SMHS MissingData

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Scientific Methods for Health Sciences - Missing Data

Motivation

In complete-case analysis using multiple regression modeling, response results may be missing may involve automatically excluding the cases with missing response value. This leads to restricting the amount of information available in the analysis, especially if the model has many parameters that need to be estimated and many responses are potentially missing. Alternatively, missing outcomes in a regression can be handled by modeling the outcome variable to impute missing values at each iteration.

A more challenging situation in regression analysis involves missing values in predictor variables. The options here are to remove the missing values, impute them, or analytically model them by supplying distributions for the input variables.

Theory

Types of data missingness

Knowing why and how is data missing is impoetant for determining hte appropriate protocol for handling the data. There are several categories of data-missingness.

  • Missingness completely at random (MCAR). A variable is missing completely at random if the probability of missingness is the same for all units. For instance, if each respondent decides whether to answer an income question by rolling a (fair) die and refusing to answer if a a number > 3 turn up. Inference based on imputing data missing completely at random, by throwing out cases with missing data, is unbiased.
  • Missingness at random (MAR). Most missingness is not completely random. For example, different non-response rates for whites and minorities on income question may be due to socioeconomic factors. Missing at random is a more general assumption where the probability a missing variable depends only on available information. Suppose demographic variables (e.g., age, gender, race, education) are recorded for all the people in the study. Then income will be missing at random if the probability of non-response to this question depends only on these other, fully recorded variables. This process many be modeled by logistic regression with the outcome variable (Y) representing indicator of missingness ($Y=1$ for observed cases and $Y=0$ for missing cases). When an outcome variable is missing at random, a regression model can exclude the missing cases (treat them as NA’s), if it controls for all the variables that affect the probability of missingness for the outcome. In our case, regression models of income would have to include predictors for ethnicity to avoid possible non-response bias.
  • Non-random missingness": When the data missingness depends on unobserved predictors, this indicates non-random gaps in the observed data, dues to information that may not be available, which may also be predictive of the missing values. For instance, highly-educated (high-income?) people may be less likely to respond to income" questions. So, college degree may have predictive value for income. Another example is a new clinical treatment that causes side-effects which may cause attrition of participants (patients drop out of study) dependent on their level of ability to deal with the side effects. Non-random missingness has to be explicitly modeled, otherwise, bias would creep into the scientific inference and impact the results of the study.
  • Missingness that depends on the missing value itself. If the probability of missingness depends on the (potentially missing) variable itself the situation is a bit more interesting. For example, higher earners may be less likely to reveal their income. In these situations, missing-data have to be modeled or accounted for by including more predictors in the missing-data

model to bringing it closer to missing at random situation. For example, whites and highly-educated participants may have higher-than-average incomes and we can control for such predictors to correct for higher rates of non-response (missingness) among higher-income people. Sometime, the missing data situation may require predictive models extrapolating beyond the range of the observed data.

Example

Suppose we are interested in identifying patterns, relations and associations between demographic, clinical and cognitive variables in a cohort of traumatic brain injury (TBI) patients. The table below shows the raw data. Notice the missing values in this table. Imputing the missing data would allow us to use all cases in our analysis of the multivariate relations using the completed dataset.

Raw TBI data

The variables in the table include: id=participant ID; age=age; sex=gender; mechanism=type of TBI injury; field.gcs=field Glasgow Coma Scale; er.gcs=emergency room Glasgow Coma Scale; icu.gcs=intensive care unit Glasgow Coma Scale; worst.gcs=lowest Glasgow Coma Scale; 6m.gose=Extended Glasgow Outcome Scale score at 6-month follow up; 2013.gose=Extended Glasgow Outcome Scale score in 2013; skull.fx=skull fracture criterion for impact-induced head injury; temp.injury=injury characteristic; surgery=index of surgery; spikes.hr=EEG spikes per hour; min.hr=min EEG per hour; max.hr=max EEG spikes per hour; acute.sz=indicator of seizure at acute state; late.sz=indicator of seizure at chronic state; ever.sz=indicator of seizures at any time.

id age sex mechanism field.gcs er.gcs icu.gcs worst.gcs 6m.gose 2013.gose skull.fx temp.injury surgery spikes.hr min.hr max.hr acute.sz late.sz ever.sz
1 19 Male Fall 10 10 10 10 5 5 0 1 1 . . . 1 1 1
2 55 Male Blunt . 3 3 3 5 7 1 1 1 168.74 14 757 0 1 1
3 24 Male Fall 12 12 8 8 7 7 1 0 0 37.37 0 351 0 0 0
4 57 Female Fall 4 4 6 4 3 3 1 1 1 4.35 0 59 0 0 0
5 54 Female Peds_vs_Auto 14 11 8 8 5 7 0 1 1 54.59 0 284 0 0 0
6 16 Female MVA 13 7 7 7 7 8 1 1 1 75.92 7 180 0 1 1
7 21 Male Fall 3 3 6 3 3 3 1 0 1 . . . 0 0 0
8 25 Male Fall 3 4 3 3 3 3 0 1 0 5.26 0 88 0 1 1
9 30 Male GSW 3 9 3 3 3 5 1 1 1 43.88 0 367 0 1 1
10 38 Male Fall 3 6 6 3 3 3 1 1 1 45.6 4 107 0 1 1
11 43 Male Blunt 8 7 7 7 6 7 1 0 1 7.76 0 72 0 0 0
12 40 Male Fall 12 14 14 12 7 8 0 1 1 26.64 0 125 0 0 0
13 21 Male MVA 12 13 9 9 7 7 1 0 1 . . . 0 1 1
14 35 Female MVA 6 5 6 5 5 7 1 1 0 65.14 0 655 1 1 1
15 59 Male Peds_vs_Auto 14 14 0 0 8 8 1 1 0 . . . 0 0 0
16 32 Male MCA 5 6 3 3 4 5 1 0 0 . . . 0 0 0
17 31 Male MVA 7 3 9 3 5 7 1 0 0 3.82 0 28 0 0 0
18 57 Male MVA 4 3 7 3 3 3 0 1 1 . . . 0 1 1
19 18 Male Blunt 4 3 6 3 5 3 1 1 1 . . . 0 1 1
20 48 Male Bike_vs_Auto 3 8 7 3 5 7 0 0 0 . . . 0 0 0
21 19 Male GSW 15 15 3 3 . 6 1 0 1 . . . 1 1 1
22 22 Male Fall 3 3 3 3 2 2 1 1 1 9.7 0 80 0 1 1
23 20 Male Peds_vs_Auto 15 14 13 13 5 8 1 1 1 . . . 0 1 1
24 41 Male MVA 3 3 6 3 3 7 1 0 0 . . . 0 0 0
25 27 Male MCA 15 13 6 6 6 7 1 0 1 . . . 0 0 0
26 23 Male MVA 14 14 7 7 4 7 1 1 1 . . . 0 0 0
27 36 Male MCA 3 3 3 3 5 6 0 0 0 . . . 0 1 1
28 83 Female Fall 14 14 9 9 . 5 0 1 1 208.92 42 641 1 1 1
29 26 Male MCA 5 7 5 5 6 7 0 1 0 . . . 0 0 0
30 21 Male Fall 14 14 14 14 5 7 0 1 1 294 30 1199 1 1 1
31 23 Male MCA 12 13 13 12 . 7 1 0 1 . . . 0 0 0
32 45 Male MCA 6 6 6 6 3 6 0 0 1 . . . 0 0 0
33 18 Male Bike_vs_Auto 8 8 7 7 7 7 0 0 0 7.14 0 20 0 1 1
34 34 Male MVA 7 7 3 3 4 6 0 1 1 47.73 0 226 0 1 1
35 19 Male MVA 3 7 7 3 7 8 0 0 0 97.43 0 300 0 0 0
36 77 Female Peds_vs_Auto 3 6 3 3 3 3 1 1 0 7.09 0 31 0 1 1
37 75 Male Bike_vs_Auto . . . . . 8 1 0 0 5.9 0 42 0 1 1
38 25 Male Fall 14 . 6 6 8 8 0 0 1 29.61 0 175 1 0 1
39 62 Female Fall 12 8 8 8 3 3 0 1 1 6.16 0 33 0 1 1
40 41 Male MCA 7 3 7 3 5 5 1 1 1 1.66 0 23 0 1 1
41 60 Male Bike_vs_Auto 3 12 7 3 3 5 1 1 0 3.8 0 12 0 1 1
42 29 Female Peds_vs_Auto 9 14 3 3 8 7 1 0 1 . . . 0 1 1
43 48 Male Blunt 12 12 11 11 6 7 0 0 1 5.39 0 43 0 0 0
44 41 Male Peds_vs_Auto 3 3 3 3 2 2 1 1 0 1.28 0 15 1 1 1
45 34 Male Fall 6 8 3 3 3 3 1 1 1 213.84 3 824 1 1 1
46 25 Female MVA 6 8 3 3 . 7 0 1 0 1.7 0 36 0 0 0

R imputation script

The R code below illustrates the imputation of a raw data. 

###########################################
# example of multiple imputation (R MI package)
# See Docs: http://www.stat.ucla.edu/~yajima/Publication/mipaper.rev04.pdf
# 
# If you don't have data, simulate fake data
# set.seed(123)
# n <- 1000
# u1 <- rbinom(n, 1, .5); v1 <- log(rnorm(n, 5, 1)); x1 <- u1*exp(v1)
# u2 <- rbinom(n, 1, .5); v2 <- log(rnorm(n, 5, 1)); x2 <- u2*exp(v2)
# x3 <- rbinom(n, 1, prob=0.45); x4 <- ordered(rep(seq(1, 5),100)[sample(1:n, n)]); x5 <- rep(letters[1:10],10)[sample(1:n, n)]; x6 <- trunc(runif(n, 1, 10)); x7 <- rnorm(n); x8 <- factor(rep(seq(1,10),10)[sample(1:n, n)]); x9 <- runif(n, 0.1, .99); x10 <- rpois(n, 4); y <- x1 + x2 + x7 + x9 + rnorm(n)
# fakedata <- cbind.data.frame(y, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
# randomly create missing values
# dat <- mi:::.create.missing(fakedata, pct.mis=30)
##########################################################

library("mi")
# copy-paste the (raw) data from the table into a plain text file "EpiBioSData.csv"
EpiBiosData <- read.csv("~/EpiBioSData.csv", na.strings=c("",".","NA"))
# get information matrix of the data
inf <- mi.info(EpiBiosData)
# to update the variable type of a specific variable to mi.info
# inf <- update(inf, "type", list(x10="count"))
# run the imputation without data transformation
IMP <- mi(EpiBiosData, info=inf, check.coef.convergence=TRUE, add.noise=noise.control(post.run.iter=10))
#
# run the imputation with data transformation  
EpiBiosData.transformed <- mi.preprocess(EpiBiosData, inf)
#IMP <- mi(EpiBiosData.transformed, n.iter=6, check.coef.convergence=TRUE, add.noise=noise.control(post.run.iter=6))
#
# IMP <- mi(EpiBiosData.transformed, n.iter=6, add.noise=TRUE)
# no noise
# IMP <- mi(dat, info=inf, n.iter=6, add.noise=FALSE) ## NOT RUN
#
# convergence checking
converged(IMP, check = "data")  ## You should get FALSE here because only n.iter is small 
# converged(IMP, check = "coefs")
IMP.bugs1 <- bugs.mi(IMP, check = "data")    ## BUGS object to look at the R hat statistics
IMP.bugs2 <- bugs.mi(IMP, check = "coefs")   ## BUGS object to look at the R hat statistics
plot(IMP.bugs1)  ## visually check R.hat
#
# visually check the imputation
plot(IMP)
#
missing.pattern.plot(EpiBiosData, gray.scale = TRUE)
#
# to obtain the Completed/Imputed Dataset
IMP.EpiBiosData.all <- mi.completed(IMP)
#
# save results out
write.mi(IMP, format = "csv")
write.csv(IMP.EpiBiosData.all, "~/EpiBioS_MIData.csv")

Imputed Complete Data

The table below shows 3 alternative imputation results for the same TBI data (generated using the R script above). Variable indices (ID, ..., ever.sz; ID.1, ..., ever.sz.1; ID.2, ..., ever.sz.2) indicate the results of the 3 complementary multiple imputations.

ID age sex mechanism field.gcs er.gcs icu.gcs worst.gcs X6m.gose X2013.gose skull.fx temp.injury surgery spikes.hr min.hr max.hr acute.sz late.sz ever.sz ID.1 age.1 sex.1 mechanism.1 field.gcs.1 er.gcs.1 icu.gcs.1 worst.gcs.1 X6m.gose.1 X2013.gose.1 skull.fx.1 temp.injury.1 surgery.1 spikes.hr.1 min.hr.1 max.hr.1 acute.sz.1 late.sz.1 ever.sz.1 ID.2 age.2 sex.2 mechanism.2 field.gcs.2 er.gcs.2 icu.gcs.2 worst.gcs.2 X6m.gose.2 X2013.gose.2 skull.fx.2 temp.injury.2 surgery.2 spikes.hr.2 min.hr.2 max.hr.2 acute.sz.2 late.sz.2 ever.sz.2
1 19 Male Fall 10 10 10 10 5 5 0 1 1 31.33408337 17.64389893 329.4906597 1 1 1 1 19 Male Fall 10 10 10 10 5 5 0 1 1 96.74023746 18.35575322 474.5394709 1 1 1 1 19 Male Fall 10 10 10 10 5 5 0 1 1 134.3949936 13.93977114 357.0245178 1 1 1
2 55 Male Blunt 8.949465016 3 3 3 5 7 1 1 1 168.74 14 757 0 1 1 2 55 Male Blunt 4.583430169 3 3 3 5 7 1 1 1 168.74 14 757 0 1 1 2 55 Male Blunt 6.759506638 3 3 3 5 7 1 1 1 168.74 14 757 0 1 1
3 24 Male Fall 12 12 8 8 7 7 1 0 0 37.37 0 351 0 0 0 3 24 Male Fall 12 12 8 8 7 7 1 0 0 37.37 0 351 0 0 0 3 24 Male Fall 12 12 8 8 7 7 1 0 0 37.37 0 351 0 0 0
4 57 Female Fall 4 4 6 4 3 3 1 1 1 4.35 0 59 0 0 0 4 57 Female Fall 4 4 6 4 3 3 1 1 1 4.35 0 59 0 0 0 4 57 Female Fall 4 4 6 4 3 3 1 1 1 4.35 0 59 0 0 0
5 54 Female Peds_vs_Auto 14 11 8 8 5 7 0 1 1 54.59 0 284 0 0 0 5 54 Female Peds_vs_Auto 14 11 8 8 5 7 0 1 1 54.59 0 284 0 0 0 5 54 Female Peds_vs_Auto 14 11 8 8 5 7 0 1 1 54.59 0 284 0 0 0
6 16 Female MVA 13 7 7 7 7 8 1 1 1 75.92 7 180 0 1 1 6 16 Female MVA 13 7 7 7 7 8 1 1 1 75.92 7 180 0 1 1 6 16 Female MVA 13 7 7 7 7 8 1 1 1 75.92 7 180 0 1 1
7 21 Male Fall 3 3 6 3 3 3 1 0 1 97.81993169 -0.213863843 38.62625185 0 0 0 7 21 Male Fall 3 3 6 3 3 3 1 0 1 57.41204562 22.47601237 -152.4300823 0 0 0 7 21 Male Fall 3 3 6 3 3 3 1 0 1 -88.08486298 -17.52260473 -126.0982147 0 0 0
8 25 Male Fall 3 4 3 3 3 3 0 1 0 5.26 0 88 0 1 1 8 25 Male Fall 3 4 3 3 3 3 0 1 0 5.26 0 88 0 1 1 8 25 Male Fall 3 4 3 3 3 3 0 1 0 5.26 0 88 0 1 1
9 30 Male GSW 3 9 3 3 3 5 1 1 1 43.88 0 367 0 1 1 9 30 Male GSW 3 9 3 3 3 5 1 1 1 43.88 0 367 0 1 1 9 30 Male GSW 3 9 3 3 3 5 1 1 1 43.88 0 367 0 1 1
10 38 Male Fall 3 6 6 3 3 3 1 1 1 45.6 4 107 0 1 1 10 38 Male Fall 3 6 6 3 3 3 1 1 1 45.6 4 107 0 1 1 10 38 Male Fall 3 6 6 3 3 3 1 1 1 45.6 4 107 0 1 1
11 43 Male Blunt 8 7 7 7 6 7 1 0 1 7.76 0 72 0 0 0 11 43 Male Blunt 8 7 7 7 6 7 1 0 1 7.76 0 72 0 0 0 11 43 Male Blunt 8 7 7 7 6 7 1 0 1 7.76 0 72 0 0 0
12 40 Male Fall 12 14 14 12 7 8 0 1 1 26.64 0 125 0 0 0 12 40 Male Fall 12 14 14 12 7 8 0 1 1 26.64 0 125 0 0 0 12 40 Male Fall 12 14 14 12 7 8 0 1 1 26.64 0 125 0 0 0
13 21 Male MVA 12 13 9 9 7 7 1 0 1 -139.5137892 -33.84480983 19.23090912 0 1 1 13 21 Male MVA 12 13 9 9 7 7 1 0 1 125.7529181 19.14860131 291.9026199 0 1 1 13 21 Male MVA 12 13 9 9 7 7 1 0 1 -12.93052956 -11.43761507 39.10220788 0 1 1
14 35 Female MVA 6 5 6 5 5 7 1 1 0 65.14 0 655 1 1 1 14 35 Female MVA 6 5 6 5 5 7 1 1 0 65.14 0 655 1 1 1 14 35 Female MVA 6 5 6 5 5 7 1 1 0 65.14 0 655 1 1 1
15 59 Male Peds_vs_Auto 14 14 0 0 8 8 1 1 0 104.0330205 28.99974405 718.6130268 0 0 0 15 59 Male Peds_vs_Auto 14 14 0 0 8 8 1 1 0 158.5435588 11.79083406 788.0040332 0 0 0 15 59 Male Peds_vs_Auto 14 14 0 0 8 8 1 1 0 70.32014857 -4.21119291 -20.90694906 0 0 0
16 32 Male MCA 5 6 3 3 4 5 1 0 0 99.20158013 -17.25973621 351.0875441 0 0 0 16 32 Male MCA 5 6 3 3 4 5 1 0 0 -217.7065141 3.020094958 -464.0898326 0 0 0 16 32 Male MCA 5 6 3 3 4 5 1 0 0 -33.098168 -0.137931315 487.9378096 0 0 0
17 31 Male MVA 7 3 9 3 5 7 1 0 0 3.82 0 28 0 0 0 17 31 Male MVA 7 3 9 3 5 7 1 0 0 3.82 0 28 0 0 0 17 31 Male MVA 7 3 9 3 5 7 1 0 0 3.82 0 28 0 0 0
18 57 Male MVA 4 3 7 3 3 3 0 1 1 -149.9422408 -30.42385829 -302.9962493 0 1 1 18 57 Male MVA 4 3 7 3 3 3 0 1 1 56.13694368 18.8199818 -62.49856966 0 1 1 18 57 Male MVA 4 3 7 3 3 3 0 1 1 45.55341087 4.468479615 -213.454323 0 1 1
19 18 Male Blunt 4 3 6 3 5 3 1 1 1 40.39410742 -36.87895336 97.37341326 0 1 1 19 18 Male Blunt 4 3 6 3 5 3 1 1 1 -106.5749596 5.559437069 -1149.613796 0 1 1 19 18 Male Blunt 4 3 6 3 5 3 1 1 1 51.18634141 -1.937828826 -342.6008879 0 1 1
20 48 Male Bike_vs_Auto 3 8 7 3 5 7 0 0 0 118.8000347 32.36213678 -73.13271061 0 0 0 20 48 Male Bike_vs_Auto 3 8 7 3 5 7 0 0 0 -87.77082486 3.717360906 -4.392630662 0 0 0 20 48 Male Bike_vs_Auto 3 8 7 3 5 7 0 0 0 108.2372319 0.187220054 519.1251498 0 0 0
21 19 Male GSW 15 15 3 3 9.25042468 6 1 0 1 40.13687855 -14.22895294 736.3143588 1 1 1 21 19 Male GSW 15 15 3 3 7.223305755 6 1 0 1 18.46733942 25.54649386 -315.4151426 1 1 1 21 19 Male GSW 15 15 3 3 3.828147759 6 1 0 1 111.5912998 17.80387347 200.2606779 1 1 1
22 22 Male Fall 3 3 3 3 2 2 1 1 1 9.7 0 80 0 1 1 22 22 Male Fall 3 3 3 3 2 2 1 1 1 9.7 0 80 0 1 1 22 22 Male Fall 3 3 3 3 2 2 1 1 1 9.7 0 80 0 1 1
23 20 Male Peds_vs_Auto 15 14 13 13 5 8 1 1 1 143.8993295 9.086586358 410.1307881 0 1 1 23 20 Male Peds_vs_Auto 15 14 13 13 5 8 1 1 1 68.95037612 -3.634136214 745.7692261 0 1 1 23 20 Male Peds_vs_Auto 15 14 13 13 5 8 1 1 1 17.52584031 4.326014737 307.7486916 0 1 1
24 41 Male MVA 3 3 6 3 3 7 1 0 0 36.38713558 -7.70043125 397.1825116 0 0 0 24 41 Male MVA 3 3 6 3 3 7 1 0 0 16.44376591 -3.227208192 318.7734905 0 0 0 24 41 Male MVA 3 3 6 3 3 7 1 0 0 39.56564601 2.069381684 695.0459207 0 0 0
25 27 Male MCA 15 13 6 6 6 7 1 0 1 89.67182293 -5.545616243 290.1814949 0 0 0 25 27 Male MCA 15 13 6 6 6 7 1 0 1 17.66215864 4.730421601 191.3041522 0 0 0 25 27 Male MCA 15 13 6 6 6 7 1 0 1 67.26462511 8.869208934 468.9527863 0 0 0
26 23 Male MVA 14 14 7 7 4 7 1 1 1 46.02145191 -13.18053664 91.69057998 0 0 0 26 23 Male MVA 14 14 7 7 4 7 1 1 1 39.36793917 12.35289402 405.9565656 0 0 0 26 23 Male MVA 14 14 7 7 4 7 1 1 1 154.8598602 30.03873428 384.849982 0 0 0
27 36 Male MCA 3 3 3 3 5 6 0 0 0 57.6777688 2.679615385 664.0843475 0 1 1 27 36 Male MCA 3 3 3 3 5 6 0 0 0 -90.21498545 -17.3682012 -26.4769941 0 1 1 27 36 Male MCA 3 3 3 3 5 6 0 0 0 -50.90586656 -6.319652137 352.0473406 0 1 1
28 83 Female Fall 14 14 9 9 4.636755103 5 0 1 1 208.92 42 641 1 1 1 28 83 Female Fall 14 14 9 9 6.242101503 5 0 1 1 208.92 42 641 1 1 1 28 83 Female Fall 14 14 9 9 2.05329258 5 0 1 1 208.92 42 641 1 1 1
29 26 Male MCA 5 7 5 5 6 7 0 1 0 -13.37057197 -14.89381792 152.0008772 0 0 0 29 26 Male MCA 5 7 5 5 6 7 0 1 0 91.7509579 -0.870090941 529.0874936 0 0 0 29 26 Male MCA 5 7 5 5 6 7 0 1 0 -0.534176227 -9.783851967 490.89377 0 0 0
30 21 Male Fall 14 14 14 14 5 7 0 1 1 294 30 1199 1 1 1 30 21 Male Fall 14 14 14 14 5 7 0 1 1 294 30 1199 1 1 1 30 21 Male Fall 14 14 14 14 5 7 0 1 1 294 30 1199 1 1 1
31 23 Male MCA 12 13 13 12 2.860415458 7 1 0 1 74.98397791 13.22365165 155.338988 0 0 0 31 23 Male MCA 12 13 13 12 3.086836617 7 1 0 1 -11.96623577 -7.703251349 530.2622312 0 0 0 31 23 Male MCA 12 13 13 12 5.904815799 7 1 0 1 16.65737111 2.374428875 436.7728378 0 0 0
32 45 Male MCA 6 6 6 6 3 6 0 0 1 104.8995511 -16.52390582 483.006168 0 0 0 32 45 Male MCA 6 6 6 6 3 6 0 0 1 -80.67017517 -15.81483739 116.5352423 0 0 0 32 45 Male MCA 6 6 6 6 3 6 0 0 1 71.76729005 -1.066523637 893.1056629 0 0 0
33 18 Male Bike_vs_Auto 8 8 7 7 7 7 0 0 0 7.14 0 20 0 1 1 33 18 Male Bike_vs_Auto 8 8 7 7 7 7 0 0 0 7.14 0 20 0 1 1 33 18 Male Bike_vs_Auto 8 8 7 7 7 7 0 0 0 7.14 0 20 0 1 1
34 34 Male MVA 7 7 3 3 4 6 0 1 1 47.73 0 226 0 1 1 34 34 Male MVA 7 7 3 3 4 6 0 1 1 47.73 0 226 0 1 1 34 34 Male MVA 7 7 3 3 4 6 0 1 1 47.73 0 226 0 1 1
35 19 Male MVA 3 7 7 3 7 8 0 0 0 97.43 0 300 0 0 0 35 19 Male MVA 3 7 7 3 7 8 0 0 0 97.43 0 300 0 0 0 35 19 Male MVA 3 7 7 3 7 8 0 0 0 97.43 0 300 0 0 0
36 77 Female Peds_vs_Auto 3 6 3 3 3 3 1 1 0 7.09 0 31 0 1 1 36 77 Female Peds_vs_Auto 3 6 3 3 3 3 1 1 0 7.09 0 31 0 1 1 36 77 Female Peds_vs_Auto 3 6 3 3 3 3 1 1 0 7.09 0 31 0 1 1
37 75 Male Bike_vs_Auto 13.73432996 14.02844584 12.08707554 6.608860636 5.076496724 8 1 0 0 5.9 0 42 0 1 1 37 75 Male Bike_vs_Auto 1.439149068 9.833777842 1.828027302 -0.395951549 8.130388643 8 1 0 0 5.9 0 42 0 1 1 37 75 Male Bike_vs_Auto 4.627381629 11.70604238 4.818391501 2.101228568 7.755182097 8 1 0 0 5.9 0 42 0 1 1
38 25 Male Fall 14 18.45286032 6 6 8 8 0 0 1 29.61 0 175 1 0 1 38 25 Male Fall 14 7.292553675 6 6 8 8 0 0 1 29.61 0 175 1 0 1 38 25 Male Fall 14 9.021238862 6 6 8 8 0 0 1 29.61 0 175 1 0 1
39 62 Female Fall 12 8 8 8 3 3 0 1 1 6.16 0 33 0 1 1 39 62 Female Fall 12 8 8 8 3 3 0 1 1 6.16 0 33 0 1 1 39 62 Female Fall 12 8 8 8 3 3 0 1 1 6.16 0 33 0 1 1
40 41 Male MCA 7 3 7 3 5 5 1 1 1 1.66 0 23 0 1 1 40 41 Male MCA 7 3 7 3 5 5 1 1 1 1.66 0 23 0 1 1 40 41 Male MCA 7 3 7 3 5 5 1 1 1 1.66 0 23 0 1 1
41 60 Male Bike_vs_Auto 3 12 7 3 3 5 1 1 0 3.8 0 12 0 1 1 41 60 Male Bike_vs_Auto 3 12 7 3 3 5 1 1 0 3.8 0 12 0 1 1 41 60 Male Bike_vs_Auto 3 12 7 3 3 5 1 1 0 3.8 0 12 0 1 1
42 29 Female Peds_vs_Auto 9 14 3 3 8 7 1 0 1 43.10920277 -12.88149901 504.4628083 0 1 1 42 29 Female Peds_vs_Auto 9 14 3 3 8 7 1 0 1 206.9761351 13.04583926 -237.7973505 0 1 1 42 29 Female Peds_vs_Auto 9 14 3 3 8 7 1 0 1 117.2635425 -5.753348151 233.8244434 0 1 1
43 48 Male Blunt 12 12 11 11 6 7 0 0 1 5.39 0 43 0 0 0 43 48 Male Blunt 12 12 11 11 6 7 0 0 1 5.39 0 43 0 0 0 43 48 Male Blunt 12 12 11 11 6 7 0 0 1 5.39 0 43 0 0 0
44 41 Male Peds_vs_Auto 3 3 3 3 2 2 1 1 0 1.28 0 15 1 1 1 44 41 Male Peds_vs_Auto 3 3 3 3 2 2 1 1 0 1.28 0 15 1 1 1 44 41 Male Peds_vs_Auto 3 3 3 3 2 2 1 1 0 1.28 0 15 1 1 1
45 34 Male Fall 6 8 3 3 3 3 1 1 1 213.84 3 824 1 1 1 45 34 Male Fall 6 8 3 3 3 3 1 1 1 213.84 3 824 1 1 1 45 34 Male Fall 6 8 3 3 3 3 1 1 1 213.84 3 824 1 1 1
46 25 Female MVA 6 8 3 3 8.135915557 7 0 1 0 1.7 0 36 0 0 0 46 25 Female MVA 6 8 3 3 7.477618429 7 0 1 0 1.7 0 36 0 0 0 46 25 Female MVA 6 8 3 3 6.093298745 7 0 1 0 1.7 0 36 0 0 0

See also


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