`casebase`

is an R package for fitting flexible and fully
parametric hazard regression models to survival data with single event
type or multiple competing causes via logistic and multinomial
regression. Our formulation allows for arbitrary functional forms of
time and its interactions with other predictors for time-dependent
hazards and hazard ratios. From the fitted hazard model, we provide
functions to readily calculate and plot cumulative incidence and
survival curves for a given covariate profile. This approach
accommodates any log-linear hazard function of prognostic time,
treatment, and covariates, and readily allows for non-proportionality.
We also provide a plot method for visualizing incidence density via
population time plots.

You can install the released version of casebase from CRAN with:

`install.packages("casebase")`

And the development version from GitHub with:

```
# install.packages("devtools")
::install_github("sahirbhatnagar/casebase") devtools
```

See the package website for example usage of the functions. This includes

- Fitting Smooth Hazard Functions
- Competing Risks Analysis
- Population Time Plots
- Customizing Population Time Plots
- Plot Hazards and Hazard Ratios
- Plot Cumulative Incidence and Survival Curves

This is a basic example which shows you some of the main
functionalities of the `casebase`

package. We use data from
the estrogen plus progestin trial from the Womenâ€™s Health
Initiative (included in the `casebase`

package). This
randomized clinical trial investigated the effect of estrogen plus
progestin (`estPro`

) on coronary heart disease (CHD) risk in
16,608 postmenopausal women who were 50 to 79 years of age at base line.
Participants were randomly assigned to receive `estPro`

or
`placebo`

. The primary efficacy outcome of the trial was CHD
(nonfatal myocardial infarction or death due to CHD).

```
library(casebase)
#> See example usage at http://sahirbhatnagar.com/casebase/
library(visreg)
library(splines)
data("eprchd")
```

We first visualize the data with a population time plot. For each treatment arm, we plot the observed person time in gray, and the case series as colored dots. It gives us a good visual representation of the incidence density:

`plot(popTime(eprchd, exposure = "treatment"))`

We model the hazard as a function of time, treatment arm and their interaction:

```
<- transform(eprchd,
eprchd treatment = factor(treatment, levels = c("placebo","estPro")))
<- fitSmoothHazard(status ~ treatment*ns(time, df = 3),
fit data = eprchd,
time = "time")
summary(fit)
#> Fitting smooth hazards with case-base sampling
#>
#> Sample size: 16608
#> Number of events: 324
#> Number of base moments: 32400
#> ----
#>
#> Call:
#> fitSmoothHazard(formula = status ~ treatment * ns(time, df = 3),
#> data = eprchd, time = "time")
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -0.2441 -0.1474 -0.1368 -0.1272 3.1398
#>
#> Coefficients:
#> Estimate Std. Error z value
#> (Intercept) -5.87406 0.30068 -19.536
#> treatmentestPro 0.65528 0.37780 1.734
#> ns(time, df = 3)1 -0.37685 0.36055 -1.045
#> ns(time, df = 3)2 0.82888 0.73435 1.129
#> ns(time, df = 3)3 1.33620 0.34430 3.881
#> treatmentestPro:ns(time, df = 3)1 0.01662 0.48792 0.034
#> treatmentestPro:ns(time, df = 3)2 -1.42088 0.94245 -1.508
#> treatmentestPro:ns(time, df = 3)3 -1.04687 0.48685 -2.150
#> Pr(>|z|)
#> (Intercept) < 2e-16 ***
#> treatmentestPro 0.082832 .
#> ns(time, df = 3)1 0.295935
#> ns(time, df = 3)2 0.259015
#> ns(time, df = 3)3 0.000104 ***
#> treatmentestPro:ns(time, df = 3)1 0.972831
#> treatmentestPro:ns(time, df = 3)2 0.131645
#> treatmentestPro:ns(time, df = 3)3 0.031533 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 3635.4 on 32723 degrees of freedom
#> Residual deviance: 3615.6 on 32716 degrees of freedom
#> AIC: 3631.6
#>
#> Number of Fisher Scoring iterations: 7
```

Since the output object from `fitSmoothHazard`

inherits
from the `glm`

class, we see a familiar result when using the
function `summary`

.

The treatment effect on the hazard is somewhat difficult to interpret because of its interaction with the spline term on time. In these situations, it is often more instructive to visualize the relationship. For example, we can easily plot the hazard function for each treatment arm:

```
plot(fit, hazard.params = list(xvar = "time", by = "treatment"))
#> Conditions used in construction of plot
#> treatment: placebo / estPro
#> offset: 0
```

We can also plot the time-dependent hazard ratio and 95% confidence band:

```
<- quantile(eprchd$time,
newtime probs = seq(0.01, 0.99, 0.01))
# reference category
<- data.frame(treatment = factor("placebo",
newdata levels = c("placebo", "estPro")),
time = newtime)
plot(fit,
type = "hr",
newdata = newdata,
var = "treatment",
increment = 1,
xvar = "time",
ci = T,
rug = T)
```

We can also calculate and plot the cumulative incidence function:

```
<- absoluteRisk(object = fit,
smooth_risk newdata = data.frame(treatment = c("placebo", "estPro")))
plot(smooth_risk, id.names = c("placebo", "estPro"))
```

The `casebase`

package uses the following hierarchy of
classes for the output of `fitSmoothHazard`

:

```
casebase:
singleEventCB:
- glm
- gam
- cv.glmnet
CompRisk:
- vglm
```

The class `singleEventCB`

is an `S3`

class, and
we also keep track of the classes appearing below. The class
`CompRisk`

is an `S4`

class that inherits from
`vglm`

.

This package is makes use of several existing packages including:

`VGAM`

for fitting multinomial logistic regression models`survival`

for survival models`ggplot2`

for plotting the population time plots`data.table`

for efficient handling of large datasets

Other packages with similar objectives but different parametric forms:

```
citation('casebase')
#>
#> To cite casebase in publications use:
#>
#> Bhatnagar S, Turgeon M, Islam J, Saarela O, Hanley J (2020).
#> _casebase: Fitting Flexible Smooth-in-Time Hazards and Risk
#> Functions via Logistic and Multinomial Regression_. R package
#> version 0.9.0, <URL:
#> https://CRAN.R-project.org/package=casebase>.
#>
#> Hanley, James A., and Olli S. Miettinen. Fitting
#> smooth-in-time prognostic risk functions via logistic
#> regression. International Journal of Biostatistics 5.1
#> (2009): 1125-1125.
#>
#> Saarela, Olli. A case-base sampling method for estimating
#> recurrent event intensities. Lifetime data analysis 22.4
#> (2016): 589-605.
#>
#> If competing risks analyis is used, please also cite
#>
#> Saarela, Olli, and Elja Arjas. Non-parametric Bayesian
#> Hazard Regression for Chronic Disease Risk Assessment.
#> Scandinavian Journal of Statistics 42.2 (2015): 609-626.
#>
#> To see these entries in BibTeX format, use 'print(<citation>,
#> bibtex=TRUE)', 'toBibtex(.)', or set
#> 'options(citation.bibtex.max=999)'.
```

- Issues: https://github.com/sahirbhatnagar/casebase/issues
- Pull Requests: https://github.com/sahirbhatnagar/casebase/
- e-mail: sahir.bhatnagar@gmail.com, max.turgeon@umanitoba.ca

You can see the most recent changes to the package in the NEWS file

Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.