Last updated: 2020-12-03

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Load packages

library(tidyverse)

library(coxme)
library(lme4)
library(brms)
library(tidybayes)

library(kableExtra)
library(knitrhooks) # install with devtools::install_github("nathaneastwood/knitrhooks")

output_max_height() # a knitrhook option

options(stringsAsFactors = FALSE)

Load data

# load desiccation resistance data
DesRes <- read.csv("data/3.DesRes.csv") %>% 
  # add event (all flies died)
  mutate(EVENT = 1,
         LINE = paste0(Treatment, substr(Replicate, 2, 2)))

# calculate survival times
# paste time and date
DesRes$d <- paste(DesRes$Death_date, DesRes$Death_time, sep = ' ')

# experiment start time
start_timeDes <- "04/02/2017 12:00"

DesRes$survival.time <- as.numeric(strptime(DesRes$d, format = "%d/%m/%Y %H") - strptime(start_timeDes, format = "%d/%m/%Y %H"))

des.surv <- Surv(DesRes$survival.time, DesRes$EVENT)


# load starvation resistance data
StaRes <- read.csv("data/3.StarvRes.csv") %>% 
  # add event (all flies died)
  mutate(EVENT = 1,
         LINE = paste0(Treatment, substr(Replicate, 2, 2)))

# calculate survival times
# paste time and date
StaRes$d <- paste(StaRes$Death_date, StaRes$Death_time, sep = ' ')

# experiment start time
start_timeSta <- "04/02/2017 12:00"

StaRes$survival.time <- as.numeric(strptime(StaRes$d, format = "%d/%m/%Y %H") - strptime(start_timeSta, format = "%d/%m/%Y %H"))

sta.surv <- Surv(StaRes$survival.time, StaRes$EVENT)

Inspecting the raw data

bind_rows(
  DesRes %>% 
  select(Treatment, Sex, survival.time) %>% mutate(var = 'Desiccation'),
  StaRes %>% 
  select(Treatment, Sex, survival.time) %>% mutate(var = 'Starvation')
) %>% 
  ggplot(aes(x = survival.time, y = Sex, fill = Treatment)) +
  geom_boxplot() +
  scale_fill_brewer(palette = 'Set1', direction = -1, name = "") +
  labs(x = 'Survival time (hours)') +
  facet_wrap(~var, ncol = 2) +
  theme_bw() +
  theme(legend.position = 'top') +
  NULL

Version Author Date
c175be4 Martin Garlovsky 2020-12-03
df61dde Martin Garlovsky 2020-12-03

Figure 1: Survival time in hours for flies in each treatment split by sex.

Fit the model for desiccation/starvation resistance

Plot the survival curves and median survival times

Version Author Date
df61dde Martin Garlovsky 2020-12-03

Version Author Date
df61dde Martin Garlovsky 2020-12-03
# median eclosion times
survfit(Surv(survival.time, EVENT) ~ Treatment + Sex, data = DesRes)
Call: survfit(formula = Surv(survival.time, EVENT) ~ Treatment + Sex, 
    data = DesRes)

                     n events median 0.95LCL 0.95UCL
Treatment=M, Sex=f 108    108     38      38      42
Treatment=M, Sex=m 111    111     32      32      34
Treatment=P, Sex=f 114    114     40      38      42
Treatment=P, Sex=m 105    105     32      32      34
survfit(Surv(survival.time, EVENT) ~ Treatment + Sex, data = StaRes)
Call: survfit(formula = Surv(survival.time, EVENT) ~ Treatment + Sex, 
    data = StaRes)

   5 observations deleted due to missingness 
                     n events median 0.95LCL 0.95UCL
Treatment=M, Sex=f 118    118     56      52      60
Treatment=M, Sex=m 120    120     40      38      44
Treatment=P, Sex=f 117    117     66      62      68
Treatment=P, Sex=m 120    120     42      40      42

Next we need to check that the ‘proportional hazards’ assumption is not violated before fitting the full model.

Version Author Date
df61dde Martin Garlovsky 2020-12-03

Version Author Date
df61dde Martin Garlovsky 2020-12-03

For both desiccation and starvation we see crossing hazards for the male survival curves. We will therefore fit accelerated failure time (AFT) models with a Weibull distribution and a frailty term to account for replicates within each treatment. We can define the degrees of freedom explicitly

Fit the Accelerated failure time models

weibull.des <- survreg(Surv(survival.time, EVENT) ~ Treatment * Sex + frailty(LINE, df = 6), 
                       data = DesRes, dist = "weibull")


weibull.sta <- survreg(Surv(survival.time, EVENT) ~ Treatment * Sex + frailty(LINE, df = 6), 
                       data = StaRes, dist = "weibull")


bind_rows(anova(weibull.des), anova(weibull.sta)) %>% 
  cbind(Parameter = c('Null', 'Treatment', 'Sex', '`frailty(LINE)`', 'Treatment x Sex')) %>% 
  mutate(across(1:5, round, 3)) %>% 
  select(Parameter, Df, `Resid. Df`, Deviance, `Pr(>Chi)`) %>% 
  filter(Parameter!='`frailty(LINE)`') %>% 
  kable() %>% 
  kable_styling() %>% 
  kable_styling(full_width = FALSE) %>%
  group_rows("Desiccation", 1, 4) %>%
  group_rows("Starvation", 5, 8)
Parameter Df Resid. Df Deviance Pr(>Chi)
Desiccation
Null NA 436.000 NA NA
Treatment 1.000 435.000 3.849 0.050
Sex 1.000 434.000 154.904 0.000
Treatment x Sex 1.010 429.020 8.682 0.003
Starvation
Null NA 473.000 NA NA
Treatment 1.000 472.000 2.290 0.130
Sex 1.000 471.000 208.841 0.000
Treatment x Sex 1.017 466.025 20.486 0.000

We see equivocal support for a treatment effect for desiccation resistance and no effect for starvation resistance. For both assays there is support for a sex effect and a treatment x sex interaction.

Calculate hazard ratios

We can use the following equation to translate the AFT coeffiecnts (\(\beta\)) to a hazard ratio (\(\alpha\)): \[ \beta = -\alpha * p \] where \(p\) is the shape (a.k.a. scale) parameter. We can also calculate standard errors… Hazard ratios give the probability of the event occuring compared to ‘control’ in our case compared to Monogamy females. Hazard ratios > 1 indicate increased hazard (i.e. increased probability of event compared to control), hazard ratio < 1 indicate decreased hazard.

# function to get hazard ratios and standard errors
hazR <- function(mod) {
  
  a = c(coefficients(summary(mod)))
  coef = (a * -1 * 1/mod$scale)
  HazardRatio = exp(coef)
  
  b = summary(mod)$table[, 2]
  se = (b * -1 * 1/mod$scale)
  HR.se = exp(se)
  
  return(data.frame(round(cbind(HazardRatio, HR.se), 3)[-c(1,5), ]))
  
}

For both desiccation and starvation resistance Polyandrous females live longer than Monogamy females (although not significantly so). Males die sooner than females, and Polyandry males die sooner than Monogamy males.

bind_rows(hazR(weibull.des), hazR(weibull.sta)) %>% as.tibble() %>% 
  cbind(Parameter = c('Treatment', 'Sex', 'Treatment x Sex')) %>% 
  select(Parameter, `Hazard ratio` = HazardRatio, `Std. Err.` = HR.se) %>% 
  kable() %>% 
  kable_styling() %>% 
  kable_styling(full_width = FALSE) %>%
  group_rows("Desiccation", 1, 3) %>%
  group_rows("Starvation", 4, 6)
Parameter Hazard ratio Std. Err.
Desiccation
Treatment 0.736 0.354
Sex 2.872 0.866
Treatment x Sex 1.834 0.815
Starvation
Treatment 0.628 0.437
Sex 3.870 0.878
Treatment x Sex 2.354 0.831

sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Mojave 10.14.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] knitrhooks_0.0.4 knitr_1.30       kableExtra_1.3.1 tidybayes_2.3.1 
 [5] brms_2.14.4      Rcpp_1.0.5       lme4_1.1-23      Matrix_1.2-18   
 [9] coxme_2.2-16     bdsmatrix_1.3-4  survival_3.2-7   forcats_0.5.0   
[13] stringr_1.4.0    dplyr_1.0.2      purrr_0.3.4      readr_1.4.0     
[17] tidyr_1.1.2      tibble_3.0.4     ggplot2_3.3.2    tidyverse_1.3.0 

loaded via a namespace (and not attached):
  [1] readxl_1.3.1         backports_1.1.10     workflowr_1.6.2     
  [4] plyr_1.8.6           igraph_1.2.6         splines_4.0.3       
  [7] svUnit_1.0.3         crosstalk_1.1.0.1    rstantools_2.1.1    
 [10] inline_0.3.16        digest_0.6.25        htmltools_0.5.0     
 [13] rsconnect_0.8.16     fansi_0.4.1          magrittr_2.0.1      
 [16] openxlsx_4.2.2       modelr_0.1.8         RcppParallel_5.0.2  
 [19] matrixStats_0.57.0   xts_0.12.1           prettyunits_1.1.1   
 [22] colorspace_1.4-1     blob_1.2.1           rvest_0.3.6         
 [25] ggdist_2.3.0         haven_2.3.1          xfun_0.19           
 [28] callr_3.5.1          crayon_1.3.4         jsonlite_1.7.1      
 [31] zoo_1.8-8            glue_1.4.2           survminer_0.4.8     
 [34] gtable_0.3.0         webshot_0.5.2        V8_3.4.0            
 [37] distributional_0.2.1 car_3.0-10           pkgbuild_1.1.0      
 [40] rstan_2.21.2         abind_1.4-5          scales_1.1.1        
 [43] mvtnorm_1.1-1        DBI_1.1.0            rstatix_0.6.0       
 [46] miniUI_0.1.1.1       viridisLite_0.3.0    xtable_1.8-4        
 [49] foreign_0.8-80       km.ci_0.5-2          stats4_4.0.3        
 [52] StanHeaders_2.21.0-6 DT_0.16              htmlwidgets_1.5.2   
 [55] httr_1.4.2           threejs_0.3.3        RColorBrewer_1.1-2  
 [58] arrayhelpers_1.1-0   ellipsis_0.3.1       pkgconfig_2.0.3     
 [61] loo_2.3.1            farver_2.0.3         dbplyr_1.4.4        
 [64] labeling_0.3         tidyselect_1.1.0     rlang_0.4.8         
 [67] reshape2_1.4.4       later_1.1.0.1        munsell_0.5.0       
 [70] cellranger_1.1.0     tools_4.0.3          cli_2.1.0           
 [73] generics_0.0.2       broom_0.7.1          ggridges_0.5.2      
 [76] evaluate_0.14        fastmap_1.0.1        yaml_2.2.1          
 [79] processx_3.4.4       fs_1.5.0             zip_2.1.1           
 [82] survMisc_0.5.5       nlme_3.1-149         whisker_0.4         
 [85] mime_0.9             projpred_2.0.2       xml2_1.3.2          
 [88] compiler_4.0.3       bayesplot_1.7.2      shinythemes_1.1.2   
 [91] rstudioapi_0.11      gamm4_0.2-6          curl_4.3            
 [94] ggsignif_0.6.0       reprex_0.3.0         statmod_1.4.34      
 [97] stringi_1.5.3        highr_0.8            ps_1.4.0            
[100] Brobdingnag_1.2-6    lattice_0.20-41      nloptr_1.2.2.2      
[103] markdown_1.1         KMsurv_0.1-5         shinyjs_2.0.0       
[106] vctrs_0.3.4          pillar_1.4.6         lifecycle_0.2.0     
[109] bridgesampling_1.0-0 data.table_1.13.0    httpuv_1.5.4        
[112] R6_2.4.1             promises_1.1.1       rio_0.5.16          
[115] gridExtra_2.3        codetools_0.2-16     boot_1.3-25         
[118] colourpicker_1.1.0   MASS_7.3-53          gtools_3.8.2        
[121] assertthat_0.2.1     rprojroot_1.3-2      withr_2.3.0         
[124] shinystan_2.5.0      mgcv_1.8-33          parallel_4.0.3      
[127] hms_0.5.3            grid_4.0.3           coda_0.19-4         
[130] minqa_1.2.4          rmarkdown_2.4        carData_3.0-4       
[133] ggpubr_0.4.0         git2r_0.27.1         shiny_1.5.0         
[136] lubridate_1.7.9      base64enc_0.1-3      dygraphs_1.1.1.6