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Multilevel and Continuous Pleural Fluid pH Likelihood Ratios for Evaluating Malignant Pleural Effusions^*

^* From the Division of Pulmonary and Critical Care Medicine (Dr. Heffner), Medical University of South Carolina, Charleston, NC; School of Law (Mr. Heffner), University of Texas, Austin, TX; and Lovelace Health Systems and the University of New Mexico School of Medicine (Dr. Brown), Albuquerque, NM.

Correspondence to: John E. Heffner, MD, FCCP, Medical University of South Carolina, Division of Pulmonary and Critical Care Medicine – 812 CSB, 96 Jonathan Lucas St, PO Box 250623, Charleston, SC 29425; e-mail: heffnerj{at}musc.edu

	Abstract

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
Study objective: Expert consensus recommends testing pleural fluid for pH to assist the selection of patients with malignant pleural effusions for pleurodesis. Although published studies report an association between pleural fluid pH and patient outcomes after pleurodesis, clinicians have no definitive information on how to use pH to select patients for pleurodesis. Thus, we quantitatively assessed different methods for deriving likelihood ratios from pleural fluid pH and evaluated the potential role of pH in selecting patients for pleurodesis.

Data sources: MEDLINE, systematic reviews, article reference lists, and contact with primary authors.

Study selection: Studies that assessed the impact of pleural fluid pH on survival and pleurodesis failure rates among patients with malignant pleural effusions.

Data extraction: Primary authors provided their data in electronic spreadsheets.

Data synthesis: Retrieved data sets included survival and pleurodesis failure rates for 417 patients and 433 patients, respectively. Binary, multilevel, and continuous likelihood ratios were calculated to estimate the likelihood of death within 3 months of pleurodesis or pleurodesis failure rates. Values for the likelihood ratios were compared for each of the three strategies, and relative clinical and statistical significance were assessed. Pleural fluid pH had marginal performance for identifying patients with < 3-month anticipated survival; binary likelihood ratios provided as much information as the multilevel and continuous strategies. Likelihood ratios for identifying patients likely to fail pleurodesis were clinically useful. Continuous likelihood ratios provided statistically more information as compared with the multilevel and binary strategies.

Conclusions: Pleural fluid pH has marginal value for estimating death within 3 months of pleurodesis, and binary likelihood ratios (cut point ≤ 7.20) perform as well as the other strategies assessed. Pleural fluid pH provides more useful information for estimating the likelihood of pleurodesis failure for which continuous likelihood ratios provide the most information as compared with binary or multilevel likelihood ratios.

Key Words: diagnostic testing • malignant • pH • pleura • pleural effusions

	Introduction

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
Malignant pleural effusions commonly complicate the clinical course of patients with a variety of thoracic and extrathoracic cancers. Although these effusions may be incidental findings in some patients, many patients experience disabling symptoms of dyspnea with the accumulation of moderate-to-large volumes of pleural fluid. Pleurodesis offers these patients palliation of symptoms by draining pleural effusions and producing a pleural symphysis that prevents the reaccumulation of malignant fluid.¹ Unfortunately, pleurodesis may fail in up to 40% of patients.² Moreover, the median survival of patients after pleurodesis is 4 months with many patients surviving only a few weeks, which limits opportunities for many patients to experience sufficient benefits from pleurodesis to justify its expense, discomforts, and potential complications.³ Consequently, the American Thoracic Society (ATS)/European Respiratory Society (ERS) consensus statement on malignant effusions emphasizes the importance of careful patient selection to avoid performing pleurodesis for patients who are likely to fail the procedure or die soon after the pleurodesis is performed.¹

No predictive models exist, however, to identify appropriate patients for pleurodesis. Several reports have observed an association between a low pleural fluid pH and failure of pleurodesis.^{4 5 6 7 8 9} Additional studies have observed a direct correlation between pleural fluid pH and survival.^{4 10 11 12 13} On the basis of these studies, the ATS/ERS statement on malignant pleural effusions recommends the adjunctive use of pleural fluid pH with other clinical factors to select patients for pleurodesis.¹ Expert opinion has suggested that patients with pleural fluid pH values less than a cut-off value of 7.20 should not be considered for pleurodesis.¹⁴

Unfortunately, the use of a single cut-off value dichotomizes patients and loses much of the diagnostic information contained within continuous numeric test results, such as pH.¹⁵ Dichotomization treats pH results just below and those extremely below the cut-off point the same. Experts in diagnostic test research recommend a Bayesian approach, wherein pH test results would be used to calculate likelihood ratios,¹⁶ which allow clinicians to estimate the posttest probabilities of a condition from their pretest clinical suspicions that the condition exists. A likelihood ratio for any test result value is calculated by dividing the number of patients with that test result who have a target condition by the number of patients with the test result who do not have the target condition. A clinician’s estimate of the pretest odds that a patient has a target condition can be multiplied by the likelihood ratio for a given test result, which computes the posttest odds. Likelihood ratios can be derived as binary likelihood ratios using a single cut-off test result value, multilevel likelihood ratios for intervals (or "strata") of test result values, or as continuous likelihood ratios calculated for discrete values of a pH test result.

We have previously reported the results of meta-analyses that examined the largest available data set to our knowledge of pleural fluid pH from patients with malignant effusions to determine the operating characteristics of pH binary strategy for selecting patients for pleurodesis.^{3 17} In the present report, we use the data set from this meta-analysis to calculate multilevel and continuous likelihood ratios for estimating the probability of successful pleurodesis and survival < 3 months for patients with malignant effusions. We also considered whether continuous likelihood ratios provide more clinically and statistically significant information as compared to multilevel and binary likelihood ratios.

	Materials and Methods

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
We performed a MEDLINE search to retrieve articles that reported pleural fluid pH and clinical outcome for patients with malignant pleural effusions. We also reviewed the reference lists of the retrieved articles and the investigators’ files for additional relevant reports. The primary investigators of retrieved articles were contacted to determine if additional data sets existed, published or unpublished, that reported pleural fluid pH and outcome for malignant effusions. To be included in this study, retrieved articles had to report pleural fluid test results in a manner that linked an individual patient’s pleural fluid pH with survival or the success vs failure of pleurodesis. Contacted investigators were invited to send us their data in spreadsheet format.

Received data were entered into statistical software (JMP; SAS Institute; Cary, NC), In addition to survival data measured in months, patients were categorized by the "success" or "failure" of pleurodesis. A successful pleurodesis was defined as complete or partial radiographic resolution of a malignant effusion with improvement of dyspnea to a degree that subsequent pleural fluid drainage was not required. A pleurodesis failure encompassed all other patients.

For the determination of multilevel likelihood ratios, pleural fluid pH values were grouped into four ordinal strata: pH ≤ 7.00, pH > 7.00 to ≤ 7.20, pH > 7.20 to ≤ 7.40, and pH > 7.40. Multilevel likelihood ratios with 95% confidence intervals (CIs) were calculated for each rank by the method of Simel and coworkers.¹⁸ Binary likelihood ratios were also calculated for the binary testing strategy recommended by expert consensus for identifying patients who were likely to fail pleurodesis or die within a short interval after pleurodesis. This strategy dichotomizes patients with a pH cut-off point of 7.20 and identifies patients with a pH value ≤ 7.20 as having a higher probability of dying within 3 months and a higher probability of failing pleurodesis.

Continuous likelihood ratios were derived from logistic regression. Simple logistic regression was used to model pleural fluid pH test results as an estimate of survival < 3 months and as an estimate of failure of pleurodesis. A survival < 3 months was selected because expert consensus recommends avoiding pleurodesis for patients with short expected survivals.¹ Continuous likelihood ratios and their 95% CIs were calculated from the regression equation parameters of the model using discrete pleural fluid pH values.¹⁹ This method uses the following equation to calculate continuous likelihood ratios: exp[ß(measured pH - x’)], wherein the variable "measured pH" represents a discrete pH value for which a continuous likelihood ratio is being calculated. The logistic regression model derived the constant ß, along with , using the pH values of the data set as estimates of < 3-months survival and failure of pleurodesis.¹⁹ The variable x’ represents the pH value for which the log odds at the prevalence of survival < 3 months or pleurodesis failure equals + ßx’ in the data set. The equation x’ = (ln[p’/(1 – p’)] – )/ß was used to calculate x’, wherein p’ is the prevalence in the data set of survival < 3 months or pleurodesis failure.

The following equation was used to calculate 95% CIs for continuous likelihood ratios: exp[(ß ± 1.96SE(ß))(x – x’)], wherein x is the measured pH and SE is the standard error for ß derived from logistic regression.¹⁹ Statistical differences between the multilevel and continuous likelihood ratios in estimating outcome were analyzed by a previously reported method that fits a logistic regression model with the multilevel ordinal predictor and the same model with the addition of the continuous pH predictor.¹⁹ A likelihood ratio test (referring to the logistic regression test rather than the likelihood ratios derived in this study) compared the two models to derive a ² test with 1 degree of freedom. The difference between the ² statistic for the multilevel likelihood ratios from the two models generated a ² statistic, which was used to estimate the statistical significance of the added predictive ability provided by continuous likelihood ratios.

The continuous and multilevel likelihood ratios derived from the described methods were compared to the likelihood ratio derived from a binary testing strategy (cut-off value ≤ 7.20) to determine relative clinical advantages. These relative clinical benefits were qualitatively estimated by inspecting the degree by which likelihood ratios differed between testing strategies across a range of pH values.¹⁹ Relative clinical advantages were also estimated between a strategy that used multilevel as compared to continuous likelihood ratios. Clinical advantages were examined by comparing the range of continuous likelihood ratios for the lowest and highest pH values in the four ordinal pH strata with the multilevel likelihood ratios calculated for the same strata.¹⁹ Clinical advantages of the two testing strategies were also compared qualitatively by examining their plots across the range of continuous pH values. In determining clinical significance, we asked if the degrees of differences in likelihood ratios calculated by the different methods were sufficiently large to cause clinicians to make different decisions in clinical practice.

	Results

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
The MEDLINE and literature search identified the same data sources that we previously reported in our earlier meta-analyses^{3 17} of the utility of pleural fluid pH for predicting survival^{4 5 6 8 20 21 22 23 24} and pleurodesis failure.^{4 5 6 7 8 9 10 11 20 23 25} One additional data set of previously unpublished data were included in both analyses (F. Rodriquez-Panadero, MD; personal communication; November 1998). There were 417 patients in the data set used for estimating survival and 433 patients in the data set used for estimating survival < 3 months.

The clinical characteristics of the 417 patients in the database used to calculate likelihood ratios for survival were previously reported.³ The median survival in this group was 4 months, and the prevalence of survival < 3 months was 41.0%. Multilevel likelihood ratios for survival with 95% CIs for the four ordinal pH strata are shown in Table 1 with the number of patients in each pH test result strata. Using the binary pH cut point of 7.20 for identifying patients with poor survival resulted in a binary likelihood ratio for pH values ≤ 7.20 of 1.70 (95% CI, 1.20 to 2.41) and for pH values > 7.20 of 0.31 (95% CI, 0.24 to 0.41) for estimating death within 3 months. These binary likelihood ratios were similar to the multilevel likelihood ratios for survival across the range of pH values (Table 1) . For example, a patient with a pleural fluid pH of 7.10 has a binary likelihood ratio of 1.70 (95% CI, 1.20 to 2.41) for death within 3 months of pleurodesis as compared with a multilevel likelihood ratio of 1.60 (95% CI, 1.06 to 2.42).

By using the above-derived equations, continuous likelihood ratios were calculated for the highest and lowest pH values in each of the strata used to calculate multilevel likelihood ratios for survival and pleurodesis failure (Tables 1 , 2) . These continuous likelihood ratio results were calculated to allow comparisons with binary and multilevel likelihood ratios for similar pleural fluid pH results. As shown in Tables 1 , 2 , continuous likelihood ratios differed from the multilevel likelihood ratios calculated for each strata and from the binary likelihood ratios. For instance, the binary likelihood ratio for death within 3 months at a pH value of 7.21 is 0.30, as compared with a multilevel likelihood ratio of 0.82 and a continuous likelihood ratio of 1.19 (Table 1) . The curves for the continuous likelihood ratios as a function of measured pH and the values for multilevel likelihood ratios within each pH interval are shown in Figures 1 , 2 . Multilevel likelihood ratios both over and under estimated the continuous likelihood ratios within each of the pH strata.

View larger version (11K): [in this window] [in a new window] [Download PPT slide]   Figure 1.. Multilevel (staircase lines) and continuous (curved lines) likelihood ratios for pleural fluid pH as an estimate of death within 3 months. Horizontal lines mark the likelihood ratio of 1.

View larger version (12K): [in this window] [in a new window] [Download PPT slide]   Figure 2.. Multilevel (staircase lines) and continuous (curved lines) likelihood ratios for pleural fluid pH as an estimate of failure of pleurodesis. Horizontal lines mark the likelihood ratio of 1.

In qualitatively examining the differences of multilevel vs continuous likelihood ratios for estimating survival shown in Figure 1 and Table 1 , we concluded that differences in likelihood ratio values were not sufficiently large to be clinically important. In inspecting the likelihood ratio values of the different strategies for estimating pleurodesis failure (Fig 2 , Table 2 ), differences appeared sufficiently large to provide a clinically important degree of added information by using the continuous likelihood ratio strategy. No association was found between the specific pleurodesis agent used and any of the measured end points.

	Discussion

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
The present study derives equations for calculating continuous likelihood ratios from pleural fluid pH that estimate the likelihood of death within 3 months of pleurodesis or failure of pleurodesis for patients with malignant pleural effusions. Pleural fluid pH had marginal value for estimating the likelihood of death within 3 months, and the binary likelihood strategy using a cut-off point of ≤ 7.20 provided as much information as the multilevel and continuous likelihood ratio strategies. For estimating pleurodesis failure, however, pleural fluid pH provided useful information to assist clinical decision making if continuous likelihood ratios, as opposed to the binary or multilevel strategies, were used to calculate posttest probabilities.

The results of this study assist clinicians in understanding the value of pH in selecting patients for pleurodesis and how pH values should be used to estimate posttest probabilities. Although the ATS/ERS statement on malignant pleural effusions recommends consideration of pleural fluid pH as an adjunctive test for estimating survival, the present study suggests that pH has little value for this purpose. As demonstrated in Figure 1 , continuous likelihood ratios follow a shallow curve across the range of pH values observed in malignant effusions. Consequently, extremely high as compared with extremely low pleural fluid pH results do not generate sufficiently different likelihood ratios to have an important impact on patient selection for pleurodesis. This observation agrees with our previous report that only 54% of patients with a low pH value < 7.28 die within 3 months.³ We can now extend these observations of the poor predictive value of pH on the basis of the present study to the entire range of pleural fluid pH results encountered in clinical practice.

It is clear from the results of this study that dichotomizing patients with a pleural fluid pH cut point of 7.20 and denying pleurodesis for patients with a pH values ≤ 7.20 on the basis of an estimated poor survival, as suggested by some experts, is unwarranted. If physicians choose to follow ATS/ERS recommendations and use pleural fluid pH as adjunctive data to estimate survival, they should adopt a Bayesian approach.¹⁵ This approach uses likelihood ratios to calculate the posttest probability of early death from a clinician’s estimates of the pretest probability. Our data demonstrate that clinicians who employ this approach can use the simple binary likelihood ratio strategy (likelihood ratio of 1.70 for pH values ≤ 7.20) because it performs as well as multilevel or continuous likelihood ratios in estimating early deaths. For example, a physician who estimates a 50% pretest probability of death within 3 months would calculate a 63% posttest probability if pleural fluid pH was < 7.20 (^{see Appendix} for equations). The modest increase in probability illustrates the marginal impact of pH on estimates of patient survival.

In contrast, pleural fluid pH provides more information for estimating pleurodesis failure. Multilevel likelihood ratios (Table 2) and the curve for the continuous likelihood ratios (Fig 2) for estimating failure increase to a greater degree from high to low pH values as compared to likelihood ratios for estimating death. Consequently, likelihood ratios associated with extremely low and extremely high pH values differ in their impacts on estimates of pleurodesis failure to a clinically important degree. For instance, a clinician’s 50% estimate of the pretest probability of pleurodesis failure becomes a posttest probability of 82% for a patient with a pleural fluid pH of 7.00 (continuous likelihood ratio of 4.42 from Table 2 , or use of the equation exp[– 5.019(measured pH – 7.296)]). The same 50% pretest probability for pleurodesis failure, however, decreases to a 37% posttest probability of failure if the patient has a pleural fluid pH of 7.40 (continuous likelihood ratio of 0.59 from Table 2 , or use of the equation exp[– 5.019(measured pH – 7.296)]).

In using pH to estimate pleurodesis failure, however, our data indicate that continuous likelihood ratios represent the preferred strategy because they provide more information as compared with the binary or multilevel approaches. Our study indicated that continuous likelihood ratios provided more information on the basis of a statistical comparison (² analysis) and a clinical comparison (visual inspection of Fig 2 ). Continuous likelihood ratios for pleurodesis failure can be easily calculated at the bedside by the equation exp[– 5.019(measured pH – 7.296)], which can be entered into a spreadsheet on a personal digital assistant. Equations for the calculation of likelihood ratios for a broad array of diagnostic tests will most likely be included in hospital-based computerized decision support systems as a component of computerized physician order entry in the near future.

The present study is limited by the quality of the primary studies that examined the relationship between pH and outcome for patients with malignant pleural effusions. The limitations of these primary studies have been previously discussed.^{3 17} Considering that expert consensus recommends the use of pH in decision making, the results of the present study advance our understanding of how these test results should be used in clinical practice pending future primary investigations.

In conclusion, pleural fluid pH offers only modest information for identifying patients who are likely to die within 3 months of pleurodesis. If pH is used as adjunctive information for this purpose, binary likelihood ratios quantify the marginal impact of pH on survival estimates and avoid the unwarranted exclusion of all patients with a low pH from pleurodesis. Pleural fluid pH is more useful for identifying patients likely to fail pleurodesis if continuous likelihood ratios are used to calculate posttest probabilities from pretest estimates of pleurodesis failure. We suggest that large, multicenter studies are needed to identify other explanatory variables that will supplement the modest value of pleural fluid pH in predicting outcome after pleurodesis. The present study, however, provides a quantitative estimate of the predictive value of pleural fluid pH for individual patients to avoid an overinflation of its clinical importance.

	Appendix

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 
Equations for Converting Pretest Probabilities of a Condition to Posttest Probabilities With the Use of Likelihood Ratios
Convert pretest probability to pretest odds: pretest odds = pretest probability/(1 – pretest probability).

Convert pretest odds to posttest odds: posttest odds = likelihood ratio x pretest odds.

Convert posttest odds to posttest probability: posttest probability = posttest odds/(1 + posttest odds).

Examples of the Use of Likelihood Ratios for Estimating Pleurodesis Failure

1. Binary likelihood ratios to estimate the probability of pleurodesis failure for a patient with a pleural fluid pH of 7.00:
   • If a clinician has a 30% estimate of pretest probability of failure of pleurodesis, the pretest odds becomes 0.30/(1 – 0.30), which equals 0.43.
     
   • To calculate the posttest odds of failure, the pretest odds (0.43) is multiplied by the binary likelihood ratio for the pH value of 7.00 taken from Table 2 , which 2.13. The posttest odds becomes 0.43 x 2.13 = 0.92.
     
   • The posttest probability is calculated by converting the posttest odds (0.92) into the posttest probability: 0.92/(1 + 0.92) = 0.48 or 48%.
     
   
   
2. Multilevel likelihood ratios to estimate the probability of pleurodesis failure for a patient with a pleural fluid pH of 7.00:
   • If a clinician has a 30% estimate of pretest probability of failure of pleurodesis, the pretest odds becomes 0.30/(1 – 0.30), which equals 0.43.
     
   • To calculate the posttest odds of failure, the pretest odds of failure (0.43) is multiplied by the multilevel likelihood ratio for the range of pH values that includes 7.00, which is 6.72 (Table 2) . The posttest odds is 0.43 x 6.72 = 2.89.
     
   • The posttest probability is calculated by converting the posttest odds (2.89) into the posttest probability: 2.89/(1 + 2.89) = 0.74 or 74%.
     
   
   
3. Continuous likelihood ratios to estimate the probability of pleurodesis failure for a patient with a pleural fluid pH of 7.00:
   • If a clinician has a 30% estimate of pretest probability of failure of pleurodesis, the pretest odds becomes 0.30/(1 – 0.30), which equals 0.43.
     
   • To calculate the posttest odds of pleurodesis failure, the pretest odds of failure (0.43) is multiplied by the continuous likelihood ratio for the measured pH value of 7.00. The logistic equation for pleurodesis failure, which is exp [– 5.019(measured pH – 7.296)], derives a continuous likelihood ratio of 4.41. The posttest odds becomes 0.43 x 4.41 = 1.90.
     
   • The posttest probability is calculated by converting the posttest odds (1.90) into the posttest probability: 1.90/(1 + 1.90) = 0.66 or 66%.
     
   
   

	Footnotes

 
Abbreviations: ATS = American Thoracic Society; CI = confidence interval; ERS = European Respiratory Society

This investigation was primarily performed at Medical University of South Carolina.

Received for publication June 5, 2002. Accepted for publication November 11, 2002.

	References

TOP Abstract Introduction Materials and Methods Results Discussion Appendix References

 

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This Article Abstract Full Text (PDF) Free Submit a response Alert me when this article is cited Alert me when eLetters are posted Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Add to My Personal Article Archive Download to citation manager Citing Articles Citing Articles via ISI Web of Science (6) Citing Articles via Google Scholar Google Scholar Articles by Heffner, J. E. Articles by Brown, L. K. Search for Related Content PubMed PubMed Citation Articles by Heffner, J. E. Articles by Brown, L. K.