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<!-- DFIN ActiveDisclosure(SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date      : 2020-05-11T18:49:23.8070616+00:00 -->
<!-- Version            : 5.0.1.385 -->
<!-- Package ID         : a22cc2082e99440c990dc219e865825f -->
<!-- Copyright (c) 2020 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="kod_PrincipalPaymentsOfTenantImprovementAllowancePayable" name="PrincipalPaymentsOfTenantImprovementAllowancePayable" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_LiabilityRelatedToSaleOfFutureRoyaltiesTextBlock" name="LiabilityRelatedToSaleOfFutureRoyaltiesTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_LiabilityRelatedToSaleOfFutureRoyaltiesAbstract" name="LiabilityRelatedToSaleOfFutureRoyaltiesAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_RisksAndUncertaintiesPolicyTextBlock" name="RisksAndUncertaintiesPolicyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_LiabilityRelatedToSaleOfFutureRoyaltiesPolicyTextBlock" name="LiabilityRelatedToSaleOfFutureRoyaltiesPolicyTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock" name="ScheduleOfAccruedAndOtherCurrentLiabilitiesTableTextBlock" type="nonnum:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_CappedPercentageOfRoyaltyOnFutureNetSales" name="CappedPercentageOfRoyaltyOnFutureNetSales" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_RelatedPartyTransactionOwnershipPercentageThreshold" name="RelatedPartyTransactionOwnershipPercentageThreshold" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="kod_SummaryOfSignificantAccountingPoliciesLineItems" name="SummaryOfSignificantAccountingPoliciesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_SummaryOfSignificantAccountingPoliciesTable" name="SummaryOfSignificantAccountingPoliciesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_BakerBrosAdvisorsLPMember" name="BakerBrosAdvisorsLPMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_FundingAgreementMember" name="FundingAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_AccruedResearchAndDevelopmentCurrent" name="AccruedResearchAndDevelopmentCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AccruedLegalFeesCurrent" name="AccruedLegalFeesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_RepurchaseAgreementMember" name="RepurchaseAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAmortizedCostBasisCurrent" name="AvailableForSaleDebtSecuritiesAmortizedCostBasisCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTaxCurrent" name="AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTaxCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTaxCurrent" name="AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTaxCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAmortizedCostBasisNoncurrent" name="AvailableForSaleDebtSecuritiesAmortizedCostBasisNoncurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTaxNonCurrent" name="AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTaxNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTaxNonCurrent" name="AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTaxNonCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_UnrecordedUnconditionalPurchaseObligationCancellationFees" name="UnrecordedUnconditionalPurchaseObligationCancellationFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="kod_CommitmentsAndContingenciesDisclosureLineItems" name="CommitmentsAndContingenciesDisclosureLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_CommitmentsAndContingenciesDisclosureTable" name="CommitmentsAndContingenciesDisclosureTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_LonzaMember" name="LonzaMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_PercentageOfRepurchaseOfRoyalties" name="PercentageOfRepurchaseOfRoyalties" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="kod_DescriptionOfTerminationOfRoyaltyAgreement" name="DescriptionOfTerminationOfRoyaltyAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="kod_FundsPayableUponEnrollmentOfPatients" name="FundsPayableUponEnrollmentOfPatients" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="kod_PercentageOfPatientsToBeEnrolled" name="PercentageOfPatientsToBeEnrolled" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="kod_TwoThousandEighteenEquityIncentivePlanMember" name="TwoThousandEighteenEquityIncentivePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_PerformanceBasedStockOptionsMember" name="PerformanceBasedStockOptionsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_PerformanceBasedRestrictedStockUnitMember" name="PerformanceBasedRestrictedStockUnitMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_PerformanceBasedEquityAwardsMember" name="PerformanceBasedEquityAwardsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember" name="TwoThousandEighteenAndTwoThousandFifteenEquityIncentivePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsWeightedAverageRemainingContractualTermAbstract" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsWeightedAverageRemainingContractualTermAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="kod_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueAbstract" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
</xsd:schema>
