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    toc: true
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```{r  include=FALSE }
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  cache = FALSE,
  out.width = "50%"
)
```

# Multivariate Event Times (`mets`) <img src="man/figures/logo.png" align="right" height="250" style="float:right; height:250px;"  alt="mets website">

 Implementation of various statistical models for multivariate
 event history data <doi:10.1007/s10985-013-9244-x>. Including multivariate
 cumulative incidence models <doi:10.1002/sim.6016>, and  bivariate random
 effects probit models (Liability models) <doi:10.1016/j.csda.2015.01.014>.
 Modern methods for survival analysis, including regression modelling (Cox, Fine-Gray, 
 Ghosh-Lin, Binomial regression) with fast computation of influence functions. 
 Restricted mean survival time regression and years lost for competing risks. 
 Average treatment effects and G-computation.  All functions can be used with
 clusters and will work for large data. 

## Installation
```{r load, echo=FALSE, results=FALSE}
library("mets")
```


```{r install, eval=FALSE}
install.packages("mets")
```

The development version may be installed directly from github
(requires [Rtools](https://cran.r-project.org/bin/windows/Rtools/) on windows and [development tools](https://mac.r-project.org/tools/) (+Xcode) for Mac OS
X):


```{r devinstall, eval=FALSE}
remotes::install_github("kkholst/mets", dependencies="Suggests")
```

or to get development version


```{r devinstall2, eval=FALSE}
remotes::install_github("kkholst/mets",ref="develop")
```


## Citation

To cite the `mets` package please use one of the following references

> Thomas H. Scheike and Klaus K. Holst (2022). A Practical Guide to
> Family Studies with Lifetime Data. Annual Review of Statistics and
> Its Application 9, pp. 47-69. doi: <http://dx.doi.org/10.1146/annurev-statistics-040120-024253>

> Thomas H. Scheike and Klaus K. Holst and Jacob B. Hjelmborg (2013).
> Estimating heritability for cause specific mortality based on twin studies.
> Lifetime Data Analysis. <http://dx.doi.org/10.1007/s10985-013-9244-x>

> Klaus K. Holst and Thomas H. Scheike Jacob B. Hjelmborg (2015).
> The Liability Threshold Model for Censored Twin Data.
> Computational Statistics and Data Analysis. <http://dx.doi.org/10.1016/j.csda.2015.01.014>

BibTeX:

    @Article{,
      title = {A Practical Guide to Family Studies with Lifetime Data},
      author = {Thomas H. Scheike and Klaus K. Holst},
      year = {2014},
      volume = {9},
      pages = {47-69},
      journal = {Annual Review of Statistics and Its Application},
      doi = {10.1146/annurev-statistics-040120-024253},
    }

    @Article{,
      title={Estimating heritability for cause specific mortality based on twin studies},
      author={Scheike, Thomas H. and Holst, Klaus K. and Hjelmborg, Jacob B.},
      year={2013},
      issn={1380-7870},
      journal={Lifetime Data Analysis},
      doi={10.1007/s10985-013-9244-x},
      url={http://dx.doi.org/10.1007/s10985-013-9244-x},
      publisher={Springer US},
      keywords={Cause specific hazards; Competing risks; Delayed entry;
    	    Left truncation; Heritability; Survival analysis},
      pages={1-24},
      language={English}
    }

    @Article{,
      title={The Liability Threshold Model for Censored Twin Data},
      author={Holst, Klaus K. and Scheike, Thomas H. and Hjelmborg, Jacob B.},
      year={2015},
      doi={10.1016/j.csda.2015.01.014},
      url={http://dx.doi.org/10.1016/j.csda.2015.01.014},
      journal={Computational Statistics and Data Analysis}
    }

## Examples: Twins Polygenic modelling

First considering standard twin modelling (ACE, AE, ADE, and more  models)

```{r, twinlm1}
# simulated data with pairs of observations in twins on long #data format
set.seed(1)
d <- twinsim(1000, b1=c(1,-1), b2=c(), acde=c(1,1,0,1))
# Polygenic model with Additive genetic effects, and shared and invidual environmental effects (ACE)
ace <- twinlm(y ~ 1, data=d, DZ="DZ", zyg="zyg", id="id")
ace
# An AE-model could be fitted as
ae <- twinlm(y ~ 1, data=d, DZ="DZ", zyg="zyg", id="id", type="ae")
# AIC
AIC(ae)-AIC(ace)
# To adjust for the covariates we simply alter the formula statement
ace2 <- twinlm(y ~ x1+x2, data=d, DZ="DZ", zyg="zyg", id="id", type="ace")
 ## Summary/GOF
summary(ace2)
```

## Examples: Twins Polygenic modelling time-to-events Data

In the context of time-to-events data we consider the 
"Liabilty Threshold model" with IPCW adjustment for censoring.

First we fit the bivariate probit model (same marginals in MZ and DZ twins but 
different correlation parameter). Here we evaluate the risk of getting 
cancer before the last double cancer event (95 years)

```{r bptwintime}
data(prt)
prt0 <-  force.same.cens(prt, cause="status", cens.code=0, time="time", id="id")
prt0$country <- relevel(prt0$country, ref="Sweden")
prt_wide <- fast.reshape(prt0, id="id", num="num", varying=c("time","status","cancer"))
prt_time <- subset(prt_wide,  cancer1 & cancer2, select=c(time1, time2, zyg))
tau <- 95
tt <- seq(70, tau, length.out=5) ## Time points to evaluate model in

b0 <- bptwin.time(cancer ~ 1, data=prt0, id="id", zyg="zyg", DZ="DZ", type="cor",
              cens.formula=Surv(time,status==0)~zyg, breaks=tau)
summary(b0)
```

Liability threshold model with ACE random effects structure

```{r liability_ace1}
b1 <- bptwin.time(cancer ~ 1, data=prt0, id="id", zyg="zyg", DZ="DZ", type="ace",
           cens.formula=Surv(time,status==0)~zyg, breaks=tau)
summary(b1)
```

## Examples: Twins Concordance for time-to-events Data

```{r prtcomprisk}

data(prt) ## Prostate data example (sim)

## Bivariate competing risk, concordance estimates
p33 <- bicomprisk(Event(time,status)~strata(zyg)+id(id),
                  data=prt, cause=c(2,2), return.data=1, prodlim=TRUE)

p33dz <- p33$model$"DZ"$comp.risk
p33mz <- p33$model$"MZ"$comp.risk

## Probability weights based on Aalen's additive model (same censoring within pair)
prtw <- ipw(Surv(time,status==0)~country+zyg, data=prt,
            obs.only=TRUE, same.cens=TRUE, 
            cluster="id", weight.name="w")

## Marginal model (wrongly ignoring censorings)
bpmz <- biprobit(cancer~1 + cluster(id), 
                 data=subset(prt,zyg=="MZ"), eqmarg=TRUE)

## Extended liability model
bpmzIPW <- biprobit(cancer~1 + cluster(id),
                    data=subset(prtw,zyg=="MZ"),
                    weights="w")
smz <- summary(bpmzIPW)

## Concordance
plot(p33mz,ylim=c(0,0.1),axes=FALSE, automar=FALSE,atrisk=FALSE,background=TRUE,background.fg="white")
axis(2); axis(1)

abline(h=smz$prob["Concordance",],lwd=c(2,1,1),col="darkblue")
## Wrong estimates:
abline(h=summary(bpmz)$prob["Concordance",],lwd=c(2,1,1),col="lightgray",lty=2)
```

## Examples: Cox model, RMST 

We can fit the Cox model and compute many useful summaries, such as 
restricted mean survival and  stanardized treatment effects (G-estimation).
First estimating the standardized survival 

```{r coxrmst}
 data(bmt)
 bmt$time <- bmt$time+runif(408)*0.001
 bmt$event <- (bmt$cause!=0)*1
 dfactor(bmt) <- tcell.f~tcell

 ss <- phreg(Surv(time,event)~tcell.f+platelet+age,bmt) 
 summary(survivalG(ss,bmt,50))

 sst <- survivalGtime(ss,bmt,n=50)
 plot(sst,type=c("survival","risk","survival.ratio")[1])
```

Based on the phreg we can also compute  the 
restricted mean survival time and years lost (via Kaplan-Meier estimates). The function does it 
for all times at once and can be plotted as restricted mean survival or years lost at the different
time horizons 


```{r}
 out1 <- phreg(Surv(time,cause!=0)~strata(tcell,platelet),data=bmt)
 
 rm1 <- resmean_phreg(out1, times=c(50))
 summary(rm1)
 par(mfrow=c(1, 2))
 plot(rm1,se=1)
 plot(rm1,years.lost=TRUE,se=1)
```

For competing risks the years lost can be decomposed into different causes and is 
based on the integrated Aalen-Johansen estimators for the different strata

```{r yearslostcause}
 ## years.lost decomposed into causes
 drm1 <- cif_yearslost(Event(time,cause)~strata(tcell,platelet),data=bmt,times=50)
 par(mfrow=c(1,2)); plot(drm1,cause=1,se=1); title(main="Cause 1"); plot(drm1,cause=2,se=1); title(main="Cause 2")
 summary(drm1)
```

Computations are again done for all time horizons at once as illustrated in the plot. 

## Examples: Cox model IPTW 

We can fit the Cox model with inverse probabilty of treatment weights based on 
logistic regression. The treatment weights can be time-dependent and then mutiplicative
weights are applied (see details and vignette). 

```{r coxiptw}
data(bmt)
bmt$time <- bmt$time+runif(408)*0.001
bmt$id <- seq_len(nrow(bmt))
bmt$event <- (bmt$cause!=0)*1
dfactor(bmt) <- tcell.f~tcell

fit <- phreg_IPTW(Surv(time,event)~tcell.f+cluster(id),data=bmt,treat.model=tcell.f~platelet+age) 
summary(fit)
head(IC(fit))
```

## Examples: Competing risks regression, Binomial Regression

We can fit the logistic regression model at a specific time-point with IPCW adjustment

```{r binregcif}
data(bmt); bmt$time <- bmt$time+runif(408)*0.001
# logistic regresion with IPCW binomial regression 
out <- binreg(Event(time,cause)~tcell+platelet,bmt,time=50)
summary(out)
head(IC(out))
 predict(out,data.frame(tcell=c(0,1),platelet=c(1,1)),se=TRUE)
```

## Examples: Brier-score for Binomial Regression

```{r binregbrier}
 bmt$id <- seq_len(nrow(bmt))

 ## --- competing risks CIF/Survival (default) ---
 fit <- brier_binreg(
   Event(time, cause) ~ tcell + platelet + age + cluster(id),
   data = bmt, time = 50,
   rhs = list(small = ~age, full = ~tcell + platelet + age)
 )
 summary(fit)                        ## log scale
 summary(fit, transform = exp)       ## Brier scale
```

Consequently, we can also compute Brier-score for RMST and RMTL regression for survival and competing risks data using the
outcome model specification for the binreg function (see examples). 

## Examples: Competing risks regression, Fine-Gray/Logistic link

We can fit the Fine-Gray model and the logit-link competing risks model 
(using IPCW adjustment). Starting with the logit-link model 

```{r cifreg}
data(bmt)
bmt$time <- bmt$time+runif(nrow(bmt))*0.01
bmt$id <- 1:nrow(bmt)
## logistic link  OR interpretation
 or=cifreg(Event(time,cause)~strata(tcell)+platelet+age,data=bmt,cause=1)
summary(or)
par(mfrow=c(1,2))
 ## to see baseline 
plot(or)

 # predictions 
nd <- data.frame(tcell=c(1,0),platelet=0,age=0)
pll <- predict(or,nd)
plot(pll)
```

Similarly, the Fine-Gray model can be estimated using IPCW adjustment

```{r finegrary}
 ## Fine-Gray model
 fg=cifreg(Event(time,cause)~strata(tcell)+platelet+age,data=bmt,cause=1,propodds=NULL)
 summary(fg)
## baselines 
plot(fg)
nd <- data.frame(tcell=c(1,0),platelet=0,age=0)
pfg <- predict(fg,nd,se=1)
plot(pfg,se=1)

## influence functions of regression coefficients
head(iid(fg))
```

and we can get standard errors for predictions based on the influence functions of 
the baseline and the regression coefiicients (these are used in the predict function)

```{r}
baseid <- iidBaseline(fg,time=40)
FGprediid(baseid,nd)
```

further G-estimation can be done 

```{r}
 dfactor(bmt) <- tcell.f~tcell
 fg1 <- cifreg(Event(time,cause)~tcell.f+platelet+age,bmt,cause=1,propodds=NULL)
 summary(survivalG(fg1,bmt,50))
```

## Examples: Marginal mean for recurrent events 

We can estimate the expected number of events non-parametrically and 
get standard errors for this estimator

```{r recurrentevents}
data(hfactioncpx12)
dtable(hfactioncpx12,~status)

gl1 <- recurrentMarginal(Event(entry,time,status)~strata(treatment)+cluster(id),hfactioncpx12,cause=1,death.code=2)
summary(gl1,times=1:5)
plot(gl1,se=1)
```

## Examples: Ghosh-Lin for recurrent events 

We can fit the Ghosh-Lin model for the expected number of events observed
before dying (using IPCW adjustment and get predictions)

```{r ghoslin}
data(hfactioncpx12)
dtable(hfactioncpx12,~status)

gl1 <- recreg(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,cause=1,death.code=2)
summary(gl1)

## influence functions of regression coefficients
head(iid(gl1))
```
and we can get standard errors for predictions  based on the influence functions of the baseline 
and the regression coefiicients

```{r}
 nd=data.frame(treatment=levels(hfactioncpx12$treatment),id=1)
 pfg <- predict(gl1,nd,se=1)
 summary(pfg,times=1:5)
 plot(pfg,se=1)
```

The influence functions of the baseline and regression coefficients at 
a specific time-point can be obtained 

```{r}
baseid <- iidBaseline(gl1,time=2)
dd <- data.frame(treatment=levels(hfactioncpx12$treatment),id=1)
GLprediid(baseid,dd)
```
and G-computation 

```{r}
 hfactioncpx12$age <- (50+rnorm(741)*4)[hfactioncpx12$id]

 GLout <- recreg(Event(entry,time,status)~treatment+age,data=hfactioncpx12,cause=1,death.code=2)
 summary(GLout)
 summary(survivalG(GLout,hfactioncpx12,time=4))
```


## Examples: Fixed time modelling for recurrent events 

We can fit a log-link regression model at 2 years for the expected number of events observed
before dying (using IPCW adjustment)

```{r}
data(hfactioncpx12)

e2 <- recregIPCW(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,cause=1,death.code=2,time=2)
summary(e2)
head(iid(e2))
```

## Examples: Regression for RMST/Restricted mean survival for survival and competing risks  using IPCW  

RMST can be computed using the Kaplan-Meier (via phreg) and the for competing
risks via the cumulative incidence functions, but we can also get these 
estimates via IPCW adjustment and then we can do regression 

```{r}
 ### same as Kaplan-Meier for full censoring model 
 bmt$int <- with(bmt,strata(tcell,platelet))
 out <- resmeanIPCW(Event(time,cause!=0)~-1+int,bmt,time=30,
                         cens.model=~strata(platelet,tcell),model="lin")
 estimate(out)
 head(iid(out))
 ## same as 
 out1 <- phreg(Surv(time,cause!=0)~strata(tcell,platelet),data=bmt)
 rm1 <- resmean_phreg(out1,times=30)
 summary(rm1)
 
 ## competing risks years-lost for cause 1  
 out1 <- resmeanIPCW(Event(time,cause)~-1+int,bmt,time=30,cause=1,
                       cens.model=~strata(platelet,tcell),model="lin")
 estimate(out1)
 ## same as 
 drm1 <- cif_yearslost(Event(time,cause)~strata(tcell,platelet),data=bmt,times=30)
 summary(drm1)
```

## Examples: Average treatment effects (ATE) for survival or competing risks 

We can compute ATE for survival or competing risks data for the 
probabilty of dying 

```{r}
 bmt$event <- bmt$cause!=0; dfactor(bmt) <- tcell~tcell
 brs <- binregATE(Event(time,cause)~tcell+platelet+age,bmt,time=50,cause=1,
	  treat.model=tcell~platelet+age)
 summary(brs)
 head(brs$riskDR.iid)
 head(brs$riskG.iid)
```

or the the restricted mean survival or years-lost to cause 1 

```{r}
 out <- resmeanATE(Event(time,event)~tcell+platelet,data=bmt,time=40,treat.model=tcell~platelet)
 summary(out)
 head(out$riskDR.iid)
 head(out$riskG.iid)

 out1 <- resmeanATE(Event(time,cause)~tcell+platelet,data=bmt,cause=1,time=40,
                    treat.model=tcell~platelet)
 summary(out1)
```

Here event is 0/1 thus leading to restricted mean and cause taking the values 0,1,2  produces 
regression for the years lost due to cause 1. 

## Examples: While Alive estimands for recurrent events 

We consider an RCT and aim to describe the treatment effect via while alive estimands

```{r}
data(hfactioncpx12)

dtable(hfactioncpx12,~status)
dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,death.code=2)
summary(dd)

dd <- WA_recurrent(Event(entry,time,status)~treatment+cluster(id),hfactioncpx12,time=2,
		   death.code=2,trans=.333)
summary(dd,type="log")
```


