Logistic Model Output
# Model 1 - Hypertension = beta0 + beta1*age
summary(mod1)
##
## Call:
## glm(formula = hyperten ~ age1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.132 -1.319 0.659 0.846 1.136
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.79492 0.20645 -8.69 <2e-16 ***
## age1 0.05737 0.00424 13.52 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5141.9 on 4433 degrees of freedom
## Residual deviance: 4945.2 on 4432 degrees of freedom
## AIC: 4949
##
## Number of Fisher Scoring iterations: 4
#Model 2 - Hypertension = beta0 + beta1* (current smoker)
summary(mod2)
##
## Call:
## glm(formula = hyperten ~ cursmoke1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.752 -1.511 0.697 0.877 0.877
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.2908 0.0512 25.20 < 2e-16 ***
## cursmoke1Yes -0.5330 0.0688 -7.75 9.4e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5141.9 on 4433 degrees of freedom
## Residual deviance: 5081.1 on 4432 degrees of freedom
## AIC: 5085
##
## Number of Fisher Scoring iterations: 4
#Model 3 - Hypertension = beta0 + beta1*(cigs per day)
summary(mod3)
##
## Call:
## glm(formula = hyperten ~ cigpday1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.688 -1.493 0.742 0.790 1.119
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.15003 0.04370 26.32 < 2e-16 ***
## cigpday1 -0.01445 0.00275 -5.25 0.00000016 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5101.8 on 4401 degrees of freedom
## Residual deviance: 5074.8 on 4400 degrees of freedom
## (32 observations deleted due to missingness)
## AIC: 5079
##
## Number of Fisher Scoring iterations: 4
#Model 4 - Hyptertension = beta0 + beta1*(bmi)
summary(mod4)
##
## Call:
## glm(formula = hyperten ~ bmi1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.645 -1.225 0.655 0.824 1.415
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -3.0307 0.2591 -11.7 <2e-16 ***
## bmi1 0.1601 0.0104 15.4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5118.0 on 4414 degrees of freedom
## Residual deviance: 4837.1 on 4413 degrees of freedom
## (19 observations deleted due to missingness)
## AIC: 4841
##
## Number of Fisher Scoring iterations: 4
#Model 5 - Hypertension = beta0 + beta1*(diabetes)
summary(mod5)
##
## Call:
## glm(formula = hyperten ~ diabetes1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.871 -1.620 0.792 0.792 0.792
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9988 0.0343 29.09 <2e-16 ***
## diabetes1Yes 0.5619 0.2425 2.32 0.02 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5141.9 on 4433 degrees of freedom
## Residual deviance: 5135.9 on 4432 degrees of freedom
## AIC: 5140
##
## Number of Fisher Scoring iterations: 4
#model 6 - Hypertension = beta0 + beta1*(Blood Pressure Meds)
summary(mod6)
##
## Call:
## glm(formula = hyperten ~ bpmeds1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.602 -1.602 0.806 0.806 0.806
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9587 0.0344 27.91 <2e-16 ***
## bpmeds1Yes 15.6073 199.9621 0.08 0.94
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5083.8 on 4372 degrees of freedom
## Residual deviance: 4992.1 on 4371 degrees of freedom
## (61 observations deleted due to missingness)
## AIC: 4996
##
## Number of Fisher Scoring iterations: 15
#Model 7 - Hypertension = beta0 + beta1*(Heart Rate)
summary(mod7)
##
## Call:
## glm(formula = hyperten ~ heartrte1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.179 -1.498 0.758 0.815 1.002
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.39215 0.22238 -1.76 0.078 .
## heartrte1 0.01866 0.00295 6.33 2.4e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5141.3 on 4432 degrees of freedom
## Residual deviance: 5099.6 on 4431 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 5104
##
## Number of Fisher Scoring iterations: 4
#Model 8 - Hypertension = beta0 + beta1*(Heart Attacks)
summary(mod8)
##
## Call:
## glm(formula = hyperten ~ prevmi1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.80 -1.62 0.79 0.79 0.79
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.0051 0.0342 29.35 <2e-16 ***
## prevmi1Yes 0.3958 0.2729 1.45 0.15
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5141.9 on 4433 degrees of freedom
## Residual deviance: 5139.6 on 4432 degrees of freedom
## AIC: 5144
##
## Number of Fisher Scoring iterations: 4
#Model 9 - Hypertension = beta0 + beta1*(Systolic Blood Pressure)
summary(mod9)
##
## Call:
## glm(formula = hyperten ~ sysbp1, family = binomial, data = fhs)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.184 -0.677 0.325 0.710 2.381
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -10.79750 0.42166 -25.6 <2e-16 ***
## sysbp1 0.09440 0.00347 27.2 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5141.9 on 4433 degrees of freedom
## Residual deviance: 3781.4 on 4432 degrees of freedom
## AIC: 3785
##
## Number of Fisher Scoring iterations: 6
# Model 10 - Hypertension = beta0 + beta1*(age) + beta2*(current smoker) + beta3*(cigs per day)
#+ beta4*(bmi) + beta5*(diabetes) + beta6*(blood pressure meds) + beta7*(Heart Rate)
#+ beta8*(Heart Attacks) + beta9*(Systolic Blood Pressure)
summary(mod10)
##
## Call:
## glm(formula = hyperten ~ age1 + cursmoke1 + cigpday1 + bmi1 +
## diabetes1 + bpmeds1 + heartrte1 + prevmi1 + sysbp1, family = binomial,
## data = fhs1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.163 -0.628 0.299 0.699 2.430
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.18403 0.57543 -21.17 < 2e-16 ***
## age1 0.00367 0.00525 0.70 0.48
## cursmoke1Yes -0.16833 0.12844 -1.31 0.19
## cigpday1 -0.00313 0.00523 -0.60 0.55
## bmi1 0.07023 0.01238 5.67 1.4e-08 ***
## diabetes1Yes -0.23052 0.31401 -0.73 0.46
## bpmeds1Yes 14.44913 259.60396 0.06 0.96
## heartrte1 0.00228 0.00364 0.63 0.53
## prevmi1Yes 0.17968 0.33732 0.53 0.59
## sysbp1 0.08938 0.00373 23.94 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5019.8 on 4321 degrees of freedom
## Residual deviance: 3606.3 on 4312 degrees of freedom
## AIC: 3626
##
## Number of Fisher Scoring iterations: 16
# Model 11 - Hypertension = beta0 + beta1*(age) + beta2*(current smoker) + beta3*(bmi)
#+ beta4*(blood pressure meds) + beta5*(Heart Rate) + beta6*(Heart Attacks)
#+ beta7*(Systolic Blood Pressure)
summary(mod11)
##
## Call:
## glm(formula = hyperten ~ age1 + cursmoke1 + bmi1 + bpmeds1 +
## heartrte1 + prevmi1 + sysbp1, family = binomial, data = fhs1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.158 -0.629 0.300 0.699 2.427
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.12817 0.57191 -21.21 < 2e-16 ***
## age1 0.00339 0.00522 0.65 0.5161
## cursmoke1Yes -0.22608 0.08470 -2.67 0.0076 **
## bmi1 0.06956 0.01235 5.63 1.8e-08 ***
## bpmeds1Yes 14.46643 259.13961 0.06 0.9555
## heartrte1 0.00207 0.00363 0.57 0.5679
## prevmi1Yes 0.16716 0.33718 0.50 0.6201
## sysbp1 0.08927 0.00373 23.95 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5019.8 on 4321 degrees of freedom
## Residual deviance: 3607.2 on 4314 degrees of freedom
## AIC: 3623
##
## Number of Fisher Scoring iterations: 16
# Model 12 - Hypertension = beta0 + beta1*(current smoker) + beta2*(bmi) +beta3*(blood pressure meds)
summary(mod12)
##
## Call:
## glm(formula = hyperten ~ cursmoke1 + bmi1 + bpmeds1, family = binomial,
## data = fhs1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.633 -1.187 0.651 0.834 1.435
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.6351 0.2737 -9.63 < 2e-16 ***
## cursmoke1Yes -0.3404 0.0725 -4.70 0.0000027 ***
## bmi1 0.1496 0.0106 14.07 < 2e-16 ***
## bpmeds1Yes 15.2868 189.9070 0.08 0.94
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5019.8 on 4321 degrees of freedom
## Residual deviance: 4648.0 on 4318 degrees of freedom
## AIC: 4656
##
## Number of Fisher Scoring iterations: 15
# Model 13 - Hypertension = beta0 + beta1*(current smoker) + beta2*(bmi) +beta3*(blood pressure meds)
#+ beta4*(Systolic Blood Pressure)
summary(mod13)
##
## Call:
## glm(formula = hyperten ~ cursmoke1 + bmi1 + bpmeds1 + sysbp1,
## family = binomial, data = fhs1)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.162 -0.633 0.302 0.698 2.437
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -11.91027 0.50294 -23.68 < 2e-16 ***
## cursmoke1Yes -0.23012 0.08334 -2.76 0.0058 **
## bmi1 0.06989 0.01234 5.66 1.5e-08 ***
## bpmeds1Yes 14.51555 258.93028 0.06 0.9553
## sysbp1 0.09006 0.00362 24.90 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 5019.8 on 4321 degrees of freedom
## Residual deviance: 3608.2 on 4317 degrees of freedom
## AIC: 3618
##
## Number of Fisher Scoring iterations: 16
#LRT: Model 10 vs Model 11
anova(mod10, mod11, test ="Chisq" )
## Analysis of Deviance Table
##
## Model 1: hyperten ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 + bpmeds1 +
## heartrte1 + prevmi1 + sysbp1
## Model 2: hyperten ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 + prevmi1 +
## sysbp1
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 4312 3606
## 2 4314 3607 -2 -0.891 0.64
#LRT: Model 10 vs Model 12
anova(mod10, mod12, test ="Chisq")
## Analysis of Deviance Table
##
## Model 1: hyperten ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 + bpmeds1 +
## heartrte1 + prevmi1 + sysbp1
## Model 2: hyperten ~ cursmoke1 + bmi1 + bpmeds1
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 4312 3606
## 2 4318 4648 -6 -1042 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#LRT: Model 10 vs Model 13
anova(mod10, mod13, test ="Chisq")
## Analysis of Deviance Table
##
## Model 1: hyperten ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 + bpmeds1 +
## heartrte1 + prevmi1 + sysbp1
## Model 2: hyperten ~ cursmoke1 + bmi1 + bpmeds1 + sysbp1
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 4312 3606
## 2 4317 3608 -5 -1.91 0.86
#LRT: Model 11 vs Model 12
anova(mod11, mod12, test ="Chisq")
## Analysis of Deviance Table
##
## Model 1: hyperten ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 + prevmi1 +
## sysbp1
## Model 2: hyperten ~ cursmoke1 + bmi1 + bpmeds1
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 4314 3607
## 2 4318 4648 -4 -1041 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#LRT: Model 11 vs Model 13
anova(mod11, mod13, test ="Chisq")
## Analysis of Deviance Table
##
## Model 1: hyperten ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 + prevmi1 +
## sysbp1
## Model 2: hyperten ~ cursmoke1 + bmi1 + bpmeds1 + sysbp1
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 4314 3607
## 2 4317 3608 -3 -1.01 0.8
#LRT: Model 12 vs Model 13
anova(mod12, mod13, test ="Chisq")
## Analysis of Deviance Table
##
## Model 1: hyperten ~ cursmoke1 + bmi1 + bpmeds1
## Model 2: hyperten ~ cursmoke1 + bmi1 + bpmeds1 + sysbp1
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 4318 4648
## 2 4317 3608 1 1040 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Surival Model Output
#Cox PH
# Model 14 - Hypertension = beta0 + beta1*(age) + beta2*(current smoker) + beta3*(cigs per day) +
#beta4*(bmi) + beta5*(diabetes) + beta6*(blood pressure meds)
# + beta7*(Heart Rate) + beta8*(Heart Attacks) + beta9*(Systolic Blood Pressure)
summary(mod14)
## Call:
## coxph(formula = surv ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 +
## bpmeds1 + heartrte1 + prevmi1 + sysbp1, data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age1 0.018517 1.018690 0.002342 7.91 2.7e-15 ***
## cursmoke1Yes -0.107032 0.898496 0.058835 -1.82 0.06888 .
## cigpday1 0.002619 1.002623 0.002453 1.07 0.28556
## bmi1 0.030797 1.031276 0.004347 7.09 1.4e-12 ***
## diabetes1Yes -0.064980 0.937086 0.106353 -0.61 0.54121
## bpmeds1Yes 0.311533 1.365517 0.092478 3.37 0.00076 ***
## heartrte1 0.003861 1.003869 0.001494 2.58 0.00977 **
## prevmi1Yes 0.271029 1.311313 0.124473 2.18 0.02945 *
## sysbp1 0.033332 1.033894 0.000745 44.72 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age1 1.019 0.982 1.014 1.02
## cursmoke1Yes 0.898 1.113 0.801 1.01
## cigpday1 1.003 0.997 0.998 1.01
## bmi1 1.031 0.970 1.023 1.04
## diabetes1Yes 0.937 1.067 0.761 1.15
## bpmeds1Yes 1.366 0.732 1.139 1.64
## heartrte1 1.004 0.996 1.001 1.01
## prevmi1Yes 1.311 0.763 1.027 1.67
## sysbp1 1.034 0.967 1.032 1.04
##
## Concordance= 0.837 (se = 0.007 )
## Rsquare= 0.45 (max possible= 1 )
## Likelihood ratio test= 2580 on 9 df, p=0
## Wald test = 4100 on 9 df, p=0
## Score (logrank) test = 3894 on 9 df, p=0
cox.zph(mod14)
## rho chisq p
## age1 -0.02692 2.3435 0.1258101
## cursmoke1Yes -0.00946 0.3002 0.5837457
## cigpday1 -0.00211 0.0151 0.9021304
## bmi1 0.00208 0.0133 0.9080208
## diabetes1Yes 0.01234 0.4952 0.4816144
## bpmeds1Yes -0.01861 1.1797 0.2774146
## heartrte1 -0.02419 1.8892 0.1692968
## prevmi1Yes 0.00483 0.0743 0.7851462
## sysbp1 0.09875 18.3681 0.0000182
## GLOBAL NA 24.8477 0.0031444
#Cox PH
# Model 14a - Hypertension = beta0 + beta1*(age) + beta2*(current smoker) + beta3*(cigs per day)
# + beta4*(bmi) + beta5*(diabetes) + beta6*(blood pressure meds)
# + beta7*(Heart Rate) + beta8*(Heart Attacks)
#adjusted for systolic blood pressure with strata command
summary(mod14a)
## Call:
## coxph(formula = surv ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 +
## bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1), data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age1 0.01219 1.01227 0.00246 4.96 7.1e-07 ***
## cursmoke1Yes -0.07091 0.93155 0.06086 -1.17 0.244
## cigpday1 0.00205 1.00205 0.00252 0.81 0.416
## bmi1 0.03175 1.03226 0.00482 6.59 4.4e-11 ***
## diabetes1Yes -0.05612 0.94543 0.11551 -0.49 0.627
## bpmeds1Yes 0.45949 1.58327 0.10230 4.49 7.1e-06 ***
## heartrte1 0.00308 1.00309 0.00154 2.00 0.046 *
## prevmi1Yes 0.27539 1.31704 0.13346 2.06 0.039 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age1 1.012 0.988 1.007 1.02
## cursmoke1Yes 0.932 1.073 0.827 1.05
## cigpday1 1.002 0.998 0.997 1.01
## bmi1 1.032 0.969 1.023 1.04
## diabetes1Yes 0.945 1.058 0.754 1.19
## bpmeds1Yes 1.583 0.632 1.296 1.93
## heartrte1 1.003 0.997 1.000 1.01
## prevmi1Yes 1.317 0.759 1.014 1.71
##
## Concordance= 0.588 (se = 0.067 )
## Rsquare= 0.023 (max possible= 0.984 )
## Likelihood ratio test= 101 on 8 df, p=0
## Wald test = 104 on 8 df, p=0
## Score (logrank) test = 105 on 8 df, p=0
cox.zph(mod14a)
## rho chisq p
## age1 0.026134 2.209447 0.137
## cursmoke1Yes -0.017457 0.991127 0.319
## cigpday1 0.009247 0.281423 0.596
## bmi1 0.008034 0.212408 0.645
## diabetes1Yes 0.008147 0.217254 0.641
## bpmeds1Yes -0.001569 0.008803 0.925
## heartrte1 -0.017276 0.926928 0.336
## prevmi1Yes -0.000434 0.000631 0.980
## GLOBAL NA 5.928764 0.655
#Cox PH
# Model 15 - Hypertension = beta0 + beta1*(age) + beta2*(current smoker) + beta3*(bmi)
#+ beta4*(blood pressure meds) + beta5*(Heart Rate) + beta6*(Heart Attacks)
#+ beta7*(Systolic Blood Pressure)
summary(mod15)
## Call:
## coxph(formula = surv ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 +
## prevmi1 + sysbp1, data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age1 0.018322 1.018491 0.002335 7.85 4.2e-15 ***
## cursmoke1Yes -0.059501 0.942235 0.037297 -1.60 0.1106
## bmi1 0.030797 1.031276 0.004308 7.15 8.7e-13 ***
## bpmeds1Yes 0.306502 1.358665 0.092285 3.32 0.0009 ***
## heartrte1 0.003862 1.003869 0.001492 2.59 0.0096 **
## prevmi1Yes 0.270696 1.310877 0.124296 2.18 0.0294 *
## sysbp1 0.033328 1.033890 0.000746 44.69 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age1 1.018 0.982 1.014 1.02
## cursmoke1Yes 0.942 1.061 0.876 1.01
## bmi1 1.031 0.970 1.023 1.04
## bpmeds1Yes 1.359 0.736 1.134 1.63
## heartrte1 1.004 0.996 1.001 1.01
## prevmi1Yes 1.311 0.763 1.027 1.67
## sysbp1 1.034 0.967 1.032 1.04
##
## Concordance= 0.837 (se = 0.007 )
## Rsquare= 0.449 (max possible= 1 )
## Likelihood ratio test= 2579 on 7 df, p=0
## Wald test = 4095 on 7 df, p=0
## Score (logrank) test = 3893 on 7 df, p=0
cox.zph(mod15)
## rho chisq p
## age1 -0.02574 2.1482 0.1427392
## cursmoke1Yes -0.01752 0.9900 0.3197368
## bmi1 0.00433 0.0569 0.8114995
## bpmeds1Yes -0.01796 1.0918 0.2960642
## heartrte1 -0.02383 1.8322 0.1758669
## prevmi1Yes 0.00591 0.1107 0.7393790
## sysbp1 0.09854 18.2791 0.0000191
## GLOBAL NA 24.5346 0.0009172
#Cox PH
# Model 15a - Hypertension = beta0 + beta1*(age) + beta2*(current smoker) + beta3*(bmi)
#+ beta4*(blood pressure meds) + beta5*(Heart Rate) + beta6*(Heart Attacks)
# adjust for Systolic Blood Pressure with strata command
summary(mod15a)
## Call:
## coxph(formula = surv ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 +
## prevmi1 + strata(sysbp1), data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## age1 0.01202 1.01209 0.00245 4.90 9.5e-07 ***
## cursmoke1Yes -0.03298 0.96756 0.03894 -0.85 0.397
## bmi1 0.03184 1.03235 0.00480 6.63 3.4e-11 ***
## bpmeds1Yes 0.45552 1.57700 0.10221 4.46 8.3e-06 ***
## heartrte1 0.00311 1.00311 0.00154 2.01 0.044 *
## prevmi1Yes 0.27761 1.31998 0.13333 2.08 0.037 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## age1 1.012 0.988 1.007 1.02
## cursmoke1Yes 0.968 1.034 0.896 1.04
## bmi1 1.032 0.969 1.023 1.04
## bpmeds1Yes 1.577 0.634 1.291 1.93
## heartrte1 1.003 0.997 1.000 1.01
## prevmi1Yes 1.320 0.758 1.016 1.71
##
## Concordance= 0.588 (se = 0.067 )
## Rsquare= 0.023 (max possible= 0.984 )
## Likelihood ratio test= 99.8 on 6 df, p=0
## Wald test = 103 on 6 df, p=0
## Score (logrank) test = 104 on 6 df, p=0
cox.zph(mod15a)
## rho chisq p
## age1 0.026335 2.247966 0.134
## cursmoke1Yes -0.016820 0.903549 0.342
## bmi1 0.009807 0.316598 0.574
## bpmeds1Yes -0.001644 0.009654 0.922
## heartrte1 -0.017037 0.902440 0.342
## prevmi1Yes 0.000341 0.000389 0.984
## GLOBAL NA 5.668180 0.461
#Cox PH
# Model 16 - Hypertension = beta0 + beta1*(current smoker) + beta2*(bmi) +beta3*(blood pressure meds)
summary(mod16)
## Call:
## coxph(formula = surv ~ cursmoke1 + bmi1 + bpmeds1, data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## cursmoke1Yes -0.17601 0.83861 0.03630 -4.85 0.0000012 ***
## bmi1 0.08813 1.09213 0.00421 20.93 < 2e-16 ***
## bpmeds1Yes 1.52215 4.58207 0.09121 16.69 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## cursmoke1Yes 0.839 1.192 0.781 0.90
## bmi1 1.092 0.916 1.083 1.10
## bpmeds1Yes 4.582 0.218 3.832 5.48
##
## Concordance= 0.657 (se = 0.007 )
## Rsquare= 0.153 (max possible= 1 )
## Likelihood ratio test= 716 on 3 df, p=0
## Wald test = 953 on 3 df, p=0
## Score (logrank) test = 1045 on 3 df, p=0
cox.zph(mod16)
## rho chisq p
## cursmoke1Yes 0.01137 0.411 0.52146
## bmi1 -0.04792 6.736 0.00945
## bpmeds1Yes 0.00875 0.262 0.60867
## GLOBAL NA 7.855 0.04911
#Cox PH
# Model 16a - Hypertension = beta0 + beta1*(current smoker) +beta2*(blood pressure meds)
# Adjusted for BMI with strata command
summary(mod16a)
## Call:
## coxph(formula = surv ~ cursmoke1 + strata(bmi1) + bpmeds1, data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## cursmoke1Yes -0.180 0.835 0.049 -3.68 0.00024 ***
## bpmeds1Yes 1.479 4.388 0.136 10.85 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## cursmoke1Yes 0.835 1.197 0.759 0.919
## bpmeds1Yes 4.388 0.228 3.359 5.731
##
## Concordance= 0.548 (se = 0.16 )
## Rsquare= 0.028 (max possible= 0.779 )
## Likelihood ratio test= 125 on 2 df, p=0
## Wald test = 134 on 2 df, p=0
## Score (logrank) test = 150 on 2 df, p=0
cox.zph(mod16a)
## rho chisq p
## cursmoke1Yes 0.020046 1.30144 0.254
## bpmeds1Yes 0.000674 0.00147 0.969
## GLOBAL NA 1.30144 0.522
#Cox PH
# Model 17 - Hypertension = beta0 + beta1*(current smoker) + beta2*(bmi) +beta3*(blood pressure meds)
#+ beta4*(Systolic Blood Pressure)
summary(mod17)
## Call:
## coxph(formula = surv ~ cursmoke1 + bmi1 + bpmeds1 + sysbp1, data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## cursmoke1Yes -0.098614 0.906093 0.036634 -2.69 0.00711 **
## bmi1 0.030801 1.031281 0.004305 7.16 8.3e-13 ***
## bpmeds1Yes 0.333974 1.396506 0.092231 3.62 0.00029 ***
## sysbp1 0.035497 1.036134 0.000686 51.71 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## cursmoke1Yes 0.906 1.104 0.843 0.974
## bmi1 1.031 0.970 1.023 1.040
## bpmeds1Yes 1.397 0.716 1.166 1.673
## sysbp1 1.036 0.965 1.035 1.038
##
## Concordance= 0.839 (se = 0.007 )
## Rsquare= 0.44 (max possible= 1 )
## Likelihood ratio test= 2506 on 4 df, p=0
## Wald test = 4163 on 4 df, p=0
## Score (logrank) test = 3856 on 4 df, p=0
cox.zph(mod17)
## rho chisq p
## cursmoke1Yes -0.01578 0.8066 0.3691270
## bmi1 0.00472 0.0676 0.7948323
## bpmeds1Yes -0.01960 1.3009 0.2540498
## sysbp1 0.09505 15.8808 0.0000675
## GLOBAL NA 22.8326 0.0001368
#Cox PH
# Model 17a - Hypertension = beta0 + beta1*(current smoker) + beta2*(bmi) +beta3*(blood pressure meds)
# ajdustled for Systolic Blood Pressure with the strata command
summary(mod17a)
## Call:
## coxph(formula = surv ~ cursmoke1 + bmi1 + bpmeds1 + strata(sysbp1),
## data = fhs1)
##
## n= 4322, number of events= 3166
##
## coef exp(coef) se(coef) z Pr(>|z|)
## cursmoke1Yes -0.05818 0.94348 0.03815 -1.52 0.13
## bmi1 0.03102 1.03151 0.00479 6.48 9.4e-11 ***
## bpmeds1Yes 0.47753 1.61209 0.10211 4.68 2.9e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## exp(coef) exp(-coef) lower .95 upper .95
## cursmoke1Yes 0.943 1.060 0.876 1.02
## bmi1 1.032 0.969 1.022 1.04
## bpmeds1Yes 1.612 0.620 1.320 1.97
##
## Concordance= 0.577 (se = 0.067 )
## Rsquare= 0.016 (max possible= 0.984 )
## Likelihood ratio test= 67.9 on 3 df, p=1.19e-14
## Wald test = 70.8 on 3 df, p=3e-15
## Score (logrank) test = 71.3 on 3 df, p=2.22e-15
cox.zph(mod17a)
## rho chisq p
## cursmoke1Yes -0.023375 1.749182 0.186
## bmi1 0.010831 0.385698 0.535
## bpmeds1Yes -0.000255 0.000233 0.988
## GLOBAL NA 2.399631 0.494
#LRT: Model 14 vs Model 15
anova(mod14a, mod15a)
## Analysis of Deviance Table
## Cox model: response is surv
## Model 1: ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 + bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1)
## Model 2: ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1)
## loglik Chisq Df P(>|Chi|)
## 1 -8830
## 2 -8830 0.9 2 0.64
#LRT: Model 14 vs Model 16
anova(mod14a, mod16a)
## Analysis of Deviance Table
## Cox model: response is surv
## Model 1: ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 + bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1)
## Model 2: ~ cursmoke1 + strata(bmi1) + bpmeds1
## loglik Chisq Df P(>|Chi|)
## 1 -8830
## 2 -3199 11261 6 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#LRT: Model 14 vs Model 17
anova(mod14a, mod17a)
## Analysis of Deviance Table
## Cox model: response is surv
## Model 1: ~ age1 + cursmoke1 + cigpday1 + bmi1 + diabetes1 + bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1)
## Model 2: ~ cursmoke1 + bmi1 + bpmeds1 + strata(sysbp1)
## loglik Chisq Df P(>|Chi|)
## 1 -8830
## 2 -8846 32.7 5 0.0000043 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#LRT: Model 15 vs Model 16
anova(mod15a, mod16a)
## Analysis of Deviance Table
## Cox model: response is surv
## Model 1: ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1)
## Model 2: ~ cursmoke1 + strata(bmi1) + bpmeds1
## loglik Chisq Df P(>|Chi|)
## 1 -8830
## 2 -3199 11262 4 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#LRT: Model 15 vs Model 17
anova(mod15a, mod17a)
## Analysis of Deviance Table
## Cox model: response is surv
## Model 1: ~ age1 + cursmoke1 + bmi1 + bpmeds1 + heartrte1 + prevmi1 + strata(sysbp1)
## Model 2: ~ cursmoke1 + bmi1 + bpmeds1 + strata(sysbp1)
## loglik Chisq Df P(>|Chi|)
## 1 -8830
## 2 -8846 31.8 3 0.00000057 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#LRT: Model 16 vs Model 17
anova(mod16a, mod17a)
## Analysis of Deviance Table
## Cox model: response is surv
## Model 1: ~ cursmoke1 + strata(bmi1) + bpmeds1
## Model 2: ~ cursmoke1 + bmi1 + bpmeds1 + strata(sysbp1)
## loglik Chisq Df P(>|Chi|)
## 1 -3199
## 2 -8846 11294 1 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1