Transposition Rates of Mycobacterium tuberculosis IS6110 Restriction Fragment Length Polymorphism Patterns

To determine the rate at which IS6110 restriction fragment lengthpolymorphism (RFLP) patterns in Mycobacterium tuberculosis changeover time, we applied a smooth nonparametric survival modelto several data sets, including data from previous publicationson the rate of change. The results strongly suggest a simpleparametric model, with an instantaneous change at time zeroand essentially a zero rate of change thereafter. Our interpretationof the results is that at the time of collection of the firstisolate, more than one strain is present. We speculate thatthe selection of mutant strains is most likely during rapidgrowth, revival of the dormant bacteria, and/or adaptation toa new host. The parameter most accurately describing changingRFLP patterns is the proportion of isolates with band changes,rather than the half-life or the rate of change.

INTRODUCTION

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Introduction

Restriction fragment length polymorphisms (RFLPs) associatedwith insertions of the IS6110 element into the genome of Mycobacteriumtuberculosis are an important tool in epidemiological studiesof tuberculosis. It is of practical and theoretical importanceto know the rate of change of these fingerprints. A fundamentalcomplication is that the data are inherently interval censored:one can determine that a fingerprint changed during some interval,but not the exact time point at which the change occurred. Thiscomplicates the application of survival analysis to this typeof data. de Boer et al. (1) assumed an exponential survivalmodel (constant hazard), integrated over observation intervals,and estimated the constant hazard by maximum likelihood. Tanakaet al. (6) refined this analysis by introducing proportionalityto the copy number. The validity of the assumption that therate of change is constant over time has not yet been examined.In this paper, we report the extent to which this assumptionis supported by data from The Netherlands, Vietnam, and SouthAfrica as well as by published data from San Francisco, Calif.,and Germany. In addition, we explore whether there are alternativesthat provide a better explanation of the observed data.

MATERIALS AND METHODS

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Materials and Methods

The following data sets were available and were used for ouranalysis: serial isolates from 544 tuberculosis patients inThe Netherlands, 25 (5%) of which showed a change in the follow-upfingerprint (1); serial isolates from 75 tuberculosis patientsin Vietnam with relapses (a repeat episode of tuberculosis afterbeing declared cured) or treatment failures (remaining smearand culture positive after 5 or 8 months of treatment), 15 (20%)of which showed a change in the fingerprint of the second episode(5); and serial isolates from 345 tuberculosis patients in SouthAfrica, 15 (4%) of which showed a change in the subsequent DNAfingerprint (7).

In addition, we used the following isolates from two publishedreports on the rate of change of IS6110 RFLP patterns: serialisolates taken at least 90 days apart from 49 tuberculosis patientsin San Francisco, 12 (24%) of which showed a change in the IS6110RFLP pattern of the isolate from the second episode (8); andserial isolates from 56 tuberculosis patients in Germany, 5(9%) of which showed an alteration in the follow-up isolate(4). For the data presented by Yeh et al. (8), we obtained numbersby using the histograms in their paper. Hence, the data wererounded to 50 days for our analysis.

For the data from The Netherlands, details are given in an articleby de Boer et al. (1). The hazard was defined as the probabilityof a change occurring during a discrete time interval, e.g.,10 days. First we developed a smooth nonparametric algorithmfor hazard estimation. In this approach, the hazard for eachtime interval is estimated as a smooth positive function thatmaximizes the likelihood of the data, using a penalized maximumlikelihood algorithm (3). This procedure was applied to eachof the five data sets. Special software was written for thisanalysis by using Matlab (available upon request).

We compared the results of the nonparametric approach (whichimplies no assumptions about changes of the hazard over time)with the following parametric models: (i) constant hazard (whichhas been used to date in publications on this subject), (ii)exponentially declining hazard, and (iii) an almost immediatechange at the origin (a "hazard impulse") followed by a constanthazard. We call the latter the impulse model.

The constant hazard model has only one parameter, the levelof the hazard. The second model assumes an exponentially decayinghazard and has two parameters: one is the initial level of thehazard and the other is the rate of decline of this hazard overtime. The last model has two parameters as well: one is theinitial proportion changed and the other is the constant hazardover the period thereafter.

These four explanatory models were compared by using log likelihoods.

RESULTS

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Results

For the nonparametric approach without assumptions about changesin the hazard over time, four of the five data sets showed thesame remarkable pattern: a high initial hazard that droppedsharply within a short time (a few weeks or months). For thedata from The Netherlands, the hazard showed an initial strongchange in the first 200 days (Fig. 1). If we used only the intervalsof <100 days, we still saw a very sharp peak near the origin(Fig. 2). This pattern was similar for data from Vietnam, CapeTown, South Africa, and San Francisco, Calif., but differentfor data from Germany (data not shown). The data set from Germanyis sparse, as it includes data for only 5 patients (of 49) witha change in IS6110 fingerprints. By experimenting with the data,we found that adding or removing only one fingerprint changehad a strong influence on the estimated hazard curve.

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FIG. 1. Dutch data. Individual intervals are shown sorted, with increases in length from bottom to top. Left, no change; right, change in RFLP.

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FIG. 2. Dutch data (first 100 days). Individual intervals are shown sorted, with increases in length from bottom to top. Left, no change; right, change in RFLP.

A comparison of the likelihoods of the models showed that theconstant hazard assumption gave the poorest results, while theother three models had similar likelihood values (Table 1; Fig.3). It should be noted here that the exponential model showeda very steep decline of the hazard, which was close to zerowithin a few weeks.

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TABLE 1. Log likelihoods of hazard models^a

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FIG. 3. Model estimates for Dutch data (left panel) and corresponding probabilities of change in RFLP fingerprints (right panel). Full lines, nonparametric model; dashed lines, constant hazard model; dash-dot lines, exponential hazard model; dotted lines, impulse model.

DISCUSSION

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Discussion

This study suggests that, contrary to previous assumptions,changes in RFLP patterns are strongly time-dependent. The datacan be more easily explained by an instantaneous change at timezero or by a steep decline of the hazard than by assuming aconstant rate of change. Of the three alternative, and moreor less equivalent, models, we think the impulse model is themost attractive for its simple interpretation.

The interpretation of the impulse model is that most changesin RFLP patterns occur before diagnosis and that the rate ofchange during treatment is extremely low. We offer two hypothesesto explain this. First, the rate of change may be proportionalto the growth rate of mycobacteria. If this is true, the rateof change during latency should be close to zero. Alternatively(or in addition), adaptation to a new host gives rise to selectionpressure and thus may lead to the selection of strains withanother RFLP pattern if such a change is accompanied by functionalchanges in the expression of particular genes. If adaptationto a new host is the main mechanism, no further change shouldbe observed among failure cases. If rapid growth is the majorexplanation, another impulse may be expected upon treatmentfailure or a relapse.

Since the rate of change during treatment appears to be extremelylow, the proportion of isolates that changed, rather than thehalf-life or rate of change, should be the parameter of interest.The proportion of isolates with changes in the IS6110 RFLP mayvary between settings, possibly due to differences in the delaybetween the onset of disease and the diagnosis. This suggeststhat the proportion changed, which can be determined at diagnosisby the fingerprinting of multiple single-strike colonies, mightbe used as an indicator of the mean delay. However, this proposalfirst needs validation.

The strength of the evidence strongly depends on the intervalsbetween serial isolates. The Dutch data contain relatively manyshort intervals, and in that case, the difference in likelihoodbetween the impulse model and the constant hazard model is large.It would be worthwhile to gather more and stronger evidenceby investigating RFLP fingerprints repeatedly within short intervalsfor many patients to estimate the rate of change during thevery early phase of treatment. Repeated isolates at the verystart of treatment would also allow us to check the hypothesisthat a mixture of strains of M. tuberculosis is already presentat that moment. That such mixed populations do occur has beenshown in a study of low-intensity bands (2).

A consequence of our findings is that it does not make muchsense to investigate relationships between the rate of changeand patient characteristics or specifics of the RFLP pattern,such as the number of (changed) bands. The rate of change isso high that knowing more about it adds little information.Instead, further research should focus on the changed fraction.In general, it will be hard to get reliable estimates, as thiswill involve studying subgroups of the already small fraction,about 5%, that shows a change. Very large groups of patientswill be needed for such studies.

FOOTNOTES

* Corresponding author. Mailing address: Leiden University Medical Centre, Department of Medical Statistics, P.O. Box 9604, 2300 RC Leiden, The Netherlands. Phone and fax: 31 71 527 6814. E-mail: p.eilers{at}lumc.nl.

REFERENCES

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