Applied Epidemiologic Analysis

Applied Epidemiologic AnalysisFall 2002

Applied Epidemiologic Analysis

Patricia Cohen, Ph.D.

Henian Chen, M.D., Ph. D.

Teaching Assistants

Julie Kranick Sylvia TaylorChelsea Morroni Judith Weissman


Lecture 12Multiple time point assessments in epidemiology: purposes, questions, and analyses

GOALS:

To understand some of the reasons for longitudinal analysis in epidemiology

To outline the circumstances in which a survival analytic method, a Poisson regression method, a repeated measure ANOVA method, a GEE method, or a multilevel method may be selected

To understand the connection between multilevel methods for clustered data and for longitudinal data in terms of the kinds of questions that may be answered.


Epidemiology and longitudinal analysis

• In a sense all epidemiological analysis is longitudinal.

• Its goals are nearly always determination of potential causes for which temporal priority is a necessity (all other analyses being, in a sense, subsidiary to this goal).

• It has an emphasis on rates, which are intrinsically longitudinal.


Matching data and analytic model

Data: Time to some event such as disease onset or diagnosis

Analytic choices depend on– Whether you have exact person-time units for those who do

experience the outcome (disease) and for those who do not experience it a time over which they were observed before censoring (end of study, loss to follow-up, experience of an incompatible outcome such as death)

– Sample size

– Appropriateness of a parametric assumption (e.g. shape of time distribution)

– Proportion of the sample getting the outcome


Matching data and analysis (rate models)

Parametric Minimum

cell N

Limit on %

censored Effect index

Life table No Yes Yes Curves/survival

rate

Kaplan-Meier No Yes Yes Curves/survival

rate

Cox regression Semi No Yes Hazard ratio

Poisson regression

Yes No No Log prob. change

Data include person-time for both cases and referent participants (time to censoring)


Matching data and analytic model (risk and change models)

Two time-point data

Dependent variable

Binary Scaled Effect Measure

Logistic regression

Yes No Odds change

Probit regression

Yes No Probability change

OLS No Yes Unit change Three + time-points

GEE (logistic) Yes No Mean odds change

Repeat ANOVA No Yes Mean difference Mean change difference

Multilevel Yes Yes Any of the above related to mean DV and any desired change function


Alternative longitudinal designs

A. Designs in which measurement of exposures, including timing, are retrospective

B. Nested case-control studies with prospective measurement of exposure and confounders and matched timing for cases and controls

C. Cohort studies in which data on exposures are gathered prospectively and disease outcomes are assessed in subsequent follow-up


Retrospective studies

• Designs in which measurement of exposures, including timing, are retrospective (gathered at a single time point in case-referent and cross-sectional cohort studies), or based on collection of pre-existing records.

• Accuracy of measurement is a problem, especially when it is based on recall.

• When exposures or confounders are themselves time-dependent or time-varying there can be considerable problems in producing an unbiased estimate of exposure effect. How will we know how much of the exposure is attributable to the confounder and how much may have preceded it?

• There may be effects of the exposure on a (partial) confounder, or even of the disease influencing exposures and/or confounders over time.


Nested case-control studies

One method of attempting to control at least some of these problems:

– prospective measurement of exposure and confounders

– matched timing for cases and controls.


Longitudinal cohort studies

• Data on exposures gathered prospectively

• Disease outcomes gathered in follow-up

Disease2 =

B0 + BDDisease1 + BCConfounders1 + BEExposure1 + ε

• In studies of disorders or conditions that change over time, earlier disease status can be included in the estimate of the effect of exposure on persistence or new onset to ensure temporal priority.


Appropriate time intervals between measures

The biologically plausible period between the exposure and disease needs to be taken into account.


Frequently changing exposures, frequently recurrent diseases, and varying biological indicators

When studying the relationship between variables that may change over fairly short time periods, it is useful to include more than two measurement points.

1. To inform about average changes in variables over time/ trials/ age

2. To improve inferences about the direction and magnitude of influences of one variable or set of variables on another by establishing sequence

3. To inform about individual or group differences in change over time and variables that relate to these differences


Repeated assessments designed to inform about average changes in variables over time/ trials/ age.

In the past these studies would often be analyzed by repeated measure analysis of variance (ANOVA)

• Data collected for every study participant at each point in time

• Problems because of difficulties managing missing data and no means of coping with variations in timing of assessments

Currently, these studies will almost invariably be analyzed with a multilevel analysis program

• Missing data are readily handled, including “censored” data

• Timing of data collection can vary from participant to participant

• Depending on the number of time points included, the kinds of questions about relationships of predictors to changes in outcomes that can be addressed are substantially increased

• Time-varying predictors can be included in the analysis

• Autocorrelation can be included in the analysis


Repeated measures with binary outcomes

• One solution is analysis by Generalized Estimation Equations:

• These models assume that in the population the correlation between DV and predictors is constant over time and provide overall estimates of DV effects under that assumption.

• The other major solution is to employ logistic (or some other link function appropriate for binary data) in multilevel regression analysis.


Longitudinal analysis of changes in indices of obesity from age 8 years to age 18 years

Dal S, Labarthe DR, Grunbaum JA, Harrist RB, Mueller WH. 2002. American Journal of Epidemiology, 156, 720-729.

Goals of study:

To examine growth patterns of obesity indices of 678 children studied at 4 month intervals for 4 years, beginning ages 8,11, and 14.

To compare these patterns for males and females and for Black and White Children.


Figure 5. Sex- and race-specific trajectories of the sum of two skinfold measurements


Lawson CC, LeMasters GK, Levin LS, Liu JH. 2002. Pregnancy hormone metabolite patterns, pregnancy symptoms, and coffee consumption. American Journal of Epidemiology, 156, 428-437.

Goals of study

To determine relationships between:

1. Pregnancy hormone metabolites (PHM) & concurrent coffee consumption (CC)

2. PHM and concurrent pregnancy symptoms (PS)

3. Pregnancy symptoms and coffee consumption

4. Pre-pregnancy coffee consumption and PHM


Study design

• Study subjects: 100 nonsmoking women enrolled on average in the 6th week of pregnancy who had been pre-pregnancy coffee drinkers, recruited from advertising in public and health service locations.

• Data collected retrospectively back to date of last menstrual period and prospectively through week 12.


Pregnancy hormones, symptoms, andcoffee consumption



Analyses to answer study questions regarding relationships between:

Pregnancy hormone metabolites (PHM) & concurrent coffee consumption (CC)

- Carried out by a multilevel analysis of the relationship between weekly coffee consumption (treated as DV) and (time-varying) PHM, partialing pre-pregnancy coffee consumption and smoking history. Two of three PHM were related to current coffee consumption.



Other study findings determining relationships between:

PHM and concurrent pregnancy symptoms (PS) Weekly changes in these variables were strongly related in multilevel models.

Nausea and appetite loss were not related to current coffee consumption, but more vomiting was associated with less coffee consumption.

Pre-pregnancy coffee consumption was related to lower mean level of one of the pregnancy hormones (a not anticipated finding).


Time-series analysis

• This set of techniques may be thought of as analogous to ecological analysis of clustered data: they are studies of changes in one unit over time.

• They are the backbone of econometric analyses and equally relevant to the analysis of effects of changes in public policy/ public health programs on aggregate public health.

• The study we examined last week that looked at regional differences in family planning policy and service availability and regional differences in sexual activity and contraceptive use by young women might have been a time series if data pre and post policy/service changes had been available.


Modeling changes in CD4+ T- Lymphocyte counts after the start of highly active antiretroviral therapy and the relation with risk of opportunistic infections

Binquet C, Chene G, Jacqmin-Gadda H, Journot V, Saves M, Lacoste D, Dabis, F et al., American Journal of Epidemiology,

Question: Is there a minimal duration of CD4+ cell count increase before its impact on opportunistic infection?

Design: 553 HIV patients treated with at least one protease inhibitor and studied at least twice over the next months with regard to CD4+ counts and opportunistic infection.


Evolution of CD4+ T lymphocity count among HIV+ patients on antiretroviral therapy


Antiretroviral therapy and CD4+ counts

• Conclusions: There was a delay in the response to the treatment over the first 4 months, including a delay in the decline of rate of opportunistic infection and in the relationship of CD4+ increase to this decline.

• After the fourth month, greater increase in CD4+ counts were related to decline in opportunistic infection

• Unfavorable trend in CD4+ trend after four months is an indication of drug failure and suggests therapy change.


TIME SERIES ANALYSES AND MULTILEVEL LONGITUDINAL STUDIES

If data are available both at the individual and aggregate level we may still focus on the effects over time, using multilevel analyses.

– Purposes and designs vary: May have designs that estimate effects of service system or legislative policy change on health indicators: Quasi-experimental designs may look at sudden change in time-trends.

– As in clustered data, a major purpose may be to see whether there are effects of “fixed” individual unit differences in the relationship among variables including time. Is there a difference in the slope (linear increase or decrease) of some disease marker over time associated with an exposure?

If a time series is based on aggregated data we may think of it as comparable to ecological analyses with data only at the clustered level.


Epidemiology of pertussis in a West African community before and after introduction of a widespread vaccination program

• How did the vaccination program affect the incidence of pertussis between 1984 and 1996 in an area within Senegal?

• How did these effects impact children of different ages?


Pertussis in a West African community



• Conclusion: periodic epidemics of pertussis were dampened by vaccination.


Pertussis in a West African community: trends in age groups

Note that in contrast to the previous graph, these rates are per 1000, and differences are smaller, numbers being partly due to decline in number of children.



Conclusion: Age effects were larger among older children in the earliest vaccinations, but were relatively equal among age groups thereafter.

Pertussis is a major cause of childhood morbidity and mortality globally. Even among those who did not receive booster shots there was a decline in mortality if there were subsequent infections.

There also appeared to be a herd immunity effect of vaccination, although the level receiving even one dose was never much over 40%.

This study has data only at the aggregate level, and is thus rather like ecological studies, without the ability to examine individual differences (e.g. in number of vaccination doses effects or in the duration over which immunity effects associated with specific numbers is effective).

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Applied Epidemiologic Analysis