This dataset, originally discussed in McGilchrist and Aisbett (1991), describes the first and second (possibly right censored) recurrence time of infection in kidney patients using portable dialysis equipment. In addition, information on the risk variables age, sex and disease type is provided.
Format
A data frame of 76 observations containing information on the following 7 variables.
- time
The time to first or second recurrence of the infection, or the time of censoring
- recur
A factor of levels
1or2indicating if the infection recurred for the first or second time for this patient- censored
Either
0or1, where0indicates no censoring of recurrence time and1indicates right censoring- patient
The patient number
- age
The age of the patient
- sex
The sex of the patient
- disease
A factor of levels
other, GN, AN, andPKDspecifying the type of disease
Source
McGilchrist, C. A., & Aisbett, C. W. (1991). Regression with frailty in survival analysis. Biometrics, 47(2), 461-466.
Examples
# \dontrun{
## performing surivival analysis using the "weibull" family
fit1 <- brm(time | cens(censored) ~ age + sex + disease,
data = kidney, family = weibull, init = "0")
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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summary(fit1)
#> Family: weibull
#> Links: mu = log
#> Formula: time | cens(censored) ~ age + sex + disease
#> Data: kidney (Number of observations: 76)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept 3.79 0.53 2.80 4.86 1.00 4705 3366
#> age -0.00 0.01 -0.02 0.02 1.00 3238 2725
#> sexfemale 1.60 0.34 0.92 2.29 1.00 3304 3019
#> diseaseGN -0.05 0.42 -0.89 0.79 1.00 2352 2804
#> diseaseAN -0.51 0.40 -1.33 0.27 1.00 2656 2689
#> diseasePKD 1.35 0.60 0.20 2.58 1.00 2660 2954
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape 0.98 0.10 0.79 1.18 1.00 3751 3008
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
plot(fit1)
## adding random intercepts over patients
fit2 <- brm(time | cens(censored) ~ age + sex + disease + (1|patient),
data = kidney, family = weibull(), init = "0",
prior = set_prior("cauchy(0,2)", class = "sd"))
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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#> Warning: There were 3 divergent transitions after warmup. See
#> https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> to find out why this is a problem and how to eliminate them.
#> Warning: Examine the pairs() plot to diagnose sampling problems
summary(fit2)
#> Warning: There were 3 divergent transitions after warmup. Increasing adapt_delta above 0.8 may help. See http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> Family: weibull
#> Links: mu = log
#> Formula: time | cens(censored) ~ age + sex + disease + (1 | patient)
#> Data: kidney (Number of observations: 76)
#> Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
#> total post-warmup draws = 4000
#>
#> Multilevel Hyperparameters:
#> ~patient (Number of levels: 38)
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(Intercept) 0.54 0.25 0.06 1.01 1.00 708 1145
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept 3.75 0.59 2.63 4.89 1.00 3565 2962
#> age -0.00 0.01 -0.03 0.02 1.00 2214 2190
#> sexfemale 1.61 0.38 0.86 2.36 1.00 2961 2482
#> diseaseGN -0.09 0.48 -1.01 0.84 1.00 2229 2523
#> diseaseAN -0.51 0.46 -1.43 0.40 1.00 2274 2450
#> diseasePKD 1.00 0.71 -0.40 2.34 1.00 1869 2625
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape 1.12 0.16 0.84 1.45 1.00 1086 1828
#>
#> Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
#> and Tail_ESS are effective sample size measures, and Rhat is the potential
#> scale reduction factor on split chains (at convergence, Rhat = 1).
plot(fit2)
# }