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 3.77 0.51 2.79 4.83 1.00 5647 3027
#> age -0.00 0.01 -0.02 0.02 1.00 3085 3056
#> sexfemale 1.60 0.34 0.91 2.25 1.00 3496 2381
#> diseaseGN -0.05 0.42 -0.85 0.77 1.00 2589 3095
#> diseaseAN -0.52 0.41 -1.30 0.28 1.00 2566 3091
#> diseasePKD 1.35 0.60 0.19 2.53 1.00 2356 2544
#>
#> 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 3549 2936
#>
#> 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 2 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 2 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) 0.55 0.24 0.06 1.01 1.00 838 1602
#>
#> Regression Coefficients:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> Intercept 3.74 0.57 2.63 4.93 1.00 3361 2714
#> age -0.00 0.01 -0.03 0.02 1.00 2128 2227
#> sexfemale 1.62 0.40 0.81 2.40 1.00 2538 2454
#> diseaseGN -0.12 0.48 -1.06 0.86 1.00 2184 2094
#> diseaseAN -0.53 0.47 -1.45 0.42 1.00 2158 1845
#> diseasePKD 0.98 0.73 -0.43 2.42 1.00 1740 1829
#>
#> Further Distributional Parameters:
#> Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> shape 1.12 0.15 0.84 1.45 1.00 1323 2455
#>
#> 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)
# }