SMHS MissingData Appendix
Contents
SMHS Missing Data - Appendix
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. Period, ".", indicates missing data.
| 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 we don't have real or observed or derived data, we can simulate fake data # See this SOCR Data/Activity: Predictive Big Data Analytics, Modeling and Visualization of Clinical, Genetic and Imaging Data for Parkinson’s Disease # # Alternatively use the example below. # 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 # (1) Convert to a missing_data.frame mdf <- missing_data.frame(EpiBiosData) # warnings about missingness patterns show(mdf) # (2) change things mdf <- change(mdf, y = "spikes.hr", what = "transformation", to = "identity") # (3) look deeper summary(mdf) hist(mdf) image(mdf) # imputations <- mi(mdf) hist(imputations) data.frames <- complete(imputations, 5) lapply(data.frames, summary) # To cast the imputed numbers as integers (not necessary, but may be useful) indx <- sapply(data.frames\([[5]]\), is.numeric) # get the indices of numeric columns data.frames\([[5]]\)[indx] <- lapply(data.frames\([[5]]\)[indx], function(x) as.numeric(as.integer(x))) # cast each value as integer # # save results out # write.mi(data.frames\([[5]]\), format = "csv") write.csv(data.frames\([[5]]\), "C:\\Users\\Dinov\\Desktop\\EpiBioS_MIData.csv") # # Complete Data analytics: ression functions: # lm.mi(); glm.mi(); polr.mi(); bayesglm.mi(); bayespolr.mi(); lmer.mi(); glmer.mi() # fit <- lm.mi(ever.sz ~ surgery + worst.gcs + sex + age, IMP) # fit1 <- lm.mi(ever.sz.1 ~ surgery.1 + worst.gcs.1 + sex.1 + age.1, IMP) # fit2 <- lm.mi(ever.sz.2 ~ surgery.2 + worst.gcs.2 + sex.2 + age.2, IMP) display(fit)
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
- Back to the Missing Data Section
- The SOCR Simulated HELP data activity provides additional missing data management examples.
- Multiple Imputation FAQs.
- SOCR Home page: http://www.socr.umich.edu
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