introduction statistics are increasingly prevalent in medical practice, and for those doing...

Introduction

• Statistics are increasingly prevalent in medical practice, and for those doing research, statistical issues are fundamental. It is extremely important therefore, to understand basic statistical ideas relating to research design and data analysis, and to be familiar with the most commonly used methods of analysis.

• Although data analysis is certainly an important part of the statistical process, there is an equally vital role to be played in the design of the research project. Without a properly designed study, the subsequent analysis may be unsafe, and/or a complete waste of time and resources.

• Types of data • Descriptive statistics• Data distributions• Comparative statistics• Non-parametric tests• Paired data• Comparison of several means• Comparing proportions• Exploring the relationship between 2

variables• Correlation• Linear regression• Survival analysis

Pro

po

rtio

n o

f to

tal

Platelet count

0 100 400 1000 1500

0

.05

.1

.15

900

Types of Data

• Categorical– binary or dichotomous e.g.

diabetic/non-diabetic, smoker/non-smoker

– nominal e.g. AB/B/AB/O, short-sighted/long-sighted/normal

– ordered categorical (ordinal) e.g. stage 1/2/3/4, mild/moderate/severe

• Discrete numerical - e.g. number of children - 0/1/2/3/4/5+

• Continuous - e.g. Blood pressure, age • Other types of data

– ranks, e.g. preference between treatments– percentages, e.g. % oxygen uptake– rates or ratios, e.g. numbers of infant

deaths/1000– scores, e.g. Apgar score for evaluating new-

born babies– visual analogue scales, e.g. perception of pain– survival data – two components, outcome and

time to outcome

Descriptive Statistics • For continuous variables there are a

number of useful descriptive statistics– Mean - equal to the sum of the observations

divided by the number of observations, also known as the arithmetic mean

– Median - the value that comes half-way when the data are ranked in order

– Mode - the most common value observed – Standard Deviation - is a measure of the

average deviation (or distance) of the observations from the mean

– Standard Error of the mean - is measure of the uncertainty of a single sample mean as an estimate of the population mean

Data Distributions

• Frequency distribution – If there are more than about 20

observations, a useful first step in summarizing quantitative data is to form a frequency distribution. This is a table showing the number of observations at different values or within certain ranges. If this is then plotted as a bar diagram a frequency distribution is obtained.

0 - 66.061.0 - 62.057.0 - 58.053.0 - 54.049.0 - 50.045.0 - 46.041.0 - 42.037.0 - 38.033.0 - 34.029.0 - 30.025.0 - 26.021.0 - 22.017.0 - 18.0

Histogram of patient ages for HD

Frequency

80

70

60

50

40

30

20

10

0

Std. Dev = 11.43

Mean = 34.3

N = 1712.00

The Normal Distribution • In practice it is found that a reasonable

description of many variables is provided by the normal distribution (Gaussian distribution). The curve of the normal distribution is symmetrical about the mean and bell-shaped. The bell is tall and narrow for small standard deviations, and short and wide for large ones.

PARAP

90.0

85.0

80.0

75.0

70.0

65.0

60.0

55.0

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.0

0.0

paraprotein in myeloma

Frequency

20

18

16

14

12

10

8

6

4

2

0

Std. Dev = 18.81

Mean = 33.0

N = 103.00

PARAP

90.0

85.0

80.0

75.0

70.0

65.0

60.0

55.0

50.0

45.0

40.0

35.0

30.0

25.0

20.0

15.0

10.0

5.0

0.0

20

18

16

14

12

10

8

6

4

2

0

Std. Dev = 18.81

Mean = 33.0

N = 103.00

Duration of disease (y)

32.030.028.026.024.022.020.018.016.014.012.010.08.06.04.02.00.0

Duration of disease pre ASCT for HD

Frequency

700

600

500

400

300

200

100

0

Std. Dev = 3.90

Mean = 3.2

N = 1676.00

Descriptives

3.1813 9.515E-02

2.9946

3.3679

2.5920

1.8000

15.174

3.8954

.10

33.40

33.30

2.3000

3.115 .060

12.507 .119

Mean

Lower Bound

Upper Bound

95% ConfidenceInterval for Mean

5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

DODStatistic Std. Error

Comparative statistics • When there are two or more sets of

observations from a study there are two types of design that must be distinguished: independent or paired. The design will determine the method of statistical analysis

• If the observations are from different groups of individuals, e.g. ages of males and females, or spectacle use in diabetics/non-diabetics, then the data is independent. The sample size may vary from group to group

• If each set of observations is made on the same group of individuals, e.g. WBC count pre- and post- treatment, then the data is said to be paired. This indicates that the observations are on the same individuals rather than from independent samples, and so we have the same number of observations in each set of data

Independent data

• With independent continuous data, we are interested in the mean difference between the groups, but the variability between subjects becomes important. This is because the two sample t test (the most common test used), is based on the assumption that each set of observations is sampled from a population with a Normal Distribution, and that the variances of the two populations are the same.

Non-parametric test

• If the continuous data is not normally distributed, or the standard deviations are very different, a non-parametric alternative to the t test known as the Mann-Whitney test can be utilised (another derivation of the same test is due to Wilcoxon)

1967314N =

MMSTAGE

4.003.002.001.00

BET2MG

30

25

20

15

10

5

0

93

94107109

111752

Group Statistics

67 3.6006 1.45738 .17805

19 7.5179 5.14869 1.18119

MMSTAGE3.00

4.00

BET2MGN Mean Std. Deviation

Std. ErrorMean

Independent Samples Test

11.739 .001 -5.559 84 .000 -3.9173 .70463 -5.31852 -2.51607

-3.279 18.825 .004 -3.9173 1.19453 -6.41906 -1.41553

Equal variancesassumed

Equal variancesnot assumed

BET2MGF Sig.

Levene's Test forEquality of Variances

t df Sig. (2-tailed)Mean

DifferenceStd. ErrorDifference Lower Upper

95% ConfidenceInterval of the

Difference

t-test for Equality of Means

T-test

Mann-Whitney Test

Ranks

67 36.78 2464.50

19 67.18 1276.50

86

MMSTAGE3.00

4.00

Total

BET2MGN Mean Rank Sum of Ranks

Test Statisticsa

186.500

2464.500

-4.685

<0.0001

Mann-Whitney U

Wilcoxon W

Z

Asymp. Sig. (2-tailed)

BET2MG

Grouping Variable: MMSTAGEa.

Group Statistics

4 2.1050 .40673 .20337

31 2.7852 .96692 .17366

MMSTAGE1.00

2.00

BET2MGN Mean Std. Deviation

Std. ErrorMean


.964 .333 -1.377 33 .178 -.6802 .49411 -1.68544 .32512

-2.543 8.518 .033 -.6802 .26743 -1.29039 -.06993



BET2MGF Sig.





Difference


Test Statisticsb

27.000

37.000

-1.816

.069

.073a

Mann-Whitney U

Wilcoxon W

Z


Exact Sig. [2*(1-tailedSig.)]

BET2MG

Not corrected for ties.a.

Grouping Variable: MMSTAGEb.

122141N =

TBIDOSE

14.412

NEUTS

60

50

40

30

20

10

0

327

83416

444

577

743

3

Neutrophil engraftment following allogeneic SCT for CML

141 88.1% 19 11.9% 160 100.0%

122 95.3% 6 4.7% 128 100.0%

TBIDOSE12

14.4

NEUTSN Percent N Percent N Percent

Valid Missing Total

Cases

Descriptives

22.9787 .5816

21.8289

24.1286

22.5816

22.0000

47.692

6.9060

11.00

56.00

45.00

9.0000

1.162 .204

3.184 .406

26.6148 .5544

25.5172

27.7123

26.1184

26.0000

37.495

6.1233

15.00

53.00

38.00

7.2500

1.453 .219

4.157 .435

Mean

Lower Bound

Upper Bound


5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

Mean

Lower Bound

Upper Bound


5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

TBIDOSE12

14.4

NEUTSStatistic Std. Error

NEUTS

55.050.045.040.035.030.025.020.015.010.0

50

40

30

20

10

0

NEUTS

55.050.045.040.035.030.025.020.015.0

50

40

30

20

10

0

98128N =

TBIDOSE

14.412

PLATES

200

100

0

62302

135

561462190

66294

444371416

87327

2631084349287

43

3

Platelet engraftment following allogeneic SCT for CML

128 80.0% 32 20.0% 160 100.0%

98 76.6% 30 23.4% 128 100.0%

TBIDOSE12

14.4

PLATESN Percent N Percent N Percent

Valid Missing Total

Cases

Descriptives

32.7891 1.6694

29.4857

36.0924

30.5556

29.5000

356.703

18.8866

14.00

186.00

172.00

11.7500

5.244 .214

37.479 .425

42.8776 3.9481

35.0417

50.7134

37.1973

27.0000

1527.572

39.0842

14.00

185.00

171.00

18.0000

2.368 .244

4.780 .483

Mean

Lower Bound

Upper Bound


5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

Mean

Lower Bound

Upper Bound


5% Trimmed Mean

Median

Variance

Std. Deviation

Minimum

Maximum

Range

Interquartile Range

Skewness

Kurtosis

TBIDOSE12

14.4

PLATESStatistic Std. Error

PLATES

190.0

180.0

170.0

160.0

150.0

140.0

130.0

120.0

110.0

100.0

90.0

80.0

70.0

60.0

50.0

40.0

30.0

20.0

10.0

40

30

20

10

0

PLATES

195.0

185.0

175.0

165.0

155.0

145.0

135.0

125.0

115.0

105.0

95.0

85.0

75.0

65.0

55.0

45.0

35.0

25.0

15.0

5.0

60

50

40

30

20

10

0

Group Statistics

141 22.9787 6.9060 .5816

122 26.6148 6.1233 .5544

128 32.7891 18.8866 1.6694

98 42.8776 39.0842 3.9481

TBIDOSE12

14.4

12

14.4

NEUTS

PLATES

N Mean Std. DeviationStd. Error

Mean


2.291 .131 -4.486 261 .000 -3.6360 .8105 -5.2320 -2.0401

-4.525 260.837 .000 -3.6360 .8035 -5.2182 -2.0539

28.139 .000 -2.557 224 .011 -10.0885 3.9448 -17.8622 -2.3148

-2.354 131.572 .020 -10.0885 4.2865 -18.5679 -1.6091





NEUTS

PLATES

F Sig.





Difference


Test Statistics

6172.500 5543.500

11023.500 15554.500

-.204 -4.977

0.83 0.0006

Mann-Whitney U

Wilcoxon W

Z

P-value (2-tailed)

PLATES NEUTS

Describing continuous data

• If the data is normally distributed– Mean and standard deviation

• If the data is skewed or non-normally distributed or is from a small sample (N<20)– Median and range

Comparison of several means

• Data sets comprising more than two groups are common, and their analysis often involves the comparison of the means for the component subgroups. It is obviously possible to compare each pair of groups using t tests, but this is not a good approach. It is far better to use a single analysis that enables us to look at all the data in one go, and the method of choice is called analysis of variance

• If the data are not normally distributed or have different variances, a non-parametric equivalent to the analysis of variance can be used, and is known as the Kruskal-Wallis test

Paired data• When we have more than one group of

observations it is vital to distinguish the case where the data are paired from that where the groups are independent. Paired data arise when the same individuals are studied more than once, usually in different circumstances. Also, when we have two different groups of subjects who have been individually matched, for example in a matched pair case-control study, then we should treat the data as paired.

• A one sample t test is used to examine the data. The value t is calculated from– t = sample mean - hypothesised mean

standard error of sample mean

• In a paired analysis where one set of observations are subtracted from the other set, the hypothesised mean is zero. Thus the calculation of the t statistic reduces to – t = sample mean / standard error of sample

mean

• The non-parametric equivalent to this test is the Wilcoxon matched pairs signed rank sum test

Ratio AZU1/GAPDHSamples CD34 MNC

A1 2273 0.0379 0.4328A2 3667 0.0007 0.1021A3 2943 0.0003 0.0007A5 2334 0.014 0.0226A6 1759 0.0696 0.5604A8 2164 0.0349 0.3249

A10 3022a 0.159 0.2487

I1 1503 0.6225 0.9253I2 1684 0.0647 1.4268I5 1615 0.2571 0.2516

Wilcoxon Signed Ranks Test

Test Statisticsb

-2.599a

.009

Z


MNC - CD34

Based on negative ranks.a.

Wilcoxon Signed Ranks Testb.

Telomere length in Dyskeratosis Congenitaparent child-4.7163 -6.6238-4.7163 -5.9629-4.7163 -6.1392-3.8798 -0.6173-1.4062 -2.2264-5.1662 -5.4028-2.2144 -3.6383-4.439 -2.0056-4.2654 -6.7593-4.9991 -3.8157-0.5679 -2.5027-5.3408 -6.4229-1.2779 -5.1118-1.2779 -3.9373-4.1954 -5.9093-0.1936 0.42620.1764 -1.5093-1.0408 2.45081.0755 0.38980.1737 1.4716-2.1199 -0.4074-2.3117 1.34261.2593 1.65270.5821 1.37010.5821 -1.4691.3701 4.27721.3701 -1.2765-1.469 -1.4892-1.469 0.8735

Paired Samples Test

-.1303 2.09654 .38932 -.9278 .6672 -.335 28 .740CHILD - PARENTPair 1Mean Std. Deviation

Std. ErrorMean Lower Upper


Difference

Paired Differences

t df Sig. (2-tailed)

Paired Samples Statistics

-2.0335 29 3.13806 .58272

-1.9032 29 2.27896 .42319

CHILD

PARENT

Pair1

Mean N Std. DeviationStd. Error

Mean

Comparison of groups : continuous data

• Paired on non-paired?

• If non-paired and normally distributed with similar variances : T-test

• If non-paired non-normally distributed or with non-similar variances or very small numbers : Mann-Whitney test

• Paired data – paired t-test or Wilcoxon Signed Ranks Test

Comparing Proportions• Qualitative or categorical data is best

presented in the form of table, such that one variable defines the rows, and the categories for the other variable define the columns. Thus in a European study of ASCT for HD, patient gender was compared between the UK and Europe

• The data are arranged in a contingency table • Individuals are assigned to the appropriate

cell of the contingency table according to their values for the two variables

COUNTRYG * PSEX Crosstabulation

Count

16 610 828 1454

100 160 260

16 710 988 1714

europe

uk

COUNTRYG

Total

Female Male

PSEX

Total

COUNTRYG * PSEXG Crosstabulation

828 610 1438

57.6% 42.4% 100.0%

83.8% 85.9% 84.7%

160 100 260

61.5% 38.5% 100.0%

16.2% 14.1% 15.3%

988 710 1698

58.2% 41.8% 100.0%

100.0% 100.0% 100.0%

Count

% within COUNTRYG

% within PSEXG

Count

% within COUNTRYG

% within PSEXG

Count

% within COUNTRYG

% within PSEXG

europe

uk

COUNTRYG

Total

1.00 2.00

PSEXG

Total

Chi-squared test (2)

• A chi-squared test (2) is used to test whether there is an association between the row variable and the column variable. When the table has only two rows or two columns this is equivalent to the comparison of proportions.

• The first step in interpreting contingency table data is to calculate appropriate proportions or percentages. The chi-squared test compares the observed numbers in each of the four categories and compares them with the numbers expected if there were no difference between the distribution of patient gender

• The greater the differences between the observed and expected numbers, the larger the value of 2 and the less likely it is that the difference is due to chance

COUNTRYG * PSEXG Crosstabulation

828 610 1438

57.6% 42.4% 100.0%

83.8% 85.9% 84.7%

160 100 260

61.5% 38.5% 100.0%

16.2% 14.1% 15.3%

988 710 1698

58.2% 41.8% 100.0%

100.0% 100.0% 100.0%

Count

% within COUNTRYG

% within PSEXG

Count

% within COUNTRYG

% within PSEXG

Count

% within COUNTRYG

% within PSEXG

europe

uk

COUNTRYG

Total

1.00 2.00

PSEXG

Total

Chi-Square Tests

1.418b 1 .234

1.260 1 .262

1.428 1 .232

.246 .131

1.417 1 .234

1698

Pearson Chi-Square

Continuity Correction a

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

Value dfAsymp. Sig.(2-sided)

Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count is108.72.

b.

Fisher’s Exact Test

• When the overall total of the table is less than 20, or if it is between 20 and 40 with the smallest of the four expected values is less than 5, then Fisher’s Exact Test should be used.

Crosstab

15 15

100.0% 100.0%

88.2% 83.3%

2 1 3

66.7% 33.3% 100.0%

11.8% 100.0% 16.7%

17 1 18

94.4% 5.6% 100.0%

100.0% 100.0% 100.0%

Count

% within SURV

% within TRMV

Count

% within SURV

% within TRMV

Count

% within SURV

% within TRMV

.00

1.00

SURV

Total

DISG3.00

.00 1.00

TRMV

Total

Chi-Square Tests

5.294b 1 .021

.847 1 .357

3.905 1 .048

.167 .167

5.000 1 .025

18

Pearson Chi-Square

Continuity Correction a

Likelihood Ratio

Fisher's Exact Test

Linear-by-LinearAssociation

N of Valid Cases

DISG3.00

Value dfAsymp. Sig.(2-sided)

Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

3 cells (75.0%) have expected count less than 5. The minimum expected count is .17.b.

• The chi-squared test can also be applied to larger tables, generally called r x c tables, where r denotes the number of rows in the table, and c the number of columns.

• The standard chi-squared test for a 2 x c table is a general test to assess whether there are differences among the c proportions. When the categories in the columns have a natural order, however, a more sensitive test is to look for an increasing (or decreasing) trend in the proportions over the columns. This trend can be tested using the chi-squared test for trend.

Cesarean section

Shoe Size

<4 4 4.5 5 5.5 6 Total

Yes 5 7 6 7 8 10 43

No 17 28 36 41 46 140 308

• In the table below the relation between frequency of Cesarean section and maternal foot size is presented

• The standard chi-squared test of this 2 x 6 table gives and a 2 value of 9.29, with 5 d.f., for which P=0.098. Analysis of the data for trend gives a 2

trend = 8.02, with 1 d.f. (P=0.005). Thus there is strong evidence of a linear trend in the proportion of women giving birth by Cesarean section in relation to shoe size. This relation is not causal, but reflects that shoe size is a convenient indicator of small pelvic size

Categorical data – comparing proportions

• Studies where there are 2 groups and the total number of patients > 40 : Chi-squared test

• Studies where there are 2 groups and the total number of patients < 40 or if more than 40 and a single cell has less than 5 : Fisher’s Exact Test

• Studies where there are more than 2 groups but not ordered : - Chi-squared test

• Studies where there are more than 2 groups which are ordered : - Chi-squared test for trend

Exploring the relationship between two variables

• Three possible purposes :– a.) assess association e.g. body

weight and blood pressure – b.) prediction e.g. height and weight

– c.) assess agreement e.g. blood pressure measurement

Correlation• Method for investigating the linear

association between two continuous variables

• The association is measured by the correlation coefficient

• A correlation between two variables shows that they are associated but does not necessarily imply a ‘cause and effect’ relationship

• A t test is used to test whether the correlation coefficient obtained is significantly different from zero, or in other words whether the observed correlation could simply be due to chance

• The significance level is a function of both the size of the correlation coefficient and the number of observations. A weak correlation may therefore be statistically significant if based on a large number of observations, while a strong correlation may fail to achieve significance if there are only a few observations

Correlations

1 -.393** .620** .395**

. .000 .000 .000

121 121 121 121

-.393** 1 -.220* -.465**

.000 . .015 .000

121 121 121 121

.620** -.220* 1 .152

.000 .015 . .097

121 121 121 121

.395** -.465** .152 1

.000 .000 .097

121 121 121 121

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

BET2MG

OPG

CRP

NTX

BET2MG OPG CRP NTX

Correlation is significant at the 0.01 level (2-tailed).**.

Correlation is significant at the 0.05 level (2-tailed).*.

OPG

20100

CRP

300

200

100

0

P=0.015

BET2MG

3020100

CRP

210

180

150

120

90

60

30

0

P=<0.0001

Problems with correlation analyses

• Biological systems are multifactoral so a simple two-way correlation may not be a true reflection of what is being observed

• Spurious correlations

FOOT SIZE

12108642

READING ABILITY

110

100

90

80

70

60

50

40

30

Assessing agreement

• Neither correlation nor linear regression are appropriate

• There may be a very high correlation, but one method gives a systematically higher/lower reading

• Linear regression, the data is not independent

• The only appropriate way is to subtract one observation from the other, and plot against an index variable

Correlation between PCR and TAQman for measuring MRD

1.000

107

.739 1.000

0.0006

107 107

Pearson Correlation

Sig. (2-tailed)

N

Pearson Correlation

Sig. (2-tailed)

N

PCR

TAQ

PCR TAQ

TAQ

.7.6.5.4.3.2.10.0

PCR

.7

.6

.5

.4

.3

.2

.1

0.0

SAMPLE

120100806040200

DIFFER

.2

.1

0.0

-.1

-.2

-.3

-.4

-.5

Paired Samples Test

2.830E-02 8.117E-02 7.847E-03 1.274E-02 4.386E-02 3.606 106 0.0002PCR - TAQMean Std. Deviation

Std. ErrorMean Lower Upper


Difference

Paired Differences

t df Sig. (2-tailed)

Linear regression

• Linear regression gives the equation of the straight line that describes how the y variable increases (or decreases) with an increase in the x variable. y is commonly called the dependent variable, and x the independent, or explanatory variable

• A t test is used to test whether the gradient b differs significantly from a specified value (usually zero)

• Assumptions– for any value of x, y must be normally

distributed– the magnitude of the scatter of the

points about the regression line is the same throughout the length of the line

– the relation between the two variables should be linear

AGE

706050403020100

TLENGTH

22

20

18

16

14

12

AGE

706050403020100

Telomer length

22

20

18

16

14

12

Coefficientsa

17.893 .317 56.390 .000

-.049 .010 -.462 -4.809 .000

(Constant)

AGE

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig.

Dependent Variable: TLENGTHa.

AGE

706050403020100

Unstandardized Residual

4

3

2

1

0

-1

-2

-3

-4

Practical application

• Y = mx + c

• Telomere length = age * -0.049 + 17.89

• Substituting in the above equation for ages of 30 and 60

• 16.42 = 30*-0.049 +17.89

• 14.95 = 60*-0.049 +17.89

AGE

706050403020100

Telomer length

22

20

18

16

14

12

Survival data

• Has 2 components

• The event of interest and the time to the event

• Special statistical methods are required – it is not appropriate to use tests for categorical data

Life Table Analysis

• Survival data are usually summarised as survival or Kaplan-Meier curves

• Based on a series of conditional probabilities

• For example, the probability of a patient surviving 10 days after a transplant, is the probability of surviving nine days, multiplied by the probability of surviving the 10th day given that the patient survived the first nine days.

0 40 80 120 160 200 240 280 320

Days post BMT

0123456789

101112131415

Pat

ien

t n

um

ber

Alive

Dead

Table 1. Life table for fifteen patients who received an allogeneic stem cell transplant Time (days) Status Number at risk Probability of

survivalStandard error

16* 0 15 1.00

26 1 14 0.93 0.069

66 1 13 0.86 0.094

69* 0 12

74 1 11 0.78 0.113

82* 0 10

88 1 9 0.69 0.129

89* 0 8

117* 0 7

133* 0 6

144* 0 5

172* 0 4

252* 0 3

291* 0 2

305* 0 1

0 50 100 150 200 250 300 3500

20

40

60

80

100

Days post BMT

Pro

bab

ility

%

Outcomes suitable for Kaplan-Meier analyses

• Survival (event of interest is death, patients alive are censored)

• Disease-free survival (events of interest are either death or disease relapse, patients alive and in remission are censored)

• Primary graft failure• Acute graft versus host disease

0 1 2 3 4 5

Years post BMT

0

20

40

60

80

100

Pro

ba

bil

ity

(%

)Overall and leukaemia-free survival for 111 patients with CML

67%

LFS

OS

45%

in CP allografted with stem cells from HLA-identical sibling donors

HH/ICSM May 2003

0 60 120 180 240 300 360

Days post BMT

0

5

10

15

20

Pro

bab

ility

of

gra

ft f

ailu

re (

%)

Graft failure following BMT for 1stCP CML with a VUD

ICSM/HH April 2003

13.2 Gy (n=57)9%

14.4 Gy (n=44)0%

0 28 56 84 112 140 168 196 224 252 280 308 336 364

Days post BMT

0

20

40

60

80

100

Pro

ba

bili

ty o

f C

MV

re

ac

tiv

ati

on

(%

)CMV reactivation following BMT with a VUD

ICSM/HH May 2003

35%

43%

effect of ganciclovir treatment

prophylactic treatment (n=49)

post infection treatment (n=72)

Use of computers for data collection/analysis

• Decide what data needs collecting (for statistical purposes) and then try if appropriate design a form (this is best done in a database, eg Microsoft ACCESS)

• Get the computer to do as much of the work as possible. ie calculation of ages, surface area etc

• Think ahead to what format the spreadsheet/stats package requires the data to be in

• For analysis purposes, its much easier to work with numbers and codes, as opposed to descriptions ie instead of male/female or m/f, use 1 or 2

• Use a ‘code’ to identify missing data, eg 999 or something ‘unlikely’

• Check the data before analysis, get ‘descriptive statistics’

• Use appropriate statistical methods • Statistical packages - SPSS, BMDP,

STATA, Statgraphics, MINITAB, STATXACT, GENSTAT, SAS

Presentation of results• Where possible give actual P values rather than

ranges– ie P=0.041 rather than P<0.05

• If a P value is not significant give the actual value and not just NS– ie P=0.15 rather than P=NS

• When presenting data it may be more useful to present confidence intervals rather than a P-value– ie lens A was more durable than lens B by 2.4 days

(P=0.03), it might be more informative to write - lens A was more durable than lens B by 2.4 days (95%CI 0.3-4.5days)

• It is not necessary to give test results– ie t=33.5, 28 dof, P=0.0001

• If a continuous variable is normally distributed present, as a description of the data, the mean and standard deviation, if not normally distributed, a median and range

• Don’t quote more significant figures than necessary – ie mean patient age 34.2550 (std dev

11.4337), 34.3 (std dev 11.4) will suffice

0.000

0.200

0.400

0.600

0.800

1.000

1.200

32D xl-1 xl-2 xl-3 xl-4 xl-5 xl-6 32DP210

Cell Line

Adhesion to FN (A

490

absorbance units)

3636N =

GROUP

XL2

.8

.6

.4

.2

0.0

8

Writing the statistics section in a paper

• If power calculations were used to calculate the sample sizes, details should be given– eg Based on samples sizes of x in each arm, we

should have been able to detect a difference of y given 80% power at a significance level of 0.05.

• State which statistical tests were used (reference obscure ones). – eg in order to investigate the differences between

the groups, a t-test was used for continuous data, and a chi-squared test for categorical data

• If applicable, state whether standard deviations or standard errors are quoted

• State whether p-values are from one or two-tailed tests– eg all quoted p-values are two-tailed

• Not necessary to quote which stats package was used

Suggested Reading Material

• Essentials of Medical Statistics – Betty Kirkwood

• Practical Statistics for Medical Research– Doug Altman

• Statistical Methods in Medical Research– Armitage and Berry

Summary

• If at all possible - consult a statistician before starting your study

• Get a feel of your data by plotting results - don’t rely on descriptive statistics alone

• Use appropriate statistical tests, not those that give the ‘best’ results

introduction statistics are increasingly prevalent in medical practice, and for those doing...

Documents

set of data slide

group slide

outcome slide

error slide

mildmoderatesevere slide

wilcoxon slide

ttest slide

data analysis