The mathematical case against unipolar mania

J.psychiar. Res. Vol. 16, No.4, Printed in Great Britain.

pp.

259-265,

1981

THE MATHEMATICAL

0022.3956/81/@40259-07 $02.00/O 0 1982 Pergamon Press Ltd.

CASE AGAINST

UNIPOLAR

MANIA

B. PFOHL, * N. VASQUEZ and H . NASRALLAH University of Iowa College of Medicine, Department of Psychiatry, Iowa City, IA 52240, U.S.A. (Received 16 March 1981; revised 16 December 1981)

THE AMERICAN Psychiatric

Association’s official Diagnostic and Statistical Manual (3rd edn.) makes a distinction between patients who have had only depressions and those who have had manias with or without depression. The former is called Major Depression and the latter is called Bipolar Disorder. There is no separate classification for patients who have had one or more manias without any history of depressive episodes. It is this group, which has been referred to by some as “unipolar mania” which is the focus of the present study. The question of whether unipolar mania should be considered a distinct diagnostic entity would be easily answered if we possessed a clear understanding of the etiology of affective disorder. Barring this the next best approach is to investigate whether the knowledge that a manic patient has never had a depression tells us anything useful. Does it alter the prognosis, response to a given treatment, or pattern of familial distribution? Are there certain antecedent events in unipolar manics that are not present in bipolar manics? Three studies use this approach to investigate unipolar mania. The first is by ABRAMS and TAYLOR.’ After reviewing 50 manic probands of whom 14 had never had a depression they concluded that there was no real difference between the groups on a variety of clinical and historical variables. NURNBERGER et al2 identified 38 patients among 241 lithium clinic patients who had never had an episode of depression. They found no significant differences except that the patients without a history of depression did not attempt suicide or exhibit rapid cycling as frequently as those with a history of depression. They conclude that there is no data to support unipolar mania as a separate entity. ABRAMS et aL3 report a more sophisticated replication of their earlier study. They changed their methodology to require a minimum of two manic episodes with no history of depression for a diagnosis of unipolar depression. They found 29 unipolar manics similar to 48 bipolars on a wide variety of clinical variables. They recommend, however, that the case for unipolar mania not be dismissed at the present time since they found an excess of males among the unipolar manics as well as an increased morbid risk of unipolar depression in their relatives. Their data could also be interpreted to suggest a deficit of females among their bipolars. *Correspondence and reprint requests. 259

B. PFOHL, N. VASQUEZand H. NASRALLAH

260

A MATHEMATICAL

MODEL

Patients with a history of mania, and no depressions, obviously exist. Are they more prevalent than would be expected based on the observed distribution of manic and depressive episodes in bipolar patients? An answer to this question can be formulated by making two assumptions. The first assumption is that, among bipolar patients, manias and depressions occur with about equal frequency independent of whether the previous episode was manic or depressive. This can be fairly well supported by a number of studies. In a recent evaluation of the literature, CORYELL and WINOKUR~ review estimates’-’ of the frequency of mania as the first episode. These estimates range from 45 to 79%. Most studies list intermediate results. The second major assumption required for the mathematical model is that after any episode of mania or depression the probability of having another episode in the future is about 50%. CORYELL and WINOKUR~ review 12 studies which look at the number of single episode courses among unipolar depressed patients and bipolars. The findings cluster around 50-65% with a trend towards more multi-episode courses in more recent studies. KRAEPELIN’”

followed

459 patients

for

up to 29 years.

He

found

that 55%

of patients

went on to have a

second episode of affective illness and 30% had more than two attacks. This is consistent with the assumption that about 50% of patients go on to have a second episode and, of these, about 50% go on to have a third episode. LUNDQUIST” found that the second episode of mania is not more likely to be followed by another episode than is the first. WINOKUR” found that a history of three episodes might in fact predispose more strongly to future episodes but this would not affect the model greatly since 75% of patients have less than three episodes. The model presented here describes the consequences of the above two assumptions plus the null hypothesis that there is only one type of affective disorder-bipolar affective disorder. The use of this model to describe a theoretical distribution of diagnoses is outlined in Table 1. TABLE 1. THEORETICALNUMBEROFUIAGNOSESASSEEN

Admiwon number (n) Number of admisslons Number of diagnosis of: unipolar mania unipolar depression bipolar depression

FKOMHOSFTTALDOOR

1 1000

2 500

3 250

4 125

5 63

2000

500 500 0

125 125 250

31 31 188

8 8 109

2 2 59

661 667 667

The data in Tabie 1 assumes that patients are admitted from a population that is not experiencing any major distortions in age distribution. It further assumes that only episodes serious enough to result in admission are being counted. The assumption of a 0.5 relapse/ readmission rate has the following consequence. If a consecutive series of 1000 firstepisode admissions are collected over a period of time, then about 500 second-episode admissions would be observed over the same period of time. If the consecutive series is collected over a relatively short period of time, most of the second-episode admissions would occur in patients whose first episode occurred before the study began. In a similar fashion the number of third-, fourth- and fifth-episode admissions can be predicted. This

THE MATHEMATICAL CASE AGAINSTUNIPOLARMANIA

261

infinite series sums to 2000 admissions for affective disorder and is displayed in row 2 of Table 1. If the probability of a given episode being manic is 0.5 then we would predict that half of the 1000 single-episode admissions will be unipolar manic, The probability of having two manic episodes in a row is 0.25 so 125 of the 500 second-episode admissions will be unipolar manic. This is seen in the third row of Table 1. The number of unipolar depression cases follow the same series since the probability of an episode being depression is also 0.5. The number of admissions with a diagnosis of bipolar disorder is calculated by subtracting out admissions for unipolar depression and unipolar mania. The model allows no patient with only one episode to be diagnosed bipolar since the definition of bipolar disorder used here requires one episode of mania and one episode of depression. Each of the last three rows of Table 1 represents an infinite series which sums to the same number-667. Thus, the model, as developed so far, predicts that a consecutive series of affective disorder would find patients with unipolar mania, unipolar depression and bipolar disorder equally represented. The percent of unipolar mania admissions among all cases where there is a history of at least one manic episode is 50%. If single episode manics are not included then this proportion must be recalculated after subtracting the 500 single episode cases from the numerator and denominator. After this adjustment, we would predict that studies which exclude single episode cases will find that 20% of all admissions with a history of mania will be unipolar manic. While the consequences of the assumptions can be readily appreciated from Table 1 it is possible to develop the model with more mathematical rigor using simple algebra. This will allow the substitution of various estimates of the probability of a future episode and the probability of a given episode being manic. If the probability of a future episode is represented by r than the proportion of admissions with n episodes is: (1-f)r”-‘. If the probability of a given episode being manic is represented by p then the probability of a patient with n episodes being diagnosed as unipolar manic is: P”.

The proportion of all affective disorder admissions that will be diagnosed mania is obtained by multiplying the above two expressions and summing series: Z’(LJM) = n; 1(1-Q-’ p” = pG .

as unipolar the infinite

In a similar fashion the proportion of affective disorder admissions diagnosed as unipolar depression [P(UD)J can also be developed. The proportion of admissions with bipolar disorder [&BP)] can be calculated by simply subtracting these two proportions from one. Most studies report the proportion of unipolar manics as a proportion of all patients who have had at least one mania. By substituting and simplifying the resulting expression, this proportion is calculated as follows. = (1-r) (l-r+rp) P(UM) I-rp . P(UM) + P(BP) When both r and p are set to 0.5, the above expression predicts a proportion agrees with our tabular calculations above.

of 50% which

B. PFOHL,N. VASQUEZand H. NASRALLAH

262

All that remains is to develop a formula for predicting the proportion of unipolar manics in studies that use a definition of unipolar mania that excludes single episode cases. If only admissions with at least two episodes are considered, the following expression is the proportion of admissions with n episodes: Using this expression

(1-r)F. in the same development described P(UM) P(UM) P(UM) f P(BP)

above we get the following:

= q;$, (1-r+rp)

p(l-r)

= (1 -rp) (2-r-p

By substituting in 0.5 for bothp and r, the above expression as did the calculations from Table 1. TESTING

+ rpj ’ predicts

a proportion

of 20%

THE MODEL

It is immediately clear that the frequency of the diagnosis of unipolar depression does not fit the model. In other words the frequency of unipolar depression as compared to bipolar disorder cannot be explained by assuming that all unipolar depressives are really bipolars who, by chance, have not had a mania yet. DSM III reports that all studies to date show 1823 % of females and 8-l 1% of males have a depression at some time during their life. The same source indicates 0.4-1.2% of the population experience bipolar disorder. This does not even come close to the model. Unipolar depression as a distinct diagnostic entity is clearly supported. Turning now to the data on unipolar mania, the null hypothesis is not so quickly rejected. Table 2 shows the expected and observed proportions of unipolar manics and bipolar patients. The first three studies in Table 2 were described earlier. The study by PFOHL et al. is a chart review of admissions from 1970 to 1979. Unipolar manics with just one episode are included among the 77 patients noted. This study will be reported in detail in a future publication. TABLE2. EXPECTEDAND OBSERVED PROPORTIONS

OF UNIPOLAR

Inclusion of single

Exclusion of single episode cases episode cases (070expected)

Unipolar mania Bipolar mania

(50) (50)

(20) (80)

AND BIPOLAR PATIENTS

MANIC

Abrams

1 14 (28) 36

ACROSS

FOUR

Nurnberger Abramst 2 (Number [%I observed) 29 (37) 48

38 (16) 203

STUDIES*

Pfohl

77 (35) 144

*Brackets indicate percent. j-Excludes patients with one episode.

In reviewing the studies, the observed percents of unipolar mania range from 16 to 37%. It is surprising that the second study by ABRAMS, which uses the most restrictive definition of unipolar mania, reports the highest percent of unipolar manics despite the fact that the model predicts that the expected number of unipolar manics should drop to 20% when single episode cases are excluded. Even without the model, it is difficult to explain why a

THEMATHEMATICAL CASE AGAINST UNIPOLAR MANIA

263

more restrictive definition would identify more cases than the less restrictive definition. It may be that the investigators took extra pains in identifying and gathering information on unipolar manics. It is also possible that their well known interest in unipolar mania caused colleagues to refer unipolar mania cases to their clinical unit. In any case, in reviewing the data from all available studies, it can be concluded that the observed proportion of unipolar manics is less than or similar to what is predicted by a model that assumes that all unipolar manics are simply bipolar cases which have not had occasion to have a mania yet. If, as the second ABRAMS study suggests, cases of unipolar mania with two or more episodes were about as common as single-episode cases, the model presented here would have to be seriously reconsidered. The model predicts that the ratio of the first : second : third: fourth or greater episode cases should be 500: 125: 31: 10. This can be seen in the third row of Table 1. This prediction is tested in Table 3 using data from the 77 unipolar manics in our own study. The column labelled “Expected No. 1” results from applying the ratio just described to the total of 77 patients. A chi-square analysis shows a reasonably good fit that is not rejected at the 0.05 level.

TABLE

3.

TWO PREDICTIONS

COMPARISONOFOBSERVEDDATATO

OF FREQUENCY

OF PATIENTS

WITH

MULTIPLE

EPISODE

UNIPOLAR

MANIA

Number of episodes 1 2 3 4 Test P

Observed 65 11 1 0

Expected 57.8 14.5 3.6 1.2 x=2.96 N.S.

No.

1 Expected No. 2 38.5 19.3 9.6 9.6 x = 36.2 0.001

If unipolar mania was an entity unto itself the drop in frequency for each number of episodes would only be 50%) resulting in a distribution of 500:250: 125: 125. This assumes that unipolar manics have relapses at least as frequently as bipolars. This assumption is supported by the fact that the number of episodes per year was somewhat greater for unipolar manics than for bipolars in the study by ABRAMSet a/. 3 This distribution does not fit the data with the difference being significant at the 0.001 level. The adequacy of the mathematical model and the null hypothesis would be further supported if the distribution of a number of episodes fit for the bipolar patients. For patienis with 2, 3,4 and > 4 episodes the observed distribution was 91:28: 16: 9. This does not fit the proportion 500: 125 :31: 10 predicted in Table 2 nor does it fit the proportion of 500: 125: 31 : 10 which the unipolar mania data fit so well. The chart-review methodology must be remembered when interpreting this data. Investigators using a prospective consecutive admission design will be in a better position to gather reliable information about the number and type of past episodes to test the adequacy of this model.

B. PFOHL,N. VASQUEZ and H. NASRALLAH

264

DISCUSSION

The model presented is certainly not the only approach that could be taken to describe the data. An attempt was made to model the number of return visits as a Poisson process but this fits the data somewhat more poorly than the original model. Another complication that has not been considered is biphasic episodes. There is no consensus in the literature about how episodes should be counted. If a manic patient becomes asymptomatic and is then discharged to be readmitted for mania three weeks later should this be counted as a second episode? If the same patient is instead readmitted with a depression three weeks after discharge should this be counted as a separate episode or as part of a biphasic episode? If the depression is not sufficiently severe to result in readmission, investigators

of unipolar

mania may not ever hear about it. WINOKUR et ~1.‘~ estimated

in

one study that about 50% of episodes were biphasic. A model involving three different kinds of episodes: depressive, manic, and biphasic was considered for the present study. The model was abandoned when it proved impossible to find estimates of the probability of an episode being manic, given that it was not biphasic. We were also unable to find any other investigators who report on what proportion of episodes are biphasic. Development of such a model would probably interview and precise definitions

require data from a careful study with direct patient for relapse, recurrent episode and biphasic episode. CONCLUSION

The model and data reviewed

in this study suggest that there is little used to postulate

the existence of a separate disorder called unipolar mania to account for clinical observations. Even a conservative interpretation suggests that most studies of unipolar mania thus far have been heavily contaminated by patients who are unipolar manics simply by the fact that they have not had occasion to have a depressive episode yet. The DSM III convention of combining unipolar mania and bipolar cases under the single heading “Bipolar

disorder”

is probably

correct.

SUMMARY

A mathematical model is deveioped based on several assumptions to predict frequency of admission for apparent unipolar mania given that such patients have the same illness as bipolars. The model is compared with data from previous studies of unipolar mania and with data from the author’s own study of 77 unipolar manic patients. The observations generally supported the model. It is concluded that the DSM III convention of classifying unipolar

manics under the heading

“Bipolar

disorder”

is upheld.

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