Clinical Applications for Change-Point Analysis of Herpes Zoster Pain

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1 510 Journal of Pain and Symptom Management Vol. 23 No. 6 June 2002 Original Article Clinical Applications for Change-Point Analysis of Herpes Zoster Pain Renee A. Desmond, PhD, Heidi L. Weiss, PhD, Ramin B. Arani, PhD, Seng-jaw Soong, PhD, Martin J. Wood, MD, Paul A. Fiddian, MD, John W. Gnann, MD, and Richard J. Whitley, MD Medical Statistics Section (R.A.D., H.L.W., S.-j.S.), Department of Medicine, Comprehensive Cancer Center, University of Alabama at Birmingham, Birmingham, Alabama, USA; Janssen Research Foundation (R.B.A.), Titusville, New Jersey, USA; Departments of Infection and Tropical Medicine (M.J.W.), Birmingham Heartlands Hospital, Birmingham, UK; Sandiway (P.A.F.), UK; and Department of Pediatrics (J.W.G., R.J.W.), Children s Hospital, University of Alabama at Birmingham, Birmingham, Alabama, USA Abstract Pain is the most frequent and disabling complication of herpes zoster. The analysis of pain severity data is complicated by the nonlinear rate of resolution. Further, three distinct phases characterize pain resolution acute, subacute, and chronic. Using two clinical trial datasets as the bases for analyses, the rates of baseline pain resolution were computed across each of three phases and compared for age, severity of pain at onset, and number of lesions at baseline. The results defined transition points of for the subacute phase and days for the chronic phase. The model demonstrated a treatment effect of valiciclovir (VACV) during the subacute phase as compared to acyclovir (ACV) (P 0.006) and supports effects of age, baseline pain and number lesions on pain cessation rates in the acute phase. This model verifies three phases of zoster pain and delineates the impact of treatment and other factors on the phase-specific rates of pain cessation. J Pain Symptom Manage 2002;23: U.S. Cancer Pain Relief Committee, Key Words Herpes zoster, bootstrap, piece-wise exponential distribution, survival analysis Introduction The most disabling complication from herpes zoster in patients is prolonged pain, which occurs in about 9 34% of patients. 1 While the incidence of herpes zoster is highest in immunocompromised patients, the severity of pain is greatest in the elderly. Given that pain is the Address reprint requests to: Renee A. Desmond, PhD, Biostatistics Unit, Comprehensive Cancer Center, 1824 Sixth Avenue South, WTI 153, Birmingham, AL , USA. Accepted for publication: September 4, most frequent and severe complication of herpes zoster, this variable is the primary outcome of most clinical trials; secondary endpoints include quality-of-life parameters. Three models of pain resolution have been considered. The classic two-phase model poses difficulty in distinguishing acute from chronic pain (i.e., postherpetic neuralgia or PHN). 2 Accordingly, Wood et al. and The International Herpes Management Forum proposed a second model. This model considers pain as a continuum incorporating acute, subacute, and chronic phases in a unified Kaplan Meier survival analysis. 3 The major disadvantage of U.S. Cancer Pain Relief Committee, /01/$ see front matter Published by Elsevier, New York, New York PII S (02)

2 Vol. 23 No. 6 June 2002 Change-Point Analysis of Herpes Zoster Data 511 the latter approach is that all phases of pain are combined such that possible treatment effects specific for each phase cannot be examined separately. Others also have suggested a model of pain resolution that is divided into three phases: acute (0 30 days), subacute ( days) and chronic (120 days). 4 Using these arbitrarily defined transition points to express the switch from acute to subacute, and from subacute to chronic, phases of pain may introduce bias in the assessment of treatment effects on the duration of PHN. In most clinical studies of herpes zoster, the primary endpoint is often the rate of pain cessation between two or more treatment groups. Plausibly, the effect of a treatment may vary according to each specific phase of pain for instance, having the greatest impact on the acute phase. Therefore, the effect of any treatment regimen designed to reduce the pain of herpes zoster should be examined for each phase, while controlling for the effect of the other phases. Time to event models, such as Kaplan Meier or Cox regression, combine the phases of pain when examining treatment effects and do not specify the functional form of the survival distribution. Time-dependent covariates in Cox regression model may be one remedy to interactions between a treatment effect and time, although the transition points between phases cannot be estimated. We propose using a model that computes the relative rate of pain cessation across each specific phase of pain resolution, as well as across subgroups of interest. 5 The parameter of interest is lambda ( ) which is the slope of pain resolution. The transition point between phases and can be quantified for a specific phase and population. In clinical trials of the pain of herpes zoster, the comparison of treatment effects on the latter stages of pain are most relevant. The piece-wise exponential model unifies PHN and can help delineate covariate effects. The model-based estimates can also be used in clinical trial design in order to estimate sample sizes that may target an outcome for a specific phase while controlling for the effect of other covariates. Methods Study Population The data used for these analyses are derived from two large clinical trials of therapeutic interventions for herpes zoster. The first population consists of 1141 patients 50 years old enrolled in a controlled clinical trial of acyclovir (ACV) versus valiciclovir (VACV). 6 The Kaplan Meir survival curves for this clinical trial derived from raw data are shown in Figure 1. The second population consists of 1897 patients 18 years old enrolled in an open-labeled evaluation of VACV in the treatment of herpes zoster. 7 Cox Model The Cox proportional hazards model assumes that any patient whose value on a particular covariate is not equal to the mean value will have a hazard proportional to the hazard at time t denoted as h o (t). The proportionality of the hazard function is an assumption that cannot necessarily be substantiated. Furthermore, the form of the underlying survival function is not specified. If one postulated that a given covariate (i.e., drug intervention) had a different effect across time, the proportional hazard assumption would be violated. One possible remedy would be to add a time-dependent covariate to the model representing the interaction of the covariate and time. As an example, we can postulate two dummy variables, coded as 1 when the times were days and 120 days, respectively. Note that the investigator must specify the transition point for the interaction terms after reviewing the plot of the survival distribution. The interaction between these two variables and treatment group can be included as effects in the model. Fig. 1. Kaplan Meier curves of the time to cessation of pain in patients with herpes zoster treated with oral valiciclovir or oral acyclovir, VACV-7, valiciclovir at 1000 mg for 7 days; VACV-14, valiciclovir at 1000 mg three times daily for 14 days; ACV-7, acyclovir at 800 mg five times daily for 7 days.

3 512 Desmond et al. Vol. 23 No. 6 June 2002 Piecewise-Exponential Model Plotting the survival function on a logarithmic scale, the appropriateness of the exponential model is illustrated in Figures 2 and 3 plots of data from the two study populations on a log scale. The log-survival function is linear in time and that makes it more amenable to visually detecting differences in hazard rates or slopes in treatment groups. The shape of the survival function suggests that there are three linear phases. In each instant of time phase, the instantaneous probability of the event is the same. If the constant hazard rate is, the survival curves if S(t) e t and the expected length of survival is 1/. The phase specific model as developed by Arani 5 can be expressed in terms of the hazard function as: htλτ (,, 1, τ 2, ) = λ 1, if 0 t τ 1 λ 2, if τ 1 t τ 2 λ 3, if τ 2 t (1) where 1 ( 1, 2, 3 ) and 1 0, j 1, 2, 3 represents the hazard rate for the jth phase. Or, in terms of the survival function: Stλτ (,, 1, τ 2, ) = exp [ λ 1 t] exp [ λ 1 τ 1 λ 2 ( t τ 1 )] exp [ λ 1 τ 1 λ 2 ( τ 2 τ 1 ) λ 3 ( t τ 2 )] (2) if 0 t τ 1 if τ 1 t τ 2 if τ 2 t The computation of lambda is obtained through the maximum likelihood function and the standard error of the change-point estimate is obtained through a bootstrapping method. 5 In clinical trials, one of the main objectives is compare the efficacy of two treatments. The proposed model can be used to test a treatment effect within each phase of zoster-associated pain. The can be illustrated by the comparison of ACV and VACV in the first data set. Hence, letting X 1 if a patient is administered VACV and X 0 if ACV is administered, the hazard rate for the ith phase can be written as i ACV VACV X i and comparison of the effect amounts to testing that ACV 0 in each phase. Fig. 2. Log of the Kaplan Meier curves of time to cessation of pain for the VACV vs. ACV trial. Results Descriptive The mean age of patients in the ACV vs. VACV trial was 69 years and the majority of the patients were Caucasian, as shown in Table 1. The majority ( 50%) reported moderate pain or worse at presentation and most ( 80%) had experienced a prodrome prior to presentation. Patients in the open-labeled VACV trial had a mean age of 54 years and most reported a prodrome and either moderate or severe pain at presentation, as shown in Table 2. Cox Model Utilizing the Cox approach for the clinical trial of ACV versus VACV provides an overall treatment effect of 1.21, P That is the rate of cessation of pain among the VACV group was 20% greater than for those patients treated with ACV. The previous report of this trial 6 showed that VACV for 7 or 14 days significantly Fig. 3. Log of Kaplan Meier curves of the time to cessation of pain in patients with herpes zoster treated in the open VACV study stratified by age group ( 50 years vs. 50 years).

4 Vol. 23 No. 6 June 2002 Change-Point Analysis of Herpes Zoster Data 513 Table 1 Demographic Characteristics for ACV versus VACV Trial Characteristic VACV, 7-day n (%) VACV, 14-day n (%) ACV n (%) Sex Male 115 (29.9) 194 (50.9) 144 (38.3) Female 229 (70.1) 187 (49.1) 242 (61.7) Mean Age, yrs (range) 69 (49 93) 68 (50 99) 68 (50 98) Race White 362 (94.3) 364 (95.5) 354 (94.4) Black 13 (3.4) 10 (2.6) 12 (3.2) Other 9 (2.3) 7 (1.8) 10 (2.7) Pain at Presentation Very mild 81 (21.1) 88 (23.1) 84 (22.3) Mild 79 (20.6) 84 (22.0) 86 (22.9) Moderate 173 (45.1) 167 (43.8) 154 (41.0) Severe 49 (12.8) 39 (10.2) 49 (13.0) Missing 2 (0.5) 3 (0.8) 3 (0.8) Prodrome Present 314 (81.8) 313 (82.2) 310 (82.4) Absent 70 (18.2) 67 (17.6) 66 (17.6) Missing 0 1 (0.3) 0 Note: One 49-year-old patient was inadvertently enrolled in the study. accelerated the resolution of pain (P and P 0.03) compared to ACV respectively, so the two VACV groups were combined in the current analysis. Introduction of treatment versus time covariates into the model for the day time period and 120 day period shows that there is a larger medication effect during the subacute phase (HR (hazard ratio) 1.16 vs. HR 1.12), but the P value was not significant (P 0.36). There was no difference in treatment for the chronic phase (P 0.94). Table 2 Demographic Characteristics for Open-Labeled VACV Trial (n 1897) Characteristic n (%) Sex Males 897 (47.0) Females 1000 (53.0) Mean Age, yrs (range) 54.0 (18 95) Race White 1629 (86.0) Black 13 (1.0) Other 255 (14.0) Pain at Presentation No pain 202 (11.0) Noticeable 41 (2.0) Mild 268 (14.0) Moderate 514 (27.0) Severe 498 (26.0) Very severe 192 (10.0) Missing 182 (10.0) Prodrome Present 1581 (83.3) Absent 316 (16.7) Piecewise-Exponential Model Two analytic approaches were considered for the piecewise exponential model, one with unknown transition times and the other with known transition times of 1 30 and The bootstrap estimates of the transition times of the study populations are given in Table 3. For Study 1 (VACV vs. ACV), the transition time estimates are (SE 3.34) and (SE 11.9). For Study 2 patients (VAC ) 50 years, the transition time estimates are (SE 3.33) and (SE 3.06). Finally, the change-point estimates for Study 2 patients 50 years population are (SE 3.33) and (SE 1.29). The hazard rate estimates and standard error for each phase under estimated changepoints are tabulated in Table 4. The trend is for a decrease in hazard rate (rate of pain cessation/day) with respect to phases over time. Table 5 defines the effect of covariates phase-specific failure hazard rates using known transition times of 1 30 and for Table 3 Bootstrap Estimates ( SE) of Change Points in Study Populations Study Population 1 SE 2 SE VACV vs. ACV VACV 50 years VACV years

5 514 Desmond et al. Vol. 23 No. 6 June 2002 Table 4 Hazard Estimates for Each Phase in Study Populations Study Population 1 (SE) 2 (SE) 3 (SE) VACV vs. ACV (0.0008) (0.0006) (0.0014) VACV 50 years (0.0010) (0.0008) (0.0014) VACV years (0.0019) (0.0023) (0.0048) Study 1. VACV significantly impacted pain during the subacute phase. The hazard rates for ACV and VACV respectively are.0092 and.0124 during the subacute phase. Younger patients ( 65 years) have a significantly accelerated rate of pain cessation as compared to older patients during both the acute and subacute phases. Also, those patients who report no baseline pain but who subsequently develop pain have a significantly faster rate of pain cessation during the acute phase compared to those who report baseline pain (P 0.001). The only other significant factor is the number of lesions at clinical presentation. Patients reporting 25 lesions at presentation have a slower rate of cessation of pain during the acute phase compared to those with 25 lesions at baseline (P 0.032). Among older patients ( 50 years) in Study 2, there is a significant effect of older age ( 65 years) on the resolution of pain during the acute phase, as shown in Table 6. Patients with pain at the time of presentation also experienced a significantly slower rate of pain cessation during the acute phase compared to patients with no baseline pain (P 0.001), as in Study 1. Among younger patients in Study 2 there was also an age effect during the acute phase (Table 7). Younger patients (18 35 years) had a faster rate of pain cessation compared to patients years old during the acute phase (P 0.001). Also, baseline pain had a similar impact during the acute phase as seen previously. Taking the hazard rates from the models for Tables 6 and 7 for all patients in Study 2 and plotting by age group, the fastest pain resolution occurred among patients aged years during the acute phase (Figure 4). Patients 65 years had the slowest rate of pain resolution during the acute phase. Stratifying the Table 5 Covariate Comparison of s with Respect to Different Phases in the Clinical Trial of ACV vs. VACV by Age Group Estimate Estimate Difference P Patient Age Phase Phase Phase Baseline Pain Yes No Phase Phase Phase Treatment Group VACV ACV Phase Phase Phase Number of Lesions at Baseline Phase Phase Phase Rash Onset 48 hrs 48 hrs Phase Phase Phase

6 Vol. 23 No. 6 June 2002 Change-Point Analysis of Herpes Zoster Data 515 Table 6 Covariate Comparison of s with Respect to Different Phases in the Open VACV Study of Herpes Zoster by Age Group for Patients 50 Years Estimate Estimate Difference P Patient Age Phase Phase Phase Baseline Pain Yes No Phase Phase Phase open VACV patients on baseline pain and age group shows that older patients ( 50 years) with baseline pain have the slowest pain resolution compared to patients 50 years with no baseline pain, as shown in Figure 5. Discussion These results demonstrate that large therapeutic databases of patient with herpes zoster who are entered into prospective treatment trials predict three phases of pain resolution. The results obtained were very similar for change points and hazard estimates for each phase. The computed bootstrap estimates for the three populations overlap the definitions proposed by Dworkin and Portenoy for acute herpetic neuralgia of 30 days and postherpetic neuralgia of 120 days. 4 The classification of pain resolution into three phases would suggest that acute herpes zoster and PHN have different pathophysiologic mechanisms. Atrophy of the dorsal horn (a central nervous system change) has been found at autopsy in patients with PHN but not in those without it. 8 In the acute phase the dorsal root ganglia show inflammation, hemorrhagic necrosis, and neural loss. The subacute phase is likely a transition phase or may be a combination of both. For a review of pathogenesis consult Kost and Straus 9 and Dworkin and Portenoy. 1 This model can be applied to define drug effect such as VACV versus ACV using estimates for transition points. The model illustrated a treatment effect during the subacute phase for a clinical trial of VACV vs. ACV. It is likely that the antiviral effects would be linked during the acute and subacute phases. This information is valuable in the design of new studies of pain cessation in that the recruitment of subjects can be maximized to detect a difference during the phase in which the greatest treatment effect is to be observed. Also, the model may be useful for examining duration of treatment effects, such as that noted by Bowsher in a study of pain cessation rates at 6 months for patients receiving ami- Table 7 Covariate Comparison of s with Respect to Different Phases in the Open VACV Study of Herpes Zoster by Age Group for Patients Years Estimate Estimate Difference P Patient Age Phase Phase Phase Baseline Pain Yes No Phase Phase Phase Note: Median age was 35 years.

7 516 Desmond et al. Vol. 23 No. 6 June 2002 Fig. 4. Phase-specific pain resolution rate per day ( ) for patients in the open VACV study of herpes zoster by age at presentation and phase using standard cutpoints (0, 30, 120). triptyline therapy for 90 days after diagnosis of herpes zoster. 10 Sample size calculations could be performed based on examination of survival function distributions, change-point estimates, and hypothesized ratio of phase-specific pain cessation rates between groups. Furthermore, these analyses provide guidance for regulatory officials at the Food and Drug Administration. Effects of drugs can be specifically assigned to different phases of disease resolution. Such knowledge could be of value in the precise labeling of new medications. Fig. 5. Phase-specific pain resolution rate per day ( ) for patients in the open VACV study of herpes zoster by age at presentation and baseline pain using standard cutpoints (0, 30, 120). A recent review of herpes zoster pain suggests that the risk factors for acute zoster pain and PHN differ. 1 Wood suggested that the shape of the pain duration curve is not linear, but roughly exponential. 11 Older age is associated with a greater duration of chronic pain. 1 The current model supports an age effect on pain cessation rate as well as an effect of pain at clinical presentation and the number of lesions at baseline on pain cessation. In conclusion, this model verifies three phases of zoster pain and delineates the impact of treatment and other factors on the rate of pain cessation. References 1. Dworkin RH, Portenoy RK. Pain and its persistence in herpes zoster. Pain 1996;67: Portenoy RK, Duma G, Foley KM. Acute herpetic and postherpetic neuralgia: clinical review and current management. Ann Neurol 1986;20: Wood MJ, the Herpes Zoster Clinical Trial Consensus Group. How should zoster trials be conducted? J Antimicrobial Chemo 1995;36: Dworkin RH, Portenoy RK. Proposed classification of herpes zoster pain. Lancet 1994;343: Arani RB, Soong S-J, Weiss HL, et al. Changepoint survival analysis of pain data. Stat Med 2001; 20: Beutner KR, Friedman DJ, Forszpaniak C, et al. Valiciclovir compared with acyclovir for improved therapy for herpes zoster in immunocompetent adults. Antimicrob Agents Chemother 1995;39: Decroix J, Partsch H, Gonzalez R, et al. Factors influencing pain outcome in herpes zoster: an observational study with valaciclovir. Valiciclovir International Zoster Assessment Group (VIZA). J Eur Acad Dermatol Venereol 2000:14: Watson CPN, Deck JH, Morshead C, et al. Postherpetic neuralgia: further post-mortem studies of cases with and without pain. Pain 1991;44: Kost RG, Straus SE. Drug therapy: postherpetic neuralgia pathogenesis, treatment and prevention. N Engl J Med 1996:335: Bowsher D. The effects of pre-emptive treatment of postherpetic neuralgia with amitriptyline: a randomized, double-blind placebo-controlled trial. J Pain Symptom Manage 1997:13: Wood MJ. How should we measure pain in herpes zoster? Neurology 1995;45(Suppl 8):S61 S62.

A Mixed Model for Factors Predictive of Pain in AIDS Patients with Herpes Zoster

410 Journal of Pain and Symptom Management Vol. 17 No. 6 June 1999 Original Article A Mixed Model for Factors Predictive of Pain in AIDS Patients with Herpes Zoster Renée A. Harrison, PhD, Seng-jaw Soong,