Stats for Non-staticians

7/29/2019 Stats for Non-staticians

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Statistics for

Non-Statisticians


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THE BASIC IDEA

Statistics are used in clinical trials to make inferencesabout new treatments based on the evidence of thepatients in the trial E.g. New drug for treatment of lung cancer does it

work or not?

Ideally design trial that includes all patients with lungcancer Not really practical!!

Can only test the new treatment on a representativesample of the population

Statistics allow us to draw conclusions about the likelyeffect on the population using data from the sample


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USING STATISTICS

But what exactly do we want the

statistics to assess:-

Assess the weight of evidence that atreatment works (ordoesnt)

Give an estimate (and likely range) of the

treatment effect Test to see how likely it is that this effect

would have been seen by chance


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Statistics can neverPROVEanything

beyond anydoubt, just beyondreasonable doubt!!

BUT


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STATISTICAL DATA

ANALYSIS METHODS


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WHO TO INCLUDE?

In any clinical trial, one is likely to find:

Ineligible patients included by mistake

Protocol violators those who dont adhere tothe treatment regimen allocated

Patients who withdraw or get lost to follow-up

To avoid bias, keep these to a minimum

Follow-up all patients randomised into a trial

Should we include them in the analysis?


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INTENTION TO TREAT ANALYSIS

As a general rule, all patients randomisedshould be analysed by treatment allocated(regardless of whether they actuallyreceived this treatment)

INTENTION TO TREAT ANALYSIS

Reasons for ITT:

Avoids or certainly minimises risk of bias

Is more pragmatic reflects real life


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HYPOTHESIS TESTING

We want to compare the outcomes in differenttreatment arms (A and B)

Testing two hypotheses H0: A=B (Null hypothesis no difference) H1:AB

Calculate test statistic based on the assumption

that H0 is true (i.e. there is no real difference) Test will give us a p-value: how likely are the

collected data if H0 is true

If this is unlikely (small p-value), we reject H0


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THE LURE OF THE P-VALUE

The p-value is the probability of having observed our datawhen the null hypothesis is true

Typically if the p-value is less than 0.05, people say that thetrial gives statistically significant evidence that there is a

difference

Tend to ignore results where p-value greater than 0.05

However, 0.05 is a purely arbitrary value, and not really thatsmall one time in twenty we will reject H0 wrongly! That is state difference exists, when one doesnt (false positive)

Dont become wedded to the p-value: there is not much

difference between 0.051 and 0.049


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ESTIMATE OF TREATMENT EFFECT

Better still, use the data collected in the trial

to give an estimate of the treatment effectsize, together with a measure of how

certain we are of our estimate


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CONFIDENCE INTERVALS (CI)

To determine the true treatment effect, we calculate theconfidence interval for our point estimate

CI is a range of values within which the true treatment effectis believed to be found, with a given level of confidence.

95% CI is a range of values within which the truetreatment effect will lie 95% of the time

Generally, 95% CI is calculated as

Sample Estimate 1.96 x Standard Error

Use the confidence interval to assess the true treatmenteffect, and not just p-values


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DATA ANALYSIS

How do we do this?

What type of analysis should be performed?

Depending on the sort of outcome measure,

different types of analysis are appropriate

Because the actual analyses are now done mainlyby computer, the skill is now:-

In choosing the appropriate test

Correctly interpreting the results


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COMMON OUTCOME MEASURES

Categorical

Continuous

Survival


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CATEGORICAL DATA

Outcomes like good/bad, yes/no or present/absent

In testing categorical data, we are looking to see if

there is any relationship between the outcomecategory and the treatment given H0: No association between variables

H1: Association between variables

For categorical data, the chi-squared test isappropriate if the categories arent ordered

For ordered categories, use a trend test


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Dead Alive Total

Aspirin 804 7783 8587

No Aspirin 1016 7584 8600

Total 1820 15,367 17,187

ISIS TRIAL OF ASPIRIN TO

PREVENT MORTALITY AFTER MI

- Use chi-squared test of association to determine whether to reject the nullhypothesis of no association between aspirin and death


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Dead Alive Total

Aspirin 804 (E=909.3) 7783 (E=7677.7) 8587

No Aspirin 1016 (E=910.7) 7584 (E=7689.3) 8600

Total 1820 15,367 17,187

ISIS TRIAL OF ASPIRIN TO

PREVENT MORTALITY AFTER MI

- Use chi-squared test of association to determine whether to reject the nullhypothesis of no association between aspirin and death

- X21 = (804 909.3)2 / 909.3 + + (7584 7689.3)2 / 7689.3 = 27.26

- X21 = 27.26 (P


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MEASURES OF TREATMENT EFFECT

Tested hypothesis and found strong evidence of anassociation between aspirin use and mortality

Not very informative - is aspirin harmful orbeneficial?

Various measures of treatment effect:- Absolute Risk Reduction

Number Needed to Treat

Relative Risk

Relative Risk Reduction

Odds Ratio

Odds Reduction


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ODDS RATIO & ODDS REDUCTION

Odds ratio = (804 x 7584) / (7783 x 1016) = 0.77


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SUMMARISING BINARY DATA IN TWO

GROUP PROSPECTIVE STUDY

Risk in standard treatment (P1) and Risk in new treatment (P2)

Term Formula ISIS Example

Absolute Risk

Reduction (ARR)

P1

- P2

0.118 0.094 = 0.024

(i.e. 2.4% in favour of new Rx)

Number needed to

treat/harm (NNT/NNH)

1 / |P1 - P2| 1 / 0.024 = 41.7, so NNT = 42

(i.e. need to treat 42 patients with

aspirin in order to prevent 1 death)

Relative Risk (RR) P2 / P1 0.094 / 0.118 = 0.80 (


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CONTINUOUS DATA

Outcomes like blood pressure, weight or scores,summarised using measures of the centre and spread ofthe distribution

Measures of the centre of the distribution Mean: what we think of as an average add up all data and divide

by number of items

Median: midpoint of the data half data below median, and otherhalf above

Mode: most popular observation

Measures of spread Variance and standard deviation

Standard deviation is average distance individual observations arefrom the mean


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CONTINUOUS DATA

In continuous data, we are comparing the

means in the two groups and assessing

whether the two groups come from the

same population H0: Mean A = Mean B

H1: Mean A Mean B

Use Students t-test

ANOVA if comparing >2 treatment groups


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NORMAL DISTRIBUTION

T-test and ANOVA assumes data are Normally distributed However, if the data are very skew or have multiple peaks,

we use a non-parametric testwhich doesnt assume anyparticular shape for the data Wilcoxon Mann-Whitney

As a rule, non-parametric tests are more general, but lesssensitive


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N Mean SDTreatment A 41 91mmHg 5.5

Treatment B 43 95mmHg 5.5

STUDY COMPARING TWO ANTI-

HYPERTENSIVE DRUGS ON BP

- Use Students t-test to assess whether means are from the same population

(i.e. Mean with Treatment A = Mean with Treatment B)

Diastolic BP compared in two groups of hypertensive patients given

two different drug treatments


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TESTING FOR A DIFFERENCE

Treatment A: N=41, Mean=91mmHg, SD=5.5

Treatment B: N=43, Mean=95mmHg, SD=5.5

Use t-test to assess evidence for or against nullhypothesis (mean A = mean B)

t-test = -3.33 on 82 df (df=n1+n2-2)

P=0.0013

So there is evidence against H0 Evidence that the mean diastolic BP in the two

treatment groups are different


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MEASURE OF TREATMENT EFFECT

Tested hypothesis and found evidence that mean diastolic BP in twogroups are different

Not very informative which of treatment A or B is better?

Point estimate of the treatment effect - calculate the difference betweenthe two means and the confidence interval Difference = 91 95mmHg = -4mmHg (favours treatment A)

95% CI: -6.39 to -1.61mmHg

So the difference in mean diastolic BP between groups is statistically

significant (P=0.0013) With treatment A being more effective in reducing diastolic BP

However, the observed difference of 4mmHg in favour of treatment A,could be as small as 1.6mmHg or as large as 6.4mmHg.


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SURVIVAL DATA

Why are survival data different? Interested in studying the time between randomisation

and a subsequent event (say death)

These times are unlikely to be normally distributed

Cannot afford to wait until events have happened to allsubjects, for example until all are dead.

Some people may have left the study early and becomelost to follow up - only information we have about somepatients is that they were still alive at last follow-up.

Use survival analysis methods to analyse time toevent data, not just the number of events Take into account that not all patients may have had an

event


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KAPLAN-MEIER SURVIVAL ANALYSIS

Basic idea: we split the trial up into distinct time

intervals

In each time interval: a certain number, N, patients

enter that time period alive and still on follow-up, andsome of these, D, have an event:

Then the probability of surviving that time interval

(assuming you live that long) is (1-D/N) Multiply all these probabilities together to give the

probability of survival up to a given time point


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EXAMPLE SURVIVAL FUNCTION

Time in Weeks

120100806040200

1.0

.8

.6

.4

.2

0.0

Survival Function

Censored


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Dead Alive Median

Survival

Total

IFN 151 187 ~4 years 338

No IFN 156 180 ~4 years 336

Total 307 367 674

AIM-HIGH TRIAL OF INTERFERON

FOR MALIGNANT MELANOMA

Want to assess whether the time to death is the same for the two treatments?


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COMPARING SURVIVAL

BETWEEN GROUPS

We will have two graphs: how do we say whether

one group survives longer than the other?

Could do one test at say 1 year; compare proportions (as

before) Could keep testing at small intervals

What are the drawbacks to these methods?

Use logrank test to determine whether survival

function the same for two treatment groups

H0: Survival function/curve same for both groups

H1: Survival function/curve different across groups


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SURVIVAL IN MELANOMA:

INTERFERON VS. OBSERVATION


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MEASURE OF TREATMENT EFFECT

Assessed the evidence and found that there is no evidencethat time to death differs between the treatment groups

Despite lack of difference should still calculate pointestimate and confidence interval for treatment effect

Use cox regression to calculate hazard ratio andconfidence interval HR=0.94 (CI=0.75 1.18)

IFN non-significantly reduces the risk of death by 6%, withthe true treatment effect based on the confidence intervalranging from a 25% reduction in mortality to an adverse18% increase in mortality with IFN.


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ANALYSES GOOD PRACTICE

Report the primary/secondary outcomes as statedin the protocol Dont give minor endpoints undue prominence in the

paper

Do not explore all endpoints until you find one thatis significant (data dredging) Looking at multiple outcomes, increases chance of

finding something significant

In 20 outcomes, just by chance 1 outcome will besignificant

Is this real, or the play of chance?

Solution: Dont have too many endpoints


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ANALYSES GOOD PRACTICE

Give confidence intervals where possible,

and not just p-values

Keep subgroup analyses to a minimum

Subgroup analyses should be pre-specified

When interpreting subgroups, assess whole

picture

Do not focus upon one subgroup and

individual p-values


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FINAL WORDS

The idea of statistics is to look at the strength of

the evidence for a given hypothesis and determinethe reliability of the treatment effect observed inthe trial

Calculations are based on formulas, but the

application of the formulas and the interpretationof the results is an art rather than a science

Significance is not black and white P>0.05 is not evidence of absence of effect, merely

absence of evidence of an effect

A little common sense can go a long way inmedical statistics

If in doubt, ask a statistician!


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To call in the statistician after theexperiment is done may be no

more than asking him to perform a

post mortem examination: he maybe able to say what the experiment

died of.

Sir R.A. Fisher

Indian Statistical Congress, Sankhya, c. 1938


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BOOK LIST

Swinscow TDV and Campbell MJ. Statistics at Square One(10th edition). BMJ Books 2002

Campbell MJ. Statistics at Square Two. BMJ Books 2001

Altman D, Machin D, Bryant T and Gardner M. Statistics

with Confidence. BMJ Books 2000

Pereira-Maxwell F.A-Z of Medical Statistics. Arnold1998

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