Estimating what would be an individual's potential response to varying levels of exposure to a treatment is of high practical relevance for several important fields, such as healthcare, economics and public policy. However, existing methods for learning to estimate counterfactual outcomes from observational data are either focused on estimating average dose-response curves, or limited to settings with only two treatments that do not have an associated dosage parameter. Here, we present a novel machine-learning approach towards learning counterfactual representations for estimating individual dose-response curves for any number of treatments with continuous dosage parameters with neural networks. Building on the established potential outcomes framework, we introduce performance metrics, model selection criteria, model architectures, and open benchmarks for estimating individual dose-response curves. Our experiments show that the methods developed in this work set a new state-of-the-art in estimating individual dose-response.
Substantial interpatient variations were demonstrated in the daily doses required to obtain therapeutic gentamicin sulfate serum concentrations in 417 elderly patients. Dosages ranged from 0.3 to 22.0 mg kg day in patients with a normal serum creatinine level. Twenty-five percent of these patients required daily doses higher than the standard regimen of 5 mg kg day, and 33 required less than 3 mg kg day. The drug half-lives in these patients ranged from 0.3 to 32.7 hours, compared with previous reports of 2.5 to four hours. The distribution volumes of these patients ranged from 0.07 to 0.53 L kg, compared with reported values of 0.20 to 0.25 L kg. These wide variations in kinetic variables in elderly patients and the need to obtain narrow ranges in serum concentrations required measuring serum concentrations and individually calculating each patient's dosage requirement early in the treatment course. Doing this consistently produced optimal peak and trough serum levels. Ototoxicity did not occur in any of the patients, and nephrotoxicity may have been drug related in 2 of the elderly patients. ( JAMA 1982;248:3122-3126) ContextMore than 50 million US adults take aspirin regularly for long-term prevention of cardiovascular disease, typically either 81 mg d or 325 mg d. Controversy remains regarding the most appropriate long-term daily dose.ObjectiveTo review the mechanism of action of aspirin and the clinical literature for relationships among aspirin dosage, efficacy, and safety.Evidence AcquisitionA systematic review of the English-language literature was undertaken using MEDLINE and EMBASE (searched through February 2007) and the search term aspirin or acetylsalicylic acid and dose. The search was limited to clinical trials and was extended by a review of bibliographies of pertinent reports of original data and review articles. Published prospective studies using different aspirin dosages in the setting of cardiovascular disease were included.Evidence SynthesisAlthough pharmacodynamic data demonstrate that long-term aspirin dosages as low as 30 mg d are adequate to fully inhibit platelet thromboxane production, dosages as high as 1300 mg d are approved for use. In the United States, 81 mg d of aspirin is prescribed most commonly (60 ), followed by 325 mg d (35 ). The available evidence, predominantly from secondary-prevention observational studies, supports that dosages greater than 75 to 81 mg d do not enhance efficacy, whereas larger dosages are associated with an increased incidence of bleeding events, primarily related to gastrointestinal tract toxicity.ConclusionsCurrently available clinical data do not support the routine, long-term use of aspirin dosages greater than 75 to 81 mg d in the setting of cardiovascular disease prevention. Higher dosages, which may be commonly prescribed, do not better prevent events but are associated with increased risks of gastrointestinal bleeding. The pharmacokinetics of midazolam and its metabolites were studied in 17 patients on mechanical ventilation in a general intensive care unit who were receiving a continuous intravenous infusion of midazolam, adjusted according to the level of induced sedation. Three patients were studied twice. Serum midazolam and α-hydroxymidazolamglucuronide levels were determined during and after infusion. The sedation level was scored on a four-point scale. Half of the observed patients were still drowsy or asleep 10 hours after termination of midazolam infusion. In only one patient was midazolam serum elimination half-life 10 hours. A wide range of midazolam serum levels was associated with adequate sedation, and similarly the midazolam levels at the moment of awakening were highly variable. The serum concentration ratio of midazolam α -hydroxymidazolamglucuronide at the end of the infusion varied from 0.03 to 15.6. Renal function could account for only a part of this variation. Clinical Pharmacology and Therapeutics (1988) 43, 263–269; doi:10.1038 clpt.1988.31