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*Journal of Mathematical Sociology*, 34:146–155, 2010Copyright Taylor & Francis Group, LLCISSN: 0022-250X print/1545-5874 onlineDOI: 10.1080/00222500903221589
A Multilevel Event History Model of Social Diffusion:Medical Innovation Revisited
Noah E. FriedkinDepartment of Sociology, University of California–Santa Barbara,Santa Barbara, California, USA

*This article presents a multilevel event history model of social diffusion andapplies it to Coleman, Katz, and Menzel’s (1966) data on the adoption oftetracycline by physicians. The simplest form of a multilevel model allows arandom intercept. In the present application of this simple model to the *MedicalInnovation

*data, structured for an event history analysis, the physicians arenested in city and time. Random intercepts capture effects of contextual conditionsthat are shared by event history cases with the same city–time status. Theintercepts also reﬂect any baseline internal contagion effects, that is, the proportionof physicians in the city–time network who have adopted the drug at time *t − 1

*.*

Here, I show that Van den Bulte and Lilien’s (2001) ﬁnding of an importantcontextual effect of drug ﬁrms’ marketing effort is misleading. I also show thatthe social network in which physicians are situated signiﬁcantly contributes totheir adoptions, controlling for baseline internal contagion effects and individual-level characteristics of physicians, which have been emphasized in investigationsof these data.
Keywords: contagion, diffusion, social networks
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Coleman, Katz, and Menzel (1966) examined the contribution ofnetworks of interpersonal contact, based on discussion, advice, andfriendship relations, to the diffusion of a medical innovation—theadoption of tetracycline, a new antibiotic. Four communities ofphysicians, located in three small cities and one substantially largercity, were investigated. A physician’s adoption of the antibiotic wasascertained from the prescription records of local pharmacies, whichwere monitored during three consecutive days each month over aperiod of 17 months after the introduction of the antibiotic. Upon
Address correspondence to Noah E. Friedkin, Department of Sociology, University
of California–Santa Barbara, 2806 Ellison, Santa Barbara, CA 94106, USA. E-mail:

[email protected]
the ﬁrst appearance of a prescription, the prescribing physician wasdeﬁned as an adopter during all of the remaining time periods of thestudy. Since the antibiotic proved to be efﬁcacious, the assumptionis reasonable that a physician’s ﬁrst prescription of the antibioticimplied continued employment of it. A small fraction of physiciansadopted the antibiotic in the ﬁrst month and, by the 17th month asubstantial fraction of monitored physicians had adopted it. Colemanet al.’s analysis supported their hypothesis that the physicians’contact networks contributed to the diffusion of the drug. Subsequentanalyses of the data have provided mixed support for this claim (Burt,1987; Marsden and Podolny, 1990; Strang and Brandon Tuma, 1993;Valente, 1996; Van den Bulte and Lilien, 2001).

Van den Bulte and Lilien’s (2001) analysis of the

*Medical*
*Innovation *data presents the most startling conclusion among theanalyses that been conducted thus far. They conclude that “priorevidence of social contagion gained from the

*Medical Innovation *studyby Coleman et al. (1966) is an artifact arising from omitting theeffect of marketing efforts” (Van den Bulte and Lilien, 2001, p. 1411).

Van den Bulte and Lilien’s conclusion is based on the followingformalization of the marketing efforts of the drug companies that werepromoting the adoption of tetracycline:
where M t is the time t measure of marketing effort, 0 ≤
scalar constant, and p t is the amount of published advertising inmonth t in hundreds of pages, t = 1 2
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and so on. Two marketing effort measures were computed: onemeasure for the marketing effort of Lederle, the major pharmaceuticalcompany that promoted the antibiotic, and another for the marketingeffort of all other competing ﬁrms. Van den Bulte acknowledges(personal communication, 2008) that this formalization of the ﬁrms’marketing efforts is crucial to their conclusion. Upon request, Vanden Bulte provided the data upon which the 2001 analysis was based,including the p t measures and the corresponding values of M t .

These scores are presented in Table 1. Note Lederle’s nearly constantlevel of published advertising.

TABLE 1 The Basis of Van den Bulte and Lilien’s (2001) Measure ofMarketing Effort
Van den Bulte and Lilien (2001) estimate the parameter
value that produced the highest model likelihood
“in a model that did not feature social network exposure variables”
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(p. 1424), but that did include variables pertaining to the individualcharacteristics of those physicians who were at risk of adopting (theirprofessional age, whether they held a chief or honorary position, thenumber of journals they read, and their scientiﬁc orientation) and anindicator variable for summer months. Estimating the models withall of these individual-level variables, the summer indicator variable,and a social contagion variable (several contagion measures wereentertained in separate models), they found signiﬁcant effects of socialcontagion. Estimating the models with all of these individual levelcharacteristics, the summer indicator, a social contagion variable,and the two measures of marketing effort (1), one for Lederle andthe other for all other competing ﬁrms combined, they found nosigniﬁcant effects of social contagion, a signiﬁcant effect of theLederle’s marketing effort, and no signiﬁcant effect of the combinedmarketing effort of other competitors. These ﬁndings are reproducedin Table 2 with the data provided to me.

TABLE 2 Van den Bulte and Lilien’s 2001 Findings Replicated
∗p < 10; ∗∗p < 05; ∗∗∗p < 01; ∗∗∗∗p < 001 (two-sided).

†In Van den Bulte and Lilien’s data set, the social contagion measures are denoted
TOTCOH, BURTCOH, TOTSP, and BURTSE1, respectively, for Models 1b, 2b, 3b, and4b. See their 2001 article on the construction of these measures.

Van den Bulte and Lilien’s ﬁndings are based on a discrete time
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= 0 is a physician i who is at risk of adopting at time t − 1,
P y t = 1 y t−1 = 0 is the hazard rate for the physician’s adoption of
w y t−1 is a social contagion measure, and x t−1 is an
array of control variables. The analysis pools 125 physicians in thefour cities studied by Coleman et al. (1966). The units of analysis are947 physician-months involving all instances of physicians at risk ofadopting tetracycline in a particular month.

The

*Medical Innovation *data have served as a useful platform
for exploring alternative models of social diffusion. It would beunfortunate if Van den Bulte and Lilien’s (2001) ﬁndings misleadinglyput an end to investigations of this data set. From a nearly constantmonthly level of advertising pages for Lederle, Van den Bulte andLilien constructed a variable for Lederle that rises monotonicallyovertime to an asymptote in a fashion that mimics the overtime curveof cumulative adoptions in the pooled populations of physicians. Theirformalization of Lederle’s marketing effort generates a variable that is
a close approximation to the partial sum of a geometric series, that is,
2p + · · · + 1 − t−2p + 1 − t−1p
+ 1 − 2 + · · · + 1 − t−2 + 1 − t−1
= 0 25, arbitrarily selected values of 0 < p < 1, for example,
p = 0 001 0 01 0 03 0 06 0 12 , sufﬁce to eliminate contagion effectsbased on (3). Reducing the amount of monthly advertising from sixpages to three pages or to one page or to

*one-tenth of a page per month*also eliminates the detection of a contact network contagion effect.

Thus, it is not evident that a contextual effect of advertising exists
and, if it does, it is not evident that it accounts for the observednetwork contagion effect. Below I describe a parsimonious test of theseeffects. Contextual effects may be based on city-level conditions thatdiffer across the four cities or on time-level conditions that differacross the months in which the physicians’ adoptions were monitored.

City–time contextual effects will generate variation in the interceptsof a suitably nested random intercept model. In the absence of suchvariation, city–time contextual effects may be dismissed.

2. A RANDOM INTERCEPT EVENT HISTORY MODEL
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Physicians’ time t responses are nested within cities and time periods.

A credible approach to these data is to locate those conditionsthat are common to physicians in the city–time intercepts for thisnesting. These common conditions include Van den Bulte and Lilien’smarketing effort measures. From (2), at each time t, we have
where M t is the marketing effort measure for Lederle and M t is
the marketing effort measure for the other competitors at time t. Thevalues of these marketing effort measures vary across time periodsand are constants within time periods. Since both measures are
contextual conditions that are common to the physicians in the

*pooledfour cities *in month t − 1. If the ﬁt of this model does not improve uponthe ﬁt of the reduced model with a ﬁxed intercept, then there is littlereason to suppose that variation of marketing effort is an importantfactor in the account of physicians’ responses.

Model (5) nests physicians in time. With an elaborated

*city–time*
random intercept model, the intercepts also include city-levelcontextual effects. The intercepts of a city–time random interceptmodel also include baseline internal contagion effects, that is,
and n is the number of physicians in city c’s network. This baseline
internal contagion value is the proportion of physicians in a particularcity who have adopted the drug at time t − 1. With such an approach,contact-network contagion is disentangled from baseline-internalcontagion. The contact-network contagion test H
whether, within a city at a particular time, the variation among thephysicians in their

*weighted averaging *of the time t − 1 adoptions andnonadoptions of other physicians is associated with the hazard rate oftheir adoption of the drug at time t. The weights that are involved inthis weighted averaging are not the weights of the baseline internal
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contagion model, but weights that are determined by the structure ofthe contact network in which the physicians are embedded. Thus, inthe detection of a contact-network contribution, a city–time nestingsimultaneously addresses effects of contextual conditions and baselineinternal contagion contributions to adoption. With this elaboratednesting, if the ﬁt of the nested model with random intercepts does notimprove upon the ﬁt of the reduced model with a ﬁxed intercept, thenthere is little reason to suppose that the hazard rate of physicians’adoption of tetracycline depends on city–time variation of contextualconditions, including marketing efforts and the proportion of previousadopters in a city.

My analysis of Van den Bulte and Lilien’s (2001) measure ofmarketing effort suggests that their null ﬁnding on network contagion
effects is an artifact of the construction of their measure of marketingeffort. The monthly level of drug ﬁrms’ advertisements in professionaljournals is a contextual condition that applies to all physicians atrisk of adoption in a given month; as such, marketing effort is onecondition, among other contextual conditions, that may contributeto variation of hazard rates among physicians in different city–time contexts. The analysis of a suitably nested model with randomintercepts provides a parsimonious test of whether or not there iswarrant for entertaining hypotheses concerned with such variation.

Such warrant must be suspect if the analysis indicates no signiﬁcantdifference of ﬁt between a model that allows the intercepts to varyacross contexts and a model that does not allow for such variation.

As shown below, the hazard rate of adoption is near zero for at-riskphysicians who are not directly exposed to any adopters, regardless ofthe time and city context.

In the network-contagion component of their model, Van den
Bulte and Lilien consider four measures of physicians’ contact-network exposure to the time t − 1 adoptions and nonadoptions ofother physicians. Two of these measures employ weights based onstructural cohesion in the physicians’ contact network, and the othertwo measures employ, weights based on structural equivalence inthe network (see Van den Bulte and Lilien, 2001, on the detailedconstruction of these measures). In the event history dataset, themeasures are correlated as follows
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where BURTSE1, BURTCOH, TOTSP, and TOTCOH are theacronyms for the four contact network contagion variables in Van denBulte and Lilien’s data set. Here, I take each measure as providing acredible approach to network contagion and employ their mean values,denoted as CNET, in the analysis. Cronbach’s
Table 3 presents the ﬁndings obtained for the event history
physicians in city–time s The summer indicator and marketing effort
TABLE 3 Estimate of Network-Contagion, Controlling forPhysicians’ Personal Characteristics, with Random InterceptsBased on a Nesting of Time Periods Within Cities, inComparison to the Estimate Obtained with a Fixed Intercept
∗p < 10; ∗∗p < 05; ∗∗∗p < 01; ∗∗∗∗p < 001 (two-sided).

†LR test vs. logistic regression: chi2 2 = 4 2E − 12 Prob > chi2 =
††CNET is measured as the mean of the four network contagion
measures employed in Van den Bulte and Lilien’s analysis, i.e.,TOTCOH, BURTCOH, TOTSP, and BURTSE1 in Table 2, for whichCronbach’s

*Note: *These estimates are based on Stata 10’s xtmelogit procedure.

scores have been dropped as variables, since both are contextualvariables with scores that are shared by all at-risk physicians locatedin a particular city–time setting. The contributions of these constantsare captured by the random intercepts. The included variables are
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the remaining individual-level variables in Table 2 (professional age,professional age squared, chief or honorary position, logged numberof journals, and scientiﬁc orientation) and CNET (the mean of thefour contact network contagion measures).

The network-contagion variable has a signiﬁcant effect. The ﬁt
of the model, LL = −308 37, does not differ from the ﬁt of thereduced null model with a ﬁxed intercept. Indeed, the estimatedrandom effects u are

*trivial *with values that range from −2 30E − 16
68 , the baseline hazard rate of adoption is near zero regardless
of physicians’ city–time settings. Hence, we may constrain theintercepts with no loss of ﬁt and dismiss the hypothesis that there arecontextual differences among the city–time settings that signiﬁcantlyraise or lower the hazard rates for the physicians within thesesettings. Given trivial variation of the intercepts, the estimates
obtained for the reduced ﬁxed effects logistic model is
which assumes an intercept that is constant across cities and times,are identical to those obtained for the nested random intercept model.

The above ﬁndings support the null model’s assumption of no
signiﬁcant variation among the city–time intercepts. The ﬁndingsare inconsistent with the hypothesis that mass marketing efforts(based on advertising in professional journals) had a monotonicallyincreasing impact over time on the hazard rate of physicians’ adoptionof tetracycline. The ﬁndings are consistent with the existence ofcontact-network contagion that is net of baseline internal contagionand those individual-level variables included as controls.

My ﬁndings support the original conclusion of Coleman et al.

(1966) that physicians’ networks of interpersonal contact withother physicians contributed to physicians’ adoption of tetracycline.

Moreover, my ﬁndings strengthen Coleman et al.’s conclusion inshowing that a contact network effect is maintained in a modelthat allows a potential baseline internal contagion contribution toadoption, that is, the proportion of physicians in a city who haveadopted the drug at time t − 1.

Mainly as a matter of convenience, I have employed a summative
measure of the contact network role in adoption—CNET—based onthe four measures employed in Van den Bulte and Lilien’s (2001)
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analysis. Two of these measures emphasize features of structuralcohesion and two emphasize features of structural equivalence inthe contact networks of the physicians. Previous analyses have beenaddressed to the relative merits of a structural cohesion versusstructural equivalence approach to specifying network effects on socialdiffusion. However, since each of these two approaches draws ondifferent but correlated structural features of contact networks, itmay be useful in the future to treat them as multiple measures thatin combination provide a more reliable discrimination of the contactnetwork environments in which actors are situated. I do not discountthe theoretical importance of pursuing a more exact speciﬁcation ofhow contact networks contribute to diffusion. I suggest only that it isequally important to more ﬁrmly and impartially establish that there

*is *a contact network contribution prior to advancing assertions thatsome structural features of the contact network are more importantthan others.

I am grateful to David Strang and Nancy Tuma for comments ondrafts of this article, and to Christophe Van de Bulte for providing thedata on which the present analysis is based.

Burt, R. S. (1987). Social contagion and innovation: cohesion versus structural
equivalence.

*American Journal of Sociology*,

*92*, 1287–1335.

Coleman, J. S., Katz, E., & Menzel, H. (1966).

*Medical Innovation: A Diffusion Study*.

Marsden, P. V. & Podolny, J. 1990. Dynamic analysis of network diffusion processes.

In J. Weesie & H. Flap, (Eds.),

*Social Networks Through Time *(pp. 197–214).

Utrecht, The Netherlands: ISOR/Rijksuniversiteit Utrecht.

Strang, D. & Brandon Tuma, N. (1993). Spatial and temporal heterogeneity in diffusion.

*American Journal of Sociology*,

*99*, 614–639.

Valente, T. W. (1996). Social network thresholds in the diffusion of innovations.

*Social*
*Networks*,

*18*, 69–89.

Van den Bulte, C. & Lilien, G. L. (2001). Medical innovation revisited: social contagion
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*American Journal of Sociology*,

*106*, 1409–1435.

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Source: http://www.soc.ucsb.edu/faculty/friedkin/Reprints/JMSMedInnov.pdf

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