IZ ICL POSITION ANALYSIS

postop_data<-readr::read_csv(file = "postop_data_cleaned.csv")

retropostion_data<-postop_data %>% select(N_RETROPOSITION_MM,T_RETROPOSITION_MM,POSITION) %>% separate(POSITION,into=c("N_POSITION","T_POSITION"),sep='-')

RELATION WITH RETROPOSITION

Cart tree for N_RETROPOSITION_MM

tree<-rpart::rpart(N_POSITION~N_RETROPOSITION_MM,data=retropostion_data,control = rpart.control(minsplit = 15))
rpart.plot(tree,type=1,
           extra=101, box.palette="GnBu",
           branch.lty=3, shadow.col="gray", nn=TRUE
        )

rpart.rules(tree)

Cart tree for T_RETROPOSITION_MM

tree<-rpart::rpart(T_POSITION~.,data=retropostion_data,control = rpart.control(minsplit = 8))
rpart.plot(tree,type=1,
           extra=101, box.palette="GnBu",
           branch.lty=3, shadow.col="gray", nn=TRUE
        )

rpart.rules(tree)

CHECK DISTRIBUTION for RETROPOSITION

Media and Standard deviation and 95% CI

estimate_position<-postop_data %>% select(T_RETROPOSITION_MM,N_RETROPOSITION_MM) %>% 
  reshape2::melt() %>% 
  group_by(variable) %>% 
  summarise(mean=mean(value),sd=sd(value))

No id variables; using all as measure variables

ci_t_position<-t.test(postop_data$T_RETROPOSITION_MM,) %>% broom::tidy() %>% select(conf.low,conf.high)
ci_n_position<-t.test(postop_data$N_RETROPOSITION_MM,) %>% broom::tidy() %>% select(conf.low,conf.high)

cbind(estimate_position,rbind(ci_t_position,ci_n_position))

Histogram

postop_data %>% select(N_RETROPOSITION_MM,T_RETROPOSITION_MM) %>% reshape2::melt() %>%
  ggplot()+
  facet_wrap(~variable)+
  geom_histogram(aes(x=value),fill="skyblue",color="gray")+
  theme_bw()

No id variables; using all as measure variables

Q-Q Plots

The result of using Shapiro’s Normality test is also annotated in the plots.

shapiro_N_RETRO<-shapiro.test(postop_data$N_RETROPOSITION_MM) 
shapiro_T_RETRO <-shapiro.test(postop_data$T_RETROPOSITION_MM) 

qq_n_plot<-qplot(sample= postop_data$N_RETROPOSITION_MM,color="", main=paste0("Distribution of N_RETROPOSITION_MM\n","p_value=",shapiro_N_RETRO$p.value))+theme_bw()

qq_t_plot<-qplot(sample= postop_data$T_RETROPOSITION_MM,color="", main=paste0("Distribution of T_RETROPOSITION_MM\n","p_value=",shapiro_T_RETRO$p.value))+theme_bw()

#plotly::ggplotly(qq_n_plot)
#plotly::ggplotly(qq_t_plot)

gridExtra::grid.arrange(qq_n_plot,qq_t_plot,ncol=2,nrow=1)

Discrimnated by Eyes

postop_data %>% select(N_RETROPOSITION_MM,T_RETROPOSITION_MM,EYE) %>% reshape2::melt() %>%
  ggplot()+
  facet_grid(variable~EYE)+
  geom_histogram(aes(x=value),fill="skyblue",color="gray")+
  theme_bw()

Using EYE as id variables

nod_data<-postop_data %>% filter (EYE=="OD") %>% select(N_RETROPOSITION_MM) %>% unlist()
nos_data<-postop_data %>% filter (EYE=="OS") %>% select(N_RETROPOSITION_MM) %>% unlist()
tod_data<-postop_data %>% filter (EYE=="OD") %>% select(T_RETROPOSITION_MM) %>% unlist()
tos_data<-postop_data %>% filter (EYE=="OS") %>% select(T_RETROPOSITION_MM) %>% unlist()

shapiro_N_RETRO_OD <- shapiro.test(nod_data) 
shapiro_N_RETRO_OS <- shapiro.test(nos_data) 
shapiro_T_RETRO_OD <- shapiro.test(tod_data) 
shapiro_T_RETRO_OS <- shapiro.test(tos_data) 

nod_plot<-qplot(sample= nod_data, 
      color="", 
      main= paste0("Distribution of N_RETROPOSITION_MM for OD\n","shapiro p_value=",
               shapiro_N_RETRO_OD$p.value))+
        theme_bw()

nos_plot<-qplot(sample=nos_data,
      color="", 
      main=paste0("Distribution of N_RETROPOSITION_MM for OS\n","shapiro p_value=",
                  shapiro_N_RETRO_OS$p.value))+theme_bw()

tod_plot<-qplot(sample=tod_data, 
      color="", 
      main= paste0("Distribution of T_RETROPOSITION_MM for OD\n","shapiro p_value=",
               shapiro_T_RETRO_OD$p.value))+
        theme_bw()

tos_plot<-qplot(sample= tos_data,
      color="", 
      main=paste0("Distribution of T_RETROPOSITION_MM for OS\n","shapiro p_value=",
                  shapiro_T_RETRO_OS$p.value))+theme_bw()

gridExtra::grid.arrange(tos_plot,tod_plot,nod_plot,nos_plot)

Discriminated by Gender

postop_data %>% select(N_RETROPOSITION_MM,T_RETROPOSITION_MM,SEX) %>% reshape2::melt() %>%
  ggplot()+
  facet_grid(variable~SEX)+
  geom_histogram(aes(x=value),fill="skyblue",color="gray")+
  theme_bw()

Using SEX as id variables

nf_data<-postop_data %>% filter (SEX=="F") %>% select(N_RETROPOSITION_MM) %>% unlist()
nm_data<-postop_data %>% filter (SEX=="M") %>% select(N_RETROPOSITION_MM) %>% unlist()
tf_data<-postop_data %>% filter (SEX=="F") %>% select(T_RETROPOSITION_MM) %>% unlist()
tm_data<-postop_data %>% filter (SEX=="M") %>% select(T_RETROPOSITION_MM) %>% unlist()

shapiro_N_RETRO_F <- shapiro.test(nf_data) 
shapiro_N_RETRO_M <- shapiro.test(nm_data) 
shapiro_T_RETRO_F <- shapiro.test(tf_data) 
shapiro_T_RETRO_M <- shapiro.test(tm_data) 


nf_plot<-qplot(sample= nf_data, 
      color="", 
      main= paste0("Distribution of N_RETROPOSITION_MM for F\n","shapiro p_value=",
               shapiro_N_RETRO_F$p.value))+
        theme_bw()

nm_plot<-qplot(sample= nm_data,
      color="", 
      main=paste0("Distribution of N_RETROPOSITION_MM for M\n","shapiro p_value=",
                  shapiro_N_RETRO_M$p.value))+theme_bw()

tf_plot<-qplot(sample= tf_data, 
      color="", 
      main= paste0("Distribution of T_RETROPOSITION_MM for F\n","shapiro p_value=",
               shapiro_T_RETRO_F$p.value))+
        theme_bw()

tm_plot<-qplot(sample= tm_data,
      color="", 
      main=paste0("Distribution of T_RETROPOSITION_MM for M\n","shapiro p_value=",
                  shapiro_T_RETRO_M$p.value))+theme_bw()

gridExtra::grid.arrange(tf_plot,tm_plot,nf_plot,nm_plot)

Discriminated by IOL MODEL

postop_data %>% select(N_RETROPOSITION_MM,T_RETROPOSITION_MM,IOL_MODEL_NEW) %>% reshape2::melt() %>%
  ggplot()+
  facet_grid(variable~IOL_MODEL_NEW)+
  geom_histogram(aes(x=value),fill="skyblue",color="gray")+
  theme_bw()

Using IOL_MODEL_NEW as id variables

postop_data %>% select(N_RETROPOSITION_MM,T_RETROPOSITION_MM,IOL_MODEL_NEW) %>% reshape2::melt() %>%
  ggplot()+
  facet_grid(variable~IOL_MODEL_NEW)+
  geom_qq(aes(sample=value),fill="skyblue",color="red")+
  theme_bw()

Using IOL_MODEL_NEW as id variables

Saphiro_test for T_RETROPOSITION_NN

postop_data %>% select(T_RETROPOSITION_MM,IOL_MODEL_NEW) %>% 
  group_by(IOL_MODEL_NEW) %>% 
  nest()  %>%
  mutate(saphiro_test=purrr::map(data, ~{shapiro.test(.x$T_RETROPOSITION_MM)%>% broom::tidy()} )  ) %>% select(-data)%>% unnest(cols = c("saphiro_test"))

Saphiro_test for N_RETROPOSITION_NN

postop_data %>% select(N_RETROPOSITION_MM,IOL_MODEL_NEW) %>% 
  group_by(IOL_MODEL_NEW) %>% 
  nest()  %>%
  mutate(saphiro_test=purrr::map(data, ~{shapiro.test(.x$N_RETROPOSITION_MM)%>% broom::tidy()} )  ) %>% select(-data)%>% unnest(cols = c("saphiro_test"))

HYPOTHESIS TESTING

By EYES

Check if significant differences exist between OD and OS for N_RETROPOSITION_MM and T_RETROPOSITION_MM

rbind(
  t.test(tos_data,tod_data) %>% broom::tidy() %>% mutate(RETROPOSITION="T"), 
  t.test(nos_data,nod_data) %>% broom::tidy() %>% mutate(RETROPOSITION="N")
) %>% select(RETROPOSITION,p.value,method, alternative, conf.low, conf.high)

By GENDER

Check if significant differences exist between F and M for N_RETROPOSITION_MM and T_RETROPOSITION_MM

rbind(
  t.test(tf_data,tm_data) %>% broom::tidy() %>% mutate(RETROPOSITION="T"), 
  t.test(nf_data,nm_data) %>% broom::tidy() %>% mutate(RETROPOSITION="N")
) %>% select(RETROPOSITION,p.value,method, alternative, conf.low, conf.high)

By IOL MODELS

We use ONE WAY ANOVA instead of T-test paired

nretro_model<-postop_data %>% select(N_RETROPOSITION_MM,IOL_MODEL_NEW) %>% 
  group_by(IOL_MODEL_NEW)

anova_nretro<-oneway.test(N_RETROPOSITION_MM~IOL_MODEL_NEW,data=nretro_model) %>% broom::tidy()

Multiple parameters; naming those columns num.df, denom.df

anova_nretro$RETROPOSITION_MM <- "N"

tretro_model<-postop_data %>% select(T_RETROPOSITION_MM,IOL_MODEL_NEW) %>% 
  group_by(IOL_MODEL_NEW)

anova_tretro<-oneway.test(T_RETROPOSITION_MM~IOL_MODEL_NEW,data=tretro_model) %>%broom::tidy()

Multiple parameters; naming those columns num.df, denom.df

anova_tretro$RETROPOSITION_MM <- "T"

rbind(anova_nretro,anova_tretro) %>% select(RETROPOSITION_MM,method,p.value)

CONCLUSIONS

1. N_RETROPOSITION_MM (N_RETRO) AND T_RETROPOSITION_MM (T_RETRO) variables are clearly related with the POSITION variable in the dataset. A value. (See CART Trees). A value of N_RETRO > 0.41 and T_RETRO >0.38 is related with CP class in POSITION.
2. Both N_RETRO and T_RETRO follow a normal distribution with mean 0.43 and 0.42, respectively. (see media, sd and CI)
3. Grouping by GENDER, EYES and IOL_MODEL also show a normal distribution according to qqplots, histograms and Saphiro tests.
4. T and one-way ANOVA tests carried out over all the groups show there is no enough evidence in the data that indicate GENDER, EYES and IOL_MODEL have influence in the value of T_RETRO and N_RETRO. (see p.value) and consequently the POSTION.
5. More experiments should be conducted to get more evidence.