Statistics you can use:Practical use of statistics in reading medical research literaturePAS 610

June 21, 2005

Robert D. Hadley

PhD, PA-C

The basics:

““There are three kinds of lies: lies, damned There are three kinds of lies: lies, damned lies, and statistics.”lies, and statistics.”

Benjamin Disraeli, British politician (1804 - 1881)

The value of statistics:

Four economists are going to a meeting on the same train as four statisticians. The economists can't help noticing that the statisticians only buy a single ticket, where they bought four. When they inquire, the statisticians say, "Don't worry, you'll see."

They get on the train, and when the conductor starts in their car the four statisticians all lock themselves in the WC. When the conductor knocks on the WC door and yells "TICKET", they slide the ticket out under the door, and the conductor stamps it and slides it back. After he's gone, the statisticians emerge.

At the station on the way back from the meeting, the economists buy only one ticket, but they can't help noticing that the statisticians don't buy any. When they inquire, the statisticians say, "Don't worry, you'll see.“

As the conductor approaches their car, the economists all pile in the nearest WC and lock the door. One of the statisticians goes and knocks on the door; the economists slide the ticket out. The statisticians take the ticket and lock themselves in the WC at the other end of the car, repeating their maneuver of the previous trip. The economists get thrown off the train.

Moral: Don't use statistical methods you don't understand.

“Practical” vs. STA 570

Ways to represent dataSample vs. population

Ways to compare data e.g. Chi-square, Student’s t-test, ANOVA/

ANCOVA, Odds ratios and CI, Cox proportional hazard model, Spearman ranked correlation coefficients, multivariate regression analysis

Appropriateness of test for the way data were collected

Terms: basics

Mean Median

Quartiles, tertiles, etc. Mode Rank Nominal Ordinal Population Sample Variance Standard deviation

Normal distribution Z-scores, T-scores Correlation Parametric vs.

Nonparametric Hypothesis testing

1- vs. 2-tailed Significance levels Confidence intervals Statistical power

Terms: medical literature-specific Intention to treat Kaplan-Meier curves ROC curves Meta-analysis representations Odds ratios/Relative Risk Risk reduction Number needed to treat

Over what time period? For what outcome?

Number needed to harm

Concepts

Descriptive vs. inferential statistics Type I and II errors

DescriptiveDescriptive StatisticsStatistics DescriptiveDescriptive StatisticsStatistics

InferentialInferential StatisticsStatistics InferentialInferential StatisticsStatistics

IncludesIncludes Collecting Organizing Summarizing Presenting data

IncludesIncludes Making inferences Hypothesis testing Determining relationships Making predictions

Inferential errors

Type I (alpha)

Incorrectly reject the null hypothesis

Infer that something is significant when it is not

Type II (beta)

Incorrectly accept the null hypothesis

Infer that something is not significant when it really is

So, which is better to do?

Which way does “intention to treat” skew the inference?

Study design

Ask the right question in the right way

Statistical power

Choose the appropriate sample size

Standard deviation and Z-scores

Note: “normal” range for lab tests is ± 2 s.d.

Z and T scores in medicine

Bone density data are reported as T-scores and Z-scores. T-scores represent the number of SDs from the normal young adult mean bone density values, whereas Z-scores represent the number of SDs from the normal mean value for age- and sex-matched control subjects.

Results showing Z-scores of −2.0 or lower may suggest a secondary cause of osteoporosis.

Osteoporosis drug treatment

Data Representation

Relative risk, odds ratios, likelihood ratios, hazard ratios

Odds ratios in meta-analyses

Relative risk

What do unequal CI bars mean?

Meta-analyses

“Gold standard” is randomized, placebo-controlled, multi-center, double blind clinical trial

“Platinum standard” is a meta-analysis of multiple “gold standard” trials by different investigators addressing the same question (rarely available)

Can make use of small studies that by themselves do not achieve statistical significance

Meta-analyses

How it’s done: Search on a specific topic Use predefined inclusion/exclusion criteria

for studies that relate to topic• e.g. must be RCT, must measure same specific

outcome (like cardiovascular events), etc. Combine all studies that meet criteria Use statistics appropriate to the way data

were gathered in the included studies Arrive at a conclusion that was impossible

with the individual studies that were included

Other anti-platelet drug (Reg. 1)

Aspirin (Reg. 2)

Antiplatelet therapy for CVD

BMJBMJ 2002; 324:71-86 2002; 324:71-86

Data Representation

Kaplan-Meier survivorship, and cumulative incidence of events

Both are a cumulative measure of something happening

Kaplan-Meier

Bortezomib or High-Dose Dexamethasone for Relapsed Multiple Myeloma

N Engl J Med 2005;352:2487-98

Use of quintiles to choose cutoff points

0

1

2

3

4

Years

Cu

mu

lati

ve i

nci

den

ce (

%)

ASCOT-LLA: Trial Stopped Nearly 2 Years Early

Sever PS et al. Lancet. 2003;361:1149-1158.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

36% RRR nonfatal MI + fatal CHD(P =.0005)

Atorvastatin 10 mg No. of events: 100Placebo (diet and exercise only) No. of events: 154

All patients counseled ondiet and exercise

What is approximate NNT for 1 year?

Data Representation

2x2, PPV, Chi-Square ROC curves

ROC

Receiver operator characteristic curvesRadar operators’ ability to distinguish

signal from noise Higher area under curve (AUC),

higher reliability for a given test Plot true positives vs. false positives

ROC

ROC value: 0.65 (0.61-0.70)

Data Representation

Correlationmany statistical methods

Correlation of clinical data

Correlation of clinical data

Is r=0.16 a strong correlation?

Can we conclude that CRP and LDL are related?

Box plots (not common)

25th percentile, median and 75th percentile indicated in each box

Other interesting data representation

Neater than a true scatter plot

Simple to interpret

Nissen et al, N Engl J Med 2005;352:29-38

An example:

Peterson RC, Thomas RG, Grandman M, Bennet D, Doody R, Ferris S, et al. Vitamin E and Donepezil for the Treatment of Mild Cognitive Impairment. N Engl J Med 2005;352:2379-88.

Available at: http://content.nejm.org/cgi/content/full/352/23/2379

Questions:

What kind of study is this? How large is the study? What are the inclusion/exclusion criteria? What is the outcome measured? What is the intervention? What are the statistical tests, and are they

appropriate? What data representations are used? Is the result statistically significant? Is the result clinically significant? How does this knowledge affect my practice?