10. Statistics and data presentation

Statistics and data presentation

Valerie J.M. Watzlaf and Elaine Rubinstein


Key words

Alternative hypothesis

Anesthesia death rate

Autopsy rate

Average daily inpatient census

Average length of stay

Bar graph

Bed turnover rate

Census statistics

Coefficient of variation

Community-acquired infection


Confidence interval

Contingency table

Continuous data

Direct method of age adjustment

Discrete data


Fetal death rate

Frequency distribution

Frequency polygon

Gross death rate




Incidence rate

Infant death rate


Inpatient bed occupancy rate

Interval data

Length of stay

Level of significance

Maternal death rate




Morbidity rates

Mortality rates

Neonatal death rate

Net death rate

Nominal data

Nosocomial infection

Null hypothesis

Ordinal data

p value

Pearson correlation coefficient


Percentage of occupancy

Pie chart

Postoperative death rate

Postoperative infection rate


Prevalence rate


Random sample




Ratio data

Regression analysis

Sampling error

Standard deviation

Standardized mortality ratio

Stratified random sample

Systematic sampling

Test statistic

Tests of significance


Vital statistics

Weighted mean


AIDS—Acquired Immunodeficiency Syndrome

ALOS—Average Length of Stay

ANOVA—Analysis of Variance

CV—Coefficient of Variation

dfb—Degrees of Freedom, Between Groups

dfw—Degrees of Freedom, Within Groups

DRG—Diagnosis-Related Group

HIM—Health Information Management

ICD—International Classification of Diseases

MSB—Mean Square Between Groups

MSW—Mean Square Within Groups

NCHS—National Center for Health Statistics

SMR—Standardized Mortality Ratio

SSB—Sum of Squares Between Groups

SSW—Sum of Squares Within Groups

Student Study Guide activities for this chapter are available on the Evolve Learning Resources site for this textbook. Please visit http://evolve.elsevier.com/Abdelhak.

When you see the Evolve logo image, go to the Evolve site and complete the corresponding activity, referenced by the page number in the text where the logo appears.

Overview of statistics and data presentation

Health care organizations continuously generate health care data. These data are used internally by patients, medical staff, nursing staff, and physical, occupational, and speech therapists and externally by state and federal regulatory agencies, the Joint Commission, and insurance companies, to name just a few. No matter who the user may be, statistics and data presentation focus on answering the user’s questions while complying with the standards of the health care facility. To accomplish this goal, various methods are used to calculate specific types of statistics. Different rates, ratios, proportions, and percentages are used to evaluate mortality, autopsy, and morbidity rates and census and vital statistics.

Organizing and displaying health care data are necessary. To choose appropriate methods of displaying and analyzing data, the health information management (HIM) professional must identify the level of measurement (nominal, ordinal, interval, or ratio) for variables and determine whether data are continuous or discrete. Measures of central tendency (mean, median, mode) and dispersion (variance and standard deviation) and tests of significance are used to describe and analyze data. It is also important for the HIM professional to understand basic principles of sample size determination and to be familiar with commonly used statistical tests such as analysis of variance (ANOVA), correlation, and regression.

This chapter explains basic and advanced health care statistics that are used in the health care field. Each statistic is defined and the formula for calculating each statistic is provided along with examples of how each statistic is used. Various methods of displaying data are described and illustrated.

Role of the health information management professional

Now more than ever, health care data are being collected to serve many purposes. One primary purpose is to establish health care statistics to compare trends in incidence of disease, quality and outcomes of care, and management of health information departments; another primary purpose is to conduct epidemiological research. The HIM professional’s goal is to collect, organize, display, and interpret health care data properly to meet the needs of the users. Data can be manipulated in many ways to demonstrate one result or another. HIM professionals need a broad base of knowledge to determine which data elements should be used and when data are being analyzed appropriately or inappropriately. To do this, an understanding of health care and vital and public health statistics is necessary. Furthermore, knowledge of statistical analysis is necessary so that HIM professionals can be the forerunners in data analysis. Because HIM professionals oversee a vast array of health data, it is imperative that the interpretation of the analysis and results of health care data start with them.

The HIM professional should assume the lead in recommending and using statistical tests that promote improvement in the analysis, use, and dissemination of health care data. The HIM professional fills many diversified roles and responsibilities, such as clinical vocabulary manager, data miner, or clinical trials manager.

In each of these roles, understanding and applying the methods used to collect, analyze, display, interpret, and disseminate data are essential. Responsibilities undertaken in these roles may vary from person to person. For example, the clinical trials manager may play a clearly visible role in cancer research study analysis and interpretation of the data, the clinical vocabulary manager may play a key role in developing vocabularies and standards that can be effectively used in the design of the electronic health record, and the data miner may determine the appropriate databases to use when analyzing clinical and financial data.

The HIM professional may assume other managerial roles in which statistics are used to assess productivity in coding, transcription, correspondence, and record analysis. The HIM professional should have sufficient knowledge and skills to do the following:

Health care statistics

Vital statistics

Vital statistics include data collected for vital events in our lives, such as births and adoptions, marriages and divorces, and deaths, including fetal deaths. Birth, death, and fetal death certificates are familiar reports to HIM professionals. Although each state can determine the format and content of its certificates, the National Center for Health Statistics (NCHS) recommends standard forms that most states have adopted. The purpose of the NCHS standard forms is to have a national uniform reporting system of vital statistics. These standard forms are revised periodically. The attending physician is responsible for the completion of birth, death, and fetal death certificates. The accurate completion of these certificates is supervised by the HIM department, and a copy of the birth or death certificate is kept in the medical record. A copy of the fetal death certificate is kept in the mother’s medical record.

When the certificate is complete, the original is sent to the local registrar, who keeps a copy and forwards the original to the state registrar. At each of these stages, the certificate is checked by the registrar to make sure it is complete. Individuals can obtain from the state registrar certified copies of birth, death, and fetal death certificates. Each state sends electronic files of birth and death statistics to the NCHS. The death statistics are then compiled in the National Death Index. The Death Index is a central computerized index of death record information used for research purposes by epidemiologists and other workers involved in health care research.1 The natality, or birth, statistics are compiled in the monthly vital statistics reports, and the data files are also available for purposes of research.

Refer to your state health data center or division of vital statistics to receive state-specific information on preparing and registering vital records.

Rates, ratios, proportions, and percentages

A rate is defined as the number of individuals with a specific characteristic divided by the total number of individuals or, alternatively, as the number of times an event did occur compared with the number of times it could have occurred.

A rate contains two major elements: a numerator and a denominator. The numerator is the number of times an event did occur. The number of events under study, or the numerator alone, conveys little information. However, when the numerator is compared with the denominator or the population of people in which the event could have occurred, a rate is determined. The results of a quality improvement study showed that 20 patients with diabetes had a stroke while taking a certain medication. What does this tell you? Should this medication be discontinued in this population? The data provided here include only the numerator. To compute a rate, the denominator is needed—for this example, total number of patients with diabetes who are taking the medication. This particular example included a sample size of 1000 patients. The rate is 20 in 1000 or 2 in 100. A rate is normally expressed in the following manner: 20 in 1000, 2 in 100, 1 in 100,000, 10 in 1,000,000, and so on.

However, rates are also commonly expressed as percentages by converting the rate into a decimal and then multiplying the decimal by 100. A percentage is based on a whole divided into 100 parts. In the preceding example, the rate could also be expressed as a percentage by taking 20/1000 = 0.02 × 100 = 2% or by taking 2/100 = 0.02 × 100 = 2%. This tells us that 2% of the patients with diabetes (in the study) had a stroke while taking a certain medication. To express a fraction, such as ⅕, as a percentage, the first step is converting the fraction into a decimal by dividing the numerator, 1, by the denominator, 5, to obtain 0.20. The decimal is then converted into a percentage by multiplying the decimal by 100, which can be accomplished by moving the decimal point two places to the right. The result of this process is 20%.

A proportion and a ratio are similar to a rate. A proportion, which is a part considered in relation to the whole, is normally expressed as a fraction—20/1000, 2/100, 1/100,000, 10/1,000,000, and so on. A ratio is a comparison of one thing to another, such as births to deaths or marriages to divorces. A ratio is expressed as 20:1000, 2:100, 1:100,000, 10:1,000,000, and so on. The number of physicians relative to patients or teachers relative to students is normally expressed as a ratio. For example, if a physician group practice has 10 physicians and 1000 patients, the ratio is 10:1000, which reduces to 1:100.

Table 10-1 summarizes examples of rates, proportions, ratios, and percentages.2,3

Once percentages are calculated, they can be compared across different subgroups, as seen in Table 10-2. This table concisely shows differences among geographic areas in the percentage of elderly people by age categories. It even allows a glance toward the future by projecting percentages for the years 2010 and 2025. Comparing percentages among areas shows that Europe has the highest percentage of population aged 65 years or older (13.7% in 1990) and that it should remain the world leader for at least the next 3 decades. North America and Oceania also have relatively high percentages of elderly people, which are projected to increase substantially from 1990 to 2025.4

Mortality rates

Mortality rates are computed because they demonstrate an outcome that may be related to the quality of the health care provided. There are many types of mortality rates. Table 10-3 provides definitions and formulas for the most commonly used mortality rates.2,3

Gross death rate

The gross death rate is a crude death rate for hospital inpatients because it does not consider such factors as age, gender, race, and severity of illness, which also play an important part in death rates. The use of the gross death rate as a measure of quality in health care has been questioned because it does not take these factors into account. As long as the HIM professional is aware that other factors influence this rate and that they have not been taken into account in the calculation, the gross death rate can be a quick, useful means of analyzing mortality in hospital inpatients (see the following example of gross death rate).

Example of Gross Death Rate

The discharge analysis report of Anywhere Health Care Facility shows 752 discharges (including deaths) for October 200X. Twelve deaths were also shown in the report.

Gross death rate:=12 inpatient deaths752 discharges (including deaths)× 100= 1.60%


This means that 1.60% of total discharges from Anywhere Health Care Facility during October 200X ended in death or that the gross percentage of deaths, or the hospital death rate, for October was 1.60%.

Net death rate

The net death rate is different from the gross death rate because it does not include deaths that occurred less than 48 hours after admission to the health care facility. The net death rate is useful because it provides a more realistic account of patient deaths related to patient care provided by a specific health care facility. For example, a 90-year-old patient arrives at the emergency department with shortness of breath, chest pain, and arrhythmia. After being evaluated, the patient is admitted, and it is determined that he has had a severe myocardial infarction (see the example of net death rate).

Approximately 24 hours later, the patient has cardiac arrest and dies. This particular death would be included in the gross death rate but not the net death rate because it occurred less than 48 hours after admission. Reporting agencies sometimes request net death rates because they may provide a more realistic reflection of patient care provided than gross death rates do. However, net death rates still do not take into consideration other risk factors that may also affect death, such as age, gender, race, and so forth. Therefore, an important note is that health care facilities are not necessarily responsible for deaths that occur more than 48 hours after patients are admitted; on the other hand, health care facilities are not necessarily free of responsibility for deaths that occur within 48 hours of admission. For this reason, some health care facilities do not make use of or report the net death rate.

Another consideration when computing any mortality rate is a health care facility must decide whether newborn inpatients will be included in these calculations. This decision is up to the health care facility; however, if a facility decides that newborn inpatient deaths will be included in the numerator, all newborn discharges must also be included in the denominator.

Example of Net Death Rate

Inpatient deaths at Anywhere Health Care Facility for 200X totaled 50. Inpatient deaths that occurred less than 48 hours after admission to the facility totaled 15. Total discharges (including deaths) were 15,546.

Net death rate:=50 inpatient deaths 15 inpatient deaths<48 hours15,546 discharges (including deaths) 15 inpatient deaths<48 hours× 100= 0.23%


This means that 0.23% (fewer than 1%) of the deaths of discharges for 200X occurred more than 48 hours after admission to the health care facility, or that the net percentage of deaths or net death rate for 200X was 0.23%.

Anesthesia death rate

The anesthesia death rate can also be referred to as a cause-specific death rate because the death is determined by a physician or medical examiner to be due to a specific cause (e.g., an anesthetic agent). This rate indicates the number of deaths that are due to the administration of anesthetics for a specified period of time. If the recent anesthetic death rate is higher than the rate in previous periods, a focused evaluation may be necessary to determine why this is so (see the example of anesthesia death rate).

Example of Anesthesia Death Rate

Anywhere Health Care Facility performed 492 surgical procedures during November and administered 452 anesthetics. Deaths resulting from the administration of an anesthetic totaled two for the month.

Anesthesia death rate:=2 anesthetic deaths452 anesthetics administered× 100= 0.44%


This means that 0.44% (fewer than 1%) of anesthetics administered resulted in a patient’s death, or that the anesthesia death rate for November was 0.44%.

Postoperative death rate

The postoperative death rate may be considered a cause-specific death rate as well. This death rate indicates the number of patients who die within 10 days of surgery divided by the number of patients who underwent surgery for the period; therefore, it expresses the number of deaths that may have resulted from surgical complications. In both the anesthesia and the postoperative death rates, other risk factors, such as age, gender, race, and severity of illness, are not considered. Therefore, if it is found that these rates are higher in certain periods than in others, specific evaluations are necessary to determine whether the increase is truly due to the anesthesia or surgery or to other risk factors (see the example of postoperative death rate).

Example of Postoperative Death Rate

Surgery was performed on 492 patients in the Anywhere Health Care Facility during November, and 27 of those patients died within 10 days of surgery.

Postoperative death rate:27 postoperative deaths492 patients having surgical procedures× 100= 5.49% or 5.5%


This means that 5.5% of the patients who underwent surgery died within 10 days of the procedure or that the postoperative death rate for November was 5.5%.

Maternal death rate

Death rates are further categorized according to the type of service or department, such as the maternal mortality or death rate. A maternal death results from causes associated with pregnancy or its management but not from accidental or incidental causes unrelated to the pregnancy. The maternal death rate is the number of maternal deaths divided by the number of obstetric discharges. Again, like all the rates described previously, the maternal death rate does not take into account any other risk factors. The maternal death rate is useful because maternal deaths are rare. Therefore, if there is even one maternal death in a period, it is necessary to examine the cause of death in more detail (see the example of maternal death rate).

Neonatal, infant, and fetal death rates

The formulas for these rates are given in Table 10-3. Neonatal and infant death rates are computed to examine deaths of the neonate and infant at different stages. A neonatal death is the death of an infant within the first 27 days, 23 hours, and 59 minutes of life. An infant death is death of an infant at any time from the moment of birth through the first year of life. Both of these figures are compared with the number of neonates and infants, respectively, who were discharged and died during the same period.

Fetal death rates are computed to examine differences in the rates of early, intermediate, and late fetal deaths. The definition of early, intermediate, and late fetal deaths may vary from state to state. These deaths are distinguished by the length of gestation or the weight of the fetus.

See the example of neonatal, infant, and fetal death rates.

Example of Neonatal, Infant, and Fetal Death Rates

Anywhere Health Care Facility developed the following discharge analysis report for 200X. A segment of the report shows the following:

Live births 127

Neonatal discharges 115

Neonatal deaths (before 28 days) 2

Infant discharges 50

Infant deaths (before 1 year and at or after 28 days) 5

Intermediate fetal deaths 13

Neonatal mortality rate:=2 neonatal deaths115 neonatal discharges+ 2 neonatal deaths× 100= 1.71% or 1.7%


This means that 1.7% of the neonates discharged/died or that the neonatal mortality rate for 200X was 1.7%.

Note: Because the intermediate fetal death rate is most commonly used, an example of that rate is given.

Intermediate fetal death rate:=13 intermediate fetal deaths127 live births+13 intermediate fetal deaths× 100= 9.29% or 9.3%


This means that intermediate fetal deaths made up 9.3% of live births (excluding the live births at or before 20 weeks’ gestation), or that the intermediate fetal death rate for 200X was 9.3%.

Infant mortality rate:=5 infant deaths50 infant discharges+ 5 infant deaths× 100= 0.09% or 9.1%


This means that 9.1% of infants discharged died, or that the infant mortality rate for 200X was 9.1%.

Using and examining mortality rates

Mortality statistics and trends are analyzed and used in many ways. When trends in mortality are examined, the possible reasons for differences in mortality rates should be considered. The influences can be grouped into three variables: time, place, and person. Changes over time include the following:

Finally, the following characteristics of groups of people can also influence mortality:

All these factors must be taken into consideration when mortality trends are examined within the health care facility or across health care facilities in relation to the quality of care provided.5

When examining mortality rates within a specific population as in the gross and net death rates, it is important to show age-specific rates or to adjust for age. Mortality rates are routinely adjusted for age because it is the most important influence in relation to death. As a person ages, the likelihood that the person will die increases. Age-specific rates can be used, but it becomes difficult to make comparisons of data with four or more age levels or categories. Therefore, age adjustment is performed. Statistically, age adjustment removes the difference in composition with respect to age.1

Two methods can be used to perform age adjustment. One is the direct method of age adjustment, and the other is the indirect method of age adjustment or standardized mortality ratio (SMR). The calculations for these two methods are shown in Table 10-4.

The direct method uses a standard population and applies the age-specific rates available for each population. The expected number of deaths in the standard population is then determined. To use the direct method of age adjustment, age-specific rates must be available for both populations and the number of deaths per age category should be at least five. The indirect method, or SMR, is used more often and can be used without age-specific rates and when the number of deaths per age category is small or fewer than five. Standard rates are then applied to the populations being compared to calculate the expected number of deaths, which is compared with the observed number of deaths.6

Because the SMR is used in most national and statewide mortality reports, it is explained in more detail here. For example, in Table 10-5, hospitals across a state are examined for death rates associated with the diagnosis-related group (DRG) 127—Heart Failure and Shock.

The actual or observed number of deaths in the hospital is compared with the expected number of deaths. The expected number of deaths is taken from a comparative national database adjusted for age and patient severity for each DRG. Table 10-5 shows a sample of the hospitals that treated patients included in DRG 127 and the actual and expected number of deaths. An SMR of 1 means that the number of observed deaths and the number of expected deaths are equal, and therefore the mortality rate is equal to what is expected from national norms. An SMR less than 1 means that the observed deaths are lower than the expected deaths, and therefore the mortality rate is lower than expected from national norms. An SMR of greater than 1 means that the observed deaths are greater than the expected deaths, and therefore the mortality rate is higher than expected from national norms (see the examples of use of SMR).

Autopsy rates

Autopsy rates are computed so that the health care facility can determine the proportion of deaths in which an autopsy was performed. This enables the facility to examine why a higher or lower autopsy rate may be seen from one month to another. Autopsies are performed to determine the cause of death, to better understand the disease process, or to collect tissue samples, as in patients with Alzheimer’s disease. Autopsy rates can be further broken down to show the gross autopsy rate, or the rate of autopsies performed for total inpatient deaths; the net autopsy rate, or the rate of autopsies performed for inpatient deaths, excluding unautopsied coroner cases; and the adjusted hospital autopsy rate or the autopsy rate performed for all deaths of hospital patients whose bodies are available or brought to the hospital for autopsy (those not removed by coroners, medical examiners, and so on). Autopsies may be performed after the deaths of inpatients, outpatients, home care patients, skilled nursing care residents, patients who died at home, previous patients, and so on (see example of hospital autopsy rates). Table 10-6 presents the most commonly used autopsy rates.3

Example of Hospital Autopsy Rates

Anywhere Health Care Facility developed the following report regarding discharges, deaths, and autopsies during January 200X.

Hospital Statistics

Discharges (including deaths) 1000

Total deaths 56

Inpatient (including two coroner cases) 52

Outpatient 2

Home care 2

Autopsies 13

Inpatient 10

Outpatient 1

Home care 2

Gross autopsy rate:=10 autopsies on inpatients52 inpatient deaths× 100= 19.23% or 19.2%


This means that 19.2% of the hospital inpatients who died during January received an autopsy, or that the gross autopsy rate was 19.2%.

Net autopsy rate:=10 autopsies on inpatients52 inpatient deaths× 100 2 unautopsied coroners’ cases= 20%


This means that 20% of the hospital inpatients who died during January received an autopsy within the hospital, or that the net autopsy rate was 20%.

Hospital autopsy rate (adjusted):=13 total hospital autopsies52 inpatient deaths 2 coroner cases+ 2 outpatients+ 2 home health care patients= 54× 100= 24.07% or 24.1%


This means that 24.1% of all health care facility patients who died in January (inpatients, outpatients, and home care patients) received an autopsy within the hospital, or that the adjusted hospital autopsy rate was 24.1%.

Morbidity rates

Morbidity rates can include complication rates, such as community-acquired, hospital-acquired or nosocomial, and postoperative infection rates. They can also include comorbidity rates and the prevalence and incidence rates of disease.

Hospitals use each of these rates to study the types of disease or conditions that are present within the health care facility and to examine the quality of care provided by the facility. These rates can aid health care facilities in planning specific health care services and programs. Table 10-7 provides a summary of the more common morbidity rates and the formulas used to compute them.3

Table 10-7


Definition Formula
Complication (condition that occurs during hospital stay that extends length of stay by at least 1 day in 75% of cases)*

Total number of complicationsTotal number of discharges ×100

Nosocomial infection rate (infection that occurs >72 hours after admission to hospital)*

Total number of infections that occur>72 hours after admissionTotal discharges ×100

Postoperative infection rate*

Total number of postoperative infectionsTotal number of discharges × 100

Community-acquired infection rate (infection that occurs in community or <72 hours of admission)*

Total number of community-acquired infections that occur<72 after admissionTotal number of discharges ×100

Total infection rate (includes both nosocomial and community-acquired infections)*

Total number of community-acquired and nosocomial infectionsTotal number of discharges ×100

Comorbidity (preexisting condition that will, because of its presence with principal diagnosis, increase the length of stay by at least 1 day in 75% of cases)*

Total number of comorbiditiesTotal number of discharges for a given period ×100

Prevalence (number of people with specific disease at specified period of time; number of existing cases of disease)

Number of cases of disease present in a population atspecified time periodNumber of people in population at specified time period ×100

Incidence (number of people with disease during specified time period; number of new cases of disease)

Number of new cases of a disease occurring in populationduring a specified time periodNumber of people in population at specified time period ×100



*Numerators and denominators in each formula must be for the same time period.

Complications include infections, allergic reactions to medications, transfusion reactions, decubitus ulcers, falls, burns, and errors of medication administration. The complication rates for any of these complications can also be computed by using the formula for complication rates listed in Table 10-7.

One of the most common complications is infections. Infection rates are computed so that the health care facility can determine when infections developed and, therefore, how they may be prevented. A nosocomial, or facility-acquired, infection rate includes infections that occur more than 72 hours after admission.7 Health care facilities may be more interested in this rate because it may show infections that occur as a result of the care that is provided in the facility. Further analysis of the nosocomial infection rate may show that other risk factors, such as age, compromising conditions such as cancer, the use of chemotherapy treatment, and the overall severity of the disease, may make an individual patient more susceptible to infection. Therefore, as with several of the mortality rates, other factors play a part in the development of the nosocomial infection. The postoperative infection rate is normally calculated to pinpoint how the infection may have developed. Postoperative infection rates are important to examine because the health care facility can determine which infections occur after surgery and are probably a result of the surgical procedure.

Distinguishing between nosocomial and community-acquired infections is important because community-acquired infections are typically present less than 72 hours before admission to the health care facility. Health care facilities may be interested in this rate because it demonstrates the infections that patients probably had before admission to the facility. If the facility finds that their community-acquired infection rate is high, they may need to develop community-wide prevention programs, such as administering a vaccine for pneumonia. Health care facilities can benefit from analysis of their total infection rate (both nosocomial and community-acquired infections) to determine the additional cost, length of stay, and overall effect the infections have on the quality of care provided to the patient.

Comorbidities are preexisting conditions, such as diabetes, hypertension, and osteoporosis. Analysis of the comorbidity rate is important because comorbidities can increase the length of stay and affect the outcome of care provided. Comorbidities include some of the other risk factors that affect mortality and morbidity rates.

Mar 15, 2017 | Posted by in NURSING | Comments Off on 10. Statistics and data presentation

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