Heart-failure data

Topic of Descriptive statistics, part of Data analysis · Also in Logistic regression

Heart-failure data

Type Topic
Taught in Descriptive statistics · Logistic regression
Part Data analysis · Statistical learning
Worked examples 1

Records of 299 patients after heart failure, all with severe weakness of the left ventricle, admitted to one hospital and followed for up to a year, with 13 measurements each, among them age, anaemia, serum creatinine and the ejection fraction. It runs through the descriptive-statistics chapter and returns in logistic regression.

In Descriptive statistics

From Descriptive statistics

The running example is a study of 299 patients after heart failure, all with severe weakness of the left ventricle, admitted to one hospital and followed for up to a year. For each patient there are 13 measurements, and the questions are which of them go with death during follow-up, and which go with the ejection fraction, the fraction of the blood in the left ventricle pumped out at each beat. The R code that produces each summary is shown with it; reading data and drawing plots in R is covered in Using R.

Examples

Survival after heart failure

Worked example from Logistic regression

The following output is a supplied fit of death during follow-up on age and high-blood-pressure status, for 299 patients. Follow-up time is stored separately, so the outcome is not a common one-year event. The printed coefficients are the numbers to be interpreted. They are not re-estimated here.

Question. Read the odds ratios, the age interval, the deviance drop, and the AIC from the printed fit.

Solution. The supplied summary is

fit <- glm(death ~ age + hbp, data = heart, family = "binomial")
summary(fit)
#> Coefficients:
#>             Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.70568    0.71072  -5.214 1.85e-07
#> age          0.04618    0.01110   4.159 3.20e-05
#> hbp          0.26920    0.26487   1.016    0.309
#> Null deviance: 375.35 on 298 degrees of freedom
#> Residual deviance: 354.97 on 296 degrees of freedom
#> AIC: 360.97
#> Number of Fisher Scoring iterations: 4
confint(fit)
#>                  2.5 %      97.5 %
#> (Intercept) -5.14257577 -2.34844333
#> age          0.02483923  0.06851426
#> hbp         -0.25344324  0.78698218

Increasing age by one year at fixed blood-pressure status multiplies the modelled odds by e^{0.04618}=1.0473. Ten years multiply them by e^{0.4618}=1.59. These are odds ratios. If the baseline probability is p and the odds multiplier is a, the new probability is ap/(1-p+ap). The printed age interval, exponentiated, gives an annual odds-ratio interval of approximately (e^{0.02484},e^{0.06851})=(1.025,1.071). For high blood pressure, the interval (e^{-0.2534},e^{0.7870})=(0.78,2.20) includes one. It does not establish that the association is exactly zero.

The deviance reduction is 375.35-354.97=20.38 on two degrees of freedom. The printed AIC is the residual deviance plus twice the number of coefficients,

354.97+2(3)=360.97.

These calculations check the interpretation of the supplied numbers. They are not causal effects, and they are not probabilities of death inside a fixed horizon.

Used in

See also

Interpreting a logistic regression · Sample quantile · Interquartile range · Sample variance and standard deviation · Five-number summary and boxplot · Normal quantile plot · Data table · Summary statistics

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