# Statistics you can use Practical use of statistics

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Statistics you can use: Practical use of statistics in reading medical research literature PAS 610 June 21, 2005 Robert D. Hadley Ph. D, PA-C

The basics: “There are three kinds of lies: lies, damned 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 data l ¢ Ways to compare data l ¢ Sample vs. population 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 l ¢ ¢ ¢ ¢ Quartiles, tertiles, etc. Mode Rank Nominal Ordinal Population Sample Variance Standard deviation ¢ ¢ ¢ Normal distribution Z-scores, T-scores Correlation Parametric vs. Nonparametric Hypothesis testing l ¢ ¢ ¢ 1 - vs. 2 -tailed Significance levels Confidence intervals Statistical power

Terms: medical literaturespecific ¢ ¢ ¢ ¢ Intention to treat Kaplan-Meier curves ROC curves Meta-analysis representations Odds ratios/Relative Risk reduction Number needed to treat l Over what time period? l For what outcome? Number needed to harm

Concepts Descriptive vs. inferential statistics ¢ Type I and II errors ¢

Descriptive Statistics Includes ü Collecting ü Organizing ü Summarizing ü Presenting data 9 Inferential Statistics Includes ü Making inferences ü Hypothesis testing ü Determining relationships ü Making predictions 3/15/2018

Inferential errors ¢ Type I (alpha) ¢ Type II (beta) ¢ Incorrectly reject the null hypothesis Infer that something is significant when it is not ¢ 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 Zscores 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 Zscores represent the number of SDs from the normal mean value for age- and sexmatched 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, placebocontrolled, 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: l l 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. l l l 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 BMJ 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

ASCOT-LLA: Trial Stopped Nearly 2 Years Early Cumulative incidence (%) 4 Atorvastatin 10 mg No. of events: 100 Placebo (diet and exercise only) No. of events: 154 3 2 36% RRR nonfatal MI + fatal CHD All patients counseled on diet and exercise (P =. 0005) 1 What is approximate NNT for 1 year? 0 0. 5 1. 0 1. 5 2. 0 Years Sever PS et al. Lancet. 2003; 361: 1149 -1158. 2. 5 3. 0 3. 5

Data Representation 2 x 2, PPV, Chi-Square ¢ ROC curves ¢

ROC ¢ Receiver operator characteristic curves l Radar 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 ¢ Correlation l many 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) 25 th percentile, median and 75 th 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?

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