Daniel W.W. Biostatistics: A Foundation for Analysis in the Health Sciences

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REVIEW QUESTIONS AND EXERCISES 757

24. Velthuis et al. (A-26) conducted a study to evaluate whether the combination of passively immo-

bilized heparin-coating and standard heparization can reduce complement activation in patients

undergoing cardiac surgical intervention. The investigators note that heparin-coated extracorporeal

circuits reduce complement activation during cardiac operations, but that little in vivo information

is available on the reduction in alternative and classic pathway activation. Complement activation

initiates a systemic inﬂammatory response during and after cardiac operations and is associated

with pathophysiologic events such as postoperative cardiac depression, pulmonary capillary leak-

age, and hemolysis. Subjects were 20 patients undergoing elective cardiopulmonary bypass (CPB)

grafting randomly allocated to be treated with either heparin-coated extracorporeal circuits (H) or

uncoated circuits (U). Among the data collected were the following plasma terminal complement

complex (SC5b-9) concentrations at baseline, 10 minutes after start of CPB, at cessation of CPB,

and after the administration of protamine sulfate:

Patient Treatment Baseline 10 min CPB End CPB Protamine

1 U 0.37 0.81 1.88 2.12

2 U 0.48 0.73 3.28 3.31

3 U 0.48 0.42 2.94 1.46

4 H 0.37 0.44 1.28 3.82

5 H 0.38 0.31 0.50 0.68

6 U 0.38 0.43 1.39 5.04

7 H 0.46 0.57 1.03 1.29

8 H 0.32 0.35 0.75 1.10

9 U 0.41 0.94 1.57 2.53

10 U 0.37 0.38 2.07 1.69

11 H 0.48 0.33 1.12 1.04

12 H 0.39 0.39 1.69 1.62

13 U 0.27 0.41 1.28 2.26

14 H 0.51 0.27 1.17 1.05

15 H 0.97 0.75 1.82 1.31

16 U 0.53 1.57 4.49 2.15

17 U 0.41 0.47 1.60 1.87

18 U 0.46 0.65 1.49 1.24

19 H 0.75 0.78 1.49 1.57

20 H 0.64 0.52 2.11 2.44

Source: Dr. Henk te Velthuis. Used with permission.

25. Heijdra et al. (A-27) state that many patients with severe chronic obstructive pulmonary disease

(COPD) have low arterial oxygen saturation during the night. These investigators conducted a study

to determine whether there is a causal relationship between respiratory muscle dysfunction and

nocturnal saturation. Subjects were 20 (ﬁve females, 15 males) patients with COPD randomly

assigned to receive either target-ﬂow inspiratory muscle training (TF-IMT) at 60 percent of their

maximal inspiratory mouth pressure ( ) or sham TF-IMT at 10 percent of Among the

data collected were the following endurance times (Time, s) for each subject at the beginning of

training and 10 weeks later:

max

.PI

max

Time (s) TF-IMT Time (s) TF-IMT

60% 10%

Week 0 Week 10 Week 0 Week 10

330 544 430 476

400 590 400 320

720 624 900 650

249 330 420 330

144 369 679 486

440 789 522 369

440 459 116 110

289 529 450 474

819 1099 570 700

540 930 199 259

Source: Dr. Yvonne F. Heijdra. Used with permission.

26. The three objectives of a study by Wolkin et al. (A-28) were to determine (a) the effects of chronic

haloperidol treatment on cerebral metabolism in schizophrenic patients, (b) the relation between

negative symptoms and haloperidol-induced regional changes in cerebral glucose utilization, and

veterans’ hospital inpatients (10 black, ﬁve white, and three Hispanic) with either acute or chronic

decompensation of schizophrenia. Subjects ranged in age from 26 to 44 years, and their duration

of illness ranged from 7 to 27 years. Among the data collected were the following pretreatment

scores on the digit-symbol substitution subtest of the WAIS-R (DSY1RW) and haloperidol-induced

change in absolute left dorsolateral prefrontal cortex (DLLA3V1) and absolute right dorsolateral

prefrontal cortex (DLRA3V1) measured in units of mol glucose/100 g tissue/min:

DSY1RW DLLA3V1 DLRA3V1 DSY1RW DLLA3V1 DLRA3V1

47 18

16 0 .40

31 29

34 17 9.48 11.31

22 38

70 64

59 52

41 50

0 4.67 7.26 62

Source: Dr. Adam Wolkin. Used with permission.

27. The purpose of a study by Maltais et al. (A-29) was to compare and correlate the increase in arte-

rial lactic acid (La) during exercise and the oxidative capacity of the skeletal muscle in patients

with chronic obstructive pulmonary disease (COPD) and control subjects (C). There were nine

subjects in each group. The mean age of the patients was 62 years with a standard deviation of 5.

Control subjects had a mean age of 54 years with a standard deviation of 3. Among the data

-1.87-4.92

-9.45-10.82-7.48-9.02

-11.81-15.13-12.61-9.70

-13.61-12.19-13.01-12.12

-6.47-6.59-12.95-17.12

-2.16-5.46

-4.57-4.62-11.58-10.15

-1.71-9.59-8.08

-9.58-4.91-17.17-7.97

max

758 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS

collected were the following values for the activity of phosphofructokinase (PFK), hexokinase

(HK), and lactate dehydrogenase (LDH) for the two groups:

PFK HK LDH

C COPD C COPD C COPD

106.8 49.3 2.0 2.3 241.5 124.3

19.6 107.1 3.2 1.4 216.8 269.6

27.3 62.9 2.5 1.0 105.6 247.8

51.6 53.2 2.6 3.6 133.9 200.7

73.2 105.7 2.4 1.3 336.4 540.5

89.6 61.3 2.4 2.9 131.1 431.1

47.7 28.2 3.5 2.2 241.4 65.3

113.5 68.5 2.2 1.5 297.1 204.7

46.4 40.8 2.4 1.6 156.6 137.6

Source: Dr. François Maltais. Used with permission.

28. Torre et al. (A-30) conducted a study to determine serum levels of nitrite in pediatric patients with

human immunodeﬁciency virus type 1 (HIV-1) infection. Subjects included 10 healthy control chil-

dren (six boys and four girls) with a mean age of 9.7 years and a standard deviation of 3.3. The

remainder of the subjects were 21 children born to HIV-1-infected mothers. Of these, seven (three

boys and four girls) were affected by AIDS. They had a mean age of 6 years with a standard devia-

tion of 2.8. The remaining 14 children (seven boys and seven girls) became seronegative for HIV-1

during the ﬁrst year of life. Their mean age was 3.3 years with a standard deviation of 2.3 years.

Among the data collected were the following serum levels of nitrite ( mol/L):

Controls Seronegativized Children HIV-1-Positive Patients

0.301 0.335 0.503

0.167 0.986 0.268

0.201 0.846 0.335

0.234 1.006 0.946

0.268 2.234 0.846

0.268 1.006 0.268

0.201 0.803 0.268

0.234 0.301

0.268 0.936

0.301 0.268

0.134

0.335

0.167

0.234

Source: Dr. Donato Torre. Used with permission.

29. Seghaye et al. (A-31) analyzed the inﬂuence of low-dose aprotinin on complement activation,

leukocyte stimulation, cytokine production, and the acute-phase response in children undergoing

n  7n  14n  10

REVIEW QUESTIONS AND EXERCISES 759

cardiac operations. Inclusion criterion for the study was a noncyanotic congenital cardiac defect

requiring a relatively simple primary surgical procedure associated with a low postoperative risk.

Among the data collected were the following measurements on interleukin-6 (IL-6) and C-reactive

protein (CRP) obtained 4 and 24 hours postoperatively, respectively:

IL-6 CRP IL-6 CRP IL-6 CRP

122 32 467 53 215 50

203 39 421 29 415 41

458 63 421 44 66 12

78 7 227 24 58 14

239 62 265 31 213 9

165 22 97 12

Source: Dr. Marie-Christine Seghaye. Used with permission.

Exercises for Use with Large Data Sets Available on the Following Website:

www.wiley.com/college/daniel

1. California State Assembly Bill 2071 (AB 2071) mandated that patients at methadone clinics be

required to undergo a minimum of 50 minutes of counseling per month. Evan Kletter (A-32) col-

lected data on 168 subjects who were continuously active in treatment through the Bay Area Addic-

tion Research and Treatment (BAART) centers for 1 year prior to, and 2 years after AB 2071’s

implementation. Prior to AB 2071, BAART center counselors spent two sessions of at least

15 minutes per session per month with each client. The subjects in the study were also identiﬁed

as cocaine abusers. The observations in KLETTER are the percentages of failing a cocaine drug

test for each of the subjects pre- and post-AB 2071. For example, a pre-value of 60 implies that

the patient failed a cocaine test 60 percent of the time prior to adoption of AB 2071. Dr. Kletter

performed a Wilcoxon rank sum test to determine if the percentage of failed tests decreased sig-

niﬁcantly after the passage of AB 2071. Use the data to determine what conclusion he was able

to reach. Report the test statistic and p value.

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760 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS

8. W. H. K

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ALLIS

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EAN

D. G

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Syracuse, NY, 1996.

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A. P

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EFÈVRE

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F. Y. B

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hyde Exposure in a Guinea Pig Model,” Journal of Toxicology and Environmental Health, Part A, 65 (2002),

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ERRMANN

, H. S

CHORR

, J. P. K

NAPP

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ÜLLER

, G. S

TEIN

, and J. G

EISEL

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tathionine and Methylmalonic Acid Measurement for Diagnosis of Vitamin Deﬁciency in High-Aged Subjects,”

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LEXER

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HERYL

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OLCOMB

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ATOSHI

OZAWA

, K

ATSUJI

HIMIZU

, K

IYAMOTO

, and M

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ANAKA

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Defect by Segmental Wire Fixation in Young Athletes with Spondylolysis,” American Journal of Sports Med-

icine, 31 (2003), 359–364.

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UTZ

, K. H. W

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, S. W

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, H. H. M

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, A. C.

UDOLPH

, and H. S

CHREIBER

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with Amyotrophic Lateral Sclerosis,” American Journal of Medical Rehabilitation, 82 (2003), 597–604.

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TANI

and S

HOJI

ISHI

, “A Controlled Study of Vitrectomy for Diabetic Macular Edema,” Amer-

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OSE

and S. R. E

, “The Association of Subjective Nasal Patency with Peak Inspiratory Nasal Flow in a

Large Healthy Population,” Clinical Otolaryngology, 28 (2003), 352–354.

Prostate

125

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ETER

AMM

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ENRIK

ESTERGAARD

, C

LAUS

ÜHL

, and O

LUF

EDERSEN

, “Impaired Insulin-Stimulated

Nonoxidative Glucose Metabolism in Glucose-Tolerant Women with Previous Gestational Diabetes,” American

Journal of Obstetrics and Gynecology, 174 (1996), 722–729.

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ERNARD

UTIN

, M

ARK

ITAKER

, S

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SLAM

, T

INA

ANOS

, C

LAYTON

MITH

, and F

RANK

REIBER

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Composition Measurement in 9–11-yr-Old Children by Dual-Energy X-Ray Absorptiometry, Skinfold-Thickness

Measurements, and Bioimpedance Analysis,” American Journal of Clinical Nutrition, 63 (1996), 287–292.

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RIM

, C

ESAR

A. K

ELLER

, C

HERIE

H. D

UNPHY

, H

ORACIO

M. M

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, and J

ILL

A. O

HAR

, “Flow

Cytometric Analysis of Lung Lymphocytes in Lung Transplant Recipients,” American Journal of Respiratory

and Critical Care Medicine, 153 (1996), 1041–1046.

A-20. M

ASAKAZU

CHINOSE

, M

OTOHIKO

IURA

, H

IDEYUKI

AMAUCHI

, N

ATSUKO

AGEYAMA

, M

ASAFUMI

OMAKI

ATSUYA

YA K E

, Y

UZURU

HUCHI

, W

ATA RU

IDA

, H

IROSHI

IKI

, G

AMURA

, and K

UNIO

HIRATO

, “A

Neurokinin 1-Receptor Antagonist Improves Exercise-Induced Airway Narrowing in Asthmatic Patients,”

American Journal of Respiratory and Critical Care Medicine, 153 (1996), 936–941.

A-21. T

OMOAKI

OMIYA

and K

ENJI

UJIWARA

, “Serum Transforming Growth Factor a Level as a Marker of Hepato-

cellular Carcinoma Complicating Cirrhosis,” Cancer, 77 (1996), 1056–1060.

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AKHAEE

, L

ISA

UML

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AULETTE

ADALINO

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, and C

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, “The

Lack of Inﬂuence of Long-Term Potassium Citrate and Calcium Citrate Treatment in Total Body Aluminum

Burden in Patients with Functioning Kidneys,” Journal of the American College of Nutrition, 15 (1996),

102–106.

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H. D

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, “Outcome of Severe Congenital Hypothyroidism: Closing the Developmental Gap with Early High

Dose Levothyroxine Treatment,” Journal of Clinical Endocrinology and Metabolism, 81 (1996), 222–227.

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IOTR

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, M

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, and A

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762 CHAPTER 13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS

763

CHAPTER OVERVIEW

The focus of this chapter is on measurements and other tools that are used

in the evaluation of the health of various human groups of interest, such as

local, state, and national populations. The techniques employed are con-

cerned with certain aspects of death, disease, and fertility.

TOPICS

14.1 INTRODUCTION

14.2 DEATH RATES AND RATIOS

14.3 MEASURES OF FERTILITY

14.4 MEASURES OF MORBIDITY

14.5 SUMMARY

LEARNING OUTCOMES

After studying this chapter, the student will

1. understand the basic concepts and methodologies of epidemiology and vital

statistics and how they are used by professionals in the health sciences ﬁeld.

2. be able to describe the differences between a rate and a ratio, and to explain

when the use of each is appropriate.

3. understand the concepts of mortality, morbidity, and fertility.

4. know how to calculate useful measures from mortality, morbidity, and fertility

data.

CHAPTER

VITAL STATISTICS

14.1 INTRODUCTION

The private physician arrives at a diagnosis and treatment plan for an individual patient

by means of a case history, a physical examination, and various laboratory tests. The

community may be thought of as a living complex organism for which the public health

team is the physician. To carry out this role satisfactorily the public health team must

also make use of appropriate tools and techniques for evaluating the health status of the

community. Traditionally, these tools and techniques have consisted of the community’s

vital statistics, which include the counts of births, deaths, illnesses, and the various rates

and ratios that may be computed from them.

The idea of community-based, public health medicine as just described is most

often studied using the concepts and tools of epidemiology. Epidemiologists study the

mechanisms by which diseases and other health-related conditions arise and how they

are distributed among populations. While private physicians diagnose and treat individ-

ual patients who have a medical condition, epidemiologists and public health profession-

als are additionally interested in studying those members of a population who are well,

and how those who have an illness differ from those who are free of the illness. To that

end, the use of vital statistics and epidemiological tools are employed in determining the

prevalence of a given condition at a point in time and incidence at which new condi-

tions arise in the population. Standard epidemiological measures such as those of mor-

tality, morbidity, and fertility are explored in this chapter.

In succeeding sections we give some of the more useful and widely used rates and

ratios. Before proceeding, however, let us distinguish between the terms rate and ratio

by deﬁning each as follows.

1. Rate. Although there are some exceptions, the term rate usually is reserved to

refer to those calculations that involve the frequency of the occurrence of some

event. A rate is expressed in the form

(14.1.1)

where

the frequency with which an event has occurred during some speciﬁed

period of time

the number of persons exposed to the risk of the event during the same

period of time

some number such as 10, 100, 1000, 10,000, or 100,000

As indicated by Expression 14.1.1, the numerator of a rate is a component part of the

denominator. The purpose of the multiplier, k, called the base, is to avoid results

involving the very small numbers that may arise in the calculation of rates and to

facilitate comprehension of the rate. The value chosen for k will depend on the mag-

nitudes of the numerator and denominator.

k =

a + b =

a =

a + b

764 CHAPTER 14 VITAL STATISTICS

2. Ratio. A ratio is a fraction of the form

(14.1.2)

where k is some base as already deﬁned and both c and d refer to the frequency of

occurrence of some event or item. In the case of a ratio, as opposed to a rate, the

numerator is not a component part of the denominator. We can speak, for example,

of the person–doctor ratio or the person–hospital-bed ratio of a certain geographic

area. The values of k most frequently used in ratios are 1 and 100.

14.2 DEATH RATES AND RATIOS

The rates and ratios discussed in this section are concerned with the occurrence of death.

Death rates express the relative frequency of the occurrence of death within some spec-

iﬁed interval of time in a speciﬁc population. The denominator of a death rate is referred

to as the population at risk. The numerator represents only those deaths that occurred

in the population speciﬁed by the denominator.

1. Annual crude death rate. The annual crude death rate is deﬁned as

where the value of k is usually chosen as 1000. This is the most widely used rate

for measuring the overall health of a community. To compare the crude death rates

of two communities is hazardous, unless it is known that the communities are com-

parable with respect to the many characteristics, other than health conditions, that

inﬂuence the death rate. Variables that enter into the picture include age, race, sex,

and socioeconomic status. When two populations must be compared on the basis of

death rates, adjustments may be made to reconcile the population differences with

respect to these variables. The same precautions should be exercised when compar-

ing the annual death rates for the same community for 2 different years.

2. Annual speciﬁc death rates. It is usually more meaningful and enlightening to

observe the death rates of small, well-deﬁned subgroups of the total population.

Rates of this type are called speciﬁc death rates and are deﬁned as

where k is usually equal to 1000. Subgroups for which speciﬁc death rates may be

computed include those groups that may be distinguished on the basis of sex, race,

and age. Speciﬁc rates may be computed for two or more characteristics simulta-

neously. For example, we may compute the death rate for white males, thus obtain-

ing a race-sex speciﬁc rate. Cause-speciﬁc death rates may also be computed by

total number of deaths in a specific subgroup during a year

total population in the specific subgroup as of July 1

total number of deaths during year 1January 1 to December 312

total population as of July 1

14.2 DEATH RATES AND RATIOS 765

including in the numerator only those deaths due to a particular cause of death,

say, cancer, heart disease, or accidents. Because of the small fraction that results,

the base, k, for a cause-speciﬁc rate is usually 100,000 or 1,000,000.

3. Adjusted or standardized death rates. As we have already pointed out, the use-

fulness of the crude death rate is restricted by the fact that it does not reﬂect the

composition of the population with respect to certain characteristics by which it is

inﬂuenced. We have seen that by means of speciﬁc death rates various segments

of the population may be investigated individually. If, however, we attempt to

obtain an overall impression of the health of a population by looking at individual

speciﬁc death rates, we are soon overwhelmed by their great number.

What is wanted is a single ﬁgure that measures the forces of mortality in a popu-

lation while holding constant one or more of the compositional factors such as age, race,

or sex. Such a ﬁgure, called an adjusted death rate, is available. It is most commonly

obtained by what is known as the direct method of adjustment. The method consists

essentially of applying to a standard population speciﬁc rates observed in the popula-

tion of interest. From the resulting expected numbers we may compute an overall rate

that tells us what the rate for the population of interest would be if that population had

the same composition as the standard population. This method is not restricted to the

computation of adjusted death rates only, but may be used to obtain other adjusted rates,

for example, an adjusted birth rate. If two or more populations are adjusted in this man-

ner, they are then directly comparable on the basis of the adjustment factors. Opinions

differ as to what population should be used as the standard. The population of the United

States as of the last decennial census is frequently used. For adjustment calculations a

population of 1,000,000, reﬂecting the composition of the standard population and called

the standard million, is usually used. In the following example we illustrate the direct

method of adjustment to obtain an age-adjusted death rate.

EXAMPLE 14.2.1

The 2000 crude death rate for Georgia was 7.8 deaths per 1000 population (A-1). Let

us obtain an age-adjusted death rate for Georgia by using the 2000 United States cen-

sus as the standard population. In other words, we want a death rate that could have been

expected in Georgia if the age composition of the Georgia population had been the same

as that of the United States in 2000.

Solution: The data necessary for the calculations are shown in Table 14.2.1.

The procedure for calculating an age-adjusted death rate by the direct

method consists of the following steps.

1. The population of interest is listed (Column 2) according to age group

(Column 1).

2. The deaths in the population of interest are listed (Column 3) by age

group.

3. The age-speciﬁc death rates (Column 4) for each age group are calcu-

lated by dividing Column 3 by Column 2 and multiplying by 100,000.

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CHAPTER 14 VITAL STATISTICS