Outline1) Descriptive Statistics 2) Define “association”.3) Practice reading Table 1 for evidence of

confounding, effect modification.

4) Practice reading scatterplots for evidence of confounding effect modification.

5) Review comparing adjusted and unadjusted analysis for confounding effect modification.

6) Read STATA output:saturated model

predicted group summary is actual group summarycorrelationevidence of association from overall hypothesis test

Descriptive Statistics Goals:1) Identify measurement of data entry errors2) Characterize the methods and materials3) Assess the validity of the scientific and statistical assumptions4) Get a straight forward estimate of the association you are interested in5) Explore data to generate hypothesis for future studies

Reporting descriptive analysis:Give the reader the ability to judge the scientific evidence and the importance of your work.

Methods: Describe what you did so that the reader could reproduce your work. Results: Report what you actually realized in this repetition of the research.

Present a preliminary estimate of the association. Indicate whether this sample supported the scientific and statistical

assumptions used to do the statistical analysis.

Association : The distribution of two variables are not independentThe conditional distribution of an outcome variable changes depending on the value of the predictor.

Rather than look at the entire distribution we use a summary measure for the distribution of the outcome and compare the value of that summary measure at different values of the predictor.

http://www.originlab.com/index.aspx?go=Products/Origin/DataAnalysishttp://www.psychstat.missouristate.edu/introbook/sbk16m.htm http://faculty.elgin.edu/dkernler/statistics/ch04/4-4.html

Prior History of Cardiovascular Disease (CVD)

No Prior CVD Prior CVD All Subjects

C reactive protein (mg/L) 3.38 (5.90; 0 - 108; n=3,802 / 3,851) 4.40 (6.88; 0 - 83; n=1,131 / 1,149) 3.61 (6.15; 0 - 108; n=4,933 / 5,000)

Fibrinogen (mg/dL)

CRP: 0 mg/L 277 (48.5; 172 - 436; n=348 / 350) 290 (57.9; 180 - 540; n=78 / 78) 280 (50.5; 172 - 540; n=426 / 428)

CRP: 1 mg/L 298 (48.5; 109 - 482; n=1,238 / 1,246) 304 (52.5; 171 - 532; n=292 / 295) 299 (49.3; 109 - 532; n=1,530 / 1,541)

CRP: 2 mg/L 314 (51.2; 183 - 482; n=835 / 841) 317 (52.5; 138 - 470; n=246 / 247) 314 (51.5; 138 - 482; n=1,081 / 1,088)

CRP: 3-4 mg/L 335 (56.2; 199 - 578; n=711 / 716) 337 (64.2; 204 - 592; n=222 / 224) 336 (58.1; 199 - 592; n=933 / 940)

CRP: 5-8 mg/L 353 (62.6; 132 - 584; n=330 / 333) 365 (70.0; 235 - 662; n=126 / 128) 356 (64.9; 132 - 662; n=456 / 461)

CRP: 9-16 mg/L 377 (70.9; 190 - 624; n=222 / 223) 391 (81.5; 175 - 614; n=110 / 111) 382 (74.7; 175 - 624; n=332 / 334)

CRP: 17-32 mg/L 419 (109.2; 232 - 872; n=59 / 59) 442 (83.0; 270 - 584; n=36 / 36) 428 (100.3; 232 - 872; n=95 / 95)

CRP: > 33 mg/L 498 (115.4; 274 - 741; n=34 / 34) 522 (102.3; 367 - 695; n=12 / 12) 504 (111.5; 274 - 741; n=46 / 46)

CRP: Missing 308 (41.7; 238 - 395; n=14 / 49) 332 (50.2; 296 - 367; n=2 / 18) 311 (41.7; 238 - 395; n=16 / 67)

All Subjects 320 (64.8; 109 - 872; n=3,791 / 3,851) 334 (74.1; 138 - 695; n=1,124 / 1,149) 323 (67.3; 109 - 872; n=4,915 / 5,000)

Descriptive Statistics-

020

040

060

080

0Fi

brin

ogen

mg/

dl

0 20 40 60 80 100C reactive protein mg/L

Crp=0 mg/L Crp=1 mg/L Crp=2 mg/L Crp=3-4 mg/L Crp=5-8 mg/L

Crp=9-16 mg/L Crp=17-32 mg/L Crp>33 mg/L mean(Fib) by Crp Category

Scatter plot Fibrinogen (mg/dl) versus CRP(mg/L)

Straightforward estimate of association. CRP FibAssess the validity of your assumptions (ie confounding,

effect modification)

Straightforward estimate of association. CRP FibAssess the validity of your assumptions (ie confounding,

effect modification)

CVD

3.2

3.7

4.2

4.7

mea

n C

reac

tive

prot

ein

mg/

L

No prior CVD Prior CVDPrevious Cardiovascular Disease

Mean CRP(mg/L) versus CVD history

Straightforward estimate of association.

Assess the validity of your assumptions (ie confounding, effect modification)

CVD Level 1: CRP FIBCVD Level 2: CRP FIB

distribution of outcome is different depending on the value of the predictor.

020

4060

8010

0C

reac

tive

prot

ein

mg/

L

No prior CVD Prior CVDPrevious Cardiovascular Disease

Crp=0 mg/L Crp=1 mg/L Crp=2 mg/L Crp=3-4 mg/L Crp=5-8 mg/L

Crp=9-16 mg/L Crp=17-32 mg/L Crp>33 mg/L mean(Fib) by Crp Category

Scatter plot CRP(mg/L) versus CVD history

But wait, it is not that simple. Effect modification depends on the type of summary measure you use.

http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704-EP713_Confounding-EM/BS704-EP713_Confounding-EM_print.html

RD: no effect modification RD: effect modificationRR: yes effect modification RR: no effect modification

Distribution of POI depends on the value of confounder

With either the additive or multiplicative contrast there is effect modification.

Distribution of POI DOESN”T depend on the value of third variable

The Third Variable (again, but in pictures)

In a saturated regression model , different combinations of the beta parameters can be used to find the summary measure for each group.

Biost 518 Midterm Examination Feb 12, 2014, Page 1 of 1

. g atrophysqr= atrophy^2

. stcox atrophy atrophysqr, robust failure _d: death analysis time _t: obstime Cox regression -- Breslow method for ties No. of subjects = 735 Number of obs = 735 No. of failures = 133 Time at risk = 3630.376453 Wald chi2(2) = 22.72 Log pseudolikelihood = -843.98762 Prob > chi2 = 0.0000 | Robust _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] atrophy | 1.040706 .0291416 1.42 0.154 .985129 1.099419 atrophysqr | .9998931 .000315 -0.34 0.734 .9992759 1.000511

. stcox atrophy, robust failure _d: death analysis time _t: obstime Cox regression -- Breslow method for ties No. of subjects = 735 Number of obs = 735 No. of failures = 133 Time at risk = 3630.376453 Wald chi2(1) = 23.49 Log pseudolikelihood = -844.04581 Prob > chi2 = 0.0000

| Robust _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] atrophy | 1.030879 .0064684 4.85 0.000 1.018278 1.043635

How should I represent my predictor of interest in the regression model?

Testing the null that all regression parameters are simultaneously 0 ==0

Testing the null that all regression parameters are simultaneously 0 =0

Testing the null that only one regression parameter is 0 =0

Testing the null that only one regression parameters is 0 =0

log (𝜆 (𝑡 )∨ h𝑎𝑡𝑟𝑜𝑝 𝑦 )=𝑙𝑜𝑔 (𝜆0 (𝑡))+𝛽1( h𝑎𝑡𝑟𝑜𝑝 𝑦 )

+