Statistics in Public Health Practice: The Role of Mathematics in the Fight Against AIDS

1. Statistics in Public Health Practice: The
Role of Mathematics in the
Fight Against AIDS
Felicia P. Hardnett
Mathematical Statistician
Centers for Disease Control and Prevention
(CDC)
The findings and conclusions in this presentation are those of the author(s) and do not
necessarily represent the views of the Centers for Disease Control and Prevention.

2. Presentation Objectives
 Define public health practice
 Describe the role of the public health
statistician
 Discuss how HIV/AIDS data are
collected and used

3. Presentation Objectives
Highlight 4 different projects that
illustrate
• Statistical methods research
• Interdisciplinary collaborations
• Training and mentorship opportunities
• Important international work

4. What is Public Health?

5. What is Public Health?
 Responsibility of the American government
to protect the health and welfare of the
American people.
 Public health science is an organized
approach to understanding the health
needs of a population rather than just
individuals.
 Public health practice is a combination of
science, ethics and politics.

6. How is public health
information used?
Public health information is used by:
• Physicians to establish treatment guidelines
• Congress in making public policy decisions
• Health advocacy groups in guiding prevention
strategies
• Print and broadcast media to make the public
aware of ways to protect themselves

7. What is the Role of the Public
Health Statistician?
• Assists with the proper collection and
processing of public health information
• Mathematically analyzes public health
information.
• Asks and answers scientific questions related
to specific disease outcomes such as…

8. Scientific Questions
 What subgroups are more at risk for disease?
 Which health behaviors are most beneficial in
preventing or treating this disease?
 Which health or demographic factors are more
closely associated with disease severity?
 What is the projected public health impact of this
disease in the future?

9. Public Health Data
 Surveillance Data
• Diagnoses
• Deaths
• Other disease outcomes
 Special Studies
• Behavioral Interventions
• Vaccine/Microbicide Trials

10. HIV/AIDS
Surveillance Activity

11. Reportable Diseases
 Diseases that are considered to be of
great public health importance.
 It is the responsibility of the
healthcare provider, not the patient,
to report diagnoses to the state
health department.

12. Reportable Diseases
 Every state has its own reporting
guidelines and list of reportable
diseases
 Many of these diseases, by law, must
be reported to CDC.

13. Reportable Diseases
 Reporting guidelines are frequently
revised depending on the public
health impact of the disease.
 Strict confidentiality guidelines are in
place to protect patient privacy.

14. CDC Surveillance Activity
State Health
Department
Physician Centers for Disease Control
and Prevention

21. Possible Causes of Racial
Disparity Among Women
 Poverty
 Education
 Healthcare Access
 Differences in Risk-Taking Behavior

22. Possible Racial Disparity
Among Women
 Poverty
 Education
 Healthcare Access
 Differences in Risk-Taking Behavior

23. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Methods:
Online search of 3 databases
Eligibility criteria
• Report rates of high-risk sexual or drug use
behavior stratified by both race and gender
• Findings must be representative of U.S.
women ages 15-44
• Findings must be generalizable to the
entire United States

24. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Hypotheses:
(2)Black women are more likely to engage in
high- risk sexual activity than women of
other races.
(3)Black women are more likely to abuse
drugs (especially intravenous drugs) than
women of other races.

25. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Hypotheses:
(2)Black women are more likely to contract
other sexually-transmitted diseases thereby
facilitating HIV transmission.
(3)Black men are less likely than men of
other races to disclose same-sex behavior
which may lead to increased HIV risk
behavior with Black women.

26. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Results:
A review of multiple studies suggests that Black
women were
-just as likely or sometimes even more likely
to report consistent condom use
-no more likely to report multiple sexual
partners
-no more likely to abuse intravenous drugs

27. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Results:
However, the results do suggest that Black
women are
-more likely to report having risky sexual
partners
-more likely to have undiagnosed/untreated
STDs

28. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Results:
Also, there is considerable evidence suggesting
that Black men are less likely than men of other
races to disclose their same-sex behavior to their
female sex partners.

29. Explaining Racial Disparities in HIV/AIDS
Incidence Among Women in the U.S.-
A Literature Review
Conclusion:
Although the literature suggests some racial
differences with regard to two of the four
hypotheses, the findings were insufficient in
explaining the 20-fold difference in HIV incidence
observed between Black and White women.
Future investigations should continue to explore
these and other social and behavioral factors.

30. Possible Causes of Racial
Disparity Among Women
 Poverty
 Education
 Healthcare Access
 Differences in Risk-Taking Behavior

31. Population Attributable Risk
(PAR) Project
Goal:
To quantify the impact of social
determinants of health on racial
disparities in HIV incidence among
U.S. women.

32. Social Determinants of Health
The economic and social conditions that
influence the health of people and
communities. These conditions are shaped
by the amount of money, power, and
resources that people have, all of which are
influenced by policy choices.

33. What is PAR?
Definition
the proportion of new cases in a population
that could have been prevented if a risk
factor were neutralized.

34. Application of PAR
Formula: PAR = P(exposed) x (RR-1)
1+ P(exposed) x (RR-1)
P(exposed) is the proportion of people
exposed to the defined health risk factor.
RR stands for relative risk.

35. Application of PAR
Formula: PAR = P(exposed) x (RR-1)
1+ P(exposed) x (RR-1)
Relative Risk (RR):
The ratio of the probability of disease among
exposed vs. unexposed.

36. Application of PAR
Formula: PAR = P(exposed) x (RR-1)
1+ P(exposed) x (RR-1)
P(exposed) is the proportion of people
exposed to the risk factor.

37. Application of PAR
Methods
Using recently published U.S. Census
and HIV/AIDS surveillance data as input
values, we estimated the PAR associated
with being African-American.

38. Application of PAR
Results
• Preliminary findings indicate that as
much as 66% of new HIV/AIDS cases
among women are attributable to
being African-American.
• This corresponds to as many as 6408
of the 9708 HIV/AIDS diagnoses
among U.S. women in 2005.

39. Application of PAR
Limitations
Race itself isn’t a modifiable risk
factor.
Completely neutralizing a risk factor
isn’t possible.

40. Application of PAR
Advantage
PAR assigns an actual measure
quantifying the potential impact of
social determinants of health as it
relates to HIV/AIDS.

41. HIV/AIDS
Special Studies

42. Special Studies
 Experimental Studies
• Subjects are enrolled and assigned to
intervention/control groups
• Intervention is administered
• Data are collected on the frequency of disease
outcomes for treated and control participants
 Observational Studies
• Subjects are enrolled and followed for a period
of time
• Data collected on the frequency of disease
outcomes

43. Special Studies
 Experimental Studies
• Subjects are enrolled and assigned to
intervention/control groups
• Intervention is administered
• Data are collected on the frequency of disease
outcomes for treated and control participants
 Observational Studies
• Subjects are enrolled and followed for a period
of time
• Data collected on the frequency of disease
outcomes

44. HIV/AIDS
Experimental Studies

45. Research Process

46. HIV/AIDS Experimental Studies
 Behavioral Interventions
 Vaccine Trials

47. HIV/AIDS Behavioral
Interventions
Description
Structured training or educational
programs which aim to lower an
individual’s HIV risk by modifying
sexual decision-making and/or drug
use behavior.

48. HIV/AIDS Behavioral
Interventions
Description
These programs target specific
psychological constructs (i.e.,
mediators) based on established
psychological theories of behavior
change.

49. HIV/AIDS Behavioral
Interventions
Purpose
To inform and/or empower people to
reduce their HIV risk through
behavioral modifications.

50. What is Mediation?
 A mediating process is the
mechanism by which a behavioral
intervention causes a change in
behavior.
 A mediator explains all or part of an
intervention’s effectiveness

51. Characteristics of Mediators
“In general, a given variable may be said to
function as a mediator to the extent that it
accounts for the relationship between the
predictor (intervention) and the outcome
(behavior)…Mediators explain how
external physical events take on internal
psychological significance.”
Baron, R. M., & Kenny, D. A. The moderator-mediator variable
distinction in social psychological research: Conceptual, strategic,
and statistical considerations. Journal of Personality and Social
Psychology, 1986, 51, 1173-1182.

52. Common Mediators in
Behavioral HIV Studies
• Self-efficacy (e.g. for condom use)
• HIV/AIDS Knowledge
• Attitudes (related to protecting self,
protecting partner, about condom use)
• Intentions to use condoms
• Outcome Expectancies (beliefs about
the consequences of behavior)

53. Purpose of Mediation Analysis
in HIV Intervention Studies
 Important for basic research on
mechanisms of effect
 Mediation analyses help to identify
how an effective intervention works
and why an ineffective one does not
work

54. How is Mediation
Measured?

55. Baron and Kenny (1986)
Mediator
α β
Intervention Outcome
τ’

56. Baron and Kenny (1986)
Mediator
α β
Intervention Outcome
τ’

57. Baron and Kenny (1986)
Mediator
α β
Intervention Outcome
τ’

58. Baron and Kenny (1986)
Mediator
α β
Intervention Outcome
τ’

59. Causal Steps- Most Common
According to Baron and Kenny (1986), a variable
functions as a mediator when it meets the
following conditions:
 (a) variations in levels of the independent
variable significantly account for variations in the
presumed mediator (i.e., Path a),
 (b) variations in the mediator significantly
account for variations in the dependent variable
(i.e., Path b), and
 (c) when Paths a and b are controlled, a
previously significant relationship between the
independent and dependent variables is no longer
significant, with the strongest demonstration of
mediation occurring when Path c is zero.

60. Controversy: Does the Intervention
Effect Have to be Significant?
 A primary assumption of the Causal
Steps approach
 Ignores the potential for suppressive
effects
 For long-term processes, power may
be low to detect an intervention to
behavior effect

61. Difference in Coefficients (τ- τ’)
Y = β01 + τ X + ε1
Y = β02 + τ ’X + βZ + ε2
Y= Outcome
X= Intervention
Z= Potential Mediator
β01, β02 = Intercepts
τ = coefficient relating independent and dependent variables
(unadjusted)
τ’= coefficient relating independent and dependent variables adjusted
for mediator effect.
ε1, ε2 = Unexplained variability

62. Product of Coefficients (αβ)
Mediator
α β
Intervention Outcome
τ’
Indirect effect: αβ
Direct Effect: τ’
Total Effect: αβ + τ’

63. Statistical Test of Mediation (I)
MacKinnon et al (1995)
αβ
z' =
α σ +β σ
2 2
β
2 2
α
• z’= modified z statistic
• Empirical critical value for .05 significance is .97
rather than 1.96

64. Statistical Test of Mediation (II)
Asymmetric Confidence Limits
α β
δα = ;δβ =
σα σβ
Values of δα and δβ are compared with
critical values in tables published by
Meeker et al.
UCL= αβ + Mupper* σ αβ
LCL= αβ + Mlower * σ αβ

65. Example- SUMIT Trial
Seropositive Urban Men’s Intervention Trial
• HIV-positive men
• Study Design: 2-arm randomized trial
(“standard” intervention vs. “enhanced”
intervention)
• Outcome variables: any unprotected insertive
anal sex with negative or unknown status
partner (UIAI)
• 10 potential mediators
• Challenge: weak intervention effect

66. Original SUMIT Analysis
 Association between IV and DV was
not significant
 Formal mediation analysis was
abandoned in favor of assessing
correlates of behavior change
O’Leary, A., Hoff, C. C., Purcell, D. W., Gomez, C.A., Parsons, J. T., Hardnett,
F., Lyles, C. M. (2005). What happened in the SUMIT trial? Mediation
and behavior change. AIDS, 19, S111-S121.

67. SUMIT Re-analysis
By applying less stringent criteria and
constructing ACLs:
• Uncovered previously unidentified mediating
effects
• Identified a marginally significant suppressive
effect

68. HIV
Vaccine/Microbicide
Trials

69. Purpose
 An opinion piece was recently
published in AIDS that attempts to
explain the waning efficacy of HIV
prevention methods observed over
time.
 DHAP researchers want to consider
the possible impact on DHAP
intervention trials.

70. Background
 Two recently published trials (1
vaccine trial and 1 microbicide trial)
concluded that intervention
effectiveness decreased over time.
 The investigators attributed this to:
• Waning vaccine efficacy (vaccine trial)
• Decreasing adherence (microbicide trial)

71. Basic Assertions
 In addition to these phenomena, the
authors assert that “selection bias
due to heterogeneity in infection
risk” is another possible explanation.
 This explanation is rarely cited in the
literature as a possible explanation
for declining efficacy.

72. Selection Bias
 is a statistical bias in which there
is an error in choosing the
individuals or groups to take part
in a scientific study.
 Can cause misleading results if
treatment groups differ in terms
of a factor associated with the
outcome.

73. Selection Bias
For example, in an HIV randomized
trial, if the majority of the persons
in the treatment group were drug
free and had taken a vow of
celibacy and the persons in the
placebo group were IDU
commercial sex workers, any
difference that you may see in HIV
incidence between these two
groups cannot be directly attributed
to the intervention.

74. Illustration of a hypothetical disease
process within a population
Population at risk
# persons who never
develop disease
Time
As people become infected, the population at risk decreases over time and
eventually plateaus
The rate of decline depends on disease incidence
The curve plateaus at the number of persons who will never develop the
disease (low/no risk people)

75. Illustration of “Selection Bias” as presented
in the paper
Population at risk
High risk
Low/no risk
Time
e paper asserts:
gh risk individuals will be infected early on and will be removed from
the population at risk.
his will leave lower risk individuals in the risk population resulting in lower
disease incidence at later time points.

76. Graphical representation of disease
incidence
N0
Population at risk (N)
n
# persons who never
develop disease Time
t0 t1
Incidence= Number who become infected (n)
From t0 to t1
Number intially at risk (N0)

77. Graphical representation of declining
disease incidence as presented in paper
Population at risk (N)
n
Time
t0 t1
• Fewer cases diagnosed at a later time point because the high risk
people are gone.
• Incidence, therefore decreases.

78. Population at risk Intervention Scenario
Treatment arm
Placebo
# persons who never
develop disease Time
• If the intervention is effective, it will prolong the time before high-risk
individuals in the treatment arm will become infected.
• Incidence decline in the placebo group will be larger because those at
high risk will be quickly removed from the population at risk.

79. Intervention Scenario
Rate ratio= incidence (treatment arm)
incidence(placebo)
Population at risk
Treatment arm
Placebo
# persons who never
develop disease Time
As a result, the time-specific rate ratio will increase from a value of less than on
to a value of one or greater.
This process is termed “frailty”,“survivor bias”, “survivor cohort effect”,
“crossing of hazards” or “depletion of susceptibles”.

80. Possible Impact on Rate Measures
Weighted average of the time specific rate ratio
This value becomes increasingly attenuated as
follow-up time increases.
This occurs even if risk factors were balanced
between study arms at baseline and if effect of
intervention is constant over time.
This may cause investigators to reject an
efficacious intervention.
This may also cause investigators to overlook a
risk factor that is, in fact, harmful.

81. Frailty Project
Purpose
To measure the potential impact of
frailty in HIV vaccine/microbicide
trials.

82. Frailty Project
Method
We are designing a series of study
scenarios that
• Incorporates both the study-related and
population-related parameters of a
randomized trial
• Manipulates these parameters
• Measures the impact on final point
estimates.

83. Frailty Project
Method
Components of these scenarios will
include measures of disease incidence,
disease risk, waning immune
response/decreased adherence and
intervention effectiveness.

84. Frailty Project
Underlying model assumptions
 Equal sample sizes in both treatment
arms.
 Disease risk is balanced between
both treatment arms at the
beginning of the study.
 Non-differential loss to follow up.

85. Frailty Project
Underlying model assumptions
 The intervention is effective at
reducing the probability of disease.
 Intervention efficacy is constant
across all risk groups.
 Intervention waning/non-adherence
is constant across all risk groups and
time intervals.

86. Frailty Project
The data collection process is taking
place now. The results will be
published as a response to the
original opinion piece.

87. HIV/AIDS
in
Subsaharan Africa

88. Southern Africa
 7 out of 10 countries have adult HIV
prevalence rate of 15% or more1
• Zambia (16.5%)
• Namibia (21.3%)
• South Africa (21.5%)
• Zimbabwe (24.6%)
• Lesotho (31.7%)
• Botswana and Swaziland (over 35%)
UNAIDS, Report of the Global AIDS Epidemic, 2004
1

89. Contributing Factors
 Sexual exploitation
• Rape
• Abuse
• Sexual trafficking
Poverty
• Limited access to prevention efforts
• Limited access to healthcare
 Inadequate public health
infrastructure
 High levels of other STDs

90. HIV Epidemic in Subsaharan Africa
 10% of the
world’s population
 70% of all people
living with HIV
 More than 2
million new
infections every
year
 Some regions
have HIV
prevalence of
more than 30%.

91. Focus on Women
 57% of infected adults are women
 75% of infected young people are
women and girls

92. Kenya Medical Research
Institute (KEMRI/CDC)
 Serves as a platform for service
delivery and scientific study in
Kenya.
 Researchers measure the impact,
effectiveness and safety of
interventions.
 Collaborations between U.S. and
Kenyan researchers to enhance
scientific and analytic capacity.

93. Kenya Incidence Cohort Study
(KiCoS)
Examines trends in seroconversion
rates, healthcare access and HIV
prevention activity in the Nyanza
Province (SW Kenya) among women,
adolescents and high risk
populations.

94. Ongoing Work in Kenya
 Examining cultural barriers to
participation in HIV prevention
efforts
 Examining factors associated with
healthcare seeking behavior among
men who have sex with men (MSM)
 Examining factors associated
consistent condom use.
 The list goes on…

95. Conclusions
Many opportunities for mathematical
researchers in the field of public health
practice
• Interdisciplinary collaborations
• Training/mentorship opportunities
• Opportunities to pursue personal
research interests
• International work

96. Thank You!!