Clinical Research:Basic Statistics and Appraising

the Literature

Epidemiology and Biostatistics

Epidemiology:Study design andinterpretation

Biostatistics:Methods for analysis

Importance of Understanding Basic Statistics in Medicine

• Research– Design Studies– Plan Analyses– Data Interpretation

• Clinical Medicine– Understanding the

Literature– Evidence-based

practice

Learning the Language

• Sampling

• Variable types– Determine analysis method(s)

• Continuous• Categorical (nominal, ordinal)

• Independent vs. Correlated Data

• Parametric vs. Non-parametric

Sampling: Is the study group representative?

CAD case:Control Studyn=328/groupNon-diabeticMiddle-aged

ItalianMen

Colomba F et al. ATVB 2005; 25: 1032

0

300

600

900

1200

1500

sRA

GE

, p

g/m

L

CAD Cases

Controls

Sampling: Is the study group representative?

Dallas Heart StudyProbability-based sampleOver-sampling Minorities

Statistical Testing: PrinciplesQuestion: Is blood pressure associated with stroke?

Study 1 Study 2

Stroke

No Stroke

Average=136 mm/Hg

132 mm/Hg

Average=136 mm/Hg

132 mm/Hg

Statistical Testing: PrinciplesQuestion: Is blood pressure associated with stroke?

Study 1 Study 2

Stroke

No Stroke132 mm/Hg 132 mm/Hg

Average=136 mm/Hg

Average=136 mm/Hg

Statistical Testing

Observed effect (what we see) – Expected (under null)

Variability of the data

Test Statistic=

Use test statistic to generate a p-value

Learning the Language

• Sampling

• Variable types– Determine analysis method(s)

• Continuous• Categorical (nominal, ordinal)

• Independent vs. Correlated Data

• Parametric vs. Non-parametric

Categorical Data

• Data where the results are in categories of some qualitative trait (yes/no)– Can be nominal or ordinal

Nominal v. Ordinal

• Nominal data (no order to the categories)– Smoking status

(smoker, non-smoker)

– Hair color (blonde, red, black)

– Race (black, white, hispanic, other)

• Ordinal data (order to categories)– Med school year (1st,

2nd, 3rd, 4th)– Heart failure class

(NYHA 1, 2, 3, or 4)

Continuous Data

• Data that are quantitative and measured

• (can perform arithmetic on)

• (can be divided into smaller values)– Blood pressure– Age– Cholesterol levels

Variable Types: Ordinal, Numerical and Categorical

Svensson AM, et al. Eur Heart J 2005; 26: 1255Svensson AM, et al. Eur Heart J 2005; 26: 1255

Learning the Language

• Sampling

• Variable types– Determine anlaysis method(s)

• Continuous• Categorical (nominal, ordinal)

• Independent vs. Correlated Data

• Parametric vs. Non-parametric

Data from Independent Samples

Park L et al. Nat Med 4:1025Park L et al. Nat Med 4:1025

0

40000

80000

120000

160000

MSA sRAGE sRAGE sRAGE sRAGE MSA

Mean LesionArea

3 gIP day-1

15 gIP day-1

20 gIP day-1

40 gIP day-1

Diabetic ApoE null miceDiabetic ApoE null mice ControlApoE null mice

ControlApoE null mice

Baseline 24 Hours Baseline 24 Hours

Control GIK

0

0.5

1

1.5

2

2.5

0

0.5

1

1.5

2

2.5

Data from Repeated Measures: Correlated Data

Addo T, et al. Am J Cardiol 2004; 94: 1288Addo T, et al. Am J Cardiol 2004; 94: 1288

Learning the Language

• Sampling

• Variable types– Determine anlaysis method(s)

• Continuous• Categorical (nominal, ordinal)

• Independent vs. Correlated Data

• Parametric vs. Non-parametric

Parametric (Gaussian) Distribution

Skewed Data

Statistical Tests: What Type of Data?

Nominal Ordinal Parametric Non-Para

Continous Correlated Paired

t-test

Wilcoxon

Sign Rank

Independ t-test Wilcoxon

Rank Sum

Categorical Correlated McNemar

Test

Independ Fisher’s

Exact

Chi-square

trend test

Power and Sample Size

Power: What is it

• Power = (1-):

– The probability of rejecting the null hypothesis when it is false

– English: the probability of detecting a true association between an exposure and an outcome when there is one

Sample Size and Power: The assumptions

• Sample size:– To determine sample size, enter three parameters:

• Power : (80 or 90%)• Effect size

– Control value and variance, or event rate– dependent on parameter of interest– best to have pilot data

• Significance level () : (0.05)– 1-tailed or 2-tailed testing

• (Confounders)– Non-compliance, Cross-overs (Drop Ins/Outs), Lost to follow

up

Standards for Effect Size

• Small –20%

• Medium – 50%

• Large – 80%– only rough guidelines

• Small, medium and large are subject dependent

Adequacy of Sample: Size Matters

Total # of events Sample Size if risk 10%

Power for

25% RRR

Adequacy of size

0-50 (under 500) <10% Utterly inadequate

50-150 (1000) 10-30% Probably inadequate

150-350 (3000) 30-70% Possibly adequate,

possibly not

350-650 (6000) 70-90% Probably adequate

Over 650 (10,000) >90% Definitely Adequate

Effect of trial size on results: 24 trials of -blockade vs. Placebo

Total deaths

Mean Sample

Size

p<0.5 against

Trend against

Trend favorable

p<0.5 favorable

0-50 (255) 0 5 5 0

50-150 (861) 0 1 9 1

150-350 (2925) 0 0 1 2

350-650 N/A - - - -

Over 650 N/A - - - -

TOTAL (866) 0 6 15 3

Ways to Reduce Required Sample Size

• Higher Event Rate– High risk populations– Composite Endpoints

• Larger Effect Size• Lower power• Larger

– 1-tailed or 2

• Change analysis type– Time dependent

Sample size planning

• How much money do you have?

• How much time to you have?

• How many patients/subjects can you expect to reasonably get?

“What sample size and study design can I afford?”

The words to use to describe this

The study was designed to have >80% power to detect an effect

size of >20% with a 2-tailed significance level of 0.05, with a

planned sample size of 400 participants in each group.

Suggested Reading

• Reference texts– Dawson-Saunders B, Trapp RG. Basic and Clinical Biostatistics, Appleton

and Lange, Norwalk, CT, 2nd Edition, 1994.– Sackett DL. Clinical Epidemiology: a basic science for clinical medicine.

Little Brown, Boston, MA, 2nd Edition, 1991.

• Selected papers:– Bias

• Sackett DL. Bias in analytic research. J Chron Dis 1979; 32:51-63

– Power• Moher D, Dulberg CS, Wells GA. Statistical power, sample size, and their

reporting in randomized controlled trials. JAMA 1994; 272: 122-4.

– Subgroup analyses• Assmann SF, Pocock SJ, Enos LE, Kasten LE. Subgroup analysis and other

(mis)use of baseline data in clinical trials. Lancet 2000; 355: 1064-1069.• Yusuf S, Wittes J, Probstfield J, Tyroler HA. Analysis and interpretation of

treatment effects in subgroups of patients in randomized clinical trials. JAMA 1991; 266: 93-98.