PubHlth 640 Intermediate Biostatistics Unit 2 Regression and Correlation

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1 PubHlth 640 Intermediate Biostatistics Unit 2 Regression and Correlation Multiple Linear Regression Software: Stata v 10.1 Human p53 and Breast Cancer Risk Source: Matthews et al. Parity Induced Protection Against Breast Cancer Background: Substantial epidemiologic evidence suggests that early first pregnancy confers a reduced life time risk of breast cancer. In laboratory studies of mice, similar observations have been made. Laboratory studies of mice have also explored the relationship between parity, expression of the tumor suppressor gene p53 and subsequent breast cancer tumor development. Lesley et al hypothesized that mammary tissue cultured from women who had an early full term pregnancy would have increased levels of p53 as compared to nulliparous women and as compared to women whose first full term pregnancy was later in life. Research Question: What is the relationship of Y=p53 expression to parity and age at first pregnancy, after adjustment for current age and established breast cancer risk, specifically the following: age at first mensis, family history of breast cancer, menopausal status, and history of oral contraceptive use? Note Age at first pregnancy is considered in each of two ways: (1) continuous, in years; and (2) age at first pregnancy < 24 years versus age at first pregnancy > 24 years. Design: Observational cohort. \stata_howto\multple linear regression p53 parity.doc Page 1 of 13

2 Data file: p53paper.dta Beware! Stata is case sensitive. All variable names are lower case. Variable Label Definition/Codings p53 P53 continuous parous Parity status 1 = ever parous 0 = not pregnum Number of pregnancies 0 = 0 pregnancies 1 = 1 pregnancy 2 = 2 pregnancies 3 = 3+ pregnancies one 0/1 indicator of 1 pregnancy = 1 if (pregnum=1) 0 otherwise two 0/1 indicator of 2 pregnancies = 1 if (pregnum=2) 0 otherwise threep 0/1 indicator of 2 or more pregnancies = 1 if (pregnum=3) 0 otherwise agepreg1 Age at first pregnancy Continuous, years = missing for never parous early late 0/1 indicator first pregnancy at age < 24 0/1 indicator first pregnancy at age >24 1 = yes 0 = no = missing for never parous 1 = yes 0 = no = missing for never parous agecurr Current age continuous, years agemen Age at first mensis Continuous, years famhx01 0/1 indicator of family history of breast cancer menop 0/1 indicator of post-menopause = 1 if yes 0 otherwise oc 0/1 indicator of ever used oral = 1 if yes contraceptives 0 otherwise = 1 if any family hx of breast ca 0 otherwise \stata_howto\multple linear regression p53 parity.doc Page 2 of 13

3 Key Green: comments in stata begin with an asterisk Black: stata command syntax. Note You do NOT need to type the leading period Blue: Output I have also inserted comments. * toggle off the screen by screen pausing of output. set more off. * FILE > OPEN to read in data p53paper.dta. use "/Users/carolbigelow/Desktop/p53paper.dta". * Compact description of data set. codebook,compact Variable Obs Unique Mean Min Max Label id agecurr agecurr: age current agepreg agepreg1: age at 1st preg pregnum pregnum: number pregnancies agemen agemen: age at 1st mensis menop menop: post menopausal oc oc: oral contraceptives hrt hrt: hormone replacement cycle cycle: cycle days famhx famhx: family hx breast ca p parity parity: parity, grouped early early: early parity late late: late parity parous parous 0/1 one one: 1 pregnancy two two: 2 pregnancies threep threep: 3+ pregnancies famhx famhx01: any family hx * Characteristics of Analysis Sample. tabstat agecurr, stat(n mean sd min max) variable N mean sd min max agecurr tabstat agemen, stat(n mean sd min max) variable N mean sd min max agemen tabstat agepreg1, stat(n mean sd min max) variable N mean sd min max agepreg \stata_howto\multple linear regression p53 parity.doc Page 3 of 13

4 . tabstat p53, stat(n mean sd min max) variable N mean sd min max p Notice that the sample size is 67 instead of 68, suggesting one missing value.. tab famhx01 famhx01: any family hx Freq. Percent Cum tab hrt hrt: hormone replacement Freq. Percent Cum tab menop menop: post menopausal Freq. Percent Cum tab oc oc: oral contracepti ves Freq. Percent Cum tab parous parous 0/1 Freq. Percent Cum \stata_howto\multple linear regression p53 parity.doc Page 4 of 13

5 . tab early early: early parity Freq. Percent Cum tab late late: late parity Freq. Percent Cum tab pregnum pregnum: number pregnancies Freq. Percent Cum * Check normality of distribution of Y=p53. tabstat p53, stat(n mean sd med min max) variable N mean sd p50 min max p * identify tick marks at multiples of sd for use in histogram w overlay normal. display (1* ) display (2* ) display (3* ) display (1* ) display (2* ) display (3* ) * (optional) choose the design you want for your graphs. set scheme s1color \stata_howto\multple linear regression p53 parity.doc Page 5 of 13

6 . * Histogram of Distribution of p53 with tick marks at each sd unit. histogram p53, start(1) bin(8) frequency addlabels normal ylabel(0(5)15, grid) xlabel( "mean" "-1 sd" "-2 sd" "-3 sd" "+1 sd" "+2 sd" "+3 sd") title("histogram of Y=P53") subtitle("overlay Normal") note("p53_graph01.png") (bin=8, start=1, width=.625) Source: p53_graph01.png. * Numeical tests of normality of Y=p53. swilk p53 Shapiro-Wilk W test for normal data Variable Obs W V z Prob>z p sfrancia p53 Shapiro-Francia W' test for normal data Variable Obs W' V' z Prob>z p The non-significance of the Shapiro Wilk and the Shapiro Francia tests suggests that it is okay to assume normality of the distribution of Y=p53 \stata_howto\multple linear regression p53 parity.doc Page 6 of 13

7 . * With modest sample size of n=67, it s a good idea to do a dot plot, too. dotplot p53, msymbol(o) title("dotplot of Y=P53") subtitle("n=67") note("p53_graph02.png") Source: p53_graph02.png - Try rotating this picture in your mind by 90 degrees. This gives a better feel for the bell shape distribution of p53 values. * Step 1 - Fit one predictor models. regress p53 parous F( 1, 65) = 9.96 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = parous _cons \stata_howto\multple linear regression p53 parity.doc Page 7 of 13

8 . regress p53 one two threep F( 3, 63) = 5.58 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = one two threep _cons regress p53 agepreg1 Source SS df MS Number of obs = F( 1, 49) = 2.21 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = agepreg _cons regress p53 early late F( 2, 64) = 6.03 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = early late _cons \stata_howto\multple linear regression p53 parity.doc Page 8 of 13

9 . regress p53 agecurr F( 1, 65) = 1.19 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = agecurr _cons regress p53 agemen Source SS df MS Number of obs = F( 1, 64) = 0.98 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = agemen _cons regress p53 famhx F( 1, 65) = 0.02 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = famhx _cons regress p53 menop F( 1, 65) = 0.13 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = menop _cons \stata_howto\multple linear regression p53 parity.doc Page 9 of 13

10 . regress p53 oc F( 1, 65) = 1.13 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = oc _cons * Step 2 - Fit initial multiple predictor model using candidates from step 1. regress p53 two threep early late F( 4, 62) = 4.21 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep early late _cons * Partial F test for EARLY and LATE controlling for TWO and THREEP. testparm early late ( 1) early = 0 ( 2) late = 0 F( 2, 62) = 0.26 Prob > F = * Step 3 - Fit of the smaller model w predictors in Step 2 with adjusted p <.10. regress p53 two threep F( 2, 64) = 8.35 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep _cons \stata_howto\multple linear regression p53 parity.doc Page 10 of 13

11 - You can check the calculation of this partial F test using the two analysis of variance tables: Partial F = 2,62 = = [SS model(4 predictor model) - SS model(2 predictor model)]/ 4 -(2) SS residual(4 predictor model)/ ( n-1) -(4) [ ]/ [ ] / 62 [ ]. * Step 4 - Assess potential confounding of model by EARLY. * Fit of model without confounder. regress p53 two threep F( 2, 64) = 8.35 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep _cons * fit of model with confounder. regress p53 two threep early F( 3, 63) = 5.63 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep early _cons *partial F test of potential confounder. testparm early ( 1) early = 0 F( 1, 63) = 0.37 Prob > F = ( ) \stata_howto\multple linear regression p53 parity.doc Page 11 of 13

12 . * Step 4 - Assess potential confounding of model by LATE. * Fit of model without confounder. regress p53 two threep F( 2, 64) = 8.35 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep _cons * fit of model with confounder. regress p53 two threep late F( 3, 63) = 5.50 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep late _cons *partial F test of potential confounder. testparm late ( 1) late = 0 F( 1, 63) = 0.04 Prob > F = \stata_howto\multple linear regression p53 parity.doc Page 12 of 13

13 . * Step 5 - Investigation of Modification of TWO and THREEP effects by EARLY. * fit of smaller model again. regress p53 two threep F( 2, 64) = 8.35 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep _cons * fit of smaller model + suspected modifier. regress p53 two threep early F( 3, 63) = 5.63 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = two threep early _cons * Partial F test of suspected modifier. testparm early ( 1) early = 0 F( 1, 63) = 0.37 Prob > F = Thus, the final model contains just TWO and THREEP as predictors (see top of page): ˆ p53 = *TWO *THREEP % variance explained = 20.7% Significance of Overall F test =.0006 \stata_howto\multple linear regression p53 parity.doc Page 13 of 13