Introduction

In this study, I calculate and analyze the historical lifetimes of drugs in England over the period 1980 to 2007. I apply the estimates of drug lifetimes to two areas: to inform the time horizon for value of information analysis of drugs, and to cost-effectiveness analysis.

I am aware of just one study, by Danzon and Kim 1, which is related to the estimation of the historical lifetimes of drugs. They investigated the sales volume of drugs at the level of the individual chemical, and found that the volume of sales of individual drugs over time is generally ∩-shaped 1. The volume of drugs sold typically increases in the first decade after drug launch, reflecting the diffusion of the new drug after launch. The volume in the second decade after launch, typically after patent expiry, declines as patients switch to newer, more effective, drugs 1, 2. They found that the sales volume of “global” chemicals (defined as molecules that were available in all seven countries they studied) on average peaked at about 20 to 30 years in the UK, and generally slightly earlier in the other countries considered: Canada, Germany, France, Italy, Japan, and USA 1. Although they do not present data on the typical lifetimes of drugs, their findings suggest that lifetimes are typically more than 30 years. Nevertheless, the generality of their findings is limited by the fact that they analyzed only high volume, “global” chemicals, and that their data are now rather out of date, relating to the period 1981 to 1992.

Value of Information and Drug Lifetimes

Value of information analysis provides an analytic framework to establish the value of acquiring additional information to inform a decision problem 3. It is increasingly being used in health technology assessment 4. For example, the expected value of perfect information (EVPI) has been used to establish a necessary condition for conducting further research and for identifying research priorities 5, 6.

Methods for estimating the value of information are described in full elsewhere 7. Therefore, here, I outline only the main points. The cost-effectiveness of a treatment option j can be expressed in terms of net benefit, NBj = λQj−Cj, where λ is the cost-effectiveness threshold, and Qj and Cj are the discounted health benefit and cost, respectively. The optimal decision with current information is to choose the treatment with the maximum expected net benefit maxjEθNB(j,θ) 8. With perfect information, the parameters θ, used to estimate Qj and/or Cj, are known, hence the decision-maker should select the treatment that maximizes the net benefit given the particular value of θ, maxjNB(j,θ). Nevertheless, the net benefit NBj is uncertain because some model parameters, θ, are uncertain. The EVPI for an individual patient is the difference between the expected value of the decision made with perfect information about the θ and the decision made given uncertainty in θ7:

This can be generalized to the value of information of particular groups of parameters in the decision problem (EVPPI) and the expected value of sample information 7-9. All these measures of the value of information must consider the future patient population that can benefit from it. The population expected value of information (PEVPI) is typically calculated based on a function of the effective lifetime of the treatment, the period over which information about the decision will be useful [T], the population incidence at time t over this period (It), and the discount rate (r). For example, the PEVPI is the discounted sum of the EVPI per patient 7;

(1)

It is very important to estimate the time horizon T as accurately as possible because this is an important determinant of PEVPI (Fig. 1). Indeed, at a discount rate of 3.5%, the value currently used in England 10, assuming equal population incidence each year, the population EVPI is about 29 times greater than the per-year EVPI (defined as the EVPI per patient multiplied by the population incidence per year) as T tends to infinity (Equation 1; Fig. 1). Clearly, the time horizon has a substantial impact on estimates of PEVPI. Of course, the choice of T might not change a decision to conduct research, but in some circumstances it will. If additional research costs more than 29 times the per-year EVPI, then it will not be cost-effective to conduct this research. Notice that we do not need to specify T accurately for times greater than about 50 years, because at such times, the ratio of population to per-year EVPI is close to the asymptote of 29.

Population expected value of perfect information (EVPI) as a function of information time horizon T calibrated so that the per-year EVPI = 1. The relationship is obtained from Equation 1, with discount rate = 3.5%. The vertical lines represent the lower 95% confidence interval (CI), the mean, and the upper 95% CI of the mean drug lifetime over all drugs (see Results).

Unfortunately, the time horizon is very uncertain 11. Indeed, existing estimates, typically about 10 to 20 years, are seemingly arbitrary 12. These approaches implicitly use the time horizon as a proxy for future changes in technology, prices, and information. Given the dearth of empirical evidence for T, recent methodological literature recommends using finite time horizons with population EVPI presented for a range of possible values of T9, 12, 13.

I am aware of just one empirical estimate of the time horizon, given by Hall and Platell 14, and discussed by Philips et al. 12 in the context of the value of information. Hall and Platell 14 investigated the relationship between the probability that statements regarding general surgery are still considered true as a function of the time from when the statement was made. They estimated the half-life of the truth of such statements as 45 years, which assuming an exponential distribution, gives a mean of 64 years.

Clearly, there will be uncertainty in any estimate of the time horizon T, and this should be included in estimates of population EVPI. It is especially important to allow for uncertainty because, given discounting, the population EVPI assuming the mean value of T does not necessarily equal the EVPI weighted according to the range of values of T12. This is because lower than expected sampled values of T reduce PEVPI substantially, but higher than expected values increase PEVPI more modestly (Fig. 1).

Some types of information may apply specifically to a single health technology decision (e.g., the mean survival of patients taking a certain drug). Other information may be more general, for example, concerning the natural history of a disease 12. A shorter time horizon may be more appropriate in the former case and a longer time horizon in the latter case. In this article, I analyze the lifetimes of pharmaceutical in England in the past. I argue that this information is more appropriate for estimating the time horizon in the former case (i.e., for information concerning a single drug).

Cost-Effectiveness Analysis and Drug Lifetimes

Estimates of the future lifetimes of drugs are useful to inform two methodological frameworks for cost-effectiveness analysis that have been suggested recently: those of Salomon et al. 2 and Hoyle and Anderson 15. These frameworks both satisfy the National Institute for Health and Clinical Excellence (NICE) guidance 10 for cost-effectiveness analysis that “the time horizon should be sufficient to reflect important cost and benefit differences between the technologies being compared.”

When a decision is uncertain and there is evidence that guidance may be reversed in the future, for example, if new evidence suggests that the technology is not cost-effective or if another technological development makes it obsolete, then it may be most cost-effective to wait until the uncertainties are resolved or until additional research is reported 2, 13, 16 An option-pricing approach may be appropriate, in which the incremental cost-effectiveness ratio (ICER) is adjusted to reflect the magnitude of uncertainty in parameter values, the extent to which decision deferral is possible, and the extent to which the decision to implement is irreversible 16. Salomon et al. 2 suggest the following methodology to allow for the possibility that a further technology may be introduced in the future. Suppose we compare the cost-effectiveness of a new technology A against an existing technology (or indeed, no treatment). There are then two options: either do or do not adopt technology A. Salomon et al. 2 suggest that we could model a third option of deferred treatment with some further, more effective technology B, which is likely to be introduced several years in the future. The third option is then: do not adopt technology A, but wait several years and then adopt technology B. To model this option, we can either: 1) assume we know with complete certainty the effectiveness and cost of technology B, and when it will become available; or 2) allow for uncertainty in these quantities by stochastic modeling. Now, this article informs the expected lifetime of technology A, assuming that the technology is a drug, and that the lifetime of technology A is typical of the historical lifetimes of drugs in England. We could then estimate the date of introduction of the new, improved technology B as the expected lifetime of technology A (i.e., technology B is introduced when technology A is phased out).

In the second methodological framework, Hoyle and Anderson 15 have recently noted that economic evaluations of health technologies typically simulate only the prevalent cohort or the current incident cohort of patients. The prevalent cohort is defined as those patients eligible for the new technology at the time the technology is introduced 15. Any given patient will be eligible for the new technology from the time when the technology is first clinically appropriate (e.g., just diagnosed with multiple sclerosis and eligible for drug treatment, or when first eligible for a hip replacement) until the time when the new technology is no longer appropriate (e.g., patient dies, or the disease has reached such a severe state that the drug is no longer effective, or the patient is too old to receive a hip replacement). The incident cohort starting t years in the future (i.e., t years after the date of introduction of a technology) is defined as comprising those patients who first become eligible for the new technology (e.g., diagnosed) t years in the future 15. The prevalent cohort is small relative to the incident cohort when a technology is appropriate only for a short time window in the life of a patient, for example, for drugs or medical devices used to treat acute conditions, or for screening people at certain fixed ages 15.

When the discount rates for costs and benefits differ, as currently in The Netherlands and Belgium 15, all future incident cohorts should be modeled, because the ICER (cost per QALY or cost per life-year) assuming all future incident cohorts are different to the ICER assuming just a single incident cohort (Equation 2) 15. In particular, when the discount rate for benefits is lower than for costs, the ICER for all future incident cohorts is lower than the ICER for the first incident cohort. Next, when the prevalent cohort is large compared to a single incident cohort, both the prevalent cohort and all future incident cohorts should be modeled 15. Now, suppose this is not true, we ignore the prevalent cohort 15:

(2)

where:

•

nt = number of patients eligible for the new technology at the start of the incident cohort starting t years in the future, relative to the number of eligible patients at the start of the first year;

•

pt = probability an eligible patient is given the new technology t years in the future;

•

v C, vB = costs and benefits discount factors over a year;

•

T = expected lifetime of new technology in years.

When either ntpt is equal for all t, or follows a ∩-shaped quadratic curve over time, as is often the case with drug sales, as described above 1, simplifies to (where v stands for either vC or vB), and Equation 2 simplifies to:

(3a)

where:

(3b)

I suggest that the expected lifetime of the technology, T, and the uncertainty in T, where the technology is a drug, can be estimated by the historical lifetimes of drugs as presented in this study. The uncertainty in T can be used for the probabilistic sensitivity analysis.

The objectives of this study are to: 1) estimate the distribution function of the historical lifetimes of drugs in England, for drugs launched from 1981 to 2007; and 2) use this information to parameterize models of the value of information and cost-effectiveness of drugs.

Methods Data

I analyzed the prescription data from the Prescription Cost Analysis for England 17 for the years 1980 to 2007. Prescriptions written by general medical practitioners in England represent the vast majority of prescriptions included 17, and account for the great majority, 75%, of pharmaceutical expenditure in the NHS 18. See Online Appendix for further details of the data.

I analyzed the number of prescriptions written over time at the level of the British National Formulary (BNF) Chemical, because this is the level at which cost-effectiveness analyses are conducted by NICE in England and Wales, and by similar bodies in other countries 19. There are typically several preparations within each BNF Chemical, some branded and some generic. When a new chemical is launched, there may be just a single branded preparation. Later, when the patent expires, generic versions may become available. Before data analysis, it was necessary to correct the data for two types of inconsistency. First, sometimes the same chemical is spelled slightly differently (e.g., amlodipine besilate = amlodipine besylate, amoxicillin = amoxycillin, beclometasone dipropionate = beclomethasone dipropionate). Second, sometimes the same chemical is recorded under completely different names (e.g., alimemazine tartrate = trimeprazine tartrate, dosulepin hydrochloride = dothiepin hydrochloride).

Estimation of Drug Lifetimes

The lifetime of each chemical was defined as the latest year for which prescriptions for the chemical were written minus the launch year of the chemical. As Danzon and Kim 1, I defined the launch year of a chemical in England as the earliest year for which any prescriptions for that chemical were written in England. I analyzed the number of prescriptions written for all 455 chemicals launched from 1981 to 2007. If prescriptions were written in the latest year (2007), the lifetime of the chemical was recorded as being right censored. I discarded those chemicals with very low sales volumes, in particular those with less than 5000 prescriptions written in all years. Were these chemicals included, their estimated lifetimes may be too low, because of the low sales volumes, preparations may have prescriptions written in some years, but not recorded in the database.

I hypothesized that the lifetimes of chemicals would be influenced by three factors: the year of chemical launch, the “sales volume” of the chemical, and the therapeutic area, defined as the BNF Chapter. Therefore, a linear survival regression model of the lifetime of each chemical was fitted, with launch year, log(average number of prescriptions per year + 1) as covariates, and the 15 BNF Chapters (e.g., skin, eye, cardiovascular system, central nervous system) as a factor. Given that many chemicals were launched shortly before 2007 and were still in use in 2007, it was necessary to define the “sales volume” as some function of the number of prescriptions written in the first few years after launch. My definition was the average number of prescriptions written per year, averaged over the first four years after launch. The logarithm of the number of prescriptions was taken because the number of prescriptions is highly skewed. Several statistical distributions were used to model statistical errors: Weibull, lognormal, and log-logistic functions, using the “survreg” survival analysis function in “R” software 20. The choice of statistical distribution was assessed by the Akaike information criteria (AIC) = −2 log-likelihood + 2(P + 1), where P = 2 parameters for all distributions. Model fitting was performed by backward deletion of nonsignificant terms to obtain the minimum adequate model.

Results

Four hundred fifty-five drugs (BNF Chemicals) of medium to high sales volume were launched from the year 1981 onwards. Of these, 67 were no longer used in primary care in England in 2007 (Table 1), and therefore the lifetimes of these drugs were not censored for the statistical analysis. The lifetimes of the remaining 388 drugs were right censored.

Table 1. Lifetimes of the 67 drugs no longer used in primary care in England BNF Chemical BNF Section Launch year Lifetime (years) Prescriptions (,000s)* Acid insulin injection Drugs used in diabetes 1983 6 13 Activated dimethicone Antacids and other drugs for dyspepsia 1998 2 179 Adrenaline hydrochloride Treatment of glaucoma 1982 12 2 Almasilate Dyspep & gastroesophageal reflux disease 1983 4 18 Alprazolam Hypnotics and anxiolytics 1983 3 105 Amethocaine Local anesthesia 1998 7 6 Aminoglutethimide Sex hormones & antag in malig disease 1982 24 11 Amoxapine Antidepressant drugs 1989 17 16 Astemizole Allergic disorders 1983 18 250 Atenolol with thiazides Beta-adrenoceptor blocking drugs 1997 7 15 Betaxolol hydrochloride Beta-adrenoceptor blocking drugs 1984 20 7 Biphasic insulin injection Drugs used in diabetes 1983 15 13 Bismuth salts Preparations for haemorrhoids 1998 1 307 Bromazepam Hypnotics and anxiolytics 1982 4 49 Catheter patency solutions Drugs for genitourinary disorders 1983 23 15 Ceftibuten Antibacterial drugs 1994 6 15 Cerivastatin Lipid-regulating drugs 1997 6 383 Cimetidine with alginate Ulcer-healing drugs 1989 12 61 Cisapride Antispasmod. & other drugs alt.gut motility 1989 17 100 Cyclofenil Hypothalamic & pituitary hormones & antioest 1982 13 1 Desoximetasone Topical corticosteroids 1984 23 13 Dexfenfluramine hydrochloride Drugs used in obesity 1990 8 88 Dextropropoxyphene Analgesics 1982 21 4 Enoxacin Antibacterial drugs 1989 4 4 Fenticonazole nitrate Treatment of vaginal & vulval conditions 1995 8 10 Flosequinan Nit, calc blockers & potassium activators 1992 6 3 Flunitrazepam Hypnotics and anxiolytics 1982 4 84 Formestane Sex hormones & antag in malig disease 1993 10 7 Fosfomycin trometamol Antibacterial drugs 1994 4 6 Guar gum Drugs used in diabetes 1984 21 12 Hydroxyapatite Minerals 1981 23 11 Hydroxyethylcellulose Misc. ophthalmic preparations 1998 8 27 Indoramin hydrochloride Antihypertensive therapy 1998 6 12 Isoconazole nitrate Treatment of vaginal & vulval conditions 1981 20 38 Lactitol Laxatives 1992 11 19 Levocabastine Corti'roids & other antiinflamm. preps. 1996 11 10 Loxapine succinate Drugs used in psychoses & rel. disorders 1990 16 7 Magaldrate Dyspep & gastroesophageal reflux disease 1984 12 5 Mibefradil Nit, calc blockers & potassium activators 1997 2 10 Oxatomide Antihist, hyposensit & allergic emergen 1982 14 5 Oxitropium bromide Bronchodilators 1991 15 112 Papaverine hydrochloride Drugs for genitourinary disorders 1988 18 2 Pirbuterol acetate Bronchodilators 1983 16 32 Pirbuterol hydrochloride Bronchodilators 1983 14 23 Pirenzepine Antisecretory drugs + mucosal protectants 1982 18 10 Piretanide Diuretics 1984 14 32 Pivampicillin with pivmecillinam Antibacterial drugs 1984 11 124 Pseudoephedrine sulphate combinations Systemic nasal decongestants 1982 9 44 Remoxipride hydrochloride Drugs used in psychoses & rel. disorders 1991 7 8 Reproterol hydrochloride Bronchodilators 1981 21 30 Rofecoxib Drugs used in rheumatic diseases & gout 1999 7 999 Salcatonin Drugs affecting bone metabolism 1998 5 6 Semisodium valporate Drugs used in psychoses & rel. disorders 2001 3 48 Sertindole Drugs used in psychoses & rel. disorders 1996 4 3 Sodium pyrrolidone carboxylate Emollient & barrier preparations 1988 12 6 Somatrem Hypothalamic & pituitary hormones & antioest 1986 5 9 Suprofen Drugs used in rheumatic diseases & gout 1983 4 20 Temafloxacin hydrochloride Antibacterial drugs 1992 1 6 Terfenadine Allergic disorders 1982 22 863 Terodiline hydrochloride Drugs for genitourinary disorders 1986 7 208 Thyroxine sodium Thyroid and antithyroid drugs 1998 5 8804 Tocainide hydrochloride Antiarrhythmic drugs 1982 16 5 Troglitazone Drugs used in diabetes 1997 1 6 Urofollitropin Hypothalamic & pituitary hormones & antioest 1981 20 0 Valdecoxib Drugs used in rheumatic diseases & gout 2003 3 81 Xamoterol fumarate Sympathomimetics 1988 13 18 Yellow fever Vaccines and antisera 1991 2 7 * Average number of prescriptions per year averaged over first four years after launch. Estimated Drug Lifetimes

Variation in drug lifetimes was best explained by the Weibull function, as measured by the minimum AIC: AIC(Weibull) = 743.2, AIC(lognormal) = 744.8, AIC(log-logistic) = 743.7. Therefore, statistical errors were modeled by a Weibull distribution. Neither launch year nor BNF Chapter significantly explained any of the variation in drug lifetimes: (χ1 = 1.43, P = 0.23 and χ15 = 23.0, P = 0.08, respectively). Nevertheless, nonsignificance may be a result of the low statistical power, because of the high degree of censorship, rather than because of a true lack of association. Drug lifetimes were significantly (χ1 = 7.68, P = 0.006) shorter with lower sales volumes (log(average number of prescriptions + 1)) (2, 3).

Probability drug in use as a function of time from drug launch. The continuous stepped line is the Kaplan–Meier curve with 95% confidence interval shown by the dashed lines. The Weibull curve best fit is shown by the smooth narrow line. Figure (b) displays the same information as figure (a), but with the time axis rescaled to show the Weibull extrapolation.

Probability drug in use as a function of time from drug launch for drugs with (a) low† and (b) high sales volume. †“Low sales volume” defined as less tha