Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Patient time cost function from service use, hours per use and an hourly value of time

p(n, t_trav, t_wait, t_care, w) = C_T

Maps the number of times a patient uses each type of health service, the hours each use takes in travel, waiting and care, and an hourly value of time to the money value of the patient's time in care over a period, per visit and in total. It is the resource costing sum HE-FM-COST-001 with patient hours as the resource and the hourly value as the unit cost, so the package keeps only the steps particular to patient time, which are hours built up from service counts (HE-FM-PTC-001 and HE-CF-PTC-001), the change in an incremental cost-effectiveness ratio when the time cost is added (HE-FM-PTC-002) and a value of time that depends on employment status (HE-FM-PTC-003). Productivity cost is a different cost category. The absence records HE-FN-ABSN-001, HE-FM-ABSN-002 and HE-FM-ABSN-003 value time lost from paid work as lost output, under the human capital approach or within the friction period, whereas patient time cost values the hours spent in care whether they are taken from paid work, unpaid work or leisure, and an hour taken from paid work is counted under one heading only. A value of time from another price year is moved with HE-FM-COST-002, time costs in later years are discounted with HE-FN-DISC-001, and a national total from a mean time cost per patient follows HE-FM-COI-001. Notation follows the Patient Time Cost article.

  • Patient time cost per visit and per year from travel, waiting and care hours

    h_v = t_trav + t_wait + t_care; c_v = w * h_v; C_T = n * c_v

    Adds the hours that one use of a service takes in round-trip travel, waiting and care, values them at the hourly value of time to give a time cost per visit, and multiplies by the number of uses in the period. With n counted over a year the result is the time cost per patient-year. The article's formula sums the same product over K service types; this formula is the term for one service type, and HE-CF-PTC-001 adds the terms for several types with published time estimates. It is HE-FM-COST-001 with a single resource, patient hours, whose unit cost is w.

  • Rise in the ICER when incremental patient time cost is added to health service costs

    dC_T = C_T_new - C_T_comp; ICER_S = ICER_H + dC_T / dE; g_ICER = (ICER_S - ICER_H) / ICER_H

    Takes the incremental cost-effectiveness ratio from the health service view, computed with HE-FM-ICER-001, and adds the incremental patient time cost divided by the same QALY gain, which gives the ratio from a limited societal perspective that counts patient time. Because the QALY gain is unchanged, the rise in the ICER is the incremental time cost over the QALY gain, and the rise as a share of the health service ICER equals the incremental time cost over the incremental health service cost (both derived here from HE-FM-ICER-001). The time cost of each option comes from HE-FM-PTC-001 or HE-CF-PTC-001. In net benefit terms the same step lowers the incremental net monetary benefit of HE-FM-NMB-002 by the incremental time cost, which also covers a QALY gain of zero or below.

  • Patient time cost with time valued by employment status

    v_i = E_i * w_i + (1 - E_i) * w_hp; C_T_i = h_i * v_i

    Values a person's hours in care at the person's own hourly wage when employed for wages and at an hourly value of home production otherwise, the approach Yabroff and colleagues used in a sensitivity analysis, and multiplies by the person's hours from HE-FM-PTC-001 or HE-CF-PTC-001. The base case of the same study used one median wage for everyone, the w of HE-FM-PTC-001, so that each person's time counted equally. In that study the choice cut annual time costs for cancer survivors aged 65 and over to USD 359, against USD 913 in the base case. The value differs from the human capital value of HE-FM-ABSN-002, which values absence from paid work as lost output, usually at gross earnings including employer-paid costs.