CCHS: Regression
This tutorial is for a complex data analysis, specifically using regression techniques to analyze survey data.
Let us load necessary R packages for the analysis:
Load data
Loads a dataset and provides some quick data checks, like the dimensions and summary of weights.
Logistic for complex survey
Performs a simple logistic regression using the complex survey data, focusing on the relationship between cardiovascular disease and osteoarthritis.
Multivariable analysis
Runs a more complex logistic regression model, adding multiple covariates to better understand the relationship.
formula1 <- as.formula(I(CVD=="event") ~ OA + age + sex + married + race +
edu + income + bmi + phyact + doctor + stress +
smoke + drink + fruit + bp + diab + province + immigrate)
fit3 <- svyglm(formula1,
design = w.design,
family = binomial(logit))
publish(fit3)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.52 [1.40;1.66] < 1e-04
#> age 20-29 years Ref
#> 30-39 years 1.29 [0.98;1.69] 0.0707636
#> 40-49 years 2.74 [2.17;3.47] < 1e-04
#> 50-59 years 6.24 [4.97;7.83] < 1e-04
#> 60-64 years 9.71 [7.68;12.29] < 1e-04
#> 65 years and over 15.85 [12.57;20.00] < 1e-04
#> teen 0.46 [0.20;1.07] 0.0707295
#> sex Female Ref
#> Male 1.73 [1.60;1.88] < 1e-04
#> married not single Ref
#> single 0.97 [0.90;1.05] 0.5209444
#> race Non-white Ref
#> White 1.44 [1.19;1.75] 0.0002219
#> edu < 2ndary Ref
#> 2nd grad. 0.90 [0.80;1.00] 0.0512330
#> Other 2nd grad. 0.97 [0.83;1.13] 0.6737665
#> Post-2nd grad. 0.93 [0.85;1.02] 0.1016562
#> income $29,999 or less Ref
#> $30,000-$49,999 0.74 [0.67;0.81] < 1e-04
#> $50,000-$79,999 0.64 [0.58;0.72] < 1e-04
#> $80,000 or more 0.58 [0.51;0.66] < 1e-04
#> bmi Underweight Ref
#> healthy weight 0.86 [0.67;1.10] 0.2350526
#> Overweight 0.88 [0.69;1.12] 0.3033213
#> phyact Active Ref
#> Inactive 1.21 [1.10;1.34] 0.0001345
#> Moderate 1.08 [0.97;1.21] 0.1771985
#> doctor No Ref
#> Yes 1.75 [1.49;2.06] < 1e-04
#> stress Not too stressed Ref
#> stressed 1.30 [1.18;1.42] < 1e-04
#> smoke Never smoker Ref
#> Current smoker 1.18 [1.05;1.32] 0.0050518
#> Former smoker 1.21 [1.11;1.33] < 1e-04
#> drink Never drank Ref
#> Current drinker 0.82 [0.68;0.98] 0.0290605
#> Former driker 1.13 [0.93;1.36] 0.2133779
#> fruit 0-3 daily serving Ref
#> 4-6 daily serving 0.94 [0.86;1.03] 0.1758214
#> 6+ daily serving 1.09 [0.97;1.23] 0.1311029
#> bp No Ref
#> Yes 2.35 [2.16;2.55] < 1e-04
#> diab No Ref
#> Yes 1.86 [1.66;2.07] < 1e-04
#> province South Ref
#> North 1.21 [0.90;1.62] 0.2103030
#> immigrate not immigrant Ref
#> > 10 years 1.02 [0.89;1.16] 0.8057243
#> recent 1.06 [0.73;1.53] 0.7651069Model fit assessment
Variability explained
Pseudo-R-square values indicate how much of the total variability in the outcomes is explainable by the fitted model (analogous to R-square). For a continuous outcome, we can compute R-square, while R-square cannot be calculated when the outcome variable is categorical, nominal or ordinal. We use pseudo-R-squared measures when the dependent variable is not continuous but a likelihood function is used to fit a model. Popular Pseudo-R-square measures are:
- Cox/Snell (never reaches max 1)
- Nagelkerke R-square (scaled to max 1)
- The larger Cox & Snell estimate is the better the model.
- These Pseudo-R-square values should be interpreted with caution (if not ignored).
- They offer little confidence in interpreting the model fit.
- Survey weighted version of them are available.
- Not trivial to decide which statistic to use under complex surveys.
Evaluates the model fit using Akaike Information Criterion (AIC) and pseudo R-squared metrics.
fit3 <- svyglm(formula1,
design = w.design,
family = quasibinomial(logit))
# Family choice here is stylistic: quasibinomial suppresses the
# non-integer-#successes warning from weighted data. The design-based
# AIC (Lumley-Scott) is defined for both binomial and quasibinomial svyglm.
AIC(fit3)
#> eff.p AIC deltabar
#> 67.752064 45362.706032 2.053093
# AIC for survey weighted regressions
psrsq(fit3, method = "Cox-Snell")
#> [1] 0.06091896
psrsq(fit3, method = "Nagelkerke")
#> [1] 0.2307586
# Nagelkerke and Cox-Snell pseudo-rsquared statisticsBackward Elimination
- Model comparisons
- LRT-aprroximation
- Wald-based
Checking one by one
Checks the significance of each variable one by one and removes those that are not statistically significant.
round(sort(summary(fit3)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over bpYes
#> 0.00 0.00 0.00
#> age60-64 years age50-59 years sexMale
#> 0.00 0.00 0.00
#> diabYes OAOA income$80,000 or more
#> 0.00 0.00 0.00
#> age40-49 years income$50,000-$79,999 doctorYes
#> 0.00 0.00 0.00
#> income$30,000-$49,999 stressstressed smokeFormer smoker
#> 0.00 0.00 0.00
#> phyactInactive raceWhite smokeCurrent smoker
#> 0.00 0.00 0.01
#> drinkCurrent drinker edu2nd grad. ageteen
#> 0.03 0.05 0.07
#> age30-39 years eduPost-2nd grad. fruit6+ daily serving
#> 0.07 0.10 0.13
#> fruit4-6 daily serving phyactModerate provinceNorth
#> 0.18 0.18 0.21
#> drinkFormer driker bmihealthy weight bmiOverweight
#> 0.21 0.24 0.30
#> marriedsingle eduOther 2nd grad. immigraterecent
#> 0.52 0.67 0.77
#> immigrate> 10 years
#> 0.81
# bmiOverweight is associated with largest p-value
# but what about other categories?
regTermTest(fit3,~bmi) # coef of all bmi cat = 0
#> Wald test for bmi
#> in svyglm(formula = formula1, design = w.design, family = quasibinomial(logit))
#> F = 0.7591291 on 2 and 185579 df: p= 0.46808
fit4 <- update(fit3, .~. -bmi)
anova(fit3, fit4)
#> Working (Rao-Scott+F) LRT for bmi
#> in svyglm(formula = formula1, design = w.design, family = quasibinomial(logit))
#> Working 2logLR = 1.424634 p= 0.49071
#> (scale factors: 1.1 0.93 ); denominator df= 185579
# high p-value (in both wald and Anova) makes it more likely that you should exclude bmi
AIC(fit3,fit4)
#> eff.p AIC deltabar
#> [1,] 67.75206 45362.71 2.053093
#> [2,] 64.30460 45358.26 2.074342
round(sort(summary(fit4)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over bpYes
#> 0.00 0.00 0.00
#> age60-64 years age50-59 years sexMale
#> 0.00 0.00 0.00
#> diabYes OAOA income$80,000 or more
#> 0.00 0.00 0.00
#> age40-49 years income$50,000-$79,999 doctorYes
#> 0.00 0.00 0.00
#> income$30,000-$49,999 stressstressed smokeFormer smoker
#> 0.00 0.00 0.00
#> phyactInactive raceWhite smokeCurrent smoker
#> 0.00 0.00 0.00
#> drinkCurrent drinker edu2nd grad. age30-39 years
#> 0.03 0.05 0.07
#> ageteen eduPost-2nd grad. fruit6+ daily serving
#> 0.07 0.10 0.13
#> fruit4-6 daily serving phyactModerate provinceNorth
#> 0.17 0.17 0.21
#> drinkFormer driker marriedsingle eduOther 2nd grad.
#> 0.21 0.53 0.67
#> immigraterecent immigrate> 10 years
#> 0.76 0.81Using AIC to automate
Uses stepwise regression guided by AIC to automatically select the most important variables.
require(MASS)
formula1b <- as.formula(I(CVD=="event") ~ OA + age + sex)
fit1b <- svyglm(formula1b,
design = w.design,
family = binomial(logit))
fit5 <- stepAIC(fit1b, direction = "backward")
#> Start: AIC=47384.51
#> I(CVD == "event") ~ OA + age + sex
#> Df Deviance AIC
#> <none> 47353 47385
#> - sex 1 47634 47658
#> - OA 1 47679 47702
#> - age 6 54414 54291publish(fit5)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.81 [1.66;1.97] < 1e-04
#> age 20-29 years Ref
#> 30-39 years 1.40 [1.07;1.84] 0.01374
#> 40-49 years 3.39 [2.69;4.27] < 1e-04
#> 50-59 years 9.42 [7.55;11.76] < 1e-04
#> 60-64 years 17.78 [14.22;22.23] < 1e-04
#> 65 years and over 33.82 [27.26;41.97] < 1e-04
#> teen 0.45 [0.20;1.02] 0.05462
#> sex Female Ref
#> Male 1.57 [1.46;1.69] < 1e-04
round(sort(summary(fit5)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over age60-64 years
#> 0.00 0.00 0.00
#> age50-59 years OAOA sexMale
#> 0.00 0.00 0.00
#> age40-49 years age30-39 years ageteen
#> 0.00 0.01 0.05Using AIC, but keeping importants
Similar to the previous step but ensures certain important variables remain in the model.
formula1c <- as.formula(I(CVD=="event") ~ OA + age + sex + married + race +
edu + income + bmi + phyact + fruit + bp + diab +
doctor + stress + smoke + drink + province + immigrate)
scope <- list(upper = ~ OA + age + sex + married + race +
edu + income + bmi + phyact + fruit + bp + diab +
doctor + stress + smoke + drink + province + immigrate,
lower = ~ OA + age + sex + married + race +
edu + income + bmi + phyact + fruit + bp + diab)
fit1c <- svyglm(formula1c, design = w.design, family = binomial(logit))
fitstep <- step(fit1c, scope = scope, trace = FALSE, k = 2, direction = "backward")
# k = 2 gives the genuine AICpublish(fitstep)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.52 [1.40;1.66] < 1e-04
#> age 20-29 years Ref
#> 30-39 years 1.29 [0.98;1.70] 0.0697699
#> 40-49 years 2.74 [2.17;3.47] < 1e-04
#> 50-59 years 6.24 [4.97;7.83] < 1e-04
#> 60-64 years 9.71 [7.68;12.28] < 1e-04
#> 65 years and over 15.85 [12.57;19.98] < 1e-04
#> teen 0.46 [0.20;1.07] 0.0705660
#> sex Female Ref
#> Male 1.73 [1.60;1.88] < 1e-04
#> married not single Ref
#> single 0.97 [0.90;1.05] 0.5042496
#> race Non-white Ref
#> White 1.41 [1.18;1.70] 0.0001986
#> edu < 2ndary Ref
#> 2nd grad. 0.90 [0.80;1.00] 0.0524940
#> Other 2nd grad. 0.97 [0.83;1.13] 0.6732446
#> Post-2nd grad. 0.93 [0.85;1.02] 0.1045975
#> income $29,999 or less Ref
#> $30,000-$49,999 0.74 [0.67;0.81] < 1e-04
#> $50,000-$79,999 0.64 [0.58;0.72] < 1e-04
#> $80,000 or more 0.58 [0.51;0.66] < 1e-04
#> bmi Underweight Ref
#> healthy weight 0.86 [0.67;1.10] 0.2316915
#> Overweight 0.88 [0.69;1.12] 0.2982852
#> phyact Active Ref
#> Inactive 1.22 [1.10;1.34] 0.0001227
#> Moderate 1.08 [0.97;1.21] 0.1754422
#> fruit 0-3 daily serving Ref
#> 4-6 daily serving 0.94 [0.86;1.03] 0.1807666
#> 6+ daily serving 1.09 [0.97;1.23] 0.1295281
#> bp No Ref
#> Yes 2.35 [2.16;2.55] < 1e-04
#> diab No Ref
#> Yes 1.85 [1.66;2.07] < 1e-04
#> doctor No Ref
#> Yes 1.75 [1.49;2.05] < 1e-04
#> stress Not too stressed Ref
#> stressed 1.30 [1.18;1.42] < 1e-04
#> smoke Never smoker Ref
#> Current smoker 1.17 [1.05;1.31] 0.0053412
#> Former smoker 1.21 [1.10;1.33] < 1e-04
#> drink Never drank Ref
#> Current drinker 0.82 [0.68;0.98] 0.0254942
#> Former driker 1.12 [0.93;1.36] 0.2205315
round(sort(summary(fitstep)$coef[,"Pr(>|t|)"]),2)
#> (Intercept) age65 years and over bpYes
#> 0.00 0.00 0.00
#> age60-64 years age50-59 years sexMale
#> 0.00 0.00 0.00
#> diabYes OAOA income$80,000 or more
#> 0.00 0.00 0.00
#> age40-49 years income$50,000-$79,999 doctorYes
#> 0.00 0.00 0.00
#> income$30,000-$49,999 stressstressed smokeFormer smoker
#> 0.00 0.00 0.00
#> phyactInactive raceWhite smokeCurrent smoker
#> 0.00 0.00 0.01
#> drinkCurrent drinker edu2nd grad. age30-39 years
#> 0.03 0.05 0.07
#> ageteen eduPost-2nd grad. fruit6+ daily serving
#> 0.07 0.10 0.13
#> phyactModerate fruit4-6 daily serving drinkFormer driker
#> 0.18 0.18 0.22
#> bmihealthy weight bmiOverweight marriedsingle
#> 0.23 0.30 0.50
#> eduOther 2nd grad.
#> 0.67Assess interactions
Check biologically interesting ones.
Check one by one
Checks if there is a significant interaction effect between ‘age’ and ‘sex’.
fit8a <- update(fitstep, .~. + interaction(age,sex))
anova(fitstep, fit8a) # keep interaction
#> Working (Rao-Scott+F) LRT for interaction(age, sex)
#> in svyglm(formula = I(CVD == "event") ~ OA + age + sex + married +
#> race + edu + income + bmi + phyact + fruit + bp + diab +
#> doctor + stress + smoke + drink + interaction(age, sex),
#> design = w.design, family = binomial(logit))
#> Working 2logLR = 40.16528 p= 1.2167e-06
#> (scale factors: 1.3 1.2 1.2 0.93 0.78 0.71 ); denominator df= 185576Checks if there is a significant interaction effect between ‘sex’ and ‘diabetes’.
fit8b <- update(fitstep, .~. + interaction(sex,diab))
anova(fitstep, fit8b) # Do not keep this interaction
#> Working (Rao-Scott+F) LRT for interaction(sex, diab)
#> in svyglm(formula = I(CVD == "event") ~ OA + age + sex + married +
#> race + edu + income + bmi + phyact + fruit + bp + diab +
#> doctor + stress + smoke + drink + interaction(sex, diab),
#> design = w.design, family = binomial(logit))
#> Working 2logLR = 0.4591456 p= 0.49597
#> df=1; denominator df= 185581Checks if there is a significant interaction effect between ‘BMI’ and ‘diabetes’.
fit8c <- update(fitstep, .~. + interaction(bmi,diab))
anova(fitstep, fit8c) # keep this interaction
#> Working (Rao-Scott+F) LRT for interaction(bmi, diab)
#> in svyglm(formula = I(CVD == "event") ~ OA + age + sex + married +
#> race + edu + income + bmi + phyact + fruit + bp + diab +
#> doctor + stress + smoke + drink + interaction(bmi, diab),
#> design = w.design, family = binomial(logit))
#> Working 2logLR = 7.92727 p= 0.02533
#> (scale factors: 1.4 0.6 ); denominator df= 185580Add all significant interactions in 1 model
Updates the model to include significant interaction terms.
Note that we have 0 effect modifiers and 2 interactions. Here a statistical interaction simply means that the effect of one variable on the outcome depends on the level of another (a product term improves model fit), whereas effect modification is the causal counterpart, where the causal effect of the exposure differs across strata of a third variable. See the confounding module for the distinction between interaction and effect modification.
fit9 <- update(fitstep, .~. + interaction(age,sex) + interaction(bmi,diab))
require(jtools)
summ(fit9, confint = TRUE, digits = 3)| Observations | 185613 |
| Dependent variable | I(CVD == "event") |
| Type | Survey-weighted generalized linear model |
| Family | binomial |
| Link | logit |
| Pseudo-R² (Cragg-Uhler) | 0.233 |
| Pseudo-R² (McFadden) | 0.207 |
| AIC | 41548.160 |
| Est. | 2.5% | 97.5% | t val. | p | |
|---|---|---|---|---|---|
| (Intercept) | -5.590 | -6.046 | -5.135 | -24.069 | 0.000 |
| OAOA | 0.438 | 0.352 | 0.523 | 10.043 | 0.000 |
| age30-39 years | 0.299 | -0.118 | 0.717 | 1.405 | 0.160 |
| age40-49 years | 1.158 | 0.794 | 1.522 | 6.236 | 0.000 |
| age50-59 years | 2.181 | 1.831 | 2.531 | 12.212 | 0.000 |
| age60-64 years | 2.619 | 2.263 | 2.976 | 14.395 | 0.000 |
| age65 years and over | 3.033 | 2.680 | 3.387 | 16.833 | 0.000 |
| ageteen | -0.695 | -1.704 | 0.314 | -1.350 | 0.177 |
| sexMale | -0.028 | -0.447 | 0.390 | -0.133 | 0.895 |
| marriedsingle | -0.016 | -0.096 | 0.064 | -0.382 | 0.703 |
| raceWhite | 0.348 | 0.165 | 0.531 | 3.724 | 0.000 |
| edu2nd grad. | -0.107 | -0.217 | 0.003 | -1.906 | 0.057 |
| eduOther 2nd grad. | -0.039 | -0.192 | 0.114 | -0.498 | 0.618 |
| eduPost-2nd grad. | -0.081 | -0.173 | 0.010 | -1.746 | 0.081 |
| income$30,000-$49,999 | -0.304 | -0.400 | -0.208 | -6.215 | 0.000 |
| income$50,000-$79,999 | -0.444 | -0.552 | -0.336 | -8.034 | 0.000 |
| income$80,000 or more | -0.555 | -0.684 | -0.426 | -8.424 | 0.000 |
| bmihealthy weight | -1.406 | -2.677 | -0.135 | -2.167 | 0.030 |
| bmiOverweight | -1.110 | -2.375 | 0.154 | -1.721 | 0.085 |
| phyactInactive | 0.194 | 0.094 | 0.293 | 3.817 | 0.000 |
| phyactModerate | 0.077 | -0.034 | 0.187 | 1.353 | 0.176 |
| fruit4-6 daily serving | -0.062 | -0.155 | 0.031 | -1.313 | 0.189 |
| fruit6+ daily serving | 0.094 | -0.023 | 0.211 | 1.579 | 0.114 |
| bpYes | 0.861 | 0.778 | 0.944 | 20.354 | 0.000 |
| diabYes | 1.745 | 0.462 | 3.027 | 2.667 | 0.008 |
| doctorYes | 0.535 | 0.372 | 0.697 | 6.447 | 0.000 |
| stressstressed | 0.256 | 0.164 | 0.347 | 5.483 | 0.000 |
| smokeCurrent smoker | 0.152 | 0.039 | 0.266 | 2.628 | 0.009 |
| smokeFormer smoker | 0.177 | 0.082 | 0.272 | 3.654 | 0.000 |
| drinkCurrent drinker | -0.205 | -0.381 | -0.029 | -2.277 | 0.023 |
| drinkFormer driker | 0.116 | -0.072 | 0.303 | 1.210 | 0.226 |
| interaction(age, sex)30-39 years.Female | -0.083 | -0.622 | 0.457 | -0.300 | 0.764 |
| interaction(age, sex)40-49 years.Female | -0.302 | -0.766 | 0.161 | -1.278 | 0.201 |
| interaction(age, sex)50-59 years.Female | -0.810 | -1.258 | -0.362 | -3.543 | 0.000 |
| interaction(age, sex)60-64 years.Female | -0.787 | -1.237 | -0.337 | -3.428 | 0.001 |
| interaction(age, sex)65 years and over.Female | -0.603 | -1.035 | -0.170 | -2.733 | 0.006 |
| interaction(age, sex)teen.Female | -0.129 | -1.806 | 1.548 | -0.151 | 0.880 |
| interaction(bmi, diab)healthy weight.No | 1.380 | 0.085 | 2.675 | 2.089 | 0.037 |
| interaction(bmi, diab)Overweight.No | 1.085 | -0.204 | 2.373 | 1.650 | 0.099 |
| Standard errors: Robust |
fit9 <- update(fitstep, .~. + age:sex + bmi:diab)
publish(fit9)
#> Variable Units OddsRatio CI.95 p-value
#> OA Control Ref
#> OA 1.55 [1.42;1.69] < 1e-04
#> married not single Ref
#> single 0.98 [0.91;1.07] 0.7026897
#> race Non-white Ref
#> White 1.42 [1.18;1.70] 0.0001960
#> edu < 2ndary Ref
#> 2nd grad. 0.90 [0.81;1.00] 0.0566536
#> Other 2nd grad. 0.96 [0.83;1.12] 0.6183383
#> Post-2nd grad. 0.92 [0.84;1.01] 0.0807393
#> income $29,999 or less Ref
#> $30,000-$49,999 0.74 [0.67;0.81] < 1e-04
#> $50,000-$79,999 0.64 [0.58;0.71] < 1e-04
#> $80,000 or more 0.57 [0.50;0.65] < 1e-04
#> phyact Active Ref
#> Inactive 1.21 [1.10;1.34] 0.0001349
#> Moderate 1.08 [0.97;1.21] 0.1760803
#> fruit 0-3 daily serving Ref
#> 4-6 daily serving 0.94 [0.86;1.03] 0.1892549
#> 6+ daily serving 1.10 [0.98;1.23] 0.1142759
#> bp No Ref
#> Yes 2.37 [2.18;2.57] < 1e-04
#> doctor No Ref
#> Yes 1.71 [1.45;2.01] < 1e-04
#> stress Not too stressed Ref
#> stressed 1.29 [1.18;1.42] < 1e-04
#> smoke Never smoker Ref
#> Current smoker 1.16 [1.04;1.30] 0.0085960
#> Former smoker 1.19 [1.09;1.31] 0.0002579
#> drink Never drank Ref
#> Current drinker 0.81 [0.68;0.97] 0.0227934
#> Former driker 1.12 [0.93;1.35] 0.2264702
#> age(20-29 years): sex(Male vs Female) 0.97 [0.64;1.48] 0.8945322
#> age(30-39 years): sex(Male vs Female) 1.06 [0.75;1.49] 0.7583565
#> age(40-49 years): sex(Male vs Female) 1.32 [1.07;1.62] 0.0091527
#> age(50-59 years): sex(Male vs Female) 2.18 [1.85;2.58] < 1e-04
#> age(60-64 years): sex(Male vs Female) 2.14 [1.80;2.53] < 1e-04
#> age(65 years and over): sex(Male vs Female) 1.78 [1.58;1.99] < 1e-04
#> age(teen): sex(Male vs Female) 1.11 [0.22;5.62] 0.9033924
#> sex(Female): age(30-39 years vs 20-29 years) 1.24 [0.87;1.77] 0.2276609
#> sex(Female): age(40-49 years vs 20-29 years) 2.35 [1.75;3.16] < 1e-04
#> sex(Female): age(50-59 years vs 20-29 years) 3.94 [2.95;5.27] < 1e-04
#> sex(Female): age(60-64 years vs 20-29 years) 6.25 [4.66;8.39] < 1e-04
#> sex(Female): age(65 years and over vs 20-29 years) 11.37 [8.60;15.02] < 1e-04
#> sex(Female): age(teen vs 20-29 years) 0.44 [0.11;1.69] 0.2320840
#> sex(Male): age(30-39 years vs 20-29 years) 1.35 [0.89;2.05] 0.1599938
#> sex(Male): age(40-49 years vs 20-29 years) 3.18 [2.21;4.58] < 1e-04
#> sex(Male): age(50-59 years vs 20-29 years) 8.85 [6.24;12.56] < 1e-04
#> sex(Male): age(60-64 years vs 20-29 years) 13.73 [9.61;19.61] < 1e-04
#> sex(Male): age(65 years and over vs 20-29 years) 20.77 [14.59;29.57] < 1e-04
#> sex(Male): age(teen vs 20-29 years) 0.50 [0.18;1.37] 0.1769155
#> bmi(Underweight): diab(Yes vs No) 5.72 [1.59;20.63] 0.0076561
#> bmi(healthy weight): diab(Yes vs No) 1.44 [1.19;1.75] 0.0002221
#> bmi(Overweight): diab(Yes vs No) 1.93 [1.70;2.20] < 1e-04
#> diab(No): bmi(healthy weight vs Underweight) 0.97 [0.76;1.25] 0.8394972
#> diab(No): bmi(Overweight vs Underweight) 0.97 [0.76;1.25] 0.8400722
#> diab(Yes): bmi(healthy weight vs Underweight) 0.25 [0.07;0.87] 0.0302066
#> diab(Yes): bmi(Overweight vs Underweight) 0.33 [0.09;1.17] 0.0852377basic.model <- eval(fit5$call[[2]])
basic.model
#> I(CVD == "event") ~ OA + age + sex
#> attr(,"variables")
#> list(I(CVD == "event"), OA, age, sex)
#> attr(,"factors")
#> OA age sex
#> I(CVD == "event") 0 0 0
#> OA 1 0 0
#> age 0 1 0
#> sex 0 0 1
#> attr(,"term.labels")
#> [1] "OA" "age" "sex"
#> attr(,"order")
#> [1] 1 1 1
#> attr(,"intercept")
#> [1] 1
#> attr(,"response")
#> [1] 1
#> attr(,".Environment")
#> <environment: R_GlobalEnv>
#> attr(,"predvars")
#> list(I(CVD == "event"), OA, age, sex)
#> attr(,"dataClasses")
#> I(CVD == "event") OA age sex
#> "logical" "factor" "factor" "factor"
#> (weights)
#> "numeric"
aic.int.model <- eval(fit9$call[[2]])
aic.int.model
#> I(CVD == "event") ~ OA + age + sex + married + race + edu + income +
#> bmi + phyact + fruit + bp + diab + doctor + stress + smoke +
#> drink + age:sex + bmi:diabSaving data
Saves the final regression models for future use.
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