Toward a quantitative characterization of patient-therapist communication

Toward a Quantitative Characterization of Patient-Therapist Communication

P. E. RAPP

Department of Physiology and Biochemistry, The Medical College of Pennsylvania, Philadelphia, Pennsylvania M. A. JIMI~NEZ-MONTANO

Center for Biological Research, University of Veracruz, Veracruz, Mexico R. J. LANGS

Nathan S. Kline Institute for Psychiatric Research, Orangeburg, New York L. THOMSON

C. G. Jung Foundation for Analytical Psychology, New York, New York AND

A. I. MEES

Department of Mathematics, University of Western Australia, Nedlands, Australia Received 25 June 1990; revised 22 January 1991

ABSTRACT The efficacy of psychotherapy, in its many and varied forms, is one of the most intensely contested issues in clinical practice. Though many theories have been advanced, quantitative evidence in their defense is limited. This contribution is directed to relatively unambitious objectives. Rather than establish yet another qualitative theory of psychotherapeutic practice, we wish to contribute to the construction of research methodologies that can quantitatively characterize the dynamic patterns of patient-therapist communication. It is hoped that a theoretical understanding of psychotherapy might eventually emerge naturally from a growing body of quantitative data.

MATHEMATICAL BIOSCIENCES 105:207-227 (1991) ©Elsevier Science Publishing Co., Inc., 1991 655 Avenue of the Americas, New York, NY 10010

207 0025-5564/91/$03.50

208 1.

P.E. RAPP ET AL. INTRODUCTION

A series of six questions has motivated this investigation. (1) Are there quantitatively discernible patterns in patient-therapist communication during psychotherapy sessions? (2) Assuming that they exist, do the patterns observed in early consultations correlate with the initial diagnosis? (3) What subject matter is important in characterizing patient-therapist communication? (4) What do patterns in the manifest content of patient-therapist dialogue suggest about unconscious processing of emotionally sensitive material? (5) Do patterns of communication change during the course of psychotherapy? (6) Assuming that changes in communication do occur during the course of therapy, do these changes correlate with the clinically perceived success or failure of the therapy? 2.

CONTENT ANALYSIS

Methods developed here are extensions of previous research using transcripts of patient-therapist dialogue (protocol analysis). An abstract and largely qualitative account of protocol analysis has been given by Ericsson and Simon [1]. Matarazzo, Wiens, and their colleagues have quantitatively examined behavior during interviews to attempt to discover which of two or more topics is of greater concern (saliency) to an interviewee [2, 3]. Measuring speech variables (mean duration of utterance, mean reaction time, mean percentage of interruptions) and frequency and duration of eye contact [4-6], they found that interviewees talk with longer mean duration of utterance when talking about a high saliency topic. As a specific application of these procedures, experiments were performed to study the use of nonverbal behaviors in identifying interviewee deception [7]. Their results were promising, but previous research indicated that the interviewer must exercise care during the course of the interview because these variables can be influenced by interviewer behavior [8]. Therefore the value of this procedure in establishing interviewee veracity is uncertain. Matarazzo and Wiens measured verbal behaviors, such as duration of utterance, that do not indicate directly anything about the content of the protocol. A similar approach was followed by Winefield and her colleagues [9], who counted the number of words exchanged by the patient and the therapist. In this study, she found that as the therapy progressed the therapist talked more frequently and for longer periods of time. Word count alone provided limited insights into the therapeutic process, however.

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By examining the content of the transcripts, Winefield also found that the asymmetry in status as assessed by Stiles verbal response mode analysis [10] decreased. Winefield suggests that this implies that patient and therapist communication became increasingly similar as the therapy progressed. The limitations in the study of word counts unaccompanied by content analysis can be generalized to other studies of non-content behavior in psychotherapy. (Non-content behavior refers to nonverbal behavior such as posture and eye contact and to verbal behaviors such as latency and duration of utterance that do not depend on what was said.) While measures such as word count, latency, and gaze behavior offer a useful partial characterization of the process, any detailed examination of psychotherapy must address the content, as well as the structure, of the interaction. For this reason, content analysis, which has had a long history of application to communication research [11] and the humanities [12], has been applied to psychotherapy research. As summarized by Lolas et al. [13], content analysis in behavioral research is a three-step process. First, the content characteristics to be measured must be specified. Second, rules for identifying these characteristics must be established. Third, correlations between the content of the protocol and the subject's behavior must be examined. The simplest form of content analysis is to determine the frequency of specified single words in the transcript. This form of analysis has the advantage of being automated. The principal disadvantage is the restriction to specific and isolated words. Equivalent concepts, expressed with a different vocabulary, will be undetected; further, context and contextual meaning cannot be identified. An example of word frequency is EVA (electronic verbal analysis) [13, 14]. A specific application of this system is its application to an anxiety topics dictionary. It was found that the frequency in the protocol of anxiety-related words correlated with the shame and separation anxiety scores obtained with a more sophisticated content analysis technique, the Gottschalk-Gleser content analysis scales [13]. The Gottschalk-Gleser content analysis procedure is one of the most sophisticated tools of its kind in use in psychiatric research [15]. Rather than a single word, the grammatical clause is the unit of analysis. In its standardized form the procedure analyzes a 5-min monologue. The content is scored on a series of scales including anxiety, hostility, depression, social alienation, cognitive and intellectual impairment, human relations, and hope. Anxiety is scored on six subcategories (death anxiety, mutilation anxiety, separation anxiety, guilt anxiety, shame, and diffuse nonspecific anxiety), and hostility is scored on four subcategories (outwardly directed-overt, outwardly directed-covert, self-directed, and ambivalent hostility). The psychiatric applications of Gottschalk-Gleser content analy-

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sis include prediction of outcome of patients at a mental health crisis clinic [16], prediction of patient compliance with therapy recommendations [17], and assessments of cognitive impairment [18]. The procedure has also been found to be successful in evaluation of psychological aspects of medical illness [19]. Examples include studies of the psychological dimension of mastectomy [20] and diabetes [21]. The hope scale of the analysis spectrum has been used in predicting the longevity of cancer patients receiving radiation therapy [22]. Applications of content analysis have not been limited to medical questions. Tolz [23] and Stiles et al. [24] have used these procedures to analyze political speeches. M c G a u g h e y and Stiles [25] have used it to analyze courtroom testimony. Finally, we should note the intricate efforts by Dahl and his associates [26-29] to investigate linguistic variables and their correlates in psychoanalytic sessions. Using a variety of complex quantitative measures, this group has shown a number of patterns and correlations between linguistic measures in working versus resistant sessions, among other areas of interest. This pioneering work suggests the value of quantification and sequential analyses, though the measures used and their implications differ greatly from those to be presented here. Decades of research with content analysis techniques have established their reliability and utility in a wide variety of applications. The methods presented in this p a p e r can be regarded as an evolute of content analysis. A limitation of conventional content analysis is that the temporal sequence of material is lost. Given the sequence-dependent structure of language and the interactional nature of psychotherapy, this is important information. O u r object is to construct a procedure that retains content information but also provides efficient and sensitive mechanisms for characterizing dynamic patterns in communication. F o r want of a better term, we would describe this as dynamic content analysis.

3.

THE DATA MATRIX

In this study, psychotherapy sessions were videotaped and then transcribed. The content of the protocols was scored line by line, in approximately 5 s intervals. [In some studies (see next section), content was scored in two-line units except when there was a change of speaker after the first line of a two-line unit.] F o r each line, scores were recorded in response to a series of questions. For example, the question " W h o was speaking?" would elicit a score of 1 if the patient was speaking and a score of 2 if the therapist was speaking. " W h a t was the time frame of the statement?" would elicit a score of 1 if the statement referred to the present therapy session, and other scores for different temporal references (2 = recent past, 3 = nonchildhood past, 4 = childhood, 5 = future, and 6 = indefinite time

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frame). Most of the questions were objective. Some of the questions required subjective scoring on a four- or seven-point scale. Issues of scoring reliability have been addressed elsewhere [30, 31]. Reliability for items investigated is quite good. Although the selection of scoring items cannot be discussed in detail here, it can be noted that the items were selected as surface indications of pschodynamics and systems dynamics, including the means by which we process emotionally charged information. The initial scoring items are derived from a theory of conscious and unconscious communication developed by Langs [32]. The dynamic and interactional nature of this theory, as well as its definition of unconscious expression, has been a major factor in the evolution of the mathematical models to be presented here. In the study described in this paper, 14 items were scored in two-line units. A n outline of the scoring criteria is given in A p p e n d i x 1. In a more detailed investigation, 60 items were scored. Items a p p r o p r i a t e to psychotherapy are considered here. However, the items scored can be changed according to specific objectives of the study. Studies of political speeches, for example, and court transcripts would require a modified spectrum of scored items.

Column N u m b e r 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 1 2 2 2 1 4 2 1 6 2 1 8 1 2 9 2 1 11 2 1 12 1 3 14 1 3 16 2 1 17 1 2 1 9 1 3 21 1 5 2 2 2 6 23 1 6

2 0 0 0 0 3 3 0 0 0 1 2 3 0 0 3 0 2 1 0 0 3 0 1 1 0 0 3 0 1 3 0 0 2 1 1 1 0 0 3 0 1 1 0 0 2 0 3 1 0 0 3 0 3 0 0 0 3 1 1 1 0 0 3 0 2 1 5 1 0 0 0 4 1 0 0 2 0 2 0 0 0 0 1 1 1 1 4 0 0 0 4

2 0 2 0 2 1

02 01 01 0 3

2

1 1 1 2 1 0 4 1 0 0 1 3 0 -2 2 3 2 -2 2 0 0 0 4 3 1 -2 2 4 1 - - 2 2 - - 3 1 1 --1 3 0 0 04 4 0 -2 2 1

0

-

0 1 0 0 0 0 0 0 0 0 0 0 0 0

FIG. 1. First 15 rows of the data matrix of Case A. The scoring scheme follows the procedure outlined in Appendix 1. The protocol was scored in two line units except in those instances where a change of speaker occurred between the first and second line of a two-line unit.

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Each protocol contains between 700 and 1000 lines. The sequence of numbers generated by each line becomes a row in a matrix. Each column therefore corresponds to a different scored item. For example, in Case A of the next section, 14 items were scored in two-line units, resulting in a 384 x 14 matrix (see Figure 1). The problem now becomes how to search for dynamic structure in these matrices. 4.

C O M P L E X I T Y M E A S U R E S OF C O M M U N I C A T I O N

4.1. QUANTITATIVE CHARACTERIZATION OF COMPLEXITY Each column of the data matrix corresponds to a different scored item. For example, column 2 records scores indicating who is speaking. The dynamic pattern of who is speaking, patient or therapist, is specified by the sequence of l's and 2's in this column. Similarly, column 3 gives the history of temporal references in the dialogue. Thus, each column constitutes a sequential message describing a specific verbal behavior. Subsequent sections of this paper will describe the analysis of data contained in more than one column. We consider now how to characterize message sequences contained in a single column. For specificity, we will describe the analysis of column 2 (Who is speaking?). With the exception of column 1, which records line numbers, these ideas generalize to other columns. As shown in Figure 1, the column 2 message from Case A is 1 , 2 , 2 , 2 , 1, 2 , 2 , 1, 1, 2, 1, 1 . . . . . Conventional statistical analysis is possible. For example, it is possible to determine what fraction of the time either party is speaking and the average length of a statement from the therapist or patient. However, we want to quantitatively capture not the overall statistical properties of the message but rather the dynamical structure of the exchange. One possibility is to compute the information content of the message. Consider a message composed of an alphabet of several letters where the probability of the ith letter appearing in the message is Pi. (We emphasize that our "alphabet" has letters that are interaction scores.) The Shannon information in the message [33, 34] can be calculated by the formula S = - E pi log 2 pi

where the sum is taken over all symbols of the alphabet. Information is an important standard measure of the content of a message. However, it is an incomplete characterization. Consider the following message composed from a two-symbol alphabet: M1=0000000011111111.

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Probabilities P0 and Pl are both 1/2, and therefore S = + 1. Consider a second message, M2=0101101011001001. Again P0 = Pl = 1 / 2 and S = + 1. These two messages have a very different qualitative appearance, but S is the same for both. Visual examination of the second message suggests that it is somehow more complex than the first. Recognition of the distinction between information and complexity has motivated a search for a means of quantitatively characterizing complexity. Several alternative approaches to the study of complexity have been developed. The longest history is presented by measures derived from algorithmic information theory [35-37]. Within this theoretical structure, the complexity of a message is the amount of information required to specify the message. This is often expressed in terms of the minimal size of the program that can generate the message. A message is algorithmically complex if it is incompressible; that is, if the minimal description is about the same size as the message [38]. If these definitions are used, random sequences are found to be very complex. Huberman and Hogg [39] have argued that a more meaningful definition of complexity describes a property intermediate between totally ordered systems such as a crystal and completely disordered systems such as a gas. A pertinent example that they cite is language. R a n d o m strings of letters generated by typing monkeys are algorithmically more complex than natural language, which has an internal structure and a degree of redundancy. (The computational complexity of natural language is reviewed by Barton et al. [40].) Application of H u b e r m a n - H o g g complexity is an important future direction for the analysis of psychiatric protocols. It will be instructive to compare this measure to other quantifications of complexity. In this paper we restrict attention to applications of the context-free grammar complexity [41, 42], which is a specific implementation of algorithmic complexity theory. When computing the grammar complexity of a symbol sequence, the object is to find the minimum length of the instruction set that can generate the message. The procedure constructed by Jim6nez-Montano [41] finds an upper bound on the complexity. It is an upper bound rather than the exact value because one doesn't know if the length returned by this algorithm is the smallest possible instruction set. However, the procedure is systematic and therefore provides a basis for comparisons between messages. The method is best explained by treating a specific example. We first consider the previously defined sequence M 2. The sequence is scanned for repeated symbol pairs. A new symbol is defined and is used to replace the original repeated pair. In M 2 the pair (0,1) is repeated six times. This pair

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is replaced by the symbol a. The original message becomes M2=0101101011001001

M2=aalaalOaOa a=01. The search for repated pairs in the revised message continues. The pair (a, a) appears twice. However, it can be shown that no compression of the instruction set is achieved if there are only two copies of the pair in the message. Therefore the search for repeated pairs ends, and the search for repeated triples begins. The triple ( a , a , 1 ) appears twice. Replacing a repeated n-tuple with a new symbol does result in compression of the message sequence even if the n-tuple appears only twice, provided that n > 3. Therefore (a, a, 1) is replaced by a new symbol.

M2=bbOaOa a=01, b=aal. In the general case, the search for larger repeated n-tuples (n = 4 , 5 , . . . ) continues until repeated fragments have been exhausted. In the present example there are no remaining repeating fragments, so the redefinition process terminates here. The message sequence and instruction set are then reexpressed in exponential form.

M2=b2OaO a a=01,

b=a21.

An upper bound on the complexity of the original message is then estimated. Two components contribute to the complexity: the number of symbols in the instruction set and their exponents. The sequence M 2 now contains five symbols (an exponent is not counted as a symbol), and the definitions of a and b both contain two symbols. Therefore, the total number of symbols in the compressed message and the instruction set is the sum 5 + 2 + 2. Under the definitions used here, repeated symbols contribute logarithmically to the estimate of complexity. There are two exponents, both 2, the exponent of b in M 2 and the exponent of a in the definition of b. The logarithmic contribution is added to the number of symbols to produce an estimate of the upper bound of the complexity. Grammar complexity of M 2 ~<5 + 2 + 2 + 2 [log 22 ] = 11. The square brackets indicate that the integer part of the logarithm is taken. Unnormalized complexity values are always integers. The discussion of complexity began with the observation that a seemingly disordered sequence like M 2 is more complex than the very ordered

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sequence M l (which has a complexity estimate of 10). Given the marked difference in the appearance of M 1 and M 2, complexity estimates of 10 and 11, respectively, do not seem remarkably different. The similarity in these two values occurs, however, because M~ and M2 are comparatively short sequences. The differences in complexity of ordered and disordered sequences becomes more pronounced as longer sequences are examined. Consider the following sequences. M a = six O's followed by six l ' s Mb=011010110010 Me = twelve O's followed by twelve l ' s Md=011100101101010001001011 M e = twenty O's followed by twenty l ' s Mr=0111001011010100010010110101101011001001. Let C ( M ) denote the grammar complexity estimate of each sequence. T h e n C ( M , ) = 9, C ( M a ) = 16,

C ( M b ) = 10,

C ( M c ) = 13

C ( M e ) = 14,

C ( M f ) = 21.

As longer sequences are considered, the disparity between ordered and disordered sequences becomes more pronounced. This can be seen more clearly by calculating the ratios

C( M~) C( Ma)

C( M,,) 1.11,

C( Mc)

C(M~) = 1.23,

and

C( me )

1.50.

4.2. RESULTS FROM TWO PROTOCOLS Two 50-min protocols have been examined. In each protocol the patient was the same. The recorded interviews were not sessions in an ongoing therapy but were 1-h consultations. In case A the therapist was a classically trained psychoanalyst using a communicative approach developed by Langs [32], and in case B the therapist was also a classically trained psychoanalyst. The two consultations were separated by 6 months. Consultation B was first. The protocols were scored in two-line units. In consultation A the resulting matrix has 384 rows. In consultation B the matrix has 401 rows. Complexity scores for each column are reported in Table 1. In order to prevent differences in the length of the protocol from magnifying differences in complexity estimates, the original complexity

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P. E. RAPP ET AL. TABLE 1 Normalized Grammar ComplexityEstimates for Two Protocols Column

Case A

Case B

1

1.00

2 3 4 5 6 7 8 9 10 11 12 13 14

0.30 0.58 0.42 0.40 0.25 0.50 0.27 0.55 0.62 0.44 0.48 0.40 0.29

1.00 0.23 0.53 0.36 0.53 0.30 0.24 0.32 0.50 0.50 0.42 0.47 0.17 0.44

Absolute Difference 0.00 0.07 0.05 0.06 0.13 0.05 0.26 0.05 0.05 0.12 0.02 0.01

0.23 0.15

measure is divided by the n u m b e r of rows in the matrix. Column 1 contains the line number. Line numbers never repeat, so each symbol in column 1 is unique. Therefore there are no repeating n-tuples in column 1, and no message compression can occur. If a message contains N nonrepeating symbols, its grammar complexity is N. If the complexity of column 1 of consultation A were to be computed, a value of 384, the n u m b e r of rows in the matrix would result. Because complexity values are normalized against the n u m b e r of rows in the matrix, a value 1 always appears for the normalized grammar complexity estimate of column 1. Given the very limited database investigated, it is impossible to draw any meaningful conclusions from these results. One can only examine Table 1 for curiosities that may or may not be upheld by systematic research. Perhaps the most remarkable observation to be obtained from Table 1 is that many of the complexity estimates for consultations A and B are similar. Marked differences in grammar complexity are observed only for continuity, C7, and the sphere to which material pertains ( t h e r a p y - n o n therapy), C13. In both instances, the protocol of consultation A presents a richer dynamical behavior. It should be stressed that complexity scores do not measure the values present in a given column but rather the complexity of the pattern of the content. The previous illustrative examples have demonstrated that it is possible to have message sequences with the same total content but different complexity estimates. However, as Table 2 indicates, consultations A and B differ in content and intensity as well as in dynamic structure.

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PATIENT-THERAPIST COMMUNICATION TABLE 2 Content Frequency for Columns 7 and 13a Column

Score

Case A

Case B

C7

- 3 - 2 - 1 0 1 2 3 4 1 2 3 4

0.000 0.034 0.026 0.229 0.063 0.115 0.531 0.002 0.216 0.596 0.094 0.094

0.000 0.005 0.002 0.047 0.020 0.020 0.905 0.000 0.005 0.943 0.032 0.020

Cl3

aSee Appendix 1 for definitions of the scores.

Consultation A displays less continuity, C 7. The frequency of moderate breaks in the flow of material and communicative exchanges in consultation A is seven times that of consultation B. Slight shifts occur 13 times as frequently, and transitional dialogue, in which there is continuity at the beginning of the line that is followed by a transition to new material, is almost five times as frequent. The result is an absence in consultation A of the dominance of directed continuity that characterizes over 90% of the material in consultation B. Column 13 specifies the sphere to which the material in the line pertains. Specific reference is made in the scoring criteria to whether or not material refers to therapy (scoring criteria are summarized in Appendix 1). For consultation B, over 90% of the material refers to situations outside of therapy, and less than 1% of the material (two lines in the protocol) is exclusively directed to therapy-related issues. This is in marked contrast to consultation A, in which 20% of the content focuses on a discussion of the therapeutic situation. Alone, complexity estimates and content frequency provide an initial but very incomplete description of the p a t i e n t - t h e r a p i s t interaction. They provide complementary information. Other techniques that can also contribute to this analysis are outlined in the next section. 5.

O T H E R ANALYSIS P R O C E D U R E S

5.1. ANALYSIS OF CORRESPONDENCE (DYNAMIC FACTOR ANALYSIS) A very large n u m b e r of additional analytic procedures can be applied to the examination of protocol matrices. Three methods that appear to be

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most promising--correspondence analysis, sequence detection, and symbolic dynamics--merit explicit mention. The analysis of large data matrices such as those generated in these studies lies within the domain of multivariate statistical analysis. Techniques having interrelated mathematical structures have been variously termed canonical analysis, multidimensional scaling, principal component analysis, factor analysis, discriminant analysis, and cluster analysis. A procedure that seems immediately applicable to these data is correspondence analysis. Using nomenclature defined by Lebart et al. [43], principal component analysis and correspondence analysis are two different forms of principal axes analysis. Principal component analysis should be used when the data are continuous, as with EEG signals, and correspondence analysis should be used for discrete data such as those generated from scoring protocols. Both methods are based on the singular value decomposition and are therefore mathematically equivalent to the Karhunen-Loeve expansion [44] and its generalizations [45, 46]. In principal axes analysis the original data matrix is subjected to an orthogonal transformation to a new coordinate system (the principal components or factors) that concentrate variance in the lowest components. After the transformation the first component contains more of the variance than the second, the second component provides the next greatest contribution to the variance, and so on. The eigenvalues of the transformation give an approximate measure of the amount of information contained in each component. The next step in the analysis is to introduce dynamics into static principal component analysis. There are at least two approaches. The first is to break the original matrix into submatrices. For example, the matrix could be divided into 100 row subunits. Correspondence analysis of each submatrix would make it possible to follow the movement of variance through the spectrum of scored items during the course of the protocol. A second approach utilizes the ability of principal component analysis to identify combinations of variables that contain the greatest amount of variance (the elements of the first principal axis). It is possible to use this identification to define a new variable composed of these elements. A dynamical characterization of the new variable using the methods employed with individual column variables of the original matrix can then be performed. 5.2. STATEMENT CLASSIFICATION Each row in the protocol contains values corresponding to the contents of one or two lines in the original transcript. Therefore one can classify a line according to its column values. For example, one could define mes-

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sages A to Z according to the following system of rules:

Message A Value = + 1 in column 2 Value = + 6 in column 5 Value = - 3 in column 7 O t h e r columns can take any value.

Message B Value = + 2 in column 2 Value = + 2 in column 5 O t h e r columns can take any value.

Message R Value = + 1 in column 2 Value = + 4 in column 3 Value = - 1 in column 8 O t h e r columns can take any value.

Message Z.

Any row not previously defined is a Z-type message.

T h e procedure must be well defined; that is, it cannot be possible for a single row to satisfy two or more definitions. T h e transcript is now reduced to a symbol sequence:

C~A~W~R~S~F~G~A--*E~J~D~. T h e classification outlined in the example was chosen arbitrarily to provide an illustration of the definition process. A meaningful classification is not arbitrary. It provides a means of systematically introducing clinical insights into the analysis of the therapeutic process. For example, a classification scheme might be constructed that would illuminate a connection between discontinuities in content and references by the therapist to a particular family member; or a classification might define message cate-

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gories according to criteria relating to the patient-therapist relationship. This type of classification structure utilizes the qualitative intuitions of the therapist, but it does so in a quantitatively explicit way that makes it possible to test the validity of these insights in the interpretation of other protocols. One can apply analysis procedures (calculation of complexity and the methods outlined in the following sections) to three types of sequences: (1) columns of the original protocol matrix, (2) sequences generated by the new variables constructed from combinations of variables identified by analysis of correspondence, and (3) symbol sequences generated by different row classification schemes. 5.3. SEQUENCE DETECTION The data in these studies are sequences of symbols. Are there repeated sequences in these patterns? This question has been treated in an indirect way in complexity calculations that search for exactly repeated n-tuples in the data. It is also possible to search for repeated sequences and their near variants (variants where the specified sequence is repeated except for some defined number of departures). Several pattern detection algorithms have been developed to search for consensus patterns in genetic control regions and to search for sequence homologies in proteins (an annotated bibliography has been given by Jungck and Friedman [47]). Methods have been based on dynamic programming [48], the analysis of finite automata [49], artificial intelligence techniques [50], and probability density functions [51]. 5.4.

SYMBOLIC DYNAMICS

We have argued that an imperfect representation of patient-therapist communication can be expressed as a sequence of symbols. This invites application of a family of related mathematical techniques called symbolic dynamics [52]. This kind of system is defined on a space of symbols Sn. It is possible to define a distance measure between sequences and to show that this measure is a metric on S n. The dynamical behavior is expressed by a shift operator ~ that advances the system in time. or(s 0

S1

S2

"'')

=(S 1

S2

S3

"'').

Crutchfield and Packard [53] have used symbolic dynamics in the analysis of continuous dynamical systems. In their analysis they begin with a dynamical system consisting of a set of states M and a map f : M --, M. A symbolic representation of the system is obtained by using a measurement partition that divides the behavior space into a finite number of states that are each associated with a symbol. They have shown that topological and metric entropies can be computed numerically using the symbol sequence

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representation of the original system. Paulus et al. [54] have applied these procedures to the analysis of rat locomotor activity patterns and have shown that behavioral changes induced by amphetamine and MDMA can be differentially characterized by entropies of corresponding symbol sequences. We do not know if these computations are feasible with the symbol sequences specified by protocol matrices. These sequences may not be long enough and the behavior of the system may be too disordered to produce convergence to a reliable entropy estimate. However, if they are feasible, an important quantitative connection between the study of human communication and dynamic analysis would be established. 6.

CONCLUSIONS

Rather than present definitive conclusions, the research outlined in this paper defines opportunities and directions for future investigation. We have shown that, building on content analysis and on a dynamic theory derived from classical psychoanalysis, it is possible to construct a quantitative representation of a patient-therapist dialogue as a matrix of symbols. It is then possible to apply a variety of mathematical techniques to extract understanding from these data. Applications of complexity measures show some promise. Other possibilities were outlined in Section 5. We anticipate that as the database of scored protocols grows and the variety and sophistication of mathematical measures increases, we will be able to begin to answer the six questions listed in Section 1 that motivated this investigation.

We would like to acknowledge the continuing support of the College Computer Center of the Medical College of Pennsylvania. P.E.R. wishes to express thanks for a Visiting Research Fellowship m the Department of Mathematics and the hospitality of Kingswood College at the University of Western Australia. M.A.J. is grateful for a Visiting Professorship at the Centro de Incestigacion Sobre Fijacion de Nitrogeno and the Centro de lnvestigacion Sobre Ingeniera Genetica Y Biotechnologia, U.N.A.M., Cuernavaca, Mexico. The advice and suggestions of T. R. Bashore and I. D. Zimmerman are gratefully acknowledged. Preliminary results from this study were presented at the annual meeting of the Society for Psychoanalytic Psychotherapy (Chicago, 1987) and at the Conference on Mathematical Models for Psychoanalysis and Psychotherapy (New York, 1988). APPENDIX 1.

STRUCTURE OF THE DATA MATRIX

The following summarizes the scoring procedure used in this study. The detailed criteria for scoring a protocol are presented in Langs et al, [31].

Column 1.

Line number

222

Column 2.

P. E. RAPP ET AL. Speaker 1 = p a t i e n t is t h e s p e a k e r 2 = t h e r a p i s t is t h e s p e a k e r

Column 3.

Time flame 1 = in s e s s i o n 2 = recent past 3 = nonchildhood past 4 = childhood 5 = future 6 = indefinite time frame

Column 4.

Individual referenced 0 = neither patient or therapist r e f e r e n c e d 1 = patient 2 = present therapist 3 = patient and therapist

Column 5.

Individual referenced 0 = n o n e o f t h e following individuals are r e f e r e n c e d 1 = other patients 2 = other psychotherapists 3 = n o n f a m i l y a u t h o r i t y figures ( d o c t o r , t e a c h e r , employer) 4 = female 5 = male 6 = p a t i e n t ' s or therapist's m o t h e r 7 = p a t i e n t ' s or therapist's father 8 = both mother and father 9 -- g r a n d p a r e n t s 10 = o t h e r relatives 11 = c h i l d r e n 12 = a n i m a l 13 = fictional c h a r a c t e r 14 -- r e f e r e n c e n o t c l e a r

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15 = family ( g e n e r a l a l l u s i o n s ) 16 = siblings 17 = f r i e n d s 18 = m e t a p h o r i c a l ' w e ' 19 = m e t a p h o r i c a l ' y o u ' 20 = lovers 21 = m e t a p h o r i c a l T 22 = s p o u s e s 23 = m e t a p h o r i c a l ' t h e y '

Column 6.

Individual referenced If a s e c o n d i n d i v i d u a l is r e f e r e n c e d , e n t e r t h e s c o r e s p e c i f i e d by t h e r u l e g o v e r n i n g c o l u m n 5. I f t h r e e o r m o r e i n d i v i d u a l s are r e f e r e n c e d , scores a r e e n t e r e d for t h e two m o s t p e r t i n e n t a n d p o w e r f u l individuals.

Column 7.

Continuity - 3 = strong break with previous material - 2 = m o d e r a t e shift -

1 = slight shift 0 = transitional 1 = material related but shifting 2 = substantial continuity 3 = clear continuity 4 = unclear

Column 8.

Agreement/disagreement - 1 = direct and overt disagreement 0 = ambiguous 1 = direct and overt agreement

Column 9.

New theme 1 = theme adds some new information 2 = m o d e r a t e a d d i t i o n of i n f o r m a t i o n 3 = s i g n i f i c a n t a d d i t i o n of i n f o r m a t i o n 4 = dramatic presentation of significant material

224 Column 10.

P. E. RAPP ET AL. Narrative image 0 = yes or n o r e s p o n s e 1 = minimal content 2 = intellectualizations 3 = fragmented images 4 = intermediate image 5 = vivid i m a g e

Column 11.

Positive t o n e 0 = tone not positive 1 = mildly p o s i t i v e 2 = moderately positive 3 = s t r o n g l y positive

Column 12.

Negative tone 0 = tone not negative - 1 = mildly n e g a t i v e -2 = moderately negative -

Column 13.

3 = strongly negative

S p h e r e to w h i c h m a t e r i a l p e r t a i n s 1 = therapy-related 2 -- s i t u a t i o n s o u t s i d e o f t h e r a p y 3 = r e f e r e n c e to b o t h t h e r a p y a n d s i t u a t i o n s o u t s i d e of therapy 4 = unclear

Column 14.

Gender/identity-related

themes

0 -- n o n e o f t h e following scores a r e a p p l i c a b l e 1 = this score is n o t u s e d 2 = this s c o r e is n o t u s e d 3 = r e f e r e n c e s to b i r t h 4 = sexual t h e m e s 5 = g e n d e r - r e l a t e d family a l l u s i o n s 6 = all o t h e r a l l u s i o n s to f a m i l y m e m b e r s

PATIENT-THERAPIST COMMUNICATION

225

7 = nonfamily social/gender interactions 8 = t h e m e s of caring 9 = g e n e r a l n o n s e x u a l b o d y allusions 10 = sexual i d e n t i t y allusions 11 = g e n e r a l , n o n s e x u a l , i d e n t i t y t h e m e s

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