 3.4543 25.6246 39.2684
Weibull Shape 0 1.0000 0.0000 1.0000 1.0000
Weibull distribution-
Fit Statistics
-2 Log Likelihood 154.835
AIC (smaller is better) 158.835
AICC (smaller is better)159.000
BIC (smaller is better) 163.497
Analysis of Maximum Likelihood Parameter Estimates
Parameter DF Estimate
Standard
Error95% Confidence LimitsChi-Square Pr > ChiSq
Intercept 1 3.4570 0.0853 3.2899 3.6241 1643.79 <.0001
Scale 1 0.4830 0.0615 0.3763 0.6199
Weibull Scale 1 31.7213 2.7047 26.8394 37.4912
Weibull Shape 1 2.0703 0.2636 1.6131 2.6573

10. Log Normal Distribution-
Fit Statistics
-2 Log Likelihood 128.013
AIC (smaller is better) 132.013
AICC (smaller is better)132.177
BIC (smaller is better) 136.674
Analysis of Maximum Likelihood Parameter Estimates
ParameterDF Estimate
Standard
Error95% Confidence LimitsChi-Square Pr > ChiSq
Intercept 1 3.4570 0.0578 3.3436 3.5703 3573.43 <.0001
Scale 1 0.4830 0.0381 0.4138 0.5637
Log logisticDistribution-
Fit Statistics
-2 Log Likelihood 139.573
AIC (smaller is better) 143.573
AICC (smaller is better)143.737
BIC (smaller is better) 148.234
Analysis of Maximum Likelihood Parameter Estimates
ParameterDF Estimate
Standard
Error95% Confidence LimitsChi-Square Pr > ChiSq
Intercept 1 3.4570 0.0969 3.2671 3.6469 1272.89 <.0001
Scale 1 0.4830 0.1005 0.3212 0.7263
Gamma Distribution-
Fit Statistics
-2 Log Likelihood 154.835
AIC (smaller is better) 160.835
AICC (smaller is better)161.169
BIC (smaller is better) 167.827

11. Analysis of Maximum Likelihood Parameter Estimates
ParameterDF Estimate
Standard
Error95% Confidence LimitsChi-Square Pr > ChiSq
Intercept 1 3.4570 0.0853 3.2899 3.6241 1643.79 <.0001
Scale 1 0.4830 0.0615 0.3763 0.6199
Shape 0 1.0000 0.0000 1.0000 1.0000
Interpretation-The AICvale of Lognormal distributionis132.013 whichisthe smallestamongstthe
otherdistributions,hence Lognormal distributionisthe appropriate model forfittingthe givendataset.
Pictorial Representation
Survival function-
Most real life survival curves are not portrayed as smooth curves as in this example. Instead,
they are usually shown as staircase curves with a "step" down each time there is a death. This is
because a real-world survival curve represents the actual experience of a particular group of
people. At the moment of each death, the proportion of survivor’s decreases and the
proportion of survivors does not change at any other time. Thus the curve steps down at each
death and is flat in between deaths which leads to the classic staircase appearance.
While a staircase does represent the actual experience of the group whose survival is portrayed
in the curve, it does not mean that the risk of an individual patient occurs in discrete steps at
specific times as shown in these curves.
With staircase curves, as the group of patients is larger, the step down caused by each death is
smaller. If the times of the deaths are plotted accurately, then we can see that as the size of the
group increases the staircase will become closer and closer to the ideal of a smooth curve

12. Interpretation-
The curves may compare results from different treatments as in the above graph. If one curve is
continuously "above" the other, as with these curves, the conclusion is that the treatment
associated with the higher curve was more effective for these patients. There are many ways
the two curves could compare. They might be very close to each other indicating there was no
difference between the treatments. If a dangerously toxic treatment resulted in more long term
survivors than a less dangerous treatment, the curve for the riskier treatment might be lower
than the other curve due to early treatment deaths, but end up further off the deck in the end.
Now from the above graph it is quite clear that the graph of R(radiotherapy) is above the rest
stating that it might be the superior treatment compared to RC and CTMtreatments. Although
for all of the treatments the survival graph is getting closer to zero in long run indicating low
survival rate for all, which is quite obvious since we are dealing with a fatal disease like breast
cancer.
Often it may be unclear whether two curves are really different or whether it is reasonable to
assume the difference between them may be just due to chance. There are tests of significance

13. for survival curves, such as the log rank test, and we will often see a "p value" given with
comparative survival curves to indicate whether the difference is statistically significant. This is
explained in the next section
Hazard Function-
The nonparametric hazard plot enables one to examine the hazard function without any
distribution assumption. This plot may indicate which parametric distribution would be
appropriate for modeling your data should you decide to use parametric estimation methods.
One can interpret the nonparametric hazard plot the same way as one would interpret the
parametric hazard plot. The major difference is that the nonparametric hazard plot is a step
function whereas the parametric hazard plot is a smoothed function.

14. Interpretation-
From the above graph it is quite evident that the hazard plot of the cancer patients getting the
treatment of CTM and RC are increasing than the cancer patients receiving the R treatment.
Hence the breast cancer patients receiving the CTM and RC treatment do not respond that well
compared to that of the treatment R, stating treatment R is much better.
Test of Homogeneity data table from SAS
Let us consider the following tests-
H0: the treatments (or characteristics) being compared are all the same vs H1: Not H0.

15. Using proc lifetest we get the following SAS output for homogeneity test-
Rank Statistics
treatment Log-RankWilcoxon
CTM 5.0743 200.00
R -6.1580 -243.00
RC 1.0837 43.00
Covariance Matrix for the Log-Rank
Statistics
treatment CTM R RC
CTM 10.5217 -5.5701 -4.9516
R -5.570113.3057 -7.7357
RC -4.9516 -7.735712.6873
Covariance Matrix for the Wilcoxon
Statistics
treatment CTM R RC
CTM 26460.0-13342.1-13118.0
R -13342.1 29660.3-16318.2
RC -13118.0-16318.2 29436.2
Test of Equality over Strata
Test Chi-Square DF
Pr >
Chi-Square
Log-Rank 3.6109 2 0.1644
Wilcoxon 2.3929 2 0.3023
-2Log(LR) 1.1913 2 0.5512
Interpretation-The ranktestsforhomogeneityindicate asignificantdifference betweenthe treatments
(p=0.1644 forthe log-ranktestandp=0.3023 for the Wilcoxontest).
The corresponding chi-square p-value of Log-rank test being 0.1644, hence at α-.05 level of
significance we accept the null hypothesis H0, stating that there is no significant difference in
the difference of the treatments.
The p-value corresponding to the chi-square value of Wilcoxon test also supports our argument.
Conclusion
When not every patient responds to a treatment, as is nearly always the case in cancer therapy,
each trial will accrue some patients who will be responders, and others who, unfortunately, will
not be responders. By random chance, some of these trials will happen to get more responders
and thus show a higher response rate than others. If the trials are small enough and there are
enough trials, probably a few of these identical trials will get a much higher response rate than
the others.

16. From the statistical homogeneity table we can conclude that the three treatments are not
much of any difference for the test subject of 76 breast cancer patients. But from the survival
graph one may argue that treatment R stands out to be little better compared to the rest.
Moreover from the hazard plot, the hazard curve of both of the treatments CTMand RC are
highly increasing compared to that of the treatment R, supporting our argument.
So with the given small data set we can conclude that although all of the treatments for the
breast cancer patients hold significantly no difference and with low survival rate, but treatment
R might edge out to be little bit better than the rest.
Recommendation
If there is a high response rate in a small trial and we conduct one more small trial of the same
treatment and also get a high response rate this is evidence that the true response rate really is
relatively high - because the chances of randomly getting a much higher response rate than the
true response rate in any one small trial is small - getting such results twice in a row is not likely.
If the trials are larger, the chance of getting misleading results in the first place is smaller. So we
can conclude that on a long run, that is if we collect more sample clinical data we might get a
clearer picture as which treatment is best or whether they have any significantly different
impact or not.