Bounded Integer Modeling of Symptom Scales Specific to Lower Urinary Tract Symptoms Secondary to Benign Prostatic Hyperplasia

Abstract

The International Prostate Symptom Score (IPSS), the quality of life (QoL) score, and the benign prostatic hyperplasia impact index (BII) are three different scales commonly used to assess the severity of lower urinary tract symptoms associated with benign prostatic hyperplasia (BPH-LUTS). Based on a phase II clinical trial including 403 patients with moderate to severe BPH-LUTS, the objectives of this study were to (i) develop traditional pharmacometric and bounded integer (BI) models for the IPSS, QoL score, and BII endpoints, respectively; (ii) compare the power and type I error in detecting drug effects of BI modeling with traditional methods through simulation; and (iii) obtain quantitative translation between scores on the three abovementioned scales using a BI modeling framework. All developed models described the data adequately. Pharmacometric modeling using a continuous variable (CV) approach was overall found to be the most robust in terms of type I error and power to detect a drug effect. In most cases, BI modeling showed similar performance to the CV approach, yet severely inflated type I error was generally observed when inter-individual variability (IIV) was incorporated in the BI variance function (g()). BI modeling without IIV in g() showed greater type I error control compared to the ordered categorical approach. Lastly, a multiple-scale BI model was developed and estimated the relationship between scores on the three BPH-LUTS scales with overall low uncertainty. The current study yields greater understanding of the operating characteristics of the novel BI modeling approach and highlights areas potentially requiring further improvement.

Keywords: BPH; BPH impact index; International Prostate Symptom Score; LUTS; Quality of life.

Fig. 1

Power and type I error in detecting a drug effect for the four developed pharmacometric models describing the International Prostate Symptom Score (IPSS) under four different simulation models and varying trial sample sizes. Five hundred trial replicates were generated under each sample size for both power and type I error estimation. Model IPSS-A used a continuous variable (CV) approach with a combined residual error model. The bounded integer (BI) model IPSS-B did not contain inter-individual variability (IIV) in the BI variance function (g()), BI model IPSS-C contained both IIV in g() as well as a Drift parameter, while IPSS-D contained IIV in g() but did not estimate a Drift parameter.

Fig. 2

– Power and type I error in detecting a drug effect for the three developed pharmacometric models describing the Quality of Life (QoL) score under four different simulation models and varying trial sample sizes. 500 trial replicates were generated under each sample size for both power and type I error estimation. Model QoL-A used an ordered categorical (OC) approach. The bounded integer (BI) model QoL-B did not contain inter-individual variability in the BI variance function (g()) while BI model QoL-C did

Fig. 3

Power and type I error in detecting a drug effect for the three developed pharmacometric models describing the BPH impact index (BII) score under three different simulation models and varying trial sample sizes. Five hundred trial replicates were generated under each sample size for both power and type I error estimation. Model BII-A used a continuous variable (CV) approach with an additive residual error model. Model BII-B used an ordered categorical (OC) approach. Bounded Integer (BI) model BII-C did not contain inter-individual variability in the BI variance function (g())

Fig. 4

Schematic representation of the relationship between scores of the International Prostate Symptom Score (IPSS), quality of life (QoL), and the benign prostatic hyperplasia impact index (BII) scales in the joint bounded integer model. The probits of the IPSS were used as reference cut-offs. The bold red and green vertical lines indicate the estimated cut-offs for the QoL and BII scores, respectively, along with their relative standard errors. Back translation of latent z-score values to observe score values allowed for mapping of scores