Statistics for the Terrified Talk 4: Analysis of Clinical Trial data 30 th September 2010

Statistics for the TerrifiedTalk 4: Analysis of Clinical Trial data

30th September 2010

Janet DunnLouise Hiller

Data types

What type of data do you have?

Categorical

2- levels More than 2 levels

Ordered

Non-

ordered

Continuous

Normally

distributed

Non-normally

distributed

Time to

event

2-level categorical (binary) data

N (%) 1 2 Row total

1 a (%) b (%) a+b

2 c (%) d (%) c+d

Column total a+c b+d n

Variable 1

Variable 2

Frequency Table

2-level categorical (binary) data - Test of association

Null hypothesis: The 2 factors are independent

Chi-squared test, with continuity correction c2=11.4 p=0.0007 Treatment and gender are NOT independent

N (%) 1 2 Row total

Male 55 (58%) 32 (33%) 87

Female 40 (42%) 66 (67%) 106

Column total 95 98 193

Treatment

Gender

2-level categorical (binary) data - Test of association


Commonly used with small numbers, Fisher’s exact test p=0.51 Treatment and gender are independent

N (%) 1 2 Row total

Male 4 (10%) 6 (17%) 10

Female 35 (90%) 30 (83%) 65


Treatment

Gender

2-level categorical (binary) data – Measure of agreementA measure of agreement between reviewers, above

that expected by chance

Kappa k=0.71 (95%CI 0.60-0.83) There is good agreement betweenreviewers

Response No response Row total

Response 74 12 86No response 8 50 58Column total 82 62 144

Reviewer 1

Reviewer 2

Altman guidelines<0.20 poor0.21 - 0.40 fair0.41 - 0.60 moderate0.61 - 0.80 good0.81 - 1.00 very good

2-level categorical (binary) data – Measure of agreementA measure of agreement between reviewers, above

that expected by chance

Kappa k=-0.04 (95%CI -0.24 - 0.15) There is poor agreement betweenreviewers

Response No response Row total

Response 35 25 60No response 25 15 40Column total 60 40 100

Reviewer 1

Reviewer 2


2-level categorical (binary) data – Exploring patterns in the data

Odds ratio (OR): the ratio of the odds of an event occurring in the 1st gp to the odds of it occurring in the 2nd gp

OR=1 - event is equally likely to occur in both gpsOR>1 - event is more likely to occur in 1st gpOR<1 - event is less likely to occur in 1st gp

OR=4.1 (95%CI 2.2-7.9) The odds of a male having a response are 4 times those of a female having a response

Yes No Row totalMale 55 20 75

Female 40 60 100Column total 95 80 175

Response

Gender

2-level categorical (binary) data – Exploring patterns in the data

Relative Risk (RR): the ratio of the risk of an event occurring in the 1st gp to the risk of it occurring in the 2nd gp

RR=1 - event is equally likely to occur in both gpsRR>1 - event is more likely to occur in 1st gpRR<1 - event is less likely to occur in 1st gp

RR=1.7 (95%CI 0.64-4.50) New trt patients are 1.7 times more likely to suffer an SAE than control patients

Yes No Row totalNew trt 10 88 98Control 6 94 100


SAE suffered

Treatment

Odds Ratio/Relative Risk plots

20.5

http://bjo.bmj.com/content/93/3/295.full

Exploring patterns in multivariate data - Logistic Regression• A statistical modelling method that describes the

relationship between a categorical response variable and 1 or more categorical and/or continuous variables

e.g. Association between bearing grudges & medical conditions

OR 95%CI pHeart attack 2.09 1.51 - 2.89 0.0001

High blood pressure 1.47 1.27 - 1.71 0.0001Heart disease 1.64 1.24 - 2.18 0.001

Epilepsy 0.86 0.55 - 1.38 0.59Stroke 0.99 0.66 - 1.49 0.96

Ordered categorical data – Test for trend Null hypothesis: No linear trend between groups

Chi-squared tests for trend c2=10.8 p=0.001 There is a linear trend between groups

N (%) 1 2 Row total

Mild 17 (20%) 32 (38.5%) 49Moderate 29 (35%) 32 (38.5%) 61Severe 38 (45%) 19 (23%) 57


Treatment

Toxicity

Ordered categorical data – Test for trend (>2 rows & columns) Null hypothesis: No linear trend between rows and

columns

Chi-squared tests for trend c2=7.1 p=0.008 There is a linear trend between rows & columns

N (%) 1mg 2mg 3mg Row total

Mild 30 (36%) 19 (23%) 18 (22%) 67Moderate 31 (37%) 32 (38.5%) 27 (33%) 90Severe 22 (27%) 32 (38.5%) 37 (45%) 91

Column total 83 83 82 248

Treatment dose

Toxicity

Ordered categorical data – Measure of agreement

A measure of agreement between reviewers, above that expected by chance

CR PR SD Row totalCR 30 12 8 50PR 17 32 20 69SD 5 22 37 64


Reviewer 1

Reviewer 2


Weighted kappa k=0.38 (95%CI 0.27-0.49) There is fair agreement between reviewers

Non-ordered categorical data - Test of association


Chi-squared test c2=0.51 p=0.78 Treatment and disease site are independent

N (%) 1 2 Row total

Head & Neck 26 (23%) 29 (26%) 55Limbs 32 (28%) 33 (30%) 65Body 55 (49%) 49 (44%) 104


Treatment

Disease site

Non-ordered categorical data – Measure of agreement

A measure of agreement between reviewers, above that expected by chance

A B C Row totalA 30 12 8 50B 17 32 20 69C 5 22 37 64


Reviewer 1

Reviewer 2


Kappa k=0.31 (95%CI 0.20-0.42) There is fair agreement between reviewers

Categorical data – RECAP.

Levels Test of association Measure of agreement

Exploring patterns in the data

2 c2 test with continuity correction;Fisher’s exact test

Kappa Odds Ratio & Relative Risk; Logistic regression

>2 (ordered) c2 test for trend Weighted kappa Not covered

>2 (non-ordered) c2 test Kappa Not covered

Data types


Categorical


Ordered

Non-

ordered

Continuous

Normally

distributed

Non-normally

distributed

Time to

event

Normally distributed data

• Data forms a bell-shaped curve• Non-significant Shapiro-Wilk test result

Mean & Standard Deviation graphTreatments

Cha

nge

over

tim

e in

QO

L (%

)

Parametric tests

• Differences between means of 2 groups– T-tests

• Differences between means of >2 groups– ANOVA– Linear regression

• Correlation– Pearson’s correlation coefficient, r

Non-normally distributed data

http://www.itl.nist.gov/div898/handbook/eda/section3/eda33d6.htm

http://www.nature.com/aja/journal/v11/n1/full/aja200817a.html

http://www.sixsigmatraining.org/non-normal

http://www.gisdevelopment.net/application/agriculture/soil/ma03214pf.htm

Box and Whisker graphs

• Outliers (observations that lie outside of the 95% CIs) are sometimes plotted individually

Box and Whisker graphs

• Parallel box plots show the differences between groups

Non-parametric tests

• Differences between medians of 2 groups– Wilcoxon rank sum test

• Differences between medians of >2 groups– Kruskal-Wallis 1-way analysis of variance test

• Correlation– Spearman’s rank order correlation coefficient, r

Transforming data

• Can transform non-normally distributed data (e.g. logarithm, square root, reciprocal) to make create normally distributed data

• Then analyse transformed data using parametric methods

http://upload.wikimedia.org/wikipedia/commons/0/00/Population_vs_area.svg

http://upload.wikimedia.org/wikipedia/commons/0/00/Population_vs_area.svg

Data types


Categorical


Ordered

Non-

ordered

Continuous

Normally

distributed

Non-normally

distributed

Time to

event

Time-to-event data

• Why is this different to other continuous data?– Censoring

TNO123456

KEY Randomisation date Date of event Censor date

Time 20* 8 8* 14 1* 16*

What time? What event?

• Start date?– Diagnosis– Surgery

• Event?– Onset / worsening of pain– Hospital discharge– Death (OS)– Relapse (RFI/DFI/ Plateau)– Relapse or death (RFS/DFS)

You need to know what you’re looking at to know how to interpret it / what to compare it to

– Randomisation– Start/End of treatment

Time-to-event data analysis (‘Survival Analysis’)

• Can be used to measure time to any event– Arthritic joint remaining pain-free post steroid injections– Elderly patient with a fractured hip remaining in hosp.

• Calculate ‘survival’ time for each patient (some may be censored times)– Recruitment takes place over time so varying lengths of

follow-up are expected• Rank these times and calculate proportions alive at

certain points, with due allowance for incomplete follow-up

• These proportions and times are plotted and overall distributions of curves compared

Time-to-event data

• Why is this different to other continuous data?– Censoring

TNO123456

KEY Randomisation date Date of event Censor date

Time 20* 8 8* 14 1* 16*

Kaplan-Meier Curves

Median survival = 1.3 years

Minimum & median FU indicate the maturity of the data

Kaplan-Meier Curves

0 1 2 3 4 5 6 7 8 9 100

25

50

75

100

ECMFCMF

Years from Surgery

% s

urvi

ving

CMF

Numbers at Risk: ECMF 1189 1171 1120 1073 1020 965 826 606 380 196 53 CMF 1202 1178 1099 1024 957 888 759 564 352 176 55

78%

84%

Undesirable comparisons of survival rates

Statistical tests for time-to-event data • Log-rank tests compare the overall distributions of

the curves (c2 and p-value presented)– Null hypothesis: all curves are samples from

populations with the same risk of the event– Compares the number of deaths observed on each

treatment arm with the number expected under the null hypothesis that the 2 survival distributions are identical

• Cox proportional hazards model (Hazard Ratio, 95% CI’s and p-value presented)– Identifies which variables from a group of several

are independently related to survival– In what order of importance– Gives you a measure of their relation to survival

Forest plots

Deaths/PatientsECMF CMF

ECMF events(O-E) Var

*Hazard Ratio & CI(ECMF : CMF)

*HR & CI(ECMF : CMF)

0.0 0.5 1.0 1.5 2.0ECMF better CMF better* 95% CI99% CI

10:1328JAN08

NOT FOR PUBLICATION OR CITATION

Trial

NEAT 231/1009 278/1012 -29.7 127.1(22.9%) (27.5%)

0.79 (0.63, 0.99)BR9601 47/180 70/190 -12.4 29.2

(26.1%) (36.8%)0.65 (0.41, 1.05)

Subtotal 278/1189 348/1202 -42.1 156.4(23.4%) (29.0%)

0.76 (0.65, 0.89)(P<.001)

= 0.9; P=.35 Interaction between 2 groups 21

Age<=50 151/713 197/699 -30.4 86.8

(21.2%) (28.2%)0.70 (0.53, 0.93)

>50 127/476 151/503 -11.3 69.5(26.7%) (30.0%)

0.85 (0.62, 1.16)

Subtotal 278/1189 348/1202 -41.8 156.3(23.4%) (29.0%)

0.77 (0.65, 0.90)(P<.001)


Menopausal Status

Pre/Peri 156/675 186/679 -18.5 85.4(23.1%) (27.4%)

0.81 (0.61, 1.06)

Post 109/444 149/467 -21.9 64.4(24.5%) (31.9%)

0.71 (0.52, 0.98)

Unknown 13/70 13/56 -1.5 6.4(18.6%) (23.2%)

0.79 (0.28, 2.18)

Subtotal 278/1189 348/1202 -41.9 156.3(23.4%) (29.0%) 0.76 (0.65, 0.89)(P<.001) = 0.6; P=.76Heterogeneity between 3 groups 2

2Performance Status

0 189/837 226/834 -25.2 103.6(22.6%) (27.1%)

0.78 (0.61, 1.01)

1/2 54/202 76/217 -9.6 32.5(26.7%) (35.0%)

0.74 (0.47, 1.17)Unknown 35/150 46/151 -7.4 20.1

(23.3%) (30.5%)0.69 (0.39, 1.23)

Subtotal 278/1189 348/1202 -42.2 156.1(23.4%) (29.0%)

0.76 (0.65, 0.89)(P<.001) = 0.3; P=.86Heterogeneity between 3 groups 2

2Surg ery

Mastectomy 163/615 217/634 -30.5 94.9(26.5%) (34.2%)

0.73 (0.56, 0.94)BCS 113/569 130/563 -12.0 60.7

(19.9%) (23.1%)0.82 (0.59, 1.14)

Subtotal 276/1184 347/1197 -42.5 155.6(23.3%) (29.0%)

0.76 (0.65, 0.89)(P<.001)


Unstratified 278/1189 348/1202 -42.3 156.4(23.4%) (29.0%)

0.76 (0.65, 0.89)(P<.001)






10:1328JAN08


Trial

NEAT 231/1009 278/1012 -29.7 127.1(22.9%) (27.5%)

0.79 (0.63, 0.99)

BR9601 47/180 70/190 -12.4 29.2(26.1%) (36.8%)

0.65 (0.41, 1.05)

Subtotal 278/1189 348/1202 -42.1 156.4(23.4%) (29.0%)

0.76 (0.65, 0.89)(P<.001) = 0.9; P=.35 Interaction between 2 groups 2

1Age

<=50 151/713 197/699 -30.4 86.8(21.2%) (28.2%)

0.70 (0.53, 0.93)

>50 127/476 151/503 -11.3 69.5(26.7%) (30.0%)

0.85 (0.62, 1.16)

Subtotal 278/1189 348/1202 -41.8 156.3(23.4%) (29.0%)


1Menopausal Status

Pre/Peri 156/675 186/679 -18.5 85.4(23.1%) (27.4%)

0.81 (0.61, 1.06)

Post 109/444 149/467 -21.9 64.4(24.5%) (31.9%)

0.71 (0.52, 0.98)

Unknown 13/70 13/56 -1.5 6.4(18.6%) (23.2%)

0.79 (0.28, 2.18)

Subtotal 278/1189 348/1202 -41.9 156.3(23.4%) (29.0%) 0.76 (0.65, 0.89)(P<.001) = 0.6; P=.76Heterogeneity between 3 groups 2

2Performance Status

0 189/837 226/834 -25.2 103.6(22.6%) (27.1%)

0.78 (0.61, 1.01)

1/2 54/202 76/217 -9.6 32.5(26.7%) (35.0%)

0.74 (0.47, 1.17)Unknown 35/150 46/151 -7.4 20.1

(23.3%) (30.5%)0.69 (0.39, 1.23)

Subtotal 278/1189 348/1202 -42.2 156.1(23.4%) (29.0%)


2Surgery

Mastectomy 163/615 217/634 -30.5 94.9(26.5%) (34.2%)

0.73 (0.56, 0.94)

BCS 113/569 130/563 -12.0 60.7(19.9%) (23.1%)

0.82 (0.59, 1.14)

Subtotal 276/1184 347/1197 -42.5 155.6(23.3%) (29.0%)


1

Unstratified 278/1189 348/1202 -42.3 156.4(23.4%) (29.0%)

0.76 (0.65, 0.89)(P<.001)






10:1328JAN08


Trial

NEAT 231/1009 278/1012 -29.7 127.1(22.9%) (27.5%)

0.79 (0.63, 0.99)

BR9601 47/180 70/190 -12.4 29.2(26.1%) (36.8%)

0.65 (0.41, 1.05)

Subtotal 278/1189 348/1202 -42.1 156.4(23.4%) (29.0%)


1Age

<=50 151/713 197/699 -30.4 86.8(21.2%) (28.2%)

0.70 (0.53, 0.93)

>50 127/476 151/503 -11.3 69.5(26.7%) (30.0%)

0.85 (0.62, 1.16)

Subtotal 278/1189 348/1202 -41.8 156.3(23.4%) (29.0%)


1Menopausal Status

Pre/Peri 156/675 186/679 -18.5 85.4(23.1%) (27.4%)

0.81 (0.61, 1.06)Post 109/444 149/467 -21.9 64.4

(24.5%) (31.9%)0.71 (0.52, 0.98)

Unknown 13/70 13/56 -1.5 6.4(18.6%) (23.2%)

0.79 (0.28, 2.18)

Subtotal 278/1189 348/1202 -41.9 156.3(23.4%) (29.0%)


2Performance Status

0 189/837 226/834 -25.2 103.6(22.6%) (27.1%)

0.78 (0.61, 1.01)

1/2 54/202 76/217 -9.6 32.5(26.7%) (35.0%)

0.74 (0.47, 1.17)Unknown 35/150 46/151 -7.4 20.1

(23.3%) (30.5%)0.69 (0.39, 1.23)

Subtotal 278/1189 348/1202 -42.2 156.1(23.4%) (29.0%)


2Surgery

Mastectomy 163/615 217/634 -30.5 94.9(26.5%) (34.2%)

0.73 (0.56, 0.94)BCS 113/569 130/563 -12.0 60.7

(19.9%) (23.1%)0.82 (0.59, 1.14)

Subtotal 276/1184 347/1197 -42.5 155.6(23.3%) (29.0%)


1

Unstratified 278/1189 348/1202 -42.3 156.4(23.4%) (29.0%)

0.76 (0.65, 0.89)(P<.001)

[Bars=95% confidence interval. Size of boxes can represent sample size]

Longitudinal data analysis

• A variable can be measured on the same patient over time (e.g. Baseline, 3 month, 6 month …)

• Can be any type of data (categorical, continuous)

Longitudinal data analysis – Summary Measures

Change from Baseline in Global QOL

CMFECMF

Change at 1 year (p=0.01)

Change at 2 years (p=0.06)

Impr

ovem

ent

Det

erio

ratio

n

TRT ATRT B

Longitudinal data analysis – Modelling

TLCO

SCO

RE (m

mol

/min

/kPa

)

Pulmonary function (TLCO score) over time

Graphs show each patient as a separate line Solid line = Trt A ptsDashed line = Trt B pts

Random effects modelling predicts the average patient score on each treatment arm

Cluster Randomised Trial data

• Patients within 1 cluster are often more likely to respond in a similar manner, and thus can not be assumed to act independently

• ICC = Intracluster Correlation Coefficient. A statistical measure of this dependence– Takes values between 0 and 1– Higher values = greater between-cluster variation.

e.g. Management within sites are consistent but, across different sites, there is wide variation

• Analysis must incorporate the effects of clustering i.e. the values of the ICC and design effect

Useful References

• Gore & Altman – Statistics in Practice

• Bland - An Introduction to Medical Statistics

• Altman - Practical Statistics for Medical Research

• Peto et al - Design and Analysis of Randomized Clinical-Trials Requiring Prolonged Observation of each patient

– 1/ Introduction and Design. British Journal of Cancer 1976. 34(6) 585-612

– 2/ Analysis and Examples. British Journal of Cancer 1977. 35(1) 1-39

Statistics for the Terrified Talk 4: Analysis of Clinical Trial data 30 th September 2010

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Transcript of Statistics for the Terrified Talk 4: Analysis of Clinical Trial data 30 th September 2010