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"content": "_cohort = 10 * 1000 # Arbitrary\n\n# Iron-deficiency anemia prevalence, children in India (any severity)\n# Global Burden of Disease 2016, see 'Supplementary data'\np_anemia = Beta(19, 22) # p15=0.38, p85=0.54; beta by quantiles not yet supported\n\n\n\ndef anemia_reduction():\n \"\"\"\n In YLDs per cohort\n \"\"\"\n # Of children with anemia, proportion with mild, moderate, and severe anemia\n p_severity = {\n \"mild\": 48 / 100,\n \"moderate\": 48 / 100,\n \"severe\": 4.1 / 100\n }\n\n # Risk ratio anemia, iron supplementation\n risk_ratio = PERT(0.3, 0.5, 1)\n\n p_cured = {}\n for severity in p_severity:\n p_cured[severity] = p_anemia * p_severity[severity] * risk_ratio\n\n yld = {\n \"mild\": 0.4 / 100,\n \"moderate\": 5.2 / 100,\n \"severe\": 15 / 100\n }\n\n yld_sum = 0\n for severity in yld:\n yld_sum += p_cured[severity] * yld[severity]\n\n return _cohort * yld_sum\n\ndef cognitive_benefits():\n \"\"\"\n In (present value of) units of increase in ln(income) per cohort.\n\n These drive most of the cost-effectiveness.\n \"\"\"\n # The intervention targets all children in a school, but we model\n # cognitive benefits as accruing only to children between ages 3-12.\n # Proportion of targeted children between ages 3-12\n p_children = 65 / 100\n\n # Change in IQ points from short-term supplementation for anemic individuals\n iq_change_sd = LogNormal(0.33 td 2)\n iq_change = iq_change_sd * 15 # Convert to IQ points: 1 SD = 15 IQ points\n\n p_wages_per_point = 1 / 100 # Percentage increase in wages/consumption for every 1 point increase in IQ\n\n # Percentage increase in wages/consumption from increase in IQ from supplementation\n p_wages = iq_change * p_wages_per_point\n\n # Speculative adjustment to assess the long-term benefit of many years of iron\n long_term_adjustment = 10 / 100\n p_wages = p_wages * long_term_adjustment\n\n # Increase in annual ln(consumption) for beneficiaries\n change_ln_cons = math.log(1 + p_wages) - math.log(1)\n\n delay_y = 12 # Average number of years between 'entering fortification program' and beginning of long term benefits\n duration_y = LogUniform(15 td 3) # Duration of long term benefits of fortification (in years)\n\n # Present Value Income Benefits\n discount_rate = Uniform(2/100, 7/100)\n pv_income = pv(discount_rate, delay_y + duration_y, -change_ln_cons) - pv(\n discount_rate, delay_y, -change_ln_cons\n ) # Unit is still changes in ln(income)\n\n # Multiplier for Resource Sharing in Households\n multiplier_resource_sharing = 2\n pv_income = pv_income * multiplier_resource_sharing\n\n # Lifetime Income Benefits for Full Cohort (including non-beneficiaries)\n return _cohort * p_children * p_anemia * pv_income\n\n\ndef altered_malaria_risk():\n \"\"\"\n In deaths per cohort\n \"\"\"\n baseline_deaths_100k = 5.14 # Baseline deaths due to malaria per 100,000 individuals 0-19 in India\n # Convert to per cohort\n baseline_deaths = baseline_deaths_100k * (_cohort / (100 * 1000))\n\n rr = PERT(1, 1.16, 1.5) # Relative risk of malaria mortality with IFA supplementation\n\n direct = baseline_deaths * (rr - 1)\n indirect_per_direct = 50 / 100\n return direct * (1 + indirect_per_direct)\n\n\ndef other_adverse_effects():\n \"\"\"\n In YLDs per cohort\n \"\"\"\n\n p_condition = {\n \"gastro\": (8 + 1 + 33 + 2 + 8) / (23 + 12 + 128 + 2 + 8),\n \"loose_stools\": (1 + 2 + 6 + 2 + 1 + 3) / (36 + 8 + 128 + 6 + 44 + 71),\n \"hard_stools\": (1 + 5 + 0 + 0 + 11 + 0 + 6 + 3) / (31 + 36 + 8 + 182 + 128 + 6 + 44 + 71),\n \"abdominal_pain\": (0 + 4 + 2 + 15 + 1 + 3 + 4) / (120 + 36 + 182 + 128 + 6 + 44 + 71),\n }\n\n yld = {\n \"gastro\": 7.4 / 100,\n \"loose_stools\": 7.4 / 100,\n \"hard_stools\": 7.4 / 100,\n \"abdominal_pain\": 1.1 / 100,\n }\n\n duration = 2 / 365\n\n yld_sum = 0\n for condition in yld:\n yld_sum += p_condition[condition] * yld[condition] * duration\n\n return _cohort * yld_sum\n\n\ndef yld_to_val(yld):\n \"\"\"\n YLDs to units of value. Arbitrary normalization.\n \"\"\"\n return 1 * yld\n\n\ndef ln_cons_to_val(ln_cons):\n \"\"\"\n Units of increase in ln(consumption) to units of value\n \"\"\"\n value_double = Uniform(0.2, 0.8) # Rule of thumb that 1 DALY = 2.5x GDP per capita would give 0.4\n value_1_ln = value_double / math.log(2)\n return value_1_ln * ln_cons\n\n\ndef death_to_val(death):\n \"\"\"\n Deaths to units of value\n \"\"\"\n return 30 * death\n\n\ndef units_value():\n \"\"\"\n In \"units of value\" per cohort (normalized to 1 unit of value = 1 YLD).\n \"\"\"\n\n anemia_ylds_averted = anemia_reduction()\n units_increase_ln_income = cognitive_benefits()\n malaria_deaths = altered_malaria_risk()\n side_effect_ylds = other_adverse_effects()\n\n u_value = {\n \"anemia\": yld_to_val(anemia_ylds_averted),\n \"income\": ln_cons_to_val(units_increase_ln_income),\n \"malaria\": -death_to_val(malaria_deaths),\n \"side_effect\": -yld_to_val(side_effect_ylds),\n }\n\n return sum(u_value.values())\n\ndef cost_effectiveness():\n \"\"\"\n Units of value per $10,000\n \"\"\"\n # Supplementation cost per person treated\n cost_p_p = 2\n cost_cohort = _cohort * cost_p_p\n val_cohort = units_value()\n return val_cohort * (10 * 1000 / cost_cohort)\n\n\ndef ratio_givedirectly():\n \"\"\"\n Cost-effectiveness ratio vs GiveDirectly\n \"\"\"\n # GiveDirectly units of increase in ln(consumption) for each $10,000 donated\n gd_ln_cons = 25\n return cost_effectiveness() / ln_cons_to_val(gd_ln_cons)\n\n\ndef pv(rate, nper, pmt):\n temp = math.pow((1 + rate), nper)\n fact = (temp - 1) / rate\n return -(pmt * fact) / temp\n\n\nvalue_per_10_000_usd = cost_effectiveness()\nmultiples_of_cash = ratio_givedirectly()"
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