diff --git a/.gitignore b/.gitignore index ed2f617..5fc4093 100644 --- a/.gitignore +++ b/.gitignore @@ -1,2 +1 @@ *_cache/ -*_files/ diff --git a/slides.Rmd b/slides.Rmd index 0bd31f6..5fad98e 100644 --- a/slides.Rmd +++ b/slides.Rmd @@ -1,12 +1,11 @@ --- title: "Slides" execute: - cache: true - freeze: auto include: true echo: false warning: false number-sections: true +toc: true --- ```{r} @@ -33,7 +32,7 @@ dat <- dat |> mutate( sex = factor(sex, levels = c(0,1), labels = c("Female","Male")), tx.type = factor(tx.type, levels = c(0,1), labels = c("Cadaveric","Living")), - # hla.match = factor(hla.match), + hla.match = factor(hla.match), # year = factor(year) ) ``` @@ -50,30 +49,26 @@ my.theme <- theme_minimal() + ) ``` -::: {.callout-warning} -There are 25 repondents with `follow.up = 0`, 21 of which with `death = 0` and -other 4 with `death = 1`. - -```{r, echo=TRUE} -dat[dat$follow.up == 0, ] |> - group_by(death) |> - summarise(n = n()) +```{r} +my.tab <- function(x) { + x |> + tab_options( + row.striping.background_color = "#F6E8C3", + table.border.top.color = "#A83262", + table.border.bottom.color = "#A83262", + column_labels.border.bottom.color = "#A83262", + table.font.size = px(16), + heading.title.font.size = px(18), + table.background.color = "#FFF4CC" + ) +} ``` -Reasons to omit them, that is, have `dat <- dat[dat$follow.up > 0,]` at the -very beginning: - -- If `death = 1`, transplant failed. They shouldn't be included in the research - question "survival rate of a *successful* tranplant". -- If `death = 0`, transplant was successful, but they were immediately removed - from populatoin at risk, contributiong nothing to the analysis. -::: - # Title -# Table of Contents (?) +# Table of Contents -# Introduction (M) +# Introduction # Method & Result @@ -81,8 +76,9 @@ very beginning: - Data source - Study population -```{r} +```{r, echo=TRUE} nrow(dat) +range(dat$year) ``` - Covariates - Outcome @@ -104,16 +100,42 @@ dat |> hla.match ~ "HLA matches, n(%)", age.donor ~ "Donor age, median (IQR)", age.rec ~ "Recipient age, median (IQR)", - cold.isc ~ "Cold ischemic time (hours), median (IQR), ", + cold.isc ~ "Cold ischemic time (hours), median (IQR)", sex ~ "Sex, n(%)" ), missing = "ifany" ) |> add_overall() |> - modify_footnote(all_stat_cols() ~ NA) + modify_footnote(all_stat_cols() ~ NA) |> + as_gt() |> + tab_style( + style = list( + cell_fill(color = "#A83262"), + cell_text(color = "white", weight = "bold") + ), + locations = cells_column_labels() + ) |> + tab_style( + style = list( + cell_fill(color = "#F8EFCB"), + cell_text(color = "#2F2F2F") + ), + locations = cells_body() + ) |> + opt_row_striping(row_striping = TRUE) |> + tab_options( + table.background.color = "#F8EFCB", + row.striping.background_color = "#EFE6D0", + table.border.top.color = "#A83262", + table.border.bottom.color = "#A83262", + column_labels.border.top.color = "#A83262", + column_labels.border.bottom.color = "#A83262", + table.font.size = px(18), + column_labels.font.weight = "bold" + ) ``` -# Elementary Analysis: Transplant Type (L) +# Table 1: By Transplant Type ## Transplant Type vs Sex @@ -190,16 +212,25 @@ plot.tx.rec <- ggplot(data = dat) + plot.tx.rec ``` +```{r} +dat[dat$tx.type == "Cadaveric", ]$age.rec |> table() +dat[dat$tx.type == "Living", ]$age.rec |> table() +``` -# Elementary Analysis: Transplant Type (Cont.) + +# Table 1: By Transplant Type ## Transplant Type vs HLA Match Living donors have less `hla.match` then cadaveric donors. ```{r, fig.width=7, fig.height=5} -ggplot(data = dat) + - geom_bar(aes(x = hla.match)) + +dat |> + mutate( + tx.type = recode(tx.type, "Cadaveric" = "Deceased") + ) |> + ggplot() + + geom_bar(aes(x = hla.match, fill = tx.type)) + facet_wrap(tx.type ~ ., ncol = 1) + labs( title = "Distribution of HLA Match by Transplant Type", @@ -207,7 +238,21 @@ ggplot(data = dat) + y = "Count", color = NULL ) + - my.theme + scale_fill_manual( + values = c( + "Deceased" = "darkorange", + "Living" = "darkgreen" + ), + labels = c( + "Deceased" = "Deceased", + "Living" = "Living" + ) + ) + + my.theme + + theme( + legend.position = "none", + strip.text = element_text(size = 12) + ) ``` @@ -242,7 +287,7 @@ plot.tx.donor <- ggplot(data = dat) + plot.tx.donor ``` -# Overall Kaplan-Meier Curve +# Overall Survival ```{r} km.all <- survfit(Surv(follow.up, death) ~ 1, data = dat) @@ -271,8 +316,8 @@ border_col <- "#D8C8A5" ``` ```{r} -times <- seq(0, 12, 2) -summary(km.all, times = times)[c("time", "n.risk", "surv")] |> +km.all.summary <- summary(km.all, times = seq(0, 12, 2)) +km.all.summary[c("time", "n.risk", "surv", "lower", "upper")] |> as.data.frame() |> gt() |> tab_header( @@ -281,33 +326,13 @@ summary(km.all, times = times)[c("time", "n.risk", "surv")] |> cols_label( time = "Follow-up Time", n.risk = "Number at Risk", - surv = "Survival Probability" - ) |> - fmt_number( - columns = surv, - decimals = 3 - ) |> - tab_options( - table.font.size = px(15), - heading.title.font.size = px(20), - column_labels.font.weight = "bold" - ) - -``` - -```{r} -summary(km.all, times = times)[c("time", "n.risk", "surv")] |> - as.data.frame() |> - gt() |> - tab_header( - title = "Overall Kaplan-Meier Survival Summary" - ) |> - cols_label( - time = "Follow-up Time", - n.risk = "Number at Risk", - surv = "Survival Probability" + surv = "Survival Probability", + lower = "Upper 95% CI", + upper = "Lower 95% CI", ) |> fmt_number(columns = surv, decimals = 3) |> + fmt_number(columns = lower, decimals = 3) |> + fmt_number(columns = upper, decimals = 3) |> fmt_number(columns = time, decimals = 0) |> tab_style( style = list( @@ -321,18 +346,234 @@ summary(km.all, times = times)[c("time", "n.risk", "surv")] |> locations = cells_body() ) |> opt_row_striping(row_striping = TRUE) |> - tab_options( - row.striping.background_color = "#F6E8C3", - table.border.top.color = "#A83262", - table.border.bottom.color = "#A83262", - column_labels.border.bottom.color = "#A83262", - table.font.size = px(16), - heading.title.font.size = px(18), - table.background.color = "#FFF4CC" + my.tab() +``` + +# Hazard by Transplant Type + +## Death distribution + + +```{r} +dat[dat$death == 1, ] |> + mutate( + first.1 = follow.up <= 1, + first.5 = follow.up <= 5, + ) |> + select(first.1, first.5) |> + summarize( + total = n(), + first.1.total = sum(first.1), + first.1.ratio = first.1.total / total * 100, + first.5.total = sum(first.5), + first.5.ratio = first.5.total / total * 100, ) ``` -# Cox Model (with intervals?) +```{r} +dat[dat$death == 1, ] |> + ggplot(aes(x = follow.up)) + + geom_histogram(bins = 50) + + labs( + title = "Distribution of Occurence of Death", + x = "Years of Follow-up", + y = "Count" + ) + + my.theme +``` + +```{r} +n.pop <- nrow(dat) +dat |> + select(follow.up, death) |> + mutate(censored = ifelse(death == 1, 0, 1)) |> + group_by(follow.up) |> + summarize( + death = sum(death), + censored = sum(censored), + .groups = "drop" + ) |> + arrange(follow.up) |> + mutate( + death.accum = cumsum(death), + death.accum.ratio = death.accum / sum(dat$death), + ) |> + ggplot() + + geom_step(aes(y = death.accum.ratio, x = follow.up)) + + labs( + title = "Cumulative Proportion of Deaths Over Follow-up", + x = "Years of Follow-up", + y = "Cumulative Proportion of Deaths" + ) + + my.theme +``` + +# Hazard Rate by Transplant Type + +```{r} +get.life.table <- function(dat, time.intervals) { + n.pop <- nrow(dat) + + dat |> + recode.dat(time.intervals) |> + group_by(fu.interval) |> + summarize( + n.censored = sum(.data$death == 0), + n.event = sum(.data$death), + ) |> + ungroup() |> + calculate.hazard(n.pop) +} + +get.life.table.by.groups <- function(dat, time.intervals, grps) { + grps |> + lapply(function(grp) { + dat |> + get.life.table.by.group(time.intervals, grp) |> + mutate( + grp.name = grp, + grp.value = pick(1)[[1]] + ) |> + select(-1) + }) |> + bind_rows() +} + +get.life.table.by.group <- function(dat, time.intervals, grp) { + dat |> + recode.dat(time.intervals) |> + group_by(fu.interval, .data[[grp]]) |> + summarize( + n.censored = sum(.data$death == 0), + n.event = sum(.data$death), + .groups = "keep" + ) |> + ungroup(fu.interval) |> + group_modify(function(df.sub, grp) { + grp.name <- names(grp) + grp.value <- grp[[1]] + n.pop <- (dat[[grp.name]] == grp.value) |> sum() + calculate.hazard(df.sub, n.pop) + }) |> + ungroup() +} + +calculate.hazard <- function(life.table, n.pop) { + n.removed <- life.table$n.event + life.table$n.censored + n.removed.accum <- c(0, cumsum(n.removed)[-length(n.removed)]) + life.table |> + mutate( + n.at.risk = n.pop - n.removed.accum, + # TODO: how to account for censored? How do we adjust for uneven interval? + hazard.rate = n.event / n.at.risk + ) +} + +recode.dat <- function(dat, time.intervals) { + df <- dat[dat$follow.up <= sum(time.intervals), ] + time.points <- cumsum(time.intervals) + df$fu.interval <- sapply(df$follow.up, function(time) { + time.points[time <= time.points][1] + }) + + df +} + +plot.hazard.rate.by.groups <- function(dat, time.intervals, grps) { + dat |> + get.life.table.by.groups(time.intervals, grps) |> + ggplot(aes(x = fu.interval, y = hazard.rate, color = grp.value)) + + geom_point() + + geom_line() + + scale_color_discrete( + labels = c( + "Cadaveric" = "Deceased", + "Living" = "Living" + ) + ) + + scale_x_continuous( + breaks = function(x) seq(floor(x[1]), ceiling(x[2]), by = 1) + ) + + labs( + title = "Hazard Rate by Transplant Type", + x = "Follow-up Year", + y = "Estimated Hazard Rate", + color = "Transplant Type" + ) + + my.theme +} +``` + +```{r, fig.width=7, fig.height=5} +time.intervals = c(rep(1/3, 3), rep(1, 4)) +plot.hazard.rate.by.groups(dat, time.intervals, "tx.type") +``` + +```{r} +get.life.table.by.group(dat, time.intervals, "tx.type") |> + select(fu.interval, tx.type, hazard.rate) |> + pivot_wider( + names_from = tx.type, + values_from = hazard.rate + ) |> + mutate( + fu.interval = case_when( + abs(fu.interval - 1/3) < 0.001 ~ "1/3", + abs(fu.interval - 2/3) < 0.001 ~ "2/3", + fu.interval %% 1 == 0 ~ as.character(as.integer(fu.interval)), + TRUE ~ as.character(fu.interval) + ), + Deceased = round(Cadaveric, 3), + Living = round(Living, 3) + ) |> + select(fu.interval, Deceased, Living) |> + gt() |> + tab_header( + title = "Estimated Hazard Rate by Transplant Type" + ) |> + cols_label( + fu.interval = "Follow-up Interval" + ) |> + cols_align( + align = "center", + columns = everything() + ) |> + tab_style( + style = list( + cell_fill(color = "#5B5FE0"), + cell_text(color = "white", weight = "bold") + ), + locations = cells_column_labels() + ) |> + tab_style( + style = list( + cell_fill(color = "#FFF2CC"), + cell_text(color = "#2F2F2F") + ), + locations = cells_body() + ) |> + tab_style( + style = cell_text( + color = "#5B5FE0", + weight = "bold", + size = px(22) + ), + locations = cells_title(groups = "title") + ) |> + tab_options( + table.background.color = "#FFF2CC", + row.striping.background_color = "#F6E7B8", + table.border.top.color = "#5B5FE0", + table.border.bottom.color = "#5B5FE0", + column_labels.border.bottom.color = "#5B5FE0", + heading.background.color = "#FFF2CC", + heading.title.font.size = px(22), + table.font.size = px(18), + column_labels.font.weight = "bold" + ) |> + opt_row_striping() +``` + # Cox Model: Transplant Type @@ -356,11 +597,11 @@ km.tx |> labels = c("Deceased", "Living") ) + labs( - title = "Survival by Donor Type", + title = "Survival by Transplant Type", x = "Years of Follow-up", y = "Survival Probability", - color = "Donor Type", - fill = "Donor Type" + color = "Transplant Type", + fill = "Transplant Type" ) + my.theme ``` @@ -452,6 +693,37 @@ km.age.rec.group <- survfit(Surv(follow.up, death) ~ age.rec.group, data = dat.age.rec.group) ``` + +```{r, fig.width=7, fig.height=7} +eme.age.rec.group$contrast |> + as.data.frame() |> + select(contrast, ratio, SE, p.value) |> + mutate( + contrast = factor(contrast), + log.ratio = log(ratio), + SE.log = SE / ratio, + low = exp(log.ratio - 1.96 * SE.log), + up = exp(log.ratio + 1.96 * SE.log) + ) |> + ggplot(aes(y = reorder(contrast, ratio))) + + geom_errorbarh(aes(xmin = low, xmax = up), height = 0.2) + + geom_point(aes(x = ratio)) + + geom_vline(xintercept = 1, linetype = "dashed") + + scale_y_discrete( + labels = function(x) { + gsub("[()]", "", x = x) + } + ) + + labs( + x = "Hazard Ratio", + y = "Recipient Age Group Comparison", + title = "Pairwise Hazard Ratios by Recipient Age Groups" + ) + + my.theme +``` + +# Cox Model: Age Recipient (Categorical) + ```{r, fig.width=7, fig.height=7} km.age.rec.group |> ggsurvfit(type = "survival") + @@ -472,34 +744,6 @@ km.age.rec.group |> my.theme ``` -```{r, fig.width=7, fig.height=7} -eme.age.rec.group$contrast |> - as.data.frame() |> - select(contrast, ratio, SE, p.value) |> - mutate( - contrast = factor(contrast), - log.ratio = log(ratio), - SE.log = SE / ratio, - low = exp(log.ratio - 1.96 * SE.log), - up = exp(log.ratio + 1.96 * SE.log) - ) |> - ggplot(aes(y = reorder(contrast, ratio))) + - geom_errorbarh(aes(xmin = low, xmax = up)) + - geom_point(aes(x = ratio)) + - geom_vline(xintercept = 1, linetype = "dashed") + - scale_y_discrete( - labels = function(x) { - gsub("[()]", "", x = x) - } - ) + - labs( - x = "Hazard Ratio", - y = "Recipient Age Group Comparison", - title = "Pairwise Hazard Ratios by Recipient Age Groups" - ) + - my.theme -``` - # Identifying Predictors ```{r} @@ -528,25 +772,24 @@ test.new.var <- function(old.vars, new.var, i=1) { ```{r, echo=TRUE} old.vars <- c() test.new.var(old.vars, "tx.type", 1) -test.new.var(old.vars, "hla.match", 1) -test.new.var(old.vars, "age.donor", 1) test.new.var(old.vars, "age.rec", 1) -test.new.var(old.vars, "cold.isc", 1) -test.new.var(old.vars, "sex", 1) +test.new.var(old.vars, "age.donor", 1) test.new.var(old.vars, "year", 1) +test.new.var(old.vars, "hla.match", 1) +test.new.var(old.vars, "sex", 1) +test.new.var(old.vars, "cold.isc", 1) ``` ## `tx.type` + ? ```{r, echo=TRUE} old.vars <- c("tx.type") -# test.new.var(old.vars, "hla.match", 2:7) -test.new.var(old.vars, "hla.match", 2) -test.new.var(old.vars, "age.donor", 2) test.new.var(old.vars, "age.rec", 2) -test.new.var(old.vars, "cold.isc", 2) -test.new.var(old.vars, "sex", 2) +test.new.var(old.vars, "age.donor", 2) test.new.var(old.vars, "year", 2) +test.new.var(old.vars, "hla.match", 2:7) +test.new.var(old.vars, "sex", 2) +test.new.var(old.vars, "cold.isc", 2) ``` `age.rec` has the smallest $p$-value @@ -556,47 +799,47 @@ test.new.var(old.vars, "year", 2) ```{r, echo=TRUE} old.vars <- c("tx.type", "age.rec") -test.new.var(old.vars, "hla.match", 3) test.new.var(old.vars, "age.donor", 3) -test.new.var(old.vars, "cold.isc", 3) -test.new.var(old.vars, "sex", 3) test.new.var(old.vars, "year", 3) -``` - -`hla.match` has the smallest $p$-value - -## `tx.type` + `age.rec` + `hla.match` + ? - -```{r, echo=TRUE} -old.vars <- c("tx.type", "age.rec", "hla.match") - -test.new.var(old.vars, "age.donor", 4) -test.new.var(old.vars, "cold.isc", 4) -test.new.var(old.vars, "sex", 4) -test.new.var(old.vars, "year", 4) +test.new.var(old.vars, "hla.match", 3:8) +test.new.var(old.vars, "sex", 3) +test.new.var(old.vars, "cold.isc", 3) ``` `age.donor` has the smallest $p$-value -## `tx.type` + `age.rec` + `hla.match` + `age.donor` + ? +## `tx.type` + `age.rec` + `age.donor` + ? ```{r, echo=TRUE} -old.vars <- c("tx.type", "age.rec", "hla.match", "age.donor") +old.vars <- c("tx.type", "age.rec", "age.donor") -test.new.var(old.vars, "cold.isc", 5) -test.new.var(old.vars, "sex", 5) -test.new.var(old.vars, "year", 5) +test.new.var(old.vars, "year", 4) +test.new.var(old.vars, "hla.match", 4:9) +test.new.var(old.vars, "sex", 4) +test.new.var(old.vars, "cold.isc", 4) ``` `year` has the smallest $p$-value -## `tx.type` + `age.rec` + `hla.match` + `age.donor` + `year` + ? +## `tx.type` + `age.rec` + `age.donor` + `year` + ? ```{r, echo=TRUE} -old.vars <- c("tx.type", "age.rec", "hla.match", "age.donor", "year") +old.vars <- c("tx.type", "age.rec", "age.donor", "year") -test.new.var(old.vars, "cold.isc", 6) -test.new.var(old.vars, "sex", 6) +test.new.var(old.vars, "hla.match", 5:10) +test.new.var(old.vars, "sex", 5) +test.new.var(old.vars, "cold.isc", 5) +``` + +`hla.match` has the smallest $p$-value + +## `tx.type` + `age.rec` + `age.donor` + `year` + `hla.match` + ? + +```{r, echo=TRUE} +old.vars <- c("tx.type", "age.rec", "age.donor", "year", "hla.match") + +test.new.var(old.vars, "sex", 11) +test.new.var(old.vars, "cold.isc", 11) ``` Neither has $p$-value less than 0.05. Stop. @@ -604,16 +847,14 @@ Neither has $p$-value less than 0.05. Stop. # Full Model ```{r} -surv.full <- Surv(follow.up + death) ~ tx.type + age.rec + hla.match + - age.donor + year +surv.full <- Surv(follow.up, death) ~ tx.type + age.rec + age.donor + year + + hla.match cox.full <- coxph(surv.full, data = dat, method = "breslow") -``` - -```{r, echo=TRUE} -cox.full +summary(cox.full) ``` ```{r, fig.width=6, fig.height=6} +print(1) tidy(cox.full, exponentiate = TRUE, conf.int = TRUE) |> mutate( term = recode( @@ -641,14 +882,60 @@ tidy(cox.full, exponentiate = TRUE, conf.int = TRUE) |> my.theme ``` -## What happened to `year`? + + + +# Proportional hazards assumption ```{r} -ggplot(data = dat) + - geom_boxplot(aes(x = factor(year), y = follow.up)) +cox.full +cox.zph(cox.full) ``` -```{r} +```{r, fig.width=15, fig.height=10} +ph_plots <- ggcoxzph( + cox.zph(cox.full), ggtheme = theme_minimal(), point.size = 5, size = 30 +) + +var.names <- c("Transplant Type", "Recipient Age", "Donor Age", "Year", + "HLA Match") + +my_ph_theme <- theme( + legend.position = "bottom", + plot.title = element_text(size = 40, face = "bold"), + axis.title = element_text(size = 35), + axis.text = element_text(size = 30), + legend.text = element_text(size = 20) +) + +for (i in seq_along(ph_plots)) { + title <- paste0("Scaled Schoenfeld Residuals: ", var.names[i]) + single_plot <- ph_plots[[i]] + my_ph_theme + labs(title = title) + print(single_plot) +} +``` + + + + + + +## What happened to `year`? + +```{r, fig.width=10, fig.height=7} +ggplot(data = dat) + + geom_boxplot(aes(x = factor(year), y = follow.up)) + + my.theme +``` + +```{r, fig.width=10, fig.height=7} +ggplot(data = dat) + + geom_boxplot(aes(x = factor(year), y = follow.up, color = factor(death))) + + my.theme +``` + + +```{r, fig.width=7, fig.height=5} ggplot(data = dat) + geom_boxplot(aes(x = factor(year), y = follow.up)) + facet_grid(death ~ .) @@ -659,8 +946,8 @@ Probabily want to omit it ## Without `year` ```{r} -surv.full.1 <- Surv(follow.up + death) ~ tx.type + age.rec + hla.match + - age.donor +surv.full.1 <- Surv(follow.up, death) ~ tx.type + age.rec + hla.match + + age.donor cox.full.1 <- coxph(surv.full.1, data = dat, method = "breslow") ``` @@ -706,25 +993,16 @@ hr.compare <- bind_rows( mutate(model = "Model without year") ) |> mutate( - term = recode( - term, - "tx.typeLiving" = "Living donor", - "age.rec" = "Recipient age", - "hla.match" = "HLA match", - "age.donor" = "Donor age", - "year" = "Transplant year" - ), - term = factor( - term, - levels = c( - "Transplant year", - "Living donor", - "Recipient age", - "Donor age", - "HLA match" - ) + term = case_when( + term == "tx.typeLiving" ~ "Living donor", + term == "age.rec" ~ "Recipient age", + term == "age.donor" ~ "Donor age", + term == "year" ~ "Transplant year", + TRUE ~ term ) ) + +hr.compare ggplot(hr.compare, aes(x = estimate, y = term, color = model)) + geom_vline(xintercept = 1, linetype = "dashed") + geom_errorbarh( @@ -746,15 +1024,6 @@ ggplot(hr.compare, aes(x = estimate, y = term, color = model)) + my.theme ``` - - - - - - - - - --- TODO: write a more generic function (UPDATE: FAILED) @@ -869,7 +1138,7 @@ dat.accum |> ``` ```{r} -dat[dat$death == 1,] |> +dat[dat$death == 1, ] |> ggplot(aes(x = follow.up)) + geom_histogram(bins = 50) ``` diff --git a/slides.html b/slides.html index b374ce6..df7baba 100644 --- a/slides.html +++ b/slides.html @@ -102,10 +102,92 @@ window.Quarto = { - +
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Reasons to omit them, that is, have dat <- dat[dat$follow.up > 0,] at the very beginning:

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    +
    +
    [1] 1990 2002
    +
    • Covariates
      • @@ -194,54 +251,54 @@ Warning

      4.2 Table (L)

      -
      - @@ -653,129 +710,129 @@ Warning -Characteristic -Overall
      +Characteristic +Overall
      N = 9,775 -Cadaveric
      +Cadaveric
      N = 5,148 -Living
      +Living
      N = 4,627 -Sex, n(%) -
      +Sex, n(%) +
      -
      +
      -
      +
      -    Female -4,014 (41%) -2,105 (41%) -1,909 (41%) +    Female +4,014 (41%) +2,105 (41%) +1,909 (41%) -    Male -5,761 (59%) -3,043 (59%) -2,718 (59%) +    Male +5,761 (59%) +3,043 (59%) +2,718 (59%) -Recipient age, median (IQR) -13 (8, 16) -13 (7, 16) -14 (9, 16) +Recipient age, median (IQR) +13 (8, 16) +13 (7, 16) +14 (9, 16) -    Unknown -9 -7 -2 +    Unknown +9 +7 +2 -Donor age, median (IQR) -33 (21, 41) -37 (31, 42) -22 (15, 37) +Donor age, median (IQR) +33 (21, 41) +37 (31, 42) +22 (15, 37) -    Unknown -113 -112 -1 +    Unknown +113 +112 +1 -HLA matches, n(%) -
      +HLA matches, n(%) +
      -
      +
      -
      +
      -    0 -784 (8.2%) -125 (2.5%) -659 (14%) +    0 +784 (8.2%) +125 (2.5%) +659 (14%) -    1 -1,504 (16%) -160 (3.2%) -1,344 (29%) +    1 +1,504 (16%) +160 (3.2%) +1,344 (29%) -    2 -1,553 (16%) -228 (4.6%) -1,325 (29%) +    2 +1,553 (16%) +228 (4.6%) +1,325 (29%) -    3 -3,778 (40%) -3,039 (61%) -739 (16%) +    3 +3,778 (40%) +3,039 (61%) +739 (16%) -    4 -1,278 (13%) -1,007 (20%) -271 (5.9%) +    4 +1,278 (13%) +1,007 (20%) +271 (5.9%) -    5 -365 (3.8%) -241 (4.9%) -124 (2.7%) +    5 +365 (3.8%) +241 (4.9%) +124 (2.7%) -    6 -279 (2.9%) -153 (3.1%) -126 (2.7%) +    6 +279 (2.9%) +153 (3.1%) +126 (2.7%) -    Unknown -234 -195 -39 +    Unknown +234 +195 +39 -Cold ischemic time (hours), median (IQR), -7 (1, 19) -1 (0, 1) -19 (13, 25) +Cold ischemic time (hours), median (IQR) +7 (1, 19) +1 (0, 1) +19 (13, 25) -    Unknown -2,250 -1,490 -760 +    Unknown +2,250 +1,490 +760 @@ -785,8 +842,8 @@ N = 4,627
    -
    -

    5 Elementary Analysis: Transplant Type (L)

    +
    +

    5 Table 1: By Transplant Type

    5.1 Transplant Type vs Sex

    sex are similar across tx.type

    @@ -811,10 +868,22 @@ N = 4,627
    +
    +
    +
    
+  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18 
+ 58 290 227 156 161 151 155 167 202 218 218 250 287 330 357 420 466 508 520
    +
    +
    +
    
+  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18 
+ 35 104 154 121 118 135 147 166 169 170 212 193 254 314 328 454 469 565 517
    +
    +
    -
    -

    6 Elementary Analysis: Transplant Type (Cont.)

    +
    +

    6 Table 1: By Transplant Type

    6.1 Transplant Type vs HLA Match

    Living donors have less hla.match then cadaveric donors.

    @@ -822,7 +891,7 @@ N = 4,627
    -

    +

    @@ -834,548 +903,43 @@ N = 4,627
    -

    +

    -
    -

    7 Overall Kaplan-Meier Curve

    +
    +

    7 Overall Survival

    -

    +

    -
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Overall Kaplan-Meier Survival Summary
    Follow-up TimeNumber at RiskSurvival Probability
    097751.000
    264510.968
    441500.953
    623980.937
    811970.919
    104920.901
    12480.888
    - -
    -
    -
    -
    -
    -
    - @@ -1812,12 +1376,14 @@ N = 4,627 - + + + @@ -1825,36 +1391,50 @@ N = 4,627 + + + + + + + + + + + + + +
    Overall Kaplan-Meier Survival SummaryOverall Kaplan-Meier Survival Summary
    Follow-up Time Number at Risk Survival ProbabilityUpper 95% CILower 95% CI
    0 9775 1.0000.9991.000
    2 6451 0.9680.9640.971
    4 4150 0.9530.9480.958
    6 2398 0.9370.9310.944
    8 1197 0.9190.9100.928
    10 492 0.9010.8880.913
    12 48 0.8880.8710.905
    @@ -1863,11 +1443,555 @@ N = 4,627
    -
    -

    8 Cox Model (with intervals?)

    +
    +

    8 Hazard by Transplant Type

    +
    +

    8.1 Death distribution

    +
    +
    +
      total first.1.total first.1.ratio first.5.total first.5.ratio
+1   465           216      46.45161           390      83.87097
    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    -
    -

    9 Cox Model: Transplant Type

    +
    +
    +

    9 Hazard Rate by Transplant Type

    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    Estimated Hazard Rate by Transplant Type
    Follow-up IntervalDeceasedLiving
    1/30.0100.022
    2/30.0030.006
    10.0030.004
    20.0060.011
    30.0050.008
    40.0060.010
    50.0050.011
    + +
    +
    +
    +
    +
    +

    10 Cox Model: Transplant Type

    Call:
@@ -1893,7 +2017,7 @@ Score (logrank) test = 47.09  on 1 df,   p=7e-12
    -

    +

    @@ -1918,8 +2042,8 @@ Score (logrank) test = 47.09 on 1 df, p=7e-12
    -
    -

    10 Cox Model: Age Recipient (Continuous)

    +
    +

    11 Cox Model: Age Recipient (Continuous)

    Call:
@@ -1946,7 +2070,7 @@ Score (logrank) test = 25.75  on 1 df,   p=4e-07
    -

    +

    @@ -2094,10 +2218,10 @@ View life table
    -
    -

    11 Cox Model: Age Recipient (Categorical)

    +
    +

    12 Cox Model: Age Recipient (Categorical)

    -
    cox.age.rec.group
    +
    cox.age.rec.group
    Call:
 coxph(formula = Surv(follow.up, death) ~ age.rec.group, data = dat.age.rec.group)
@@ -2114,9 +2238,9 @@ n= 9766, number of events= 464
    -
    eme.age.rec.group <- emmeans(cox.age.rec.group, pairwise ~ age.rec.group,
-                             type = "response")
-eme.age.rec.group
    +
    eme.age.rec.group <- emmeans(cox.age.rec.group, pairwise ~ age.rec.group,
+                             type = "response")
+eme.age.rec.group
    $emmeans
  age.rec.group response     SE  df asymp.LCL asymp.UCL
@@ -2145,28 +2269,31 @@ Tests are performed on the log scale
    -

    -
    -
    -
    -
    -
    -
    -
    -
    -

    +

    -
    -

    12 Identifying Predictors

    -
    -

    12.1 Start with nothing

    +
    +

    13 Cox Model: Age Recipient (Categorical)

    -
    old.vars <- c()
-test.new.var(old.vars, "tx.type", 1)
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +

    14 Identifying Predictors

    +
    +

    14.1 Start with nothing

    +
    +
    old.vars <- c()
+test.new.var(old.vars, "tx.type", 1)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2181,39 +2308,7 @@ n= 9775, number of events= 465 
          Wald df            p
 1 45.49594  1 1.529554e-11
    -
    test.new.var(old.vars, "hla.match", 1)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-             coef exp(coef) se(coef)      z        p
-hla.match -0.2096    0.8109   0.0351 -5.972 2.34e-09
-
-Likelihood ratio test=35.87  on 1 df, p=2.112e-09
-n= 9541, number of events= 451 
-   (234 observations deleted due to missingness)
    -
    -
    -
         Wald df            p
-1 35.6703  1 2.336993e-09
    -
    -
    test.new.var(old.vars, "age.donor", 1)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-               coef exp(coef)  se(coef)      z        p
-age.donor -0.021738  0.978497  0.003467 -6.269 3.62e-10
-
-Likelihood ratio test=38.96  on 1 df, p=4.319e-10
-n= 9662, number of events= 464 
-   (113 observations deleted due to missingness)
    -
    -
    -
          Wald df           p
-1 39.30567  1 3.62387e-10
    -
    -
    test.new.var(old.vars, "age.rec", 1)
    +
    test.new.var(old.vars, "age.rec", 1)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2229,7 +2324,74 @@ n= 9766, number of events= 464
 
          Wald df            p
 1 25.44856  1 4.543371e-07
    -
    test.new.var(old.vars, "cold.isc", 1)
    +
    test.new.var(old.vars, "age.donor", 1)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+               coef exp(coef)  se(coef)      z        p
+age.donor -0.021738  0.978497  0.003467 -6.269 3.62e-10
+
+Likelihood ratio test=38.96  on 1 df, p=4.319e-10
+n= 9662, number of events= 464 
+   (113 observations deleted due to missingness)
    +
    +
    +
          Wald df           p
+1 39.30567  1 3.62387e-10
    +
    +
    test.new.var(old.vars, "year", 1)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+         coef exp(coef) se(coef)      z     p
+year -0.03667   0.96399  0.01550 -2.366 0.018
+
+Likelihood ratio test=5.62  on 1 df, p=0.0178
+n= 9775, number of events= 465
    +
    +
    +
          Wald df          p
+1 5.595603  1 0.01800561
    +
    +
    test.new.var(old.vars, "hla.match", 1)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+               coef exp(coef) se(coef)      z        p
+hla.match1 -0.07016   0.93225  0.17301 -0.405   0.6851
+hla.match2 -0.36381   0.69503  0.17922 -2.030   0.0424
+hla.match3 -0.76176   0.46684  0.16442 -4.633 3.60e-06
+hla.match4 -0.89933   0.40684  0.20835 -4.317 1.59e-05
+hla.match5 -0.59727   0.55031  0.28740 -2.078   0.0377
+hla.match6 -0.66377   0.51491  0.31171 -2.129   0.0332
+
+Likelihood ratio test=47.36  on 6 df, p=1.584e-08
+n= 9541, number of events= 451 
+   (234 observations deleted due to missingness)
    +
    +
    +
           Wald df        p
+1 0.1644258  1 0.685114
    +
    +
    test.new.var(old.vars, "sex", 1)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+            coef exp(coef) se(coef)      z     p
+sexMale -0.08422   0.91923  0.09374 -0.898 0.369
+
+Likelihood ratio test=0.8  on 1 df, p=0.37
+n= 9775, number of events= 465
    +
    +
    +
           Wald df         p
+1 0.8072063  1 0.3689475
    +
    +
    test.new.var(old.vars, "cold.isc", 1)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2245,79 +2407,14 @@ n= 7525, number of events= 357
 
          Wald df            p
 1 22.20574  1 2.449402e-06
    -
    test.new.var(old.vars, "sex", 1)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-            coef exp(coef) se(coef)      z     p
-sexMale -0.08422   0.91923  0.09374 -0.898 0.369
-
-Likelihood ratio test=0.8  on 1 df, p=0.37
-n= 9775, number of events= 465
    -
    -
    -
           Wald df         p
-1 0.8072063  1 0.3689475
    -
    -
    test.new.var(old.vars, "year", 1)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-         coef exp(coef) se(coef)      z     p
-year -0.03667   0.96399  0.01550 -2.366 0.018
-
-Likelihood ratio test=5.62  on 1 df, p=0.0178
-n= 9775, number of events= 465
    -
    -
    -
          Wald df          p
-1 5.595603  1 0.01800561
    -
    -
    -

    12.2 tx.type + ?

    +
    +

    14.2 tx.type + ?

    -
    old.vars <- c("tx.type")
-
-# test.new.var(old.vars, "hla.match", 2:7)
-test.new.var(old.vars, "hla.match", 2)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                  coef exp(coef) se(coef)      z        p
-tx.typeLiving  0.45336   1.57359  0.11146  4.068 4.75e-05
-hla.match     -0.12459   0.88286  0.03959 -3.147  0.00165
-
-Likelihood ratio test=52.43  on 2 df, p=4.122e-12
-n= 9541, number of events= 451 
-   (234 observations deleted due to missingness)
    -
    -
    -
          Wald df           p
-1 9.905243  1 0.001648086
    -
    -
    test.new.var(old.vars, "age.donor", 2)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.478191  1.613154  0.106660  4.483 7.35e-06
-age.donor     -0.013523  0.986568  0.003745 -3.611 0.000305
-
-Likelihood ratio test=59.05  on 2 df, p=1.506e-13
-n= 9662, number of events= 464 
-   (113 observations deleted due to missingness)
    -
    -
    -
         Wald df            p
-1 13.0412  1 0.0003047131
    -
    -
    test.new.var(old.vars, "age.rec", 2)
    +
    old.vars <- c("tx.type")
+
+test.new.var(old.vars, "age.rec", 2)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2334,7 +2431,78 @@ n= 9766, number of events= 464
 
          Wald df            p
 1 33.06396  1 8.917646e-09
    -
    test.new.var(old.vars, "cold.isc", 2)
    +
    test.new.var(old.vars, "age.donor", 2)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z        p
+tx.typeLiving  0.478191  1.613154  0.106660  4.483 7.35e-06
+age.donor     -0.013523  0.986568  0.003745 -3.611 0.000305
+
+Likelihood ratio test=59.05  on 2 df, p=1.506e-13
+n= 9662, number of events= 464 
+   (113 observations deleted due to missingness)
    +
    +
    +
         Wald df            p
+1 13.0412  1 0.0003047131
    +
    +
    test.new.var(old.vars, "year", 2)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                  coef exp(coef) se(coef)      z        p
+tx.typeLiving  0.63806   1.89281  0.09563  6.672 2.52e-11
+year          -0.03310   0.96744  0.01548 -2.138   0.0325
+
+Likelihood ratio test=51.69  on 2 df, p=5.967e-12
+n= 9775, number of events= 465
    +
    +
    +
          Wald df         p
+1 4.573044  1 0.0324788
    +
    +
    test.new.var(old.vars, "hla.match", 2:7)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                  coef exp(coef) se(coef)      z       p
+tx.typeLiving  0.39047   1.47768  0.12688  3.078 0.00209
+hla.match1    -0.08836   0.91543  0.17308 -0.510 0.60970
+hla.match2    -0.36329   0.69539  0.17919 -2.027 0.04263
+hla.match3    -0.50800   0.60170  0.18299 -2.776 0.00550
+hla.match4    -0.65400   0.51996  0.22221 -2.943 0.00325
+hla.match5    -0.39435   0.67412  0.29410 -1.341 0.17997
+hla.match6    -0.51481   0.59761  0.31489 -1.635 0.10208
+
+Likelihood ratio test=56.78  on 7 df, p=6.605e-10
+n= 9541, number of events= 451 
+   (234 observations deleted due to missingness)
    +
    +
    +
         Wald df          p
+1 14.7018  6 0.02270728
    +
    +
    test.new.var(old.vars, "sex", 2)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                  coef exp(coef) se(coef)      z       p
+tx.typeLiving  0.64499   1.90597  0.09558  6.748 1.5e-11
+sexMale       -0.08657   0.91707  0.09374 -0.924   0.356
+
+Likelihood ratio test=47.95  on 2 df, p=3.87e-11
+n= 9775, number of events= 465
    +
    +
    +
           Wald df         p
+1 0.8528929  1 0.3557352
    +
    +
    test.new.var(old.vars, "cold.isc", 2)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2351,65 +2519,15 @@ n= 7525, number of events= 357
 
           Wald df         p
 1 0.5357515  1 0.4641988
    -
    test.new.var(old.vars, "sex", 2)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                  coef exp(coef) se(coef)      z       p
-tx.typeLiving  0.64499   1.90597  0.09558  6.748 1.5e-11
-sexMale       -0.08657   0.91707  0.09374 -0.924   0.356
-
-Likelihood ratio test=47.95  on 2 df, p=3.87e-11
-n= 9775, number of events= 465
    -
    -
    -
           Wald df         p
-1 0.8528929  1 0.3557352
    -
    -
    test.new.var(old.vars, "year", 2)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                  coef exp(coef) se(coef)      z        p
-tx.typeLiving  0.63806   1.89281  0.09563  6.672 2.52e-11
-year          -0.03310   0.96744  0.01548 -2.138   0.0325
-
-Likelihood ratio test=51.69  on 2 df, p=5.967e-12
-n= 9775, number of events= 465
    -
    -
    -
          Wald df         p
-1 4.573044  1 0.0324788
    -

    age.rec has the smallest \(p\)-value

    -
    -

    12.3 tx.type + age.rec + ?

    +
    +

    14.3 tx.type + age.rec + ?

    -
    old.vars <- c("tx.type", "age.rec")
-
-test.new.var(old.vars, "hla.match", 3)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.512664  1.669733  0.112875  4.542 5.58e-06
-age.rec       -0.048268  0.952878  0.008688 -5.556 2.77e-08
-hla.match     -0.113954  0.892299  0.039929 -2.854  0.00432
-
-Likelihood ratio test=81.92  on 3 df, p=< 2.2e-16
-n= 9535, number of events= 450 
-   (240 observations deleted due to missingness)
    -
    -
    -
          Wald df           p
-1 8.144605  1 0.004318947
    -
    -
    test.new.var(old.vars, "age.donor", 3)
    +
    old.vars <- c("tx.type", "age.rec")
+
+test.new.var(old.vars, "age.donor", 3)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2427,43 +2545,7 @@ n= 9655, number of events= 463
 
          Wald df          p
 1 6.508773  1 0.01073435
    -
    test.new.var(old.vars, "cold.isc", 3)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z       p
-tx.typeLiving  0.489852  1.632075  0.170731  2.869 0.00412
-age.rec       -0.025545  0.974779  0.010019 -2.550 0.01078
-cold.isc       0.005637  1.005653  0.006709  0.840 0.40085
-
-Likelihood ratio test=35.04  on 3 df, p=1.194e-07
-n= 7519, number of events= 357 
-   (2256 observations deleted due to missingness)
    -
    -
    -
          Wald df         p
-1 0.705761  1 0.4008547
    -
    -
    test.new.var(old.vars, "sex", 3)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.695122  2.003953  0.096164  7.229 4.88e-13
-age.rec       -0.050004  0.951226  0.008569 -5.835 5.37e-09
-sexMale       -0.130416  0.877730  0.094113 -1.386    0.166
-
-Likelihood ratio test=80.63  on 3 df, p=< 2.2e-16
-n= 9766, number of events= 464 
-   (9 observations deleted due to missingness)
    -
    -
    -
          Wald df         p
-1 1.920263  1 0.1658277
    -
    -
    test.new.var(old.vars, "year", 3)
    +
    test.new.var(old.vars, "year", 3)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
@@ -2481,248 +2563,423 @@ n= 9766, number of events= 464
 
          Wald df          p
 1 4.680122  1 0.03051359
    -
    -

    hla.match has the smallest \(p\)-value

    -
    -
    -

    12.4 tx.type + age.rec + hla.match + ?

    -
    -
    old.vars <- c("tx.type", "age.rec", "hla.match")
-
-test.new.var(old.vars, "age.donor", 4)
    +
    test.new.var(old.vars, "hla.match", 3:8)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
 
                    coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.408204  1.504113  0.121727  3.353 0.000798
-age.rec       -0.043716  0.957225  0.008875 -4.926 8.39e-07
-hla.match     -0.107306  0.898251  0.040127 -2.674 0.007491
-age.donor     -0.008810  0.991229  0.003859 -2.283 0.022443
+tx.typeLiving  0.439788  1.552378  0.129107  3.406 0.000658
+age.rec       -0.048395  0.952758  0.008687 -5.571 2.53e-08
+hla.match1    -0.065986  0.936144  0.173137 -0.381 0.703116
+hla.match2    -0.339580  0.712069  0.179741 -1.889 0.058856
+hla.match3    -0.479802  0.618906  0.184469 -2.601 0.009295
+hla.match4    -0.617490  0.539296  0.223835 -2.759 0.005803
+hla.match5    -0.362744  0.695764  0.294632 -1.231 0.218257
+hla.match6    -0.410614  0.663243  0.315392 -1.302 0.192946
 
-Likelihood ratio test=85.46  on 4 df, p=< 2.2e-16
-n= 9433, number of events= 449 
-   (342 observations deleted due to missingness)
    -
    -
    -
          Wald df          p
-1 5.211086  1 0.02244331
    -
    -
    test.new.var(old.vars, "cold.isc", 4)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z      p
-tx.typeLiving  0.349594  1.418492  0.182948  1.911 0.0560
-age.rec       -0.023299  0.976970  0.010119 -2.302 0.0213
-hla.match     -0.071073  0.931394  0.044036 -1.614 0.1065
-cold.isc       0.006428  1.006449  0.006717  0.957 0.3386
-
-Likelihood ratio test=33.68  on 4 df, p=8.682e-07
-n= 7381, number of events= 352 
-   (2394 observations deleted due to missingness)
    -
    -
    -
           Wald df         p
-1 0.9158816  1 0.3385587
    -
    -
    test.new.var(old.vars, "sex", 4)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.515100  1.673806  0.112902  4.562 5.06e-06
-age.rec       -0.048944  0.952234  0.008721 -5.612 2.00e-08
-hla.match     -0.112940  0.893204  0.039936 -2.828  0.00468
-sexMale       -0.094882  0.909480  0.095783 -0.991  0.32188
-
-Likelihood ratio test=82.9  on 4 df, p=< 2.2e-16
+Likelihood ratio test=86.59  on 8 df, p=2.288e-15
 n= 9535, number of events= 450 
    (240 observations deleted due to missingness)
    -
           Wald df         p
-1 0.9812753  1 0.3218842
    +
         Wald df          p
+1 13.1233  6 0.04111916
    -
    test.new.var(old.vars, "year", 4)
    +
    test.new.var(old.vars, "sex", 3)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
 
                    coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.494911  1.640353  0.113403  4.364 1.28e-05
-age.rec       -0.048129  0.953011  0.008689 -5.539 3.04e-08
-hla.match     -0.122559  0.884654  0.040341 -3.038  0.00238
-year          -0.035190  0.965422  0.015831 -2.223  0.02622
+tx.typeLiving  0.695122  2.003953  0.096164  7.229 4.88e-13
+age.rec       -0.050004  0.951226  0.008569 -5.835 5.37e-09
+sexMale       -0.130416  0.877730  0.094113 -1.386    0.166
 
-Likelihood ratio test=86.88  on 4 df, p=< 2.2e-16
-n= 9535, number of events= 450 
-   (240 observations deleted due to missingness)
    +Likelihood ratio test=80.63 on 3 df, p=< 2.2e-16 +n= 9766, number of events= 464 + (9 observations deleted due to missingness)
    -
          Wald df          p
-1 4.941346  1 0.02622161
    +
          Wald df         p
+1 1.920263  1 0.1658277
    +
    +
    test.new.var(old.vars, "cold.isc", 3)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z       p
+tx.typeLiving  0.489852  1.632075  0.170731  2.869 0.00412
+age.rec       -0.025545  0.974779  0.010019 -2.550 0.01078
+cold.isc       0.005637  1.005653  0.006709  0.840 0.40085
+
+Likelihood ratio test=35.04  on 3 df, p=1.194e-07
+n= 7519, number of events= 357 
+   (2256 observations deleted due to missingness)
    +
    +
    +
          Wald df         p
+1 0.705761  1 0.4008547

    age.donor has the smallest \(p\)-value

    -
    -

    12.5 tx.type + age.rec + hla.match + age.donor + ?

    +
    +

    14.4 tx.type + age.rec + age.donor + ?

    -
    old.vars <- c("tx.type", "age.rec", "hla.match", "age.donor")
-
-test.new.var(old.vars, "cold.isc", 5)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z      p
-tx.typeLiving  0.355582  1.427011  0.188970  1.882 0.0599
-age.rec       -0.021491  0.978738  0.010298 -2.087 0.0369
-hla.match     -0.067709  0.934532  0.044223 -1.531 0.1257
-age.donor     -0.003508  0.996499  0.004230 -0.829 0.4069
-cold.isc       0.004519  1.004530  0.006774  0.667 0.5047
-
-Likelihood ratio test=34.04  on 5 df, p=2.333e-06
-n= 7347, number of events= 351 
-   (2428 observations deleted due to missingness)
    -
    -
    -
          Wald df         p
-1 0.445129  1 0.5046572
    -
    -
    test.new.var(old.vars, "sex", 5)
    +
    old.vars <- c("tx.type", "age.rec", "age.donor")
+
+test.new.var(old.vars, "year", 4)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
 
                    coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.411943  1.509748  0.121783  3.383 0.000718
-age.rec       -0.044462  0.956512  0.008914 -4.988  6.1e-07
-hla.match     -0.106379  0.899084  0.040136 -2.650 0.008038
-age.donor     -0.008675  0.991362  0.003862 -2.246 0.024677
-sexMale       -0.092710  0.911458  0.095941 -0.966 0.333885
+tx.typeLiving  0.571096  1.770207  0.107278  5.324 1.02e-07
+age.rec       -0.044243  0.956721  0.008718 -5.075 3.87e-07
+age.donor     -0.009313  0.990730  0.003793 -2.456   0.0141
+year          -0.031516  0.968975  0.015475 -2.037   0.0417
 
-Likelihood ratio test=86.39  on 5 df, p=< 2.2e-16
+Likelihood ratio test=87.47  on 4 df, p=< 2.2e-16
+n= 9655, number of events= 463 
+   (120 observations deleted due to missingness)
    +
    +
    +
         Wald df          p
+1 4.14746  1 0.04169701
    +
    +
    test.new.var(old.vars, "hla.match", 4:9)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z       p
+tx.typeLiving  0.343744  1.410218  0.135594  2.535 0.01124
+age.rec       -0.044106  0.956853  0.008869 -4.973 6.6e-07
+age.donor     -0.008401  0.991634  0.003842 -2.187 0.02878
+hla.match1    -0.060302  0.941480  0.173155 -0.348 0.72765
+hla.match2    -0.319994  0.726153  0.179955 -1.778 0.07537
+hla.match3    -0.457366  0.632949  0.185204 -2.470 0.01353
+hla.match4    -0.580080  0.559853  0.224649 -2.582 0.00982
+hla.match5    -0.327698  0.720580  0.295711 -1.108 0.26779
+hla.match6    -0.399931  0.670366  0.316127 -1.265 0.20584
+
+Likelihood ratio test=89.74  on 9 df, p=1.834e-15
 n= 9433, number of events= 449 
    (342 observations deleted due to missingness)
    -
           Wald df         p
-1 0.9337712  1 0.3338849
    +
          Wald df          p
+1 11.68364  6 0.06941019
    -
    test.new.var(old.vars, "year", 5)
    +
    test.new.var(old.vars, "sex", 4)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
 
                    coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.397903  1.488700  0.121903  3.264  0.00110
-age.rec       -0.043831  0.957116  0.008875 -4.939 7.87e-07
-hla.match     -0.115648  0.890789  0.040537 -2.853  0.00433
-age.donor     -0.008325  0.991709  0.003854 -2.160  0.03078
-year          -0.033109  0.967433  0.015844 -2.090  0.03664
+tx.typeLiving  0.574554  1.776338  0.107419  5.349 8.86e-08
+age.rec       -0.045101  0.955901  0.008757 -5.150 2.60e-07
+age.donor     -0.009501  0.990544  0.003799 -2.501   0.0124
+sexMale       -0.127413  0.880370  0.094265 -1.352   0.1765
 
-Likelihood ratio test=89.84  on 5 df, p=< 2.2e-16
-n= 9433, number of events= 449 
-   (342 observations deleted due to missingness)
    +Likelihood ratio test=85.12 on 4 df, p=< 2.2e-16 +n= 9655, number of events= 463 + (120 observations deleted due to missingness)     
          Wald df         p
-1 4.367128  1 0.0366387
    +1 1.826933 1 0.1764903 +
    +
    test.new.var(old.vars, "cold.isc", 4)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z       p
+tx.typeLiving  0.475677  1.609104  0.178023  2.672 0.00754
+age.rec       -0.023171  0.977095  0.010194 -2.273 0.02303
+age.donor     -0.004841  0.995171  0.004205 -1.151 0.24970
+cold.isc       0.003780  1.003787  0.006755  0.559 0.57583
+
+Likelihood ratio test=36.13  on 4 df, p=2.722e-07
+n= 7480, number of events= 356 
+   (2295 observations deleted due to missingness)
    +
    +
    +
           Wald df        p
+1 0.3130214  1 0.575832

    year has the smallest \(p\)-value

    -
    -

    12.6 tx.type + age.rec + hla.match + age.donor + year + ?

    +
    +

    14.5 tx.type + age.rec + age.donor + year + ?

    -
    old.vars <- c("tx.type", "age.rec", "hla.match", "age.donor", "year")
-
-test.new.var(old.vars, "cold.isc", 6)
    -
    -
    Call:
-coxph(formula = new.surv, data = dat, method = "breslow")
-
-                   coef exp(coef)  se(coef)      z      p
-tx.typeLiving  0.381855  1.464999  0.189901  2.011 0.0443
-age.rec       -0.021369  0.978857  0.010295 -2.076 0.0379
-hla.match     -0.073960  0.928708  0.044568 -1.660 0.0970
-age.donor     -0.002981  0.997024  0.004226 -0.705 0.4806
-year          -0.037375  0.963315  0.019227 -1.944 0.0519
-cold.isc       0.002743  1.002747  0.006825  0.402 0.6878
-
-Likelihood ratio test=37.86  on 6 df, p=1.195e-06
-n= 7347, number of events= 351 
-   (2428 observations deleted due to missingness)
    -
    -
    -
           Wald df         p
-1 0.1615171  1 0.6877636
    -
    -
    test.new.var(old.vars, "sex", 6)
    +
    old.vars <- c("tx.type", "age.rec", "age.donor", "year")
+
+test.new.var(old.vars, "hla.match", 5:10)
    Call:
 coxph(formula = new.surv, data = dat, method = "breslow")
 
                    coef exp(coef)  se(coef)      z        p
-tx.typeLiving  0.401829  1.494556  0.121963  3.295 0.000985
-age.rec       -0.044602  0.956378  0.008916 -5.003 5.66e-07
-hla.match     -0.114750  0.891589  0.040546 -2.830 0.004653
-age.donor     -0.008185  0.991848  0.003857 -2.122 0.033833
-year          -0.033222  0.967324  0.015844 -2.097 0.036011
-sexMale       -0.094191  0.910109  0.095956 -0.982 0.326293
+tx.typeLiving  0.330259  1.391328  0.135752  2.433  0.01498
+age.rec       -0.044176  0.956785  0.008869 -4.981 6.32e-07
+age.donor     -0.007886  0.992145  0.003836 -2.056  0.03978
+year          -0.034415  0.966170  0.015880 -2.167  0.03022
+hla.match1    -0.087933  0.915822  0.173602 -0.507  0.61249
+hla.match2    -0.352526  0.702910  0.180569 -1.952  0.05090
+hla.match3    -0.504964  0.603527  0.186678 -2.705  0.00683
+hla.match4    -0.625722  0.534875  0.225828 -2.771  0.00559
+hla.match5    -0.364687  0.694414  0.296524 -1.230  0.21874
+hla.match6    -0.456586  0.633442  0.317208 -1.439  0.15004
 
-Likelihood ratio test=90.8  on 6 df, p=< 2.2e-16
+Likelihood ratio test=94.45  on 10 df, p=6.975e-16
+n= 9433, number of events= 449 
+   (342 observations deleted due to missingness)
    +
    +
    +
          Wald df         p
+1 13.08326  6 0.0417326
    +
    +
    test.new.var(old.vars, "sex", 5)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z        p
+tx.typeLiving  0.574624  1.776462  0.107327  5.354 8.60e-08
+age.rec       -0.045294  0.955716  0.008759 -5.171 2.33e-07
+age.donor     -0.009119  0.990922  0.003795 -2.403   0.0163
+year          -0.031699  0.968798  0.015475 -2.048   0.0405
+sexMale       -0.129147  0.878844  0.094284 -1.370   0.1708
+
+Likelihood ratio test=89.33  on 5 df, p=< 2.2e-16
+n= 9655, number of events= 463 
+   (120 observations deleted due to missingness)
    +
    +
    +
          Wald df         p
+1 1.876286  1 0.1707569
    +
    +
    test.new.var(old.vars, "cold.isc", 5)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z      p
+tx.typeLiving  0.509289  1.664108  0.179269  2.841 0.0045
+age.rec       -0.023037  0.977226  0.010191 -2.261 0.0238
+age.donor     -0.004381  0.995629  0.004202 -1.043 0.2971
+year          -0.036400  0.964254  0.018995 -1.916 0.0553
+cold.isc       0.002027  1.002029  0.006812  0.298 0.7660
+
+Likelihood ratio test=39.84  on 5 df, p=1.608e-07
+n= 7480, number of events= 356 
+   (2295 observations deleted due to missingness)
    +
    +
    +
           Wald df         p
+1 0.0885476  1 0.7660318
    +
    +
    +

    hla.match has the smallest \(p\)-value

    +
    +
    +

    14.6 tx.type + age.rec + age.donor + year + hla.match + ?

    +
    +
    old.vars <- c("tx.type", "age.rec", "age.donor", "year", "hla.match")
+
+test.new.var(old.vars, "sex", 11)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z        p
+tx.typeLiving  0.334671  1.397480  0.135776  2.465  0.01371
+age.rec       -0.044917  0.956077  0.008908 -5.043 4.59e-07
+age.donor     -0.007753  0.992277  0.003838 -2.020  0.04341
+year          -0.034523  0.966066  0.015880 -2.174  0.02970
+hla.match1    -0.088750  0.915074  0.173601 -0.511  0.60919
+hla.match2    -0.350775  0.704142  0.180587 -1.942  0.05209
+hla.match3    -0.501788  0.605447  0.186640 -2.689  0.00718
+hla.match4    -0.624023  0.535784  0.225726 -2.765  0.00570
+hla.match5    -0.361475  0.696648  0.296530 -1.219  0.22284
+hla.match6    -0.450811  0.637111  0.317311 -1.421  0.15540
+sexMale       -0.092818  0.911359  0.095967 -0.967  0.33345
+
+Likelihood ratio test=95.39  on 11 df, p=1.457e-15
 n= 9433, number of events= 449 
    (342 observations deleted due to missingness)
           Wald df         p
-1 0.9635531  1 0.3262933
    +1 0.9354639 1 0.3334471 +
    +
    test.new.var(old.vars, "cold.isc", 11)
    +
    +
    Call:
+coxph(formula = new.surv, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z      p
+tx.typeLiving  0.310337  1.363884  0.201059  1.544 0.1227
+age.rec       -0.021521  0.978709  0.010287 -2.092 0.0364
+age.donor     -0.002701  0.997303  0.004215 -0.641 0.5216
+year          -0.038176  0.962544  0.019265 -1.982 0.0475
+hla.match1     0.070810  1.073377  0.218390  0.324 0.7458
+hla.match2    -0.100219  0.904639  0.221242 -0.453 0.6506
+hla.match3    -0.285575  0.751582  0.227967 -1.253 0.2103
+hla.match4    -0.314582  0.730094  0.262605 -1.198 0.2309
+hla.match5    -0.132791  0.875648  0.351300 -0.378 0.7054
+hla.match6    -0.279719  0.755996  0.359291 -0.779 0.4363
+cold.isc       0.002472  1.002475  0.006832  0.362 0.7175
+
+Likelihood ratio test=40.14  on 11 df, p=3.39e-05
+n= 7347, number of events= 351 
+   (2428 observations deleted due to missingness)
    +
    +
    +
           Wald df         p
+1 0.1308801  1 0.7175212

    Neither has \(p\)-value less than 0.05. Stop.

    -
    -

    13 Full Model

    +
    +

    15 Full Model

    -
    cox.full
    Call:
 coxph(formula = surv.full, data = dat, method = "breslow")
 
-                    coef  exp(coef)   se(coef)      z       p
-tx.typeLiving  0.0734859  1.0762534  0.0253724  2.896 0.00378
-age.rec        0.0154431  1.0155630  0.0020497  7.534 4.9e-14
-hla.match     -0.0210826  0.9791381  0.0086077 -2.449 0.01431
-age.donor     -0.0009874  0.9990131  0.0008841 -1.117 0.26405
-year           0.4429003  1.5572171  0.0057586 76.910 < 2e-16
+  n= 9433, number of events= 449 
+   (342 observations deleted due to missingness)
 
-Likelihood ratio test=8440  on 5 df, p=< 2.2e-16
-n= 9433, number of events= 9433 
+                   coef exp(coef)  se(coef)      z Pr(>|z|)    
+tx.typeLiving  0.330259  1.391328  0.135752  2.433  0.01498 *  
+age.rec       -0.044176  0.956785  0.008869 -4.981 6.32e-07 ***
+age.donor     -0.007886  0.992145  0.003836 -2.056  0.03978 *  
+year          -0.034415  0.966170  0.015880 -2.167  0.03022 *  
+hla.match1    -0.087933  0.915822  0.173602 -0.507  0.61249    
+hla.match2    -0.352526  0.702910  0.180569 -1.952  0.05090 .  
+hla.match3    -0.504964  0.603527  0.186678 -2.705  0.00683 ** 
+hla.match4    -0.625722  0.534875  0.225828 -2.771  0.00559 ** 
+hla.match5    -0.364687  0.694414  0.296524 -1.230  0.21874    
+hla.match6    -0.456586  0.633442  0.317208 -1.439  0.15004    
+---
+Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+
+              exp(coef) exp(-coef) lower .95 upper .95
+tx.typeLiving    1.3913     0.7187    1.0663    1.8154
+age.rec          0.9568     1.0452    0.9403    0.9736
+age.donor        0.9921     1.0079    0.9847    0.9996
+year             0.9662     1.0350    0.9366    0.9967
+hla.match1       0.9158     1.0919    0.6517    1.2870
+hla.match2       0.7029     1.4227    0.4934    1.0014
+hla.match3       0.6035     1.6569    0.4186    0.8702
+hla.match4       0.5349     1.8696    0.3436    0.8327
+hla.match5       0.6944     1.4401    0.3883    1.2417
+hla.match6       0.6334     1.5787    0.3402    1.1795
+
+Concordance= 0.644  (se = 0.015 )
+Likelihood ratio test= 94.45  on 10 df,   p=7e-16
+Wald test            = 96.48  on 10 df,   p=3e-16
+Score (logrank) test = 99.11  on 10 df,   p=<2e-16
    +
    +
    +
    +
    +
    [1] 1
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +

    16 Proportional hazards assumption

    +
    +
    +
    Call:
+coxph(formula = surv.full, data = dat, method = "breslow")
+
+                   coef exp(coef)  se(coef)      z        p
+tx.typeLiving  0.330259  1.391328  0.135752  2.433  0.01498
+age.rec       -0.044176  0.956785  0.008869 -4.981 6.32e-07
+age.donor     -0.007886  0.992145  0.003836 -2.056  0.03978
+year          -0.034415  0.966170  0.015880 -2.167  0.03022
+hla.match1    -0.087933  0.915822  0.173602 -0.507  0.61249
+hla.match2    -0.352526  0.702910  0.180569 -1.952  0.05090
+hla.match3    -0.504964  0.603527  0.186678 -2.705  0.00683
+hla.match4    -0.625722  0.534875  0.225828 -2.771  0.00559
+hla.match5    -0.364687  0.694414  0.296524 -1.230  0.21874
+hla.match6    -0.456586  0.633442  0.317208 -1.439  0.15004
+
+Likelihood ratio test=94.45  on 10 df, p=6.975e-16
+n= 9433, number of events= 449 
    (342 observations deleted due to missingness)
    +
    +
              chisq df       p
+tx.type    2.46  1 0.11651
+age.rec   36.40  1 1.6e-09
+age.donor 10.84  1 0.00099
+year       4.00  1 0.04537
+hla.match 12.87  6 0.04507
+GLOBAL    56.91 10 1.4e-08
    +
    -

    +

    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +

    -
    -

    13.1 What happened to year?

    +
    +

    16.1 What happened to year?

    -

    +

    @@ -2731,29 +2988,43 @@ n= 9433, number of events= 9433
    -

    +

    +
    +
    +
    +
    +
    +
    +
    +
    +

    Probabily want to omit it

    -
    -

    13.2 Without year

    +
    +

    16.2 Without year

    -
    cox.full.1
    +
    cox.full.1
    Call:
 coxph(formula = surv.full.1, data = dat, method = "breslow")
 
-                    coef  exp(coef)   se(coef)      z        p
-tx.typeLiving  0.0037484  1.0037554  0.0254736  0.147   0.8830
-age.rec        0.0139177  1.0140150  0.0020498  6.790 1.12e-11
-hla.match     -0.0854685  0.9180821  0.0089546 -9.545  < 2e-16
-age.donor      0.0023071  1.0023098  0.0008657  2.665   0.0077
+                   coef exp(coef)  se(coef)      z       p
+tx.typeLiving  0.343744  1.410218  0.135594  2.535 0.01124
+age.rec       -0.044106  0.956853  0.008869 -4.973 6.6e-07
+hla.match1    -0.060302  0.941480  0.173155 -0.348 0.72765
+hla.match2    -0.319994  0.726153  0.179955 -1.778 0.07537
+hla.match3    -0.457366  0.632949  0.185204 -2.470 0.01353
+hla.match4    -0.580080  0.559853  0.224649 -2.582 0.00982
+hla.match5    -0.327698  0.720580  0.295711 -1.108 0.26779
+hla.match6    -0.399931  0.670366  0.316127 -1.265 0.20584
+age.donor     -0.008401  0.991634  0.003842 -2.187 0.02878
 
-Likelihood ratio test=172.9  on 4 df, p=< 2.2e-16
-n= 9433, number of events= 9433 
+Likelihood ratio test=89.74  on 9 df, p=1.834e-15
+n= 9433, number of events= 449 
    (342 observations deleted due to missingness)
    @@ -2761,16 +3032,40 @@ n= 9433, number of events= 9433
    -

    +

    +
    +
    # A tibble: 19 × 8
+   term            estimate std.error statistic p.value conf.low conf.high model
+   <chr>              <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl> <chr>
+ 1 Living donor       1.39    0.136       2.43  1.50e-2    1.07      1.82  Full…
+ 2 Recipient age      0.957   0.00887    -4.98  6.32e-7    0.940     0.974 Full…
+ 3 Donor age          0.992   0.00384    -2.06  3.98e-2    0.985     1.000 Full…
+ 4 Transplant year    0.966   0.0159     -2.17  3.02e-2    0.937     0.997 Full…
+ 5 hla.match1         0.916   0.174      -0.507 6.12e-1    0.652     1.29  Full…
+ 6 hla.match2         0.703   0.181      -1.95  5.09e-2    0.493     1.00  Full…
+ 7 hla.match3         0.604   0.187      -2.71  6.83e-3    0.419     0.870 Full…
+ 8 hla.match4         0.535   0.226      -2.77  5.59e-3    0.344     0.833 Full…
+ 9 hla.match5         0.694   0.297      -1.23  2.19e-1    0.388     1.24  Full…
+10 hla.match6         0.633   0.317      -1.44  1.50e-1    0.340     1.18  Full…
+11 Living donor       1.41    0.136       2.54  1.12e-2    1.08      1.84  Mode…
+12 Recipient age      0.957   0.00887    -4.97  6.60e-7    0.940     0.974 Mode…
+13 hla.match1         0.941   0.173      -0.348 7.28e-1    0.671     1.32  Mode…
+14 hla.match2         0.726   0.180      -1.78  7.54e-2    0.510     1.03  Mode…
+15 hla.match3         0.633   0.185      -2.47  1.35e-2    0.440     0.910 Mode…
+16 hla.match4         0.560   0.225      -2.58  9.82e-3    0.360     0.870 Mode…
+17 hla.match5         0.721   0.296      -1.11  2.68e-1    0.404     1.29  Mode…
+18 hla.match6         0.670   0.316      -1.27  2.06e-1    0.361     1.25  Mode…
+19 Donor age          0.992   0.00384    -2.19  2.88e-2    0.984     0.999 Mode…
    +
    -

    +

    @@ -2782,18 +3077,18 @@ n= 9433, number of events= 9433
    -
    -

    14 Old

    +
    +

    17 Old

    -
    -

    14.1 Death & Censored

    +
    +

    17.1 Death & Censored

    -
    dat |>
-  group_by(death) |>
-  summarise(
-    n = n(),
-    percentage = n() / nrow(dat) * 100
-  )
    +
    dat |>
+  group_by(death) |>
+  summarise(
+    n = n(),
+    percentage = n() / nrow(dat) * 100
+  )
    # A tibble: 2 × 3
   death     n percentage
@@ -2807,7 +3102,7 @@ n= 9433, number of events= 9433
 
    
 
    
 
    
-
    
+
    
 
    
 
    
 
    
@@ -2816,7 +3111,7 @@ n= 9433, number of events= 9433
 
    
 
    
 
    
-
    
+
    
 
    
 
    
 
    
@@ -2834,7 +3129,7 @@ n= 9433, number of events= 9433
 8          4        38      11        2     0 2002 Female Cadaveric         0
 9          0        23      10        6     0 2002 Female    Living         0
 10         3        26       1        1     0 2002   Male Cadaveric         0
-11        NA        42      18       NA     0 2002   Male Cadaveric         0
+11      <NA>        42      18       NA     0 2002   Male Cadaveric         0
 12         4        39       9       NA     0 2002 Female Cadaveric         0
 13         3        34      13       NA     0 2002   Male Cadaveric         0
 14         3        NA      14        2     0 2002 Female Cadaveric         0
@@ -2863,11 +3158,11 @@ n= 9433, number of events= 9433
    -
    -

    14.2 Cox Model - Age as a Continuous Variable

    +
    +

    17.2 Cox Model - Age as a Continuous Variable

    -
    cox.age.rec <- coxph(Surv(follow.up, death) ~ age.rec, data = dat)
-cox.age.rec |> summary()
    +
    cox.age.rec <- coxph(Surv(follow.up, death) ~ age.rec, data = dat)
+cox.age.rec |> summary()
    Call:
 coxph(formula = Surv(follow.up, death) ~ age.rec, data = dat)
@@ -2890,66 +3185,66 @@ Score (logrank) test = 25.75  on 1 df,   p=4e-07
    -
    -

    14.3 Cox Model - Age as a Categorical Variable

    +
    +

    17.3 Cox Model - Age as a Categorical Variable

              chisq df       p
-tx.type    2.46  1 0.11654
-age.rec   36.09  1 1.9e-09
-hla.match  8.63  1 0.00331
-age.donor 10.88  1 0.00097
-year       3.96  1 0.04666
-GLOBAL    52.00  5 5.4e-10
    +tx.type 2.46 1 0.11643 +age.rec 36.41 1 1.6e-09 +hla.match 12.88 6 0.04498 +age.donor 10.85 1 0.00099 +year 4.01 1 0.04535 +GLOBAL 56.93 10 1.4e-08
    -

    +

    -

    +

    -

    +

    -

    +

    -

    +

    -

    +

    -
    -

    14.4 Table 1 (L)

    -
    -

    14.4.1 HLA match hla.match

    +
    +

    17.4 Table 1 (L)

    +
    +

    17.4.1 HLA match hla.match

    
@@ -2961,7 +3256,7 @@ GLOBAL    52.00  5 5.4e-10
    -

    +

    @@ -2970,7 +3265,7 @@ GLOBAL 52.00 5 5.4e-10
    -

    +

    @@ -3002,14 +3297,14 @@ Note
    -
    -

    14.4.2 Donor age age.donor

    +
    +

    17.4.2 Donor age age.donor

    -
    mean(dat$age.donor, na.rm = TRUE)
    +
    mean(dat$age.donor, na.rm = TRUE)
    [1] 31.29952
    -
    median(dat$age.donor, na.rm = TRUE)
    +
    median(dat$age.donor, na.rm = TRUE)
    [1] 33
    @@ -3018,7 +3313,7 @@ Note
    -

    +

    @@ -3027,7 +3322,7 @@ Note
    -

    +

    @@ -3036,7 +3331,7 @@ Note
    -

    +

    @@ -3045,7 +3340,7 @@ Note
    -

    +

    @@ -3054,7 +3349,7 @@ Note
    -

    +

    @@ -3073,14 +3368,14 @@ Note
    -
    -

    14.4.3 Recipient Age age.rec

    +
    +

    17.4.3 Recipient Age age.rec

    -
    mean(dat$age.rec, na.rm = TRUE)
    +
    mean(dat$age.rec, na.rm = TRUE)
    [1] 11.64653
    -
    median(dat$age.rec, na.rm = TRUE)
    +
    median(dat$age.rec, na.rm = TRUE)
    [1] 13
    @@ -3089,103 +3384,27 @@ Note
    -

    -
    -
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -
    -
    -
    -
    -

    14.4.4 Cold Ischemia Time cold.isc

    -
    -
    mean(dat$cold.isc, na.rm = TRUE)
    -
    -
    [1] 10.85967
    -
    -
    median(dat$cold.isc, na.rm = TRUE)
    -
    -
    [1] 7
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -
    -
    -
    -
    -
    -

    -
    -
    -

    14.4.5 Transplant Type tx.type

    -
    -
    
-Cadaveric    Living      <NA> 
-     5148      4627         0
    +
    +
    +
    +

    +
    +
    -
    dat$tx.type |> table()
    -
    -
    
-Cadaveric    Living 
-     5148      4627
    +
    +
    +
    +

    +
    +
    @@ -3197,25 +3416,28 @@ Cadaveric Living
    -
    -
    -

    14.4.6 Year year

    -
    -
    -
    
-1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 
- 728  734  666  736  787  813  789  745  740  842  706  834  655
    -
    -
    -

    +

    +
    +
    +

    17.4.4 Cold Ischemia Time cold.isc

    +
    +
    mean(dat$cold.isc, na.rm = TRUE)
    +
    +
    [1] 10.85967
    +
    +
    median(dat$cold.isc, na.rm = TRUE)
    +
    +
    [1] 7
    +
    +
    @@ -3243,21 +3465,94 @@ Cadaveric Living
    +
    +
    +

    17.4.5 Transplant Type tx.type

    +
    +
    +
    
+Cadaveric    Living      <NA> 
+     5148      4627         0
    +
    +
    +
    +
    dat$tx.type |> table()
    +
    +
    
+Cadaveric    Living 
+     5148      4627
    +
    +
    -

    +

    +
    +
    +
    +
    +
    +
    +

    17.4.6 Year year

    +
    +
    +
    
+1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 
+ 728  734  666  736  787  813  789  745  740  842  706  834  655
    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +
    +
    +

    +
    +
    +
    +
    +
    +
    +
    +
    +

    -
    -

    14.5 Kaplan-Meier

    -
    -

    14.5.1 Overall (L)

    +
    +

    17.5 Kaplan-Meier

    +
    +

    17.5.1 Overall (L)

    Call: survfit(formula = Surv(follow.up, death) ~ 1, data = dat)
@@ -3272,41 +3567,41 @@ Cadaveric    Living
 
    
 
    
 
    
-
    
+
    -
    -

    14.5.2 tx.type (M)

    +
    +

    17.5.2 tx.type (M)

    -

    +

    -
    -

    14.6 Cox Model

    -
    -

    14.6.1 death Distribution (?)

    +
    +

    17.6 Cox Model

    +
    +

    17.6.1 death Distribution (?)

    -

    +

    -
    -

    14.6.2 Overall (L)

    +
    +

    17.6.2 Overall (L)

    @@ -3335,17 +3630,17 @@ Note
    -
    -

    14.6.3 tx.type (M)

    +
    +

    17.6.3 tx.type (M)

    -
    -

    14.6.4 age (continuous) (L)

    +
    +

    17.6.4 age (continuous) (L)

    -
    -

    14.6.5 age (categorical) (M)

    +
    +

    17.6.5 age (categorical) (M)

    -
    -

    14.6.6 Full model (L)

    +
    +

    17.6.6 Full model (L)

    Call:
@@ -3355,20 +3650,30 @@ coxph(formula = Surv(follow.up, death) ~ hla.match + tx.type,
   n= 9541, number of events= 451 
    (234 observations deleted due to missingness)
 
-                  coef exp(coef) se(coef)      z Pr(>|z|)    
-hla.match     -0.12460   0.88285  0.03959 -3.148  0.00165 ** 
-tx.typeLiving  0.45336   1.57359  0.11146  4.068 4.75e-05 ***
+                  coef exp(coef) se(coef)      z Pr(>|z|)   
+hla.match1    -0.08845   0.91535  0.17308 -0.511  0.60933   
+hla.match2    -0.36340   0.69531  0.17919 -2.028  0.04256 * 
+hla.match3    -0.50810   0.60164  0.18298 -2.777  0.00549 **
+hla.match4    -0.65410   0.51991  0.22221 -2.944  0.00324 **
+hla.match5    -0.39445   0.67405  0.29410 -1.341  0.17985   
+hla.match6    -0.51491   0.59755  0.31489 -1.635  0.10201   
+tx.typeLiving  0.39049   1.47771  0.12688  3.078  0.00209 **
 ---
 Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 
               exp(coef) exp(-coef) lower .95 upper .95
-hla.match        0.8828     1.1327    0.8169    0.9541
-tx.typeLiving    1.5736     0.6355    1.2648    1.9578
+hla.match1       0.9153     1.0925    0.6520    1.2850
+hla.match2       0.6953     1.4382    0.4894    0.9879
+hla.match3       0.6016     1.6621    0.4203    0.8612
+hla.match4       0.5199     1.9234    0.3363    0.8037
+hla.match5       0.6740     1.4836    0.3787    1.1996
+hla.match6       0.5976     1.6735    0.3224    1.1077
+tx.typeLiving    1.4777     0.6767    1.1524    1.8949
 
-Concordance= 0.611  (se = 0.014 )
-Likelihood ratio test= 52.43  on 2 df,   p=4e-12
-Wald test            = 51.54  on 2 df,   p=6e-12
-Score (logrank) test = 53.06  on 2 df,   p=3e-12
    +Concordance= 0.613 (se = 0.014 ) +Likelihood ratio test= 56.79 on 7 df, p=7e-10 +Wald test = 57.08 on 7 df, p=6e-10 +Score (logrank) test = 59.51 on 7 df, p=2e-10 
    Call:
@@ -3379,21 +3684,41 @@ coxph(formula = Surv(follow.up, death) ~ hla.match * tx.type,
    (234 observations deleted due to missingness)
 
                             coef exp(coef) se(coef)      z Pr(>|z|)  
-hla.match               -0.08577   0.91780  0.07828 -1.096   0.2732  
-tx.typeLiving            0.59989   1.82192  0.27919  2.149   0.0317 *
-hla.match:tx.typeLiving -0.05232   0.94902  0.09086 -0.576   0.5647  
+hla.match1                0.8094    2.2467   0.8165  0.991   0.3215  
+hla.match2                1.1371    3.1176   0.7530  1.510   0.1311  
+hla.match3                0.4217    1.5245   0.7140  0.591   0.5548  
+hla.match4                0.1094    1.1156   0.7341  0.149   0.8816  
+hla.match5                0.4754    1.6087   0.7820  0.608   0.5432  
+hla.match6                0.5836    1.7925   0.8021  0.728   0.4669  
+tx.typeLiving             1.3801    3.9752   0.7218  1.912   0.0559 .
+hla.match1:tx.typeLiving -0.9614    0.3823   0.8355 -1.151   0.2498  
+hla.match2:tx.typeLiving -1.6578    0.1905   0.7762 -2.136   0.0327 *
+hla.match3:tx.typeLiving -1.0096    0.3644   0.7461 -1.353   0.1760  
+hla.match4:tx.typeLiving -0.5175    0.5960   0.7863 -0.658   0.5105  
+hla.match5:tx.typeLiving -0.8601    0.4231   0.8805 -0.977   0.3286  
+hla.match6:tx.typeLiving -1.3342    0.2634   0.9113 -1.464   0.1432  
 ---
 Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 
-                        exp(coef) exp(-coef) lower .95 upper .95
-hla.match                  0.9178     1.0896    0.7873     1.070
-tx.typeLiving              1.8219     0.5489    1.0541     3.149
-hla.match:tx.typeLiving    0.9490     1.0537    0.7942     1.134
+                         exp(coef) exp(-coef) lower .95 upper .95
+hla.match1                  2.2467     0.4451   0.45341   11.1322
+hla.match2                  3.1176     0.3208   0.71257   13.6400
+hla.match3                  1.5245     0.6559   0.37617    6.1787
+hla.match4                  1.1156     0.8964   0.26460    4.7032
+hla.match5                  1.6087     0.6216   0.34737    7.4498
+hla.match6                  1.7925     0.5579   0.37212    8.6342
+tx.typeLiving               3.9752     0.2516   0.96600   16.3580
+hla.match1:tx.typeLiving    0.3823     2.6155   0.07435    1.9662
+hla.match2:tx.typeLiving    0.1905     5.2480   0.04162    0.8723
+hla.match3:tx.typeLiving    0.3644     2.7444   0.08443    1.5726
+hla.match4:tx.typeLiving    0.5960     1.6778   0.12763    2.7836
+hla.match5:tx.typeLiving    0.4231     2.3635   0.07533    2.3763
+hla.match6:tx.typeLiving    0.2634     3.7971   0.04414    1.5712
 
-Concordance= 0.611  (se = 0.014 )
-Likelihood ratio test= 52.77  on 3 df,   p=2e-11
-Wald test            = 52.64  on 3 df,   p=2e-11
-Score (logrank) test = 54.76  on 3 df,   p=8e-12
    +Concordance= 0.615 (se = 0.014 ) +Likelihood ratio test= 66.78 on 13 df, p=3e-09 +Wald test = 65.9 on 13 df, p=5e-09 +Score (logrank) test = 69.92 on 13 df, p=8e-10     
    Analysis of Deviance Table
@@ -3401,39 +3726,39 @@ Score (logrank) test = 54.76  on 3 df,   p=8e-12
    Model 1: ~ hla.match + tx.type Model 2: ~ hla.match * tx.type loglik Chisq Df Pr(>|Chi|) -1 -3850.6 -2 -3850.5 0.3327 1 0.5641 +1 -3848.5 +2 -3843.5 9.9891 6 0.1251
    -
    -

    14.6.7 Discussion: include year or not?

    +
    +

    17.6.7 Discussion: include year or not?

    -
    -

    14.7 Assumption Testing

    +
    +

    17.7 Assumption Testing

    ## Why Survival Analysis (L)

    Motivation: study the distribution of time to event \(T\).

    Example: time of death after kidney transplant.

    -
    - @@ -3909,7 +4234,7 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12
    -

    +

    @@ -3919,23 +4244,23 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12

    With this, all we need is to fit a linear model t ~ X or log(t) ~ X

    -
    - @@ -4417,7 +4742,7 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12
    -

    +

    @@ -4427,23 +4752,23 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12

    Scenario 1: the study ends at the year 2008?

    -
    - @@ -4925,14 +5250,14 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12
    -

    +

    -

    +

    @@ -4942,23 +5267,23 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12

    Scenario 2: respondent 3 move away; loss follow up

    -
    - @@ -5440,14 +5765,14 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12
    -

    +

    -

    +

    @@ -5458,14 +5783,14 @@ Score (logrank) test = 54.76 on 3 df, p=8e-12
    -

    +

    -
    -

    14.8 Challenges in Survival Analysis (L)

    +
    +

    17.8 Challenges in Survival Analysis (L)

    • Right Censoring: only observe the event if it occurs before a certain time.
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