SMHS MissingData Appendix

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.

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• SOCR Home page: http://www.socr.umich.edu

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