Decision analytic framework.
_A decision tree was constructed to facilitate analysis of the decision of immediate cryotherapy versus expectant management in women with LSIL proven by colposcopically guided biopsy (see Figure 1). This analysis will support estimation of the likelihood that each type of procedure (cryotherapy, LEEP, laser ablation or excision, cone excision, or hysterectomy) will be required for a patient who has been managed by following (watchful waiting) or by immediate cryotherapy.[Hamm, 1995 #177; Hamm, 1995 #176] It will also permit measurement of the expected utility of each option. In addition, this framework can serve as the basis for a cost-effectiveness analysis. Our analysis has used first the SMLTREE computer program[Siegel, 1993 #147] and more recently the DATA 3.0 program (Decision Analysis by TreeAge[TreeAge Software Inc, 1996 #275]).
_Decision analysis[Weinstein, 1980 #83] uses a decision tree to represent a decision, identifying (i) options that are available, (ii) the events that might follow those options, and (iii) the consequences of those events occurring. Thus in Figure 2, which shows the first two layers of branches of the decision tree of Figure 1, the upper option is watchful waiting, and the lower option is immediate cryotherapy. Four events may occur following the first option: cure (regression), no change, progression to CIN 2, and progression to CIN 3. The cure branch is an outcome or "terminal" node; each of the other branches would be continued (as in Figure 3) and most terminate in an "invasive procedure" branch (Figure 4). The probability of each "path" in a tree from the decision at the left to a terminal branch on the right can be calculated. The utility of the consequences at each terminal branch can be measured. Multiplication of the utility of the outcome by the probability that the outcome would occur produces an estimate of the impact of that possible outcome on the attractiveness of the option. Addition of all these impacts together produces an overall measure of how beneficial the option is.
Our analysis includes as its key elements the cure rate with each of the management plans, the possibility that the watched patient's dysplasia will regress or progress, and the procedures likely to be needed in case of (a) progression, (b) persistence of lesion, or (c) cryotherapy that does not cure the dysplasia. It is assumed that no patient will have metastatic cancer. The outcomes measured in the analysis are the dysutilities of all the procedures required to control the patient's disease and assure that cancer will not develop or, if it should develop, that it will be treated effectively. For simplicity, we use a two year time period, to represent the one- to three-year period that it may take to bring this episode of cervical dysplasia to a conclusion. There is no discounting of the dysutility of procedures that occur later rather than earlier.
_The analysis involves these steps:
Tree structure.
_Our decision tree specifies all possible paths for a patient starting with an initial identification of mild cervical dysplasia and followed until the cervical dysplasia is cured. Two options are considered: watchful following or immediate cryotherapy (Figure 1). It is assumed that all patients are cured of their cervical dysplasia within a two year period. (This time span was most common in the reports of case series in the literature, and is consistent with current clinical experience.) The tree structure includes the possibility that the cervical dysplasia may progress to cancer before it is effectively treated; these are included with the moderate or severe dysplasias that require the more invasive surgical procedures. The outcomes to be considered in the analysis are aspects the process and procedures required to cure the patients, as evaluated on a subjective scale. We do not measure life expectancy or quality of life, because we assume the patients will be cured and the treatment will not permanently affect their quality of life.
Watchful following option.
_The branches of the watchful following option are summarized as follows: a patient's mild cervical dysplasia may regress without treatment, persist, or progress (Figure 2). If it should regress without treatment, it stays cured for the full two years (by definition). If it should persist, the physician will decide at some point in the 2 year period to treat it (see Figure 3), either by doing a cryotherapy procedure or a more invasive procedure (such as LEEP or conization; see Figure 4). If the dysplasia should progress, again the physician will decide whether to use cryotherapy or a more invasive procedure. As Figure 3 shows, the probability the clinician's decision will be to perform cryotherapy is a function of the clinician's ability to adequately visualize the dysplasia with the colposcope, the extent, appearance, cytology and/or histology of the dysplasia, and the clinician's general tendency to prefer the less invasive but more uncertain cryotherapy procedure over a more invasive but more certain surgical procedure (LEEP, cone, or hysterectomy). If cryotherapy is done, the dysplasia either is cured (and stays cured during the rest of the two years) or is not cured. If a more invasive procedure is done, it is assumed to cure the dysplasia. At each branch where an invasive procedure is required or chosen, the probability that each of the 5 procedures would be used (Figure 4) differs, as is appropriate for the situation. The probabilities for each branch will be explained in a subsequent section. Note that the tree does not address the state of the dysplasia at each point. Rather it addresses the probability that each surgical procedure would be selected, whether that be for wide spread or endocervical LSIL, for HSIL, or for carcinoma in situ.
_It is worth commenting on how this analysis handles the decision how to treat a patient whose dysplasia does not regress. The choice whether to use cryotherapy or a more invasive surgical procedure is partly governed by features of the dysplasia and the cervix, but there is also a zone of clinician discretion. There is similar discretion in the choice of which surgical procedure to use. We treat the clinician's choices within these zones of discretion as chance variables, even though they technically could be considered to be decision branches (whose options would be analyzed, and the option with the highest expected value selected.[Weinstein, 1980 #83]) This is done because the analysis is from the perspective of a clinician deciding whether to follow or do immediate cryotherapy, at the moment when the patient's LSIL is first identified. The later decision about what procedure to use may be outside the decision maker's control. If the followed dysplasia should progress or if the initial cryotherapy should fail to cure the dysplasia, this clinician may refer to another. Those who receive such referrals find it reasonable to make statements such as, "In such a situation, I do option A about 40% of the time..." Taking the future decision as an event external to the decision maker, whose probability can be estimated, rather than as something within the control of the decision maker, is a faithful representation of the position of many clinicians faced with the decision how to manage a patient with mild cervical dysplasia.
Immediate cryotherapy option.
_The immediate cryotherapy treatment option can result in the patient being cured throughout the two year period, or not cured (Figure 2). Patients who are not cured with initial cryotherapy will be treated, either with a second cryotherapy procedure or with a more invasive procedure (Figures 3 and 4). If the second cryotherapy procedure does not cure the dysplasia, then a more invasive procedure will be used (Figures 3 and 4). It is assumed that the more extensive procedures such as LEEP or laser surgery will cure the cervical dysplasia without the possibility of recurrence. (Patients are followed to assure this cure has happened.)
Probabilities.
_The branches at every "chance" node in the decision tree have probabilities that sum to 1. The branch definitions and their probabilities are given in Table 1 for the branches in Figure 1, and in Table 2 for the branches in Figure 4 at each of the 17 situations where those branches are pertinent. An invasive procedure is used at 17 locations in the tree in Figure 1. The probability that each of the five procedures is used varies according to the situation. Four experienced colposcopists (1 gynecologic oncologist and 3 family physicians) collaborated to produce the probability estimates in Table 2.
Outcome measurement.
_The measure of the outcomes is expert subjective judgment of the dysutility of the procedures involved in producing those outcomes. This is the sum of ratings of (A) the cost and severity of the procedure itself, and (B) the procedure's morbidity, effect on quality of life, and possible long term effects (including the potential requirement for surgical diagnostic procedures for future cervical abnormalities). The measure is shown in Table 3 for all procedures included in the analysis. This is a ratio scale, where 0 would indicate no dysutility. The dysutility of the watchful following strategy (inconvenience and discomfort of repeated appointments, pelvic exams, and ongoing uncertainty, for two years on the average) was applied to every patient in the watchful following branch. The cost of each other procedure was accrued if it happened. After cryotherapy, it was possible to have additional cryotherapies or other procedures. Each other procedure was a terminal branch in the tree. The values in Table 3 were produced by one experienced colposcopist. A second experienced colposcopist made independent judgments which correlated r = .97 with these judgments.
Sensitivity analysis.
_Sensitivity analysis is a method of determining whether and how the results of an analysis depend on the values assumed for one (or more) of the parameters in the analysis. For example, if we assumed there is a low probability that the dysplasia will regress, immediate cryotherapy may seem to be the better management strategy. However, if there truly were a high probability that the dysplasia will regress, then watchful following may be the better strategy. In this case, it could be said that the analysis' recommendation is sensitive to the value assumed for the probability that dysplasia will regress if followed.
_We performed sensitivity analyses for the following factors: The probability that the dysplasia will regress if followed (in Table 1, variable preggfol); the proportion of non-regressing dysplasia that persists as CIN 1 rather than progressing to CIN 2 or CIN 3 (proporpersist); the proportion of progressing dysplasia that progresses to CIN 2 rather than CIN 3 (propCIN2); the probability that cryotherapy will cure dysplasia (pcurgcryo); the probability that a colposcopic exam can adequately view the cervix, post cryotherapy (pviewgimcryfail); the probability that dysplasia will require an invasive procedure rather than cryotherapy, given it can be adequately seen with colposcopy (pdisreqinvas); the probability that cryotherapy rather than an invasive procedure will be chosen, later, in situations which do not require an invasive procedure (pcryovsinvas); and finally the dysutility of watchful following compared to all the other procedures in Table 3.
_Several of the factors that we will analyze occur at multiple locations in the decision tree. For example, the probability that cryotherapy will cure dysplasia is a factor for the watchful following strategy, in the "persist as CIN 1" branch and the "progress to CIN 2" branch, and for the immediate cryotherapy strategy. Though the exact probabilities are not identical, they are related. To allow these factors to vary together in a sensitivity analysis, they are constructed as functions of a common variable. This may be seen in the third column of Table 1, where for example the probability that cryotherapy cures dysplasia, given dysplasia persists and doctor chooses cryotherapy (pcurg1cryopers) is equal to .98 * pcurgcryo. The variable pcurgcryo is the common variable for all branches in the tree where the probability cryotherapy will cure the dysplasia is a factor. The families of variables that are related in this manner are shown in Table 4. For each family, a sensitivity analysis on the first variable will vary all the probabilities in the family of related branches, in a logically coordinated manner.
_The decision tree of Figure 1 is used with the probabilities in Tables 1 and 2 to calculate the probability that each procedure (cryotherapy, LEEP, laser ablation, laser cone, cold knife cone, or hysterectomy) will be used. While it is assumed that each of the more invasive procedures would cure the patient, explicit provision is made for the possibility of recurrence after cryotherapy. For example, a patient might have two ineffective cryotherapies and ultimately require a laser cone. The probabilities with which each treatment approach would resort to each procedure to cure the patient's cervical dysplasia are shown in Table 5.
_The probabilities in Table 5 illustrate the essential tradeoff inherent in the decision between watchful following and immediate cryotherapy. With watchful following, most people (57%) are better off for they recover with no procedure, but more people require invasive surgical procedures (19.8% rather than 4.5%). Thus, 57.0% of patients are better off but 15.4% are worse off. Whether we consider watching to be better or worse than immediate cryotherapy would depend on the relative dysutilities of receiving no procedure, cryotherapy, or one of the surgical procedures.
_Calculation of the expected dysutility of a strategy involves multiplying the dysutility of each path in the decision tree that the strategy could lead to (the sum of the dysutilities of all the procedures encountered on that path) times the probability of going down that path (which is the product of all the probabilities on the path). Then the expected dysutilities of all the paths that an option could lead to are added up. Using the measures of dysutility given in Table 3, the expected dysutility of watchful waiting is 2.53 and the expected dysutility of immediate cryotherapy is worse, at 3.18. Thus the analysis would recommend watchful following rather than immediate therapy.
Sensitivity analysis.
_The conclusion that watchful waiting is superior to immediate cryotherapy depends on the assumptions of the analysis, including the numerical estimates of the probabilities (Tables 1 and 2) and the dysutilities (Tables 3). To compare the possible effects of these variables, Figure 5 shows a "tornado diagram" for 9 variables. The x-axis represents the expected dysutility of the alternative that is better in the baseline analysis, watchful following, whose expected dysutility is 2.53. More dysutility is worse. The baseline expected dysutility of the other alternative, immediate cryotherapy, is represented by the vertical dashed line at 3.175. The horizontal bar graphs show the effect that varying each variable over a range of possible values would have on the expected dysutility of watchful waiting. For example, as the probability the dysplasia would regress is increased from the most accurate estimate of .57, up to .9, the expected dysutility of watching would decrease from 2.53 to 1.35. If the probability of regressing were as low as .3, then the expected dysutility of watchful waiting would increase from 2.53 to 3.4. With the most unfavorable estimate (p = 0.3), watchful waiting would be worse than immediate cryotherapy.
_When they are varied individually, three of the factors have the potential to change the recommendation of the analysis. These are the probability the dysplasia will regress, the dysutility of the process of watchful following, and the dysutility of invasive procedures compared to cryotherapy. (a) The less likely it is that the dysplasia would regress, the less attractive is watchful following. (b) The more dysutility is attributed to the process of watchful following (repeated visits for colposcopy or Pap smear, the uncertainty of living with a possible cancer precurser), compared with the dysutilities assigned to the other procedures (as specified in Table 3), the less attractive watchful following is. (c) The more dysutility is attributed to invasive procedures, compared to cryotherapy, the less attractive watchful waiting becomes. None of the other variables displayed in Figure 5 could reverse the recommendation of the analysis if varied in isolation, even if varied far beyond realistic possibilities. (However, it is possible that assigning different values to combinations of other variables could change the recommendation.)
_The impact of each of the variables that affect the analysis' recommendation depends on the value of the others. For example, Figure 6 shows a two-way sensitivity analysis of the effects of two factors, the dysutility of the process of following and the probability that the dysplasia will regress, upon the overall dysutility of the watchful following strategy. In the upper left diagonal region, watchful following is the preferred strategy, while in the lower region immediate cryotherapy is preferred. The threshold value of each factor -- the particular value where the options are equally preferred -- is different for different values of the other factor. For example, if the dysutility of the watchful following process were 1 (1/3 as bad as cryotherapy), then the probability that the CIN 1 dysplasia would regress would have to be lower than .38 before immediate cryotherapy would be preferable to watchful following. On the other hand, if the dysutility of watchful following were 2, then immediate cryotherapy would be preferable if the probability that dysplasia would regress were less than .65.
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