Handling Missing


Data Source: 

Health data from the 1994 National Population Health Survey


Julie Bernier - julie.bernier@statcan.ca, David Haziza - david.haziza@statcan.ca, Karla Nobrega - karla.nobrega@statcan.ca, Patricia Whitridge - patricia.whitridge@statcan.ca



The data set to be studied, which uses health data from the 1994 National Population Health Survey, will have missing data to simulate non-response. In addition to studying the relationship between health status and health determinants, the student will learn about response mechanisms, non-response bias, and different methods to treat and analyze data with missing values. 


In surveys, it is virtually assured that a certain level of nonresponse will occur. There are two types of nonresponse: total (or unit) nonresponse, when no information is collected on a sampled unit, and partial (or item) nonresponse, when the absence of information is only limited to some variables. In surveys, weighting adjustment methods are commonly used to compensate for total nonresponse, while imputation is used to compensate for item nonresponse.

Weighting adjustments are used primarily to increase the survey weight of respondents in order to compensate for the nonrespondents.  Imputation, on the other hand, produces an "artificial value" to replace a missing value. The goal in both cases is to obtain approximately unbiased estimates.

There are four sections to this case study.  The student may do any or all of the four components.

Section 1: Assessing the response mechanism

The student will assess the nature of the response mechanism. There are three common classifications for response mechanisms:

  • Missing Completely at Random (MCAR) i.e. the probability of response for a variable of interest y is the same for all units in the population, this means that the probability of response does not depend on either auxiliary variables x or the variable of interest y ;
  • Missing at Random (MAR), i.e. the probability of response to a variable of interest y is related to auxiliary variable(s) x ;
  • Not Missing at Random (NMAR), i.e. the probability of response to variable of interest y is related to y or to other variables that were not studied.

Note that one can only test for missing completely at random.

Section 2: Deciding on a method to deal with the missing data

The student will consider alternatives to address missing data some of which are:

  1. Do nothing;
  2. Use only respondents with complete data;
  3. Use a weighting adjustment method;
  4. Impute value using:
  • Mean
  • Ratio
  • Regression
  • Random Hot Deck
  • Nearest Neighbour
  • Other methods

Section 3: Analysing the data

The student will study the relationship between either the Health Utilities Index (HUI) or general self perceived health and the following variables:

  • age
  • income
  • probability of depression
  • number of chronic conditions
  • number of doctor visits
  • Body Mass Index (BMI)
  • sex
  • smoking status

Section 4: Examining bias from imputation

Using the Generalized System for Imputation Simulations (GENESIS) v.1.0, SAS-8.2, the student will assess the extent of bias resulting from different imputation methods.

Data Description


This case study on missing data uses a sub-sample of the 1994 National Population Health Survey.  The context of the exercise is the relationship between health status and health predictors.  Health status is measured with either the general health question or the Health Utilities Index (HUI).  The data represent persons, aged 20-65, living in a private household in the prairie provinces. (Pregnant women were excluded in this analysis.)  Note that the "missing" data values in the data sample were removed for this case study although they are, in reality, present in the public use micro-data files.

The National Population Health Survey (NPHS) used the Labour Force Survey sampling frame to draw the initial sample of approximately 20,000 households. The survey is designed to collect information on the health of the Canadian population and related socio-demographic information. The first cycle of data collection began in 1994 and continues every second year thereafter. The sample collection is distributed over four quarterly periods followed by a follow-up period and the whole process takes a year.  The survey is designed to produce both cross-sectional and longitudinal estimates.  In each household some limited health information is collected from all household members and one person in each household is randomly selected for a more in-depth interview.

The questionnaires include content related to health status, use of health services, determinants of health, a health index, chronic conditions and activity restrictions. The use of health services is probed through visits to health care providers, both traditional and non-traditional, and the use of drugs and other medications. Health determinants include smoking, alcohol use and physical activity.  As well, a section on self-care has also been included this cycle. The socio-demographic information includes age, sex, education, ethnicity, household income and labour force status.

Research Question: 

For this case study, a survey example will be used to:

  1. Distinguish non-response mechanisms.
  2. Examine methods used to deal with non-response.
  3. Estimate bias in the presence of non-response.


Health index:

GH_Q1 In general, how would you describe your health?
DVHST94 Derived Health Status Index (3 decimal places)-HUI provisional score


AGEGRP Grouped age cohorts
SEX Respondent's sex
DVHHIN94 Derived total household income from all sources in the past 12 months
DVBMI94 Derived Body Mass Index (1 decimal place)
DVSMKT94 Derived type of smoker
DVPP94 Derived depression variable - predicted probability (2 decimal points)
NUMCHRON Sum of the following conditions:
CHRQ1_A Do you have any food allergies diagnosed by a health professional?
CHRQ1_B Do you have other allergies diagnosed by a health professional? 
CHRQ1_C Do you have asthma diagnosed by a health professional?
CHRQ1_D Do you have arthritis or rheumatism diagnosed by a health professional?
CHRQ1_E Do you have back problems (excluding arthritis) diagnosed by a health professional? 
CHRQ1_F Do you have high blood pressure diagnosed by a health professional?
CHRQ1_G Do you have migraine headaches diagnosed by a health professional? 
CHRQ1_H Do you have chronic bronchitis or emphysema diagnosed by a health professional?
CHRQ1_I  Do you have sinusitis diagnosed by a health professional? 
CHRQ1_J Do you have diabetes diagnosed by a health professional?
CHRQ1_K Do you have epilepsy diagnosed by a health professional?
CHRQ1_L Do you have heart disease diagnosed by a health professional?
CHRQ1_M Do you have cancer diagnosed by a health professional?
CHRQ1_N Do you have stomach or intestinal ulcers diagnosed by a health professional?
CHRQ1_O Do you have the effects of a stroke diagnosed by a health professional?
CHRQ1_P Do you have urinary incontinence diagnosed by a health professional?
CHRQ1_R Do you have Alzheimer's disease diagnosed by a health professional?
CHRQ1_S Do you have cataracts diagnosed by a health professional?
CHRQ1_T Do you have glaucoma diagnosed by a health professional?
CHRQ1_U Do you have any other long-term condition diagnosed by a health professional?
VISITS Sum of the following questions:
UTIL-Q2 (Not counting when ... were/was an overnight patient); in the past 12 months, how many times have/has ... seen or talked on the telephone with [fill category] about your/his/her physical, emotional or mental health

a)  General practitioner or family physician;
b)  Eye specialist (such as an ophthalmologist or optometrist);
c)  Other medical doctor (such as surgeon, allergist, gynaecologist, psychiatrist, etc.);
d)  A nurse for care or advice;
e)  Dentist or Orthodontist;
f)   Chiropractor;
g)  Physiotherapist;
h)  Social worker or counsellor;
i)   Psychologist;
j)   Speech, Audiology or Occupational Therapist.

WT6 Survey weights

See attached NPHS documentation for classes and definitions.

Data Access: 



Bourbeau R , Legare J , and Emond V. Nouvelles tables de mortalité par génération au Canada et au Québec. Document demographique no. 3. (Statistics Canada Catalogue no. 91F0015MPF) 1997.
Fellegi, I. P., and D. Holt (1976), "A Systematic Approach to Automatic Edit and Imputation", Journal of the American Statistical Association, 71, pp. 17-35.
*Kalton, G. and D. Kasprzyk (1982), "Imputing for Missing Survey Responses", Proceedings of the Survey Research Methods Section, American Statistical Association, pp. 22-31.
*Kalton, G., and Kasprzyk, D. (1986), "The treatment of missing survey data", Survey Methodology, 12, pp. 1-16.
*Kovar, J. G. and P. Whitridge (1995), "Imputation of Business Survey Data", in B. Cox, D. Binder, A. Christianson, M. Colledge, and P. Kott (eds),  Business Survey Methods, New Work: Wiley, pp. 403-420.

Lee , H., E. Rancourt and C.-E. Särndal (1991), "Experiments with Variance Estimation from Survey Data with Imputed Values", Proceedings of the Survey Research Methods Section, American Statistical Association, pp. 690-695.

*Little, R. J. A. and D. B. Rubin (1987), Statistical Analysis with Missing Data, New York : Wiley.

Lohr, S.L. (1999).  Sampling: Design and Analysis.  Duxbury Press.

Martel L, Bélanger A. An analysis of the change in dependence-free life expectancy in Canada between 1986 and 1996. Report on the Demographic Situation in Canada 1998-1999 (Statistics Canada Catalogue no. 91-209-XPE) 1999;164-86.

Mathers CD (1992) Estimating gains in health expectancy due to elimination of specified diseases. Fifth meeting of the International Network on Health Expectancy (REVES-5), Statistics Canada, Ottawa , 19-21 February 1992.

Monier A. La conjoncture demographique: l'Europe et les pays developes d'outre-mer. Population 1998;53:995-1023.

*Nordholt, E.S. (1997). Imputation: methods, simulation experiments and practical examples. Statistics Netherlands , 1-9

Nusselder WJ , van der Velden K, Sonsbeek JLA et al (1996). The elimination of selected chronic diseases in a population: the compression and expansion of morbidity. American Journal of Public Health  86(2): 187-193.

Oh, H. L. and F. J. Scheuren (1983), "Weighting Adjustment for Unit non-response", in W. G. Madow, I. Olkin, and D. B. Rubin (eds), Incomplete data in Sample Surveys, Vol. 2: Theory and Bibliographies, New York: Academic Press, pp. 143-184.
Sande, I. G. (1982), "Imputation in Surveys: Coping with Reality", American Statistician, 36, pp. 145-152.

Smith, P. J., Hoaglin, D. C., Battaglia, M. P., Rao, J. N. K., and Daniels, D. (2001), "Evaluation of Adjustment for Partial Nonresponse Bias, Applied to Provider nonresponse in the National Immunization Survey", paper presented at the Annual Meeting of the Statistical Society of Canada, Ottawa, Canada.

Torrance , George W. (1987): Utility approach to measuring health-related quality of life, Journal of Chronicle diseases, 40:6:593-600.

Torrance , George W. and Feeny, David (1989): Utilities and Quality-Adjusted Life Years, International Journal of Technology Assessment in Health Care.​