An Analysis. Jane Doe Department of Biostatistics Vanderbilt University School of Medicine. March 19, Descriptive Statistics 1

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1 An Analysis Jane Doe Department of Biostatistics Vanderbilt University School of Medicine March 19, 211 Contents 1 Descriptive Statistics 1 2 Redundancy Analysis and Variable Interrelationships 2 3 Logistic Regression Model 3 4 Test Calculations 5 5 Computing Environment 6 1 Descriptive Statistics gethdata ( support ) # Use Hmisc / gethdata to get dataset from VU DataSets wiki d s u b s e t ( support, s e l e c t=c ( age, sex, race, edu, income, hospdead, s l o s, dzgroup, meanbp, hrt ) ) l a t e x ( d e s c r i b e ( d ), f i l e = ' ' ) d 1 Variables 1 Observations age : Age n 1 missing unique 97 Mean lowest : highest: sex n missing unique 1 2 female (438, 44%), male (562, 56%) race n missing unique white black asian other hispanic Frequency % edu : Years of Education n missing unique Mean lowest : , highest: income n missing unique under $11k (39, 47%), $11-$25k (161, 25%), $25-$5k (16, 16%) >$5k (75, 12%) 1

2 2 REDUNDANCY ANALYSIS AND VARIABLE INTERRELATIONSHIPS hospdead : Death in Hospital n missing unique Sum Mean slos : Days from Study Entry to Discharge n missing unique Mean lowest : , highest: dzgroup n 1 missing unique 8 ARF/MOSF w/sepsis COPD CHF Cirrhosis Coma Colon Cancer Lung Cancer Frequency % MOSF w/malig Frequency 86 % 9 meanbp : Mean Arterial Blood Pressure Day 3 n missing unique Mean lowest : , highest: hrt : Heart Rate Day 3 n missing unique Mean lowest : , highest: Race is reduced to three levels (white, black, OTHER) because of low frequencies in other levels (minimum relative frequency set to.5). d updata ( d, r a c e = c o m b i n e. l e v e l s ( race, minlev =. 5 ) ) Input o b j e c t s i z e : 17 bytes ; 1 v a r i a b l e s Modified v a r i a b l e r a c e New o b j e c t s i z e : 1688 bytes ; 1 v a r i a b l e s 2 Redundancy Analysis and Variable Interrelationships v v a r c l u s (., data=d ) p l o t ( v ) redun ( age+sex+r a c e+edu+income+dzgroup+meanbp+hrt, data=d ) Redundancy A n a l y s i s redun ( formula = age + sex + r a c e + edu + income + dzgroup + meanbp + hrt, data = d ) n : 617 p : 8 nk : 3 Number o f NAs : 383 F r e q u e n c i e s o f Missing Values Due to Each V a r i a b l e age sex r a c e edu income dzgroup meanbp hrt Transformation o f t a r g e t v a r i a b l e s f o r c e d to be l i n e a r R 2 c u t o f f :. 9 Type : o r d i n a r y R 2 with which each v a r i a b l e can be p r e d i c t e d from a l l o t h e r v a r i a b l e s : age sex r a c e edu income dzgroup meanbp hrt No redundant v a r i a b l e s 2

3 3 LOGISTIC REGRESSION MODEL # Alternative : redun (., data = subset (d, select = -c ( hospdead, slos ))) Spearman ρ meanbp hospdead dzgroupcoma dzgroupcopd dzgroupmosf w/malig sexmale age hrt dzgroupcirrhosis dzgroupcolon Cancer dzgrouplung Cancer slos dzgroupchf income$11 $25k income$25 $5k racewhite raceblack edu income>$5k Note that the clustering of black with white is not interesting; this just means that these are mutually exclusive higher frequency categories, causing them to be negatively correlated. 3 Logistic Regression Model Here we fit a tentative binary logistic regression model. The coefficients are not very useful so they are not printed. Note: the symbolic section reference below was created by the following R comment: # see Section (*\ref{descstats}*) for descriptive statistics The label was defined in an earlier section using \section{descriptive Statistics}\label{descStats} dd d a t a d i s t ( d ) ; o p t i o n s ( d a t a d i s t= ' dd ' ) f lrm ( hospdead r c s ( age, 4 ) + sex + r a c e + dzgroup + r c s ( meanbp, 5 ), data=d ) # see Section 1 for descriptive statistics p r i n t ( f, l a t e x=true, c o e f s=false) 3

4 3 LOGISTIC REGRESSION MODEL Logistic Regression Model lrm(formula = hospdead ~ rcs(age, 4) + sex + race + dzgroup + rcs(meanbp, 5), data = d) Frequencies of Missing Values Due to Each Variable hospdead age sex race dzgroup meanbp 5 Model Likelihood Discrimination Rank Discrim. Ratio Test Indexes Indexes Obs 995 LR χ R C d.f. 17 g 1.65 D xy Pr(> χ 2 ) <.1 g r 4.98 γ.62 max deriv g p.228 τ a.227 Brier.144 l a t e x ( anova ( f ), where= ' h ', f i l e = ' ' ) # can also try where =' htbp ' Table 1: Wald Statistics for hospdead χ 2 d.f. P age Nonlinear sex race dzgroup <.1 meanbp <.1 Nonlinear <.1 TOTAL NONLINEAR <.1 TOTAL <.1 p r i n t ( p l o t ( P r e d i c t ( f ) ) ) 4

5 4 TEST CALCULATIONS race sex log odds OTHER white black age female dzgroup male meanbp ARwCOPCHFCrrComClCLnCMOw Test Calculations x 3 ; y 2 i f ( x y ) ' t h i s ' e l s e ' that ' [ 1 ] that i f ( y x ) ' that ' e l s e ' t h i s ' [ 1 ] t h i s x y [ 1 ] 9 p l o t ( r u n i f ( 2 ), r u n i f ( 2 ) ) 5

6 REFERENCES runif(2) runif(2) 5 Computing Environment These analyses were done using the following versions of R 1, the operating system, and add-on packages Hmisc 2, rms 3, and others: ˆ R version ( ), x86_64-pc-linux-gnu ˆ Base packages: base, datasets, graphics, grdevices, grid, methods, splines, stats, utils ˆ Other packages: Hmisc 3.8-3, lattice.19-17, rms 3.3-, survival ˆ Loaded via a namespace (and not attached): cluster References [1] R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 21. ISBN , available from [2] Frank E. Harrell. Hmisc: A package of miscellaneous S functions. Available from biostat.mc.vanderbilt. edu/s/hmisc, 211. [3] Frank E. Harrell. rms: S functions for biostatistical/epidemiologic modeling, testing, estimation, validation, graphics, prediction, and typesetting by storing enhanced model design attributes in the fit. Available from biostat.mc.vanderbilt.edu/rms, 211. Implements methods in Regression Modeling Strategies, New York:Springer, 21. 6